PONTIFICAL FACULTY OF PHILOSOPHY
STUDIUM GENERALE OF SAINT THOMAS AQUINAS

THE MANNER OF DEMONSTRATING
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IN NATURAL PHILOSOPHY

A DISSERTATION
Submitted to the Pontifical Faculty of Philosophy
of the Studium Generale of St. Thomas Aquinas
in Partial fulfillment of the Requirements
for the Degree of Doctor of
Philosophy

by

Rev. Melvin A. Glutz, C.P., Ph.D.

RIVER FOREST, ILLINOIS

TABLE OF CONTENTS
PAGE

INTRODUCTION ............................................................................. ix
CHAPTER
I. THE ARISTOTELIAN-THOMISTIC CONCEPT OF
DEMONSTRATION .............................
1
Intuition and Demonstration ...................................................
1
Definition of Demonstration....................................................
4
Reason for two definitions ................................................... 5
Definition from final cause .................................................
5
Definition from material cause ............................................. 12
Kinds of Demonstration ............................................................ 27
Demonstration Compared with Opinion .................................. 30
Demonstration and the “Scientific Method” ........................... 35
II. .THE SUBJECT OF NATURAL PHILOSOPHY .......... 40
Subject and Object of Science in General .......................... 40
Subject and Object of Natural Science .............................. 48
Division of the Formal Subject ........................................... 57
Procedure at the Level of Specific Essences ....................... 65
Summary.................................................................................... 65
III. CERTITUDE AND NECESSITY IN NATURAL PHI­
LOSOPHY ............................................................................... 66
Aristotle’s Idea of a Natural Science ..............
66
Certitude .................................................................................... 67
Necessity .................................................................................... 71
Summary .................................................................................... 80
IV. THE MANNER OF DEMONSTRATING IN NATURAL
PHILOSOPHY ....................................................................... 84
Place of Induction andExperience ........................................ 85
Natural Science Demonstrates through All the Causes .... 98
Nature of Aristotelian NaturalScience .............................. 100
Summary ...................................................................................... 102
V. DEMONSTRATION THROUGH FORMAL CAUSE ... 103
VL DEMONSTRATION THROUGH EFFICIENT CAUSE . 119
VII. DEMONSTRATION THROUGH MATERIALCAUSE . 139
VIII. DEMONSTRATION THROUGH FINALCAUSE .. ........... 153
SUMMARY AND CONCLUSION ................................................. 172
BIBLIOGRAPHY .............................
175
INDEX ............................
183

ΙΚΒΜ

INTRODUCTION
The Logical Positivists, with their principle of verifica­
tion,1 have laid great stress upon method, even to the point
of practically identifying meaning and method. Although
a method based on a radical sensism has not been felicitous
for philosophy, still perhaps indirectly these neo-positivists
will be of real service to philosophy by pointing out to
Thomists a weakness in their own understanding of the
philosophy of nature.
The Aristotelian logic is intended to be a method for at­
taining truth “in an orderly and easy manner and without
error.”1
2 Generally, Scholastics have been faithful to their
body of logical doctrine as logica docens, although it must
be admitted that the current manuals miss much of the
riches hidden away in St. Thomas’ Commentaries on the
Organon. However, modem Scholastics, while adhering to
their logic in principle, have not always been successful at
putting it into practice in building up the various branches
of philosophical science. Likewise, the discursive method
being used in most modern books of Thomist philosophy
tends to obscure the artificial logical procedure whereby
a demonstration is constructed.3 We may charge that sci1 Cf. H. Van Laer, Philosophico-Scientific Problems. Chap. 3,
“The Principle of Verification,” pp. 28-58.
2 “... ordinate, faciliter et sine errore.” (St. Thomas, In I Post.
Analyt., lect. 1, n. 1.) The editions of St. Thomas’ works used in this
dissertation are marked with an asterisk in the bibliography. The
Latin text will not be given in the footnotes whenever an authoritative
English translation has been used.
3 It is noteworthy that the Holy See prefers the use of the syllogis­
tic form in the presentation of prooofs. “In quaestionibus speculativis
sive Theologiae sive Philosophiae adhibeatur methodus quam scho­
lasticam vocant, non neglecta, tam in proponendis argumentis quam
in afferendis, disputandis, solvendis difficultatibus, forma syllogistica.
Hac autem methodo auditorum mentes ita excolantur, ut apti paratique efficiantur non solum ad falsa systemata erroresque antehac

(,ΗΜΗΒΜβίΜΐΜ

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Demonstrating in Natural Philosophy

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entitle logic is in practice often replaced by mere natural
logic.
Whether the above judgment is too severe need not con­
cern us now. The reasons for it will become more apparent
in the course of our study. The fact in which we are inter­
ested is that logic is only a general method applicable to
all the sciences. It has to be specified for each individual
science.
There are different ways of seeking truth; so a
man must be instructed as to how arguments are
to be received in each of the sciences. It is not
easy for a man to grasp two things at one time,
for while he is attending to them both, he can
grasp neither. So it is absurd for a man at the
same time to seek sciences and the method of sci­
ence. Therefore, one must first learn logic before
the other sciences, because logic gives the common
manner of proceeding in all the sciences. But the
method proper to each individual science should
be given toward the beginning of each science.4
Almost all of Book Two of Aristotle’s Physics is taken
up with the principles and method of the science, a thing
conspicuously absent in our manuals of natural philosophy.
It is very important in our times that we not only have

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exortos dijudicandos et refutandos, sed etiam ad discernendas et ex
veritate aestimandas sententias novas quae forte in disciplinis
theologicis vel philosophicis exoriantur.” (Sacra Congregatio de
Seminariis et Studiorum Universitatibus, “Ordinationes ad constitutionem apostolicam ‘Deus scientiarum Dominus’ de Universitatibus et
Facultatibus Studiorum ecclesiasticorum rite exsequendam.” Text
from Enchiridion de Statibus Perfectionis, η. 360.)
4 “Diversi secundum diversos modos veritatem inquirunt; ideo
oportet quod homo instruatur per quem modum in singulis scientiis
sint recipienda ea quae dicuntur.—Et quia non est facile quod homo
simul duo capiat, sed dum ad duo attendit, neutrum capere potest;
absurdum est, quod homo simul quaerat scientiam et modum qui convenit scientiae. Et propter hoc debet prius addiscere logicam quam
alias scientias, quia logica tradit communem modum procedendi in
omnibus aliis scientiis. Modus autem proprius singularum scientia­
rum, in scientiis singulis circa principium tradi debet.” (Zn II Meta.,
lect. 5, n. 335.)

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Introduction

xi

truth, but know that we have it and know how we have
attained it.® Thus, a certain amount of preoccupation with
methodology is especially necessary in a world that is has­
tening toward the quagmire of scepticism,
In the primary sources of our Aristotelian-Thomistic
tradition we have a wealth of material on the method of
building up the science of nature that we call natural phi­
losophy. This present study intends to bring to light some
of this too little known doctrine. This is not to be merely
a historical study, either of Aristotle’s or St. Thomas’ doc­
trine, although the works of these two great thinkers will
constitute our main source. We will feel free, however,
to draw from any other sources, old and new, that we find
helpful.
In order to reach the heart of our subject, the manner
of demonstrating in natural science,® we have to make a
number of preliminary considerations. First of all we must
say what is meant by the Aristotelian-Thomistic concept
of demonstration and science and how it differs from other
types of knowledge. We must clarify the meaning and ex­
tent of what we understand by the term natural science.
It is impossible to determine the method of natural phi­
losophy according to the thought of Aristotle and St. Thom­
as, unless we understand their integral view of this science.
Therefore, we will have to explain their process of begin­
ning and developing natural philosophy and also the noetic
status they claimed for it.
8 Cardinal Zigliara, in a footnote (B) to St. Thomas’ second Lectio
on the Posterior Analytics (Leonine edition, p. 143) says: “Quae
de praecognitione deque praecognitionis modo disseruntur a s. Thoma
cum Aristotele tantae sunt necessitatis, ut si quis ea non intime
penetraverit, vim naturamque demonstrationis ignoret necesse sit;
atque ideo a scientificis cognitionibus arcebitur: cum. sapiens nul­
latenus sit dicendus, qui suae scientiae rationem intimam impotens
est ostendere.” (Italics ours.)
® St. Thomas speaks of natural philosophy as “natural science.”
We will discuss in later chapters the extent of this natural science
and its relation to the experimental sciences of nature.

xii

Demonstrating in Natural Philosophy

It is our hope that our study may be some small contri­
bution to what Jacques Maritain has called “a sort of renais­
sance of the philosophy of nature.”7
7 Philosophy of Nature, p. 151.

CHAPTER I
THE ARISTOTELIAN-THOMISTIC CONCEPT
OF DEMONSTRATION
Demonstration is a crutch, whereby we compensate for
the imperfection of our intellect. An angel does not need
to demonstrate. In one intuition of an intelligible form, an
angel contemplates all that is knowable in it.1 The full light
of the angelic intelligence focusses upon its natural object
and in one act knows its essence and all its attributes.
With us men, however, it is different. Our nature holds
the lowest rung of intellectual beings. We cannot attain
the perfection of knowledge by one powerful insight into
the essence of an object. Because of the weakness of our
intellectual light we must come to full truth progressively,
by a laborious and often painful process of reasoning from
known truths to those that are unknown.12 We must also
seek our knowledge, not in the full light of immateriality,
but conformably to our nature, in the shadows of matter,
in the world of sense. The object of our knowledge is a
form hidden away in individual corporeal matter, an ob­
ject that our mind must first disengage from matter and
to which it must give an immaterial manner of existing, in
order to be one with that object in the vital act of know­
ing. Even so, that object retains connotations of the mat­
ter from which it has been drawn. It takes further proc­
esses of refinement before the mind can fathom the full in­
telligibility of its object. The goal of all its labors, the
greatest triumph it can expect, is to come to some knowl­
1 Cf. Summa Theologiae, I, q. 58, a. 3; a. 4.
«“Quaedam vero sunt inferiores (intellectus), quae ad cognitionem
veritatis perfectam venire non possunt nisi per quemdam motum,
quo ab uno in aliud discurrunt, ut ex cognitis in incognitorum notitiam
perveniant; quod est proprie humanarum animarum.” (De Veritate,
q. 15, a. 1.)
1

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2

Demonstrating in Natural Philosophy

edge of the immaterial natures existing beyond the scope
of its ordinary vision.3
It is important to realize that the act of understanding,
the act called technically intellectus? or intuition, is the
most perfect manner of knowing. It is an intus legere,s a
reading, as it were, of truth in the very essence of an ob­
ject.3 When we speak of such intuition of essence, however,
we must not form too lofty a concept of it. We do not grasp
essences directly and at a glance. Essences are known to
us only by means of their sensible manifestations or prop­
erties.
The name intellect arises from the intellect’s abil­
ity to know the most profound elements of a thing;
for to understand (intelligere) means to read what
is inside a thing {intus legere). Sense and imag­
ination know only external accidents, but the in­
tellect alone penetrates to the interior and to the
essence of a thing.7
In a sense we can say that we “reason” to essences, under­
standing by “reason” the act of the cogitative power, often
called the particular reason. This collates recurring sen­
sible manifestations and presents an experimentum, or gen■ *“Necesse est dicere quod intellectus noster intelligit materialia
abstrahendo a phantasmatibus, et per materialia sic considerata in
immaterialium aliqualem cognitionem devenimus, sicut e contra angeli
per immaterialia materialia cognoscunt.” (Summa Theol., I, q. 85,
a. 1.)
4 “Nomen intellectus dupliciter accipi potest. Uno modo secundum
quod se habet ad hoc tantum a quo primo nomen impositum fuit; et
sic dicimur proprie intelligere cum apprehendimus quidditatem rerum,
vel cum intelligimus illa quae statim nota sunt intellectui notis rerum
quidditatibus, sicut sunt prima principia, quae cognoscimus cum
terminos cognoscimus; unde et intellectus habitus principiorum
dicitur.” (De Ver., q. 1, a. 12.)
3 Summa Theol., Π-Π, q. 8, a. 1.
•“Intellectus enim simplicem et absolutam cognitionem designare
videtur; ex hoc enim aliquis intelligere dicitur quod interius in ipsa
rei essentia veritatem quodammodo legit; ratio vero discursum quem­
dam designat, quo ex uno in aliud cognoscendum anima humana per­
tingit vel pervenit.” (De Ver., q. 15, a. 1.)
T De Ver., q. 1, a. 12.

The Aristotelian-Thomistic Concept

3

eralized sense image, from which, the active intellect ab­
stracts a species representative of the essence. Moreover,
the mind does not apprehend an essence perfectly in one
act. The first concept of a thing is vague and imperfect. It
represents the essence as a something, a material being.
It takes successive acts before the mind distinguishes the
specific features and differentiates it from other beings,
thereby forming a definition. This first definition does not
exhaust the intelligibility of the essence; it is only the
start. It is the work of judgment and reasoning that rounds
out the first vague understanding of the essence and fur­
nishes us a complete definition.®
Whereas understanding is a perfect manner of knowing,
reasoning is essentially an imperfection. It is proper only
to us men. Neither God nor the angels reason. They sim­
ply understand. All that we learn by our plodding rational
processes is known in a simple glance by a higher intellect®
This distinction between understanding and reasoning
must never be lost sight of throughout our study of demon­
stration. Demonstration is a reasoning process. It puts
the finishing touches on our knowledge. It brings it to its
fullest perfection. Yet demonstration is imperfect as a man­
ner of knowing, even in us men. We have also that other
and more noble manner of knowing, understanding, which
St. Thomas calls a participation of the angel’s way of know­
ing.8
*10 Understanding is, in fact, the beginning and pre­
requisite of our reasoning process. Reasoning and demon­
stration would be impossible unless we had some simple
grasp of truth from which to start. Because of the im­
portance of this, let us read a passage where St. Thomas
clearly and concisely explains it.
Now all movement proceeds from what is at rest,
as Augustine says. For rest is the term of mo­
tion, as is said in the Physics. Thus, movement
is related to rest as to its source and its term,
8 Summa Theol., I, q. 85, a. 5.
"Ζδΐί.
10 De Ver., q. 15, a. 1.

MHM

Demonstrating in Natural Philosophy
as is reason, also, which is related to understand­
ing as movement to rest and generation to existtence.... It is related to understanding as to its'"]
source and its term. It is related to it as its source
because the human mind could not move from one
thing to another unless the movement started from
some simple perception of truth, and this perception is understanding of principles. Similarly, the
movement of reason would not reach anjrthing
certain unless there were an examination of that
which it came upon through discursive movement
of the mind. This examination proceeds to first
principles, the point to which reason pursues its
analysis. As a result, we find that understanding
is the source of reasoning in the process of dis-,
covery and its term in that of judging.11
An appreciation of the act of understanding will save
us from the mistake of wanting to have all our knowledge
demonstrated. To do so would be to destroy the very process of demonstration.12 For the present our discussion of
understanding and its difference from reasoning has pur­
posed to give us a general introductory idea of what dem­
onstration is. We have seen that it is our human way of
extending our knowledge beyond our first weak insights
into its object. It is our method of overcoming the imperfection of our composite nature and stretching out to great­
er vistas of understanding. We may say that demonstra­
tion is pressing out the pulp of knowable objects in order
to extract from them the last drops of intelligibility.
Aristotle gives two definitions of demonstration; and in
doing so he is making use of a principle which it will not
be inopportune to point out even at this early stage, since
the principle is cardinal to the manner of demonstrating in
11 De Ver., q. 15, a.1.
12 CfMetaphysics, Bk. 4, Chap. 4, 1006a 5-10: “Some indeed de­
mand that even this shall be demonstrated (principle of non-contra­
diction), but this they do through want of education, for not to
know of what things one should demand demonstration, and of what
one should not, argues want of education. For it is impossible that
there should be demonstration of absolutely everything (there would
be an infinite regress, so that there would still be no demonstration.)”

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The Aristotelian-Thomistic Concept

natural science. First, he defines demonstration by reason
of its final cause; then, through its material cause. St.
Thomas gives the following explanation, which he will re­
peat many times in the course of his commentaries on the
works of Aristotle.
In all things that are ordained to an end, the defi­
nition through final cause is the reason for the
definition through” material cause and also the
middle term for proving it. For example, because
a house is a shelter to protect us from cold and
heat, it has to be constructed of stones and wood.
So Aristotle here gives two definitions of demon­
stration: one is taken from the end of demon­
stration, which is to know (scire) ; from this is
concluded the other, which is taken from the mat­
ter of demonstration.13
By reason of its end Aristotle thus defines demonstra­
tion : “By demonstration I mean a syllogism productive of
scientific knowledge, that is, the grasp of which is eo ipso
such knowledge.”14 The Latin equivalent of this definition
is: “Demonstratio est syllogismus scientialis, idest faciens
scire.”15
With John of St. Thomas1* we may profitably consider
13 “In omnibus quae sunt propter finem, definitio, quae est per
causam finalem, est ratio definitionis, quae est per causam materialem,
et medium probans ipsam: propter hoc enim oportet ut domus fiat
ex lapidibus et lignis, quia est operimentum protegens nos a frigore
et aestu. Sic igitur Aristoteles de demonstratione dat his duas defin­
itiones: quarum una sumitur a fine demonstrationis, qui est scire;
et ex hac concluditur altera, quae sumitur a materia demonstrationis.”
(In I Post. Analyt., lect. 4. n. 2.)
14 Άπόδειξιν δε λόγω συλλογισμόν επιστημονικόν. επιστημονικόν
δε λέγω καθ' δν τω εχειν αυτόν επιστάμεθα. (Post. Analyt., Bk. 1,
Chap. 2, 71b 18.) The Greek text is that given in the Leonine
Edition of St. Thomas’ Commentary. It is the Didot text, which the
editors compared with other editions, both old and recent. Cf. p.
xxxvii. In the course of this study we will give the Greek text of
quotations from Aristotle only when it helps in an understanding of
the doctrine.
15 In I Post. Analyt., lect. 4, n. 9.
“ Cursus Philosophicus Thomisticus, (ed. Reiser), Vol. I, pp. 773,
774.

6

Demonstrating in Natural Philosophy

each element of the definition: (1) syllogismus; (2) faci­
ens (or “efficiens,” as he defines it) ; (3) scire.
Demonstration is said to be a syllogism, as designating
the form of argument required for it. Syllogism, we must
remember, is Aristotle’s own invention for the attainment
of truth. He worked out an elaborate science of formal
logic, whose parts are all orientated to the syllogism. So
all the doctrine of formal logic is presupposed for demon­
stration. We must content ourselves with merely indicat­
ing this fact in passing. It is noteworthy, however,
with respect to demonstration, that the first figure of syl­
logism is the vehicle of demonstration. It alone concludes
universally and affirmatively, enabling us to predicate a
definition or a proper attribute of our subject; and it is
by means of this figure that the other figures are resolved
to immediate premisses, of which we shall speak later.17
Demonstration is secondly a syllogism productive (effi­
ciens) of scientific knowledge. If we consider scientific
knowledge, or science, as a habit, then we say that the
habit is generated by the whole process of demonstration.
But we are here concerned with science as an act. In this
case, then, it is the premisses that are productive of the
scientific conclusion, and this in two ways: effectively and
formally.
The premisses are said to be the efficient cause of the
conclusion.
The principles of demonstration are related to
their conclusions as the active causes of natural
things are related to their effects. Hence in the
Second Book of Physics the propositions of the
syllogism are placed in the genus of efficient
cause.18
It is in the light of the premisses that the conclusion is
17 Cf. Post Analyt., Bk. 1, Chap. 14, 79a 18-33. St. Thomas In I
Post. Analyt., lect. 26.
18 “Principia autem se habent ad conclusiones in demonstrativis
sicut causae activae in naturalibus ad suos effectus (unde in II
Physicorum propositiones syllogismi ponuntur in genere causae effi­
cientis) .” (In I Post. Analyt., lect. 3, n. 1.)

The Aristotelian-Thomistic Concept

7

inferred. The premisses are extrinsic to the conclusion
and give the intellect the power to assent to the conclu­
sion.18
19 The conclusion is truly a new being, an actualization
of what was only virtually contained in the premisses.
Therefore, as in the case of any transition from potency
to act, there must be an efficient cause. The possible in­
tellect, determined by the premisses, is moved by the active
intellect to consent to the conclusion. The premisses con­
cur as instrumental causes.20 When the premisses are not
certain or the inference not clear, the motive power of the
will is needed to make the intellect assent, as happens in
the act of faith.
The premisses are said to produce the conclusion for­
mally, in that the objects known in the premisses specify
the judgments whereby the premisses are known, and so
virtually and mediately specify the assent of the conclu­
sion.21
Finally, demonstration is said to yield scientific knowl­
edge. The Latin noun scientia and the verb scire translate
the corresponding Greek επιστήμη and έπίστασθαι.22 These
are technical terms with Aristotle and have a very precise
meaning. It is significant to note that Aristotle adopted
18 Cf. John of St. Thomas, op. cit., pp. 758-762.
20 “Intellectus in actu principiorum non sufficit ad reducendum
intellectum possibilem de potentia in actum sine intellectu agente;
sed in hac reductione intellectus agens se habet sicut artifex, et
principia demonstrationis sicut instrumenta.” (Qu. Disput. De Anima,
a. 4, ad 6.)
21 “Formaliter autem ipsa obiecta seu res cognitae, quae istis
notitiis repraesentantur ipsosque actus cognoscitivos praemissarum
specificant. Et quia veritas et obiecta principiorum virtualiter con­
tinent veritates illatas, virtualiter etiam et mediate specificant
assensum conclusionis, qui explicite et formaliter tendit in ipsam
veritatem conclusionis.” (John of St. Thomas, op. cit., p. 774.) The
premisses are also the material cause of the conclusion. In II Phys.,
lect. 5, n. 9.
22 The adverb άττλως is frequently added. The Latin equivalent
is simpliciter. The Oxford translators of Aristotle’s works use the
term: “unqualified scientific knowledge” or “in an unqualified sense
of the term to know'' (71a 26; b 8.)

8

Demonstrating in Natural Philosophy

the term επιστήμη, which for Plato meant the contempla­
tion of the subsistent Ideas, a knowledge that was thought
to be immutable and eternal. The word επίστασθαι is a de­
rivative of ϊστασθαι, which means to stand or come to a
stop. In the seventh book of Physics the etymological con­
nection is brought out.
The terms “knowing” and “understanding” im­
ply that the intellect has reached a state of rest
and come to a standstill.23
The intellect is awakened to scientific inquiry “by wonder­
ing that things are as they are.” The scientific process
“must end in the contrary and, according to the proverb,
the better state,”24 that is, a state of rest and satisfaction.
What is Aristotle’s concept of this knowledge that will
perfectly quiet the mind? He says of it:
We suppose ourselves to possess unqualified scien­
tific knowledge of a thing when we think that we
know the cause on which the fact depends, as the
cause of that fact and of no other, and, further,
that the fact could not be other than it is.25
He does not attempt to prove his definition. It is not neces­
sary to do so. For in fact, it is quite evident that scientific
knowledge is such, since such knowledge is claimed both
by those who actually possess it and by those who only
think that they have it. The human mind spontaneously
searches for just such a type of truth. Therefore, Aristotle
could say in the first sentence of his Metaphysics: “All men
by nature desire to know.”2®
“ Tç> yàp ήρεμήσαι καί στήναι την διάνοιαν επίστασθαι καϊ
φρονεΐν Χόγομεν. (Physics, Bk. 7, Chap. 3, 274b 10.)
14 Metaphysics, Bk. 1, Chap. 2, 983a 14, 18.
11 Post. Analyt., Bk. 1, Chap. 2, 71b 9sq.
“ 980a 22. It is to be noted, however, that Aristotle also used the
term “science" in a broader sense as including any certain knowledge.
“Not all knowledge (επιστήμη) is demonstrative: on the contrary,
knowledge of the immediate premisses is independent of demonstra­
tion.” (Post. Analyt., Bk. 1, Chap. 3, 72b 19.) St. Thomas says of
this: /‘Sciendum est tamen quod hic Aristoteles large accipit scientiam

The Aristotelian-Thomistic Concept

9

Let us now, with the help of St. Thomas’ commentary,
try to bring out the significance of Aristotle’s definition
of science.
Scientific knowledge, as defined, means perfect knowl­
edge of a thing, a knowledge that will completely satisfy
the natural inquisitiveness of our minds. Science aims at
uncovering for us the essence of its object in all its virtual­
ity. By the act of intuition, or understanding, we come to
some imperfect knowledge of a universal essence and em­
body it in a general definition. But such a definition must
be refined and perfected by a study of the causes and prop­
erties of the object. When we note the constant recurrence
of some attribute of an object, we are led to inquire the
cause of this constancy. Why, for instance, should men be
risible, or why does the moon occasionally suffer eclipse?
Our natural desire to know is not quieted by the mere
knowledge of the existence of some fact; it seeks to know
the “why,” the cause of that fact. And when the fact is
a property of an object, the cause will be the essence of the
object. From properties we come to know essences, the
natural object of our intellect.
In the speculative sciences we search after defini­
tions, by which we understand the essences of
things through the division of a genus into differ­
ences and through the examination of a thing’s
causes and accidents, which contribute a great
deal to our knowledge of the essences.27
Not only the intrinsic causes of a thing, but the extrinsic
causes, especially the final cause, throw light on an essence.
The end is the cause of the other causes, the reason why
there should be such a form and such matter. And a uni­
vocal agent is in some way similar to its effect, according
to the dictum: “Omne agens agit sibi simile.” Therefore,
pro qualibet certitudinali cognitione, et non secundum quod scientia
dividitur contra intellectum, prout dicitur quod, scientia est conclusi­
onum et intellectus principiorum.” (In I Post. Analyt., lect. 7, n. 6.
Cf. lect. 42, n. 9; lect. 44, n. 3.)
27 In Librum Boethii De Trinitate, q. 6, a. 4, corp.

10

Demonstrating in Natural Philosophy

we do not know a thing perfectly until we know its causes.28
“The knowledge of the causes of any genus is the end at­
tained by the inquiry of the science.”29
Let us note that Aristotle has said: “We suppose our­
selves to possess unqualified scientific knowledge of a thing
when we think that we know the cause on which the fact
depends.” We are seeking, in other words, the cause of
the fact, not the cause of our knowledge of the fact, the
cause in essendo, not that in cognoscendo. To use Aris­
totle’s example, we know that the planets are near, because
they do not twinkle.30 However, non-twinkling is not the
cause of the nearness of the planets, but merely an effect
of it, which becomes for us the cause of our knowledge
of that nearness. The reason why we seek the cause in es­
sendo is that:
To have scientific knowledge of something is to
know it perfectly, which means perfectly to appre­
hend its truth. Now the principles of a thing’s
existence and of its truth are the same, as is evi­
dent from the Second Book of Metaphysics. There­
fore, if one knows perfectly, he must know the
cause of the thing known.31
In order to demonstrate a scientific conclusion, more­
over, we must know the cause of any fact under consider­
ation “as the cause of that fact and of no other.”3233The
28 With Cajetan we must understand “cause” in the broad sense
of “reason” or “virtual cause,” as when we demonstrate in metaphysics
that the immutability of God is the reason for His eternity; if God
had a cause of His eternity, it would be His immutability. Cf. note
i, Leonine Edition of St. Thomas’ Commentary on the Posterior
Analytics, p. 151; John of St. Thomas, op. cit., pp. 775-776.
33 “Nam cognitio causarum alicujus generis, est finis ad quem con­
sideratio scientiae pertingit.” (In Metaphysicam, Proenium.)
«° Post. Analyt., Bk. 1, Chap. 13, 78a 30.
51 “Scire aliquid est perfecte cognoscere ipsum, hoc autem est
perfecte apprehendere veritatem ipsius: eadem enim sunt principia
esse rei et veritatis ipsius, ut patet ex II Metaphysicae. Oportet igitur
scientem, si est perfecte cognoscens, quod cognoscat causam rei scitae.”
(In I Post. Analyt., lect. 4, n. 5. Cf. In II Meta., lect. 2, n. 298.)
33 Post. Analyt., Bk. 1, Chap. 2, 71b 11.

,

The AristotelianAThomistic Concept

11

Latin text that St. Thomas used does not contain the phrase
“and of no other.” St. Thomas’ interpretation of the other
part: “as the cause of that fact” is the following:
If one were to know the cause only, he would not
yet know the effect in act (which is unqualified
scientific knowledge), but only virtually (which
is knowledge secundum quid and as it were per
accidens). So in order to have unqualified scien­
tific knowledge, one must know also the applica­
tion of the cause to the effect.33
Finally, scientific knowledge must tell us “that the fact
could not be other than it is.”33
34 There must, in other words,
be a necessary connection manifested between the subject
and predicate of a scientific conclusion. Necessity is the
essential and specifying element of science. No other type
of knowledge would ever satisfy the natural inquiry of our
mind, for if the fact could be otherwise, then perhaps in
this case it is otherwise, and the mind is again delivered
over to wonderment.
Demonstration is said to be of necessary things and
from necessary principles. It is of necessary
things, because that which is simply demonstrated
cannot happen to be otherwise. We say simply
demonstrated in distinction from a demonstration
“ad hominem”.... But because the causes of the
conclusion in demonstrations are the premisses—
for demonstration gives knowledge in the unquali­
fied sense, which can be only by means of a cause
—then the principles of the syllogism have to be
necessary and impossible to be otherwise. For
from a non-necessary cause there cannot follow a
necessary effect.35
33 “Si autem cognosceret causam tantum, nondum cognosceret ef­
fectum in actu, quod est scire simpliciter, sed virtute tantum, quod
est scire secundum quid et quasi per accidens. Et ideo oportet scien­
tem simpliciter cognoscere etiam applicationem causae ad effectum.”
{In I Post. Analyt., lect. 4, n. 5.)
34 Post. Analyt., Bk. 1, Chap. 2, 71b 12. Cf. Nicomachean Ethics,
Bk. 6, Chap. 3, 1139b 18-24.
35 “Demonstratio enim dicitur esse necessariorum, et dicitur esse
ex necessariis. Necessariorum quidem esse dicitur, quia illud, quod

12

Demonstrating in Natural Philosophy

We can have science of contingent and mobile things,
but it must be under some aspect whereby they are neces­
sary. “Nothing is so contingent as not to have some neces­
sary aspect to it.”36 We shall treat in a later chapter the
kind of necessity to be found in material objects.
In these three notes we have the Aristolian concept of
scientific or perfect knowledge, the fruit of demonstration.
It consists of knowledge through a cause, as actually exer­
cising its causality, and as necessitating the effect. Because
science is intellectual and not sense knowledge, it is ob­
viously of a universal nature, abstracting from sensible
individuals.
Granting Aristotle’s idea of scientific knowledge, the end
of demonstration, then what kind of premisses are needed
to produce such a knowledge? In stating the conditions
of the premisses, Aristotle concludes a definition of dem­
onstration from its material cause. Putting this definition
into form, we can say that demonstration, or a scientific
syllogism, is a syllogism that proceeds from or is composed
of premisses that must be “true, primary, immediate, bet­
ter known than and prior to the conclusion, which is further
related to them as effect to cause.”37
The premisses of demonstration must be true, “for that
which is non-existent cannot be known.”38 If an alleged
fact is not true, it is non-existent, and so cannot be an ob­
ject of knowledge. Every cause, moreover, produces an
simpliciter demonstratur, non contingit aliter se habere. Dicitur
autem simpliciter demonstratum ad ejus differentiam quod demonstra­
tur in demonstratione quae est ad aliquem, et non simpliciter; quod
in quarto libro dixit demonstrare ad hominem arguentem.... Sed,
quia causae conclusionis in demonstrationibus sunt praemissae, cum
demonstratio simpliciter scire faciat, quod non est nisi per causam,
oportet etiam principia, ex quibus est syllogismus, esse necessaria quae
impossibile sunt aliter se habere. Nam ex causa non necessaria non
potest sequi effectus necessarius.” (In V Meta., lect. 6, n. 838.)
“ “Nihil enim est adeo contingens, quin in se aliquid necessarium
habeat.” (Summa Theol., I, q. 86, a. 3. Cf. q. 84, a. 1, ad 3.) Our transi.
« Post. Analyt., Bk. 1, Chap. 2, 71b 20.
71b 25.

The Aristotelian-Thomistic Concept

13

effect like unto itself; false premisses can per se produce
only a false conclusion. Per accidens, however, a true con­
clusion can come from false premisses, as in the example:
Every man is a stone. Every pearl is a man. Therefore,
every pearl is a stone.
Demonstration must likewise have premisses that are
primary and immediate. Aristotle explains his meaning
of these notes in his customary concise and cryptic man­
ner:
The premisses must be primary and indemon­
strable (i.e. immediate) ; otherwise they will re­
quire demonstration in order to be known, since
to have knowledge, if it be not accidental knowl­
edge, of things which are demonstrable, means
precisely to have a demonstration of them.... In
saying that the premisses of demonstrated knowl­
edge must be primary, I mean that they must be
the “appropriate” basic truths, for I identify pri­
mary premiss and basic truth. A “basic truth”
in a demonstration is an immediate proposition.
An immediate proposition is one which has no
other proposition prior to it.39
Aristotle seems to equate primary and immediate prem­
isses. We can, however, note some slight distinction be­
tween the two. Premisses are immediate, according to St
Thomas, when they are indemonstrable, that is, when they
have no medium whereby they can be demonstrated. They
are primary “in relation to other propositions that are
proved through them.”40 Let us, for greater clarity, quote
the remark of John of St. Thomas with regard to these
two notes:
Ibid., 71b 27-28; 72a 6-8. “Appropriate basic truths” translates
άρχων οικείων, the Latin equivalent of which is “ex propriis prin­
cipiis.”
40 “Demonstrativa scientia, idest quae per demonstrationem ac­
quiritur, procedat ex propositionibus veris, primis et immediatis, idest
quae non per aliquod medium demonstrantur, sed per seipsas sunt
manifestae (quae quidem immediatae dicuntur, in quantum carent
medio demonstrante; primae autem in ordine ad alias propositiones,
quae per eas probantur.)” (In I Post. Analyt., lect. 4, n. 10)

14

Demonstrating in Natural Philosophy

Demonstration is said to be from primary and
immediate—that is, from per se known—prem­
isses, which are not demonstrated through any
middle term.... They are primary with respect
to those (propositions) that are proved through
them; they are immediate, because they lack a
middle term to demonstrate them. Accordingly,
these two particles are not superfluous, but ex­
plain different formalities, namely that (1) a
proposition is not demonstrated by another,
which is what is meant by lacking a middle
term, and (2) it is apt to demonstrate others,
or to hold a primacy among them, which is what
is meant by being primary.41
Primary and immediate, then, are two formalities of
the same thing: of a per se known, or self-evident, propo­
sition. In general, a per se known proposition is one whose
predicate is contained in the notion of the subject.42 Every
per se known proposition is also primary and immedi41 “Dicitur ex primis et immediatis, id est ex per se notis, quae non
per aliud medium demonstrantur, ut explicat D. Thomas I Poster.
lect. 4. Et dicuntur primae respectu earum, quae per illas probantur,
immediatae vero, quia carent medio demonstrante illas, ut dicit S.
Doctor. Itaque non sunt superfluae illae duae particulae, sed explicant
diversas formalitates, scilicet propositionem non esse demonstratam
ab alio, quod est carere medio, et esse aptam demonstrare alia seu
primatum inter alia tenere, quod est esse primam.” (John of St.
Thomas, op. cit. Vol. I, p. 775.)
"“Quaelibet propositio, cuius praedicatum est in ratione subiecti,
est immediata et per se nota, quantum est in se.” (In I Post Analyt^
lect. 5, n. 7.) A proposition may be self-evident in itself, though not
to us, such as that God exists: the predicate is identical with the
subject, but not evidently so to us. Or a proposition may be selfevident both in itself and to us, such as is the principle of non-con­
tradiction, which is spontaneously known by all men. Some such selfevident propositions are known not by all men, but only by the learned,
that is, by those who know the definitions of subject and predicate and
thus know their identity. It is to be noted that sometimes a demon­
stration will proceed from a premiss that is not immediate, but proved
by another science, from which it is borrowed and accepted in place
of an immediate premiss. Ibid., and note k (Leonine). Cf. Summa
TheoL, I, q. 2, a. 1.

The Aristotelian-Thomistic Concept

15

ate.43 This is not to say that every per se proposition is
primary and immediate, for all propositions in demon­
stration, as we will show, must be per se, although they
may in some cases be conclusions through a middle term:
a mediate proposition is per se in the sense of essential,
though it is known per medium.44 The premisses of the
first of a series of demonstrations must be per se KNOWN
to us.
Since demonstration of premisses cannot proceed back­
ward to infinity, we must arrive at some propositions that
are evident to us without demonstration, at some proposi­
tions of which we are spontaneously aware that the sub-^
ject and predicate are identified or united. This of course'
does not mean that every demonstration has to have im­
mediate premisses. In a series of demonstrations in which
a premiss of one is the conclusion of a preceding, it is
sufficient that the first demonstration of the series be
from immediate premisses.45

Though the premisses of only the first demonstration
have to be immediate, all the propositions in any demon­
stration have to be per se. Therefore, we must take some
time to expand this notion of per se propositions. Since
necessity is the specifying element of science, our prem­
isses as well as our conclusion must have this element of
necessity. If one of the premisses is contingent, the con43 “Et quia omnis propositio per se nota est immediata, explicatur
negative, quatenus est immediata, et positive, quatenus est per se
nota.” (John of St. Thomas, op. cit., Vol. I, p. 767.)
44 “Circa praedicatum per se advertendum est, quod in communi
loquendo est illud, quod opponitur praedicato per accidens. Et per
accidens aliquando est idem, quod per aliud; aliquando est idem, quod
non essentialiter, sed accidentaliter et contingenter. Et similiter
per se aliquando dicitur idem quod immediate seu non per aliud; ali­
quando idem quod necessario et essentialiter.” (John of St. Thomas,
op. cit., p. 769.)
45 “Et sic oportet quod demonstratio ex immediatis procedat, vel
statim, vel per aliqua media.” (In I Post. Analyt., lect 4, n. 14. Cf.
In V. Meta., lect. 4, n. 801.)

I
ί

16

Demonstrating in Natural Philosophy

elusion will be so also, since an effect cannot be greater
than its causes.
Now, what is necessary must be predicated of a subject
per se, either as a definition or property of it. Any attri­
bute of a subject that is not per se, is merely contingent:
it can be absent. Therefore, we cannot demonstrate a
necessary inherence of it.
There are four ways in which a proposition can be per
se. But first we must observe that the preposition per
designates a causal relation; for instance, the body lives
per animam (formal cause) ; a body is colored per super­
ficiem (material cause or proper subject) ; water is heated
per ignem (efficient cause).46 Thus, when the subject is
itself the cause of the predicate, we have per se or essen­
tial predication.
The first manner of predicating per se is to attribute
to a subject something that pertains to its form or es­
sence, that is, a definition or a part of a definition. The
second manner takes the preposition per as signifying ma­
terial cause, that is, the proper subject of some form or
attribute that cannot be defined without reference to its
subject of inherence. Such a “proper passion” depends for
its being on its subject, and so can be understood only
in relation to it, as “equal” includes "number” and “iso­
cèles” includes “triangle” in their definitions.47 A third
mode is mentioned here only to exclude it: it occurs when
per se designates, not a causal relation, but rather a
“standing alone” or subsistence. Socrates, for instance,
cannot be attributed to some subject; rather, he is a sub­
ject of attribution. So we have here, not a mode of predi­
cation, but a mode of being; it does not concern demon­
stration, because it deals with the singular, whereas sci­
ence can concern only the universal, for only universals
can be defined.
46 Cf. In I Post. Analyt., lect. 10, n. 2. The analysis that follows
is taken from Post. Analyt., Bk. I, Chap. 4 and 5 and from St. Thomas’
Commentary, lect. 9-14.
« Cf. In VII Meta., lect. 4, n. 1342-1346.

’

*

* ·*

*

■»'

The Aristotelianr-Thomistic Concept

17

The fourth kind of essential predication is most im­
portant for demonstration, because it points formally to
the causal relation between subject and predicate, rather
than to the relation of predicating, as does the second
mode/8 This means that the predicate is the proper effect
of the causal action of the subject. The predicate is con­
sidered formally as an effect, not formally as a thing de­
fined in relation to its subject.49 Moreover, the predicate
will often be in the operative order: a property (e.g. a
faculty) or a proper operation of the subject, such as: the
runner ran, the doctor worked a cure. Aristotle calls this
a “consequential connection.”
If... there is a consequential connection, the
predication is essential; e.g., if a beast dies when
its throat is being cut, then its death is also es­
sentially connected with the cutting, because the
cutting was the cause of death, not death a “co­
incident” of the cutting.80
48 “Denique quartus modus dicendi per se non est modus praedi­
candi vel essendi, sed causandi, et definitur ab Aristotele: ‘Quando
aliquid inest propter ipsum,’ id est quando significatur ratio propria,
a qua causatur.” (John of St. Thomas, op. rit., p. 770.) This causal
relation, according to St. Thomas, may be efficient or any other.
“... quartum modum, secundum quod haec praepositio per designat
habitudinem causae efficientis vel cuiuscunque alterius. Et ideo dicit
quod quidquid inest unicuique propter seipsum, per se dicitur de eo.”
(In I Post. Analyt., lect. 10, n. 7.) Essence is the efficient, final and
material cause of all its proper accidents. Cf. Summa Theol., I, q. 77,
a. 6, c and ad 2. Properties are said to “emanate” from essence.
Cf. John of St. Thomas, op. rit., Vol. II, pp. 267-270.
49 The second and fourth mode of predicating do in fact usually
coincide, though there is a formal diversity. The formality of the
second mode is that of predication, founded upon the definition of
the predicate as including the subject. The fourth mode regards
rather the causal relation, in that the predicate depends for its
existence upon the subject, its proper cause. Because of the importance
of this distinction, we transcribe here a footnote from the Leonine
edition of the Commentary on the Posterior Analytics (note p, p. 178) :
"Circa quartum modum perseitatis, inquit Caietanus, diligenter ad­
verte subtilissimam s. Thomae expositionem, secundum quam iste
quartus modus distinguitur a secundo formaliter, quia perseitas
secundi est formaliter perseitas praedicationis (quatenus subiectum

18

Demonstrating in Natural Philosophy

It is to be noted that the fourth kind of essential predicate
can be accidental as regards its actual esse: the runner
need not always be running; his running is a contingent
accident. But in regard to causality, there is an essential
relation.®1
The Scholastics subdivided the modes of essential predi­
cation into per se primo and per se secundo. The first
designates that the predicate is of the definition of the
subject or a property and is convertible with it, because
it adéquates the universality of the subject. The predicate
is never found apart from the subject, nor the subject,
from the predicate. The second excludes convertibility.
This per se primo predication is at the very heart of
the Aristotelian-Thomist demonstrative theory. Aristotle
calls it καθόλου,which is translated by the Scholastics
as “universale” and by the Oxford translator as “com­
mensurate universal.” This latter is an excellent term,
and we shall make frequent use of it.
£‘ ’
Aristotle gives the following definition of the commen­
surate universal :
I term commensurately universal an attribute
which belongs to every instance of its subject,
and to every instance essentially and as such;
from which it clearly follows that all commen­
surate universals inhere necessarily in their sub­
jects.53
ponitur in ratione praedicati, uti supra dictum est), sed perseitas in
quarto modo est perseitas causalitatis formaliter (quatenus scilicet
praedicatum attribuitur subiecto ratione alicuius causalitatis). Et
quia contingit quandoque quod idem sit per se causa alicuius et per
se subiectum eiusdem, ut patet de subiecto respectu propriae passionis;
ideo quandoque secundus modus et quartus... coincidunt in unam
propositionem secundum diversas eius conditiones (ratione nempe
subtecti et ratione causalitatis). Ex. g., in hac propositione: Animal
rationale mortale est risibile, subiectum (animal) ponitur in ratione
praedicati et subiectum est propria causa illius praedicati.”
"Post. Analyt., Bk. 1, Chap. 4, 73b 13-15.
51 John of St. Thomas, op. cit., Vol. I, p. 772.
52 Post. Analyt., ibid., 73b 26.
«/Ma., 26-28.

The Aristotelian-Thomistic Concept

19

We note three elements in the commensurate universal.
(1) It applies to any random instance of its subject, that
is, to all the inferiors of a universal subject and at all
times.54 (2) It applies essentially. (3) It applies as such,
that is, the universality of the predicate must be propor­
tioned to or as broad as the universality of the subject.
The predicate must belong to the subject by reason of the
specific nature of the subject, not by reason of any generic
characteristic that it shares with other things. Or to put
it in another way: “An attribute belongs commensurate?~\
ly and universally to a subject when it can be shown to J
belong to any random instance of that subject and when /
the subject is the first thing to which it can be shown to /
belong.”55 It can be said, for example, that every rock is I
colored. But the predicate here is too broad for the sub-/
ject; it is not commensurate. Color applies to rock not*
as such (as rock), but as a surface; therefore, many otheri
beings besides rocks are colored. To have three angles )
equal to two right angles is a property commensurate J
with triangle, not however with isosceles triangle,/Like­
wise, risibility is commensurate with rationality. How­
ever, sensibility is not commensurate with man, but with
animal. Nor is sight commensurate with animal, but
rather to some unnamed universal, since not all animals
have the sense of sight. Reproduction is not commensurate
with animal, as it belongs also to vegetable, nor with liv­
ing beings, because some living beings (e.g. spiritual be­
ings) do not reproduce; it is, however, commensurate
with living bodies. Breathing, likewise, is not commen­
surate with animal.55 There are some properties that do
not belong commensurately to any particular things at
« Ibid., 73a 27-30.
65 Ibid., 73b 33. Cf. 74a 1-4: “The demonstration, in the essential
sense, of any predicate is the proof of it as belonging to this first
subject commensurately and universally: while the proof of it as
belonging to the other subjects to which it attaches is demonstration
in a secondary and unessential sense.”
58 Cf. Post. Analyt., Bk. 1, Chap. 13, 78b 15-27.

I
r

20

Demonstrating in Natural Philosophy

all, but to being as such; for instance, existence, actuality,
causality, goodness, truth. Scientific knowledge of such
can be had only in a science that treats of being as such
as its subject.
We can begin to see now what a lofty ideal of scientific
knowledge Aristotle and St. Thomas had. It is obviously
not an easy thing to come by, nor can we hope to know
everything in this perfect manner of commensurate uni­
versality. Moreover, we can expect that many errors will
be made in determining what properties and subjects are
commensurately universal. For instance, we could attri­
bute a predicate commensurately to a subject that is actu­
ally too narrow or too broad for it; that is, we could at­
tribute to a species what belongs to a genus, and vice
versa.57 How can we know when we have the commen­
surate universal? We can do no better than give the rule
in the words of Aristotle himself:
When, then, does our knowledge fail of commen­
surate universality, and when is it unqualified
knowledge? If triangle be identical in essence with
equilateral, i.e., with each or all equilaterals, then
clearly we have unqualified knowledge: if on the
other hand it be not, and the attribute belongs to
equilateral qua triangle; then our knowledge fails
of commensurate universality. “But,” it will be
asked, “does this attribute belong to the subject of
which it has been demonstrated qua triangle or
qua isosceles : What is the point at which the sub­
ject to which it belongs is primary? (i. e. to what
subject can it be demonstrated as belonging com­
mensurately and universally?”) Clearly this point
is the first term in which it is found to inhere as
the elimination of inferior differentiae proceeds.
Thus the angles of a brazen and isosceles triangle
are equal to two right angles : but eliminate brazen
and isosceles and the attribute remains. “But”—
87 Aristotle devotes Chapter 5 of the First Book of Posterior
Analytics to discussing three kinds of errors that can be made in
determining the commensurate universal. Cf. St. Thomas’ Com­
mentary, lect. 12.

The Aristotelian-Thomistic Concept

21

you may say—“eliminate figure or limit, and the
attribute vanishes.” True, but figure and limit are
not the first differentiae whose elimination de­
stroys the attribute. “Then what is the first?”
If it is triangle, it will be in virtue of triangle
that the attribute belongs to all the other subjects
of which it is predicable, and triangle is the sub­
ject to which it can be demonstrated as belonging
commensurately and universally.58
Now that we have precised the meaning of essential and
commensurately universal predication, we must see exactly
how they are used in demonstration.
Demonstration is the conclusion of a syllogism in which
an attribute is predicated commensurately of its proper
subject. Now, the proper subject is included in the defini­
tion of the attribute, as was shown above, and the proposi­
tion containing them both is in the second mode of essential
predication. The subject is also the cause of the attribute,
in the fourth mode of predication. “Hence, conclusions of
demonstration include a twofold manner of essential predi­
cation, namely the second and the fourth.”59 Formally, how­
ever, the conclusion is in the second mode.
This conclusion is proved through a middle term that is
a definition of both the subject and the attribute,80 a defini­
tion that tells us quid and propter quid.61 The major prem­
iss, then, whose predicate is the attribute and whose subject
is the definition expressing the cause of the attribute «βά
whim-subject is-thc definition oxpreaBing-the-causc of-the
aUribatfr is in the fourth mode of essential predication.
The minor premiss contains the subject of the conclusion,
to which is predicated, in the first mode of predication, its
a Ibid., Chap. 5, 74a 33-b 4. (Italics ours.)
59 “Unde conclusiones demonstrationum includunt duplicem modum
dicendi per se, scilicet secundum et quartum.” (In l Post Analyt.,
lect 10, n. 8.)
«° “Ex definitione subiecti et passionis sumatur medium demon­
strationis.” (Ibid., lect. 2, n. 3.)
81 “Omnis quaestio est quodammodo quaestio medii, quod quidem
est quod quid est et proper quid." (In II Post. Analyt., lect. 2, η. 1.)

22

Demonstrating in Natural Philosophy

own definition. The conclusion, then, is in the second
mode.®2
An example will help to clarify the above principles. Let
us take the syllogism: “Every rational animal is capable
of science. Man is a rational animal ; therefore, man is cap­
able of science.” The conclusion is the second kind of essen­
tial predication, where a property is ascribed to a commen­
surate subject. The middle term, rational animal, is a defi­
nition indicating quid, or the essential definition of man
in the minor premiss (first mode) and propter quid of the
attribute in the major premiss (fourth mode). For the
essence of the subject is the cause of all the properties that
naturally flow from it.®3
If the major premiss is not in the fourth mode, then the
middle term will not be shown as the cause of the attribute,
and the syllogism will be only explicative. The same would
hold if the conclusion were in the first mode : it would not
' predicate a proper attribute of the subject, but only its defi­
nition, which would give no new truth besides that already
known in the premisses. If, however, the definition con­
cluded is a definition by some other cause, different from
and flowing from the definition that serves as middle term,
then it is as an attribute of the subject.®4
We have now discussed three of the elements in the defi­
nition of demonstration, namely that the premisses have

λκ

'T'

“Sciendum autem est quod cum in demonstratione probetur
passio de subiecto per medium, quod est definitio, oportet quod prima
propositio, cuius praedicatum est passio et subiectum est definitio,
quae continet principia passionis, sit per se in quarto modo; secunda
autem, cuius subiectum est ipsum subiectum et praedicatum ipsa
definitio, in primo modo. Conclusio vero, in qua praedicatur passio
de subiecto, est per se in secundo modo.” (In I Post. Analyt., lect.
13, n. 3.)
®3 Cf. Note t in the Leonine edition of the Commentary on the
Post. Analyt., p. 189.
·* A good summary of the doctrine on demonstration may be found
in the little opusculum De Demonstratione. Mandonnet considers this
■work apocryphal, but Grabmann and Michelitsch, with greater proba­
bility, accept it as an authentic work of St. Thomas.

The Aristotelian-Thomistic Concept

23

to be true, primary and immediate. We still have three
more of the notes: that the premisses must be prior to,
more known than, and causes of the conclusion. The first
three elements concern the premisses in themselves; these
last three concern them in relation to the conclusion.
The premisses must be the cause of the conclusion, "be­
cause we have scientific knowledge when we know causes.”®’
We pointed out earlier that from the standpoint of the for­
mal inference, the premisses are instrumental causes of
the conclusions. From the standpoint of the scientific knowl­
edge produced, the middle term, contained in each of the
premisses, is the cause of the inherence of the attribute
in the subject, as made known in the conclusion. The mid­
dle term can be any of the four causes, depending on the
nature of the subject matter being demonstrated, for a
thing can be defined in terms of any of its causes. But, as
we have noted, in the perfect type of demonstration, demon­
stration propter quid, the cause will be the true ontological
cause of the conclusion, causa, in essendo, not just the cause
of our knowledge of the conclusion, causa in cognoscendo.
Moreover, we must have per se and proximate causes, ac­
cording to what we said above about the need of primary
and immediate premisses. A remote cause is not immedi­
ate ; it is generic and has to be contracted by a specific dif­
ference in order to be proportioned to a specific effect.
Hence, it is not convertible with the effect and therefore
lacks the note of necessary connection. However, it can
sometimes happen that a remote cause is convertible with
its effect and thus can yield a demonstration propter quid.
This is called a remote cause only by reason of position or
order;®® it is not contracted by a specific difference extrinsic
to it; rather, the further determination of it is something
that it already has intrinsically or else something that is
65 “Quia tunc scimus, cum causas cognoscimus.” {In I Post.
Analyt., lect. 4, n. 15.)
®*A cause is remote either by reason of predication, i.e., in the
logical order, when there is a relation of genus to species, or by
reason of order or position.

ί

24

Demonstrating in Natural Philosophy

merely a material condition. Hence the cause is really con­
vertible with the effect. For example, “Every spiritual sub­
stance acts by free will.” We can use this proposition to
demonstrate propter quid, even though it is a remote cause.
For a spiritual substance acts, not of itself, but through
faculties; however, these it has of itself and convertibly
with itself.®7
Finally—a point necessary with respect to metaphysics—
the cause need not be a physical cause, but it can be a meta­
physical or virtual cause, not really distinct from the ef­
fect.®8
Because the premisses are causes of the conclusion, they
must be prior and better known: prior because the causes
must precede their effect; more known because they cause
our knowledge of the conclusion and thereby must be more
perfect in the order of knowledge, according to the causal
axiom, “Propter quod unumquodque tale et illud magis.”
We must dwell for a moment on this fore-knowledge (i.e.
prior and more known) required in the premisses of dem­
onstration. We may enuntiate a general principle about it
in the words of St. Thomas: “The premisses of demon­
stration are prior and more known simply and according
to their own nature, and not in relation to us.”®9 For us,
eT Cf. Note t, IVa, Leonine Edition of the Commentary on the
Posterior Analytics, p. 239. Cf. note b, p. 234.
Cf. John of St. Thomas, op. cit., p. 775-776: “De demonstra­
tionibus propter quid, respondetur non requiri, quod semper procedant
ex causa, quae formaliter sit causa et physice, sed sufficit, quod vir­
tualiter vel metaphysice, ita quod unum se habeat ut ratio alterius,
etsi non sit causans alterum, sicut immutabilitas est ratio aeternita­
tis et perfectio bonitatis, etc. Quod vero dicitur de prima passione
respectu essentiae, respondetur illam quidem causari et dimanare ab
essentia, sed quia essentia est subiectum, de quo debet demonstrari,
non potest demonstrari de ipsa essentia nisi per ipsammet essentiam.
Unde in re caret medio, per quod demonstratur, quia est idem cum
subiecto; accipitur tamen a nobis definitio essentiae quasi medium
demonstrationis non rei, sed ratione distinctum.”
e»“Ea, ex quibus procedit demonstratio, sunt priora et notiora
simpliciter et secundum naturam, et non quoad nos." {In. I Post.
Analyt., lect. 4, n. 15.)

The Aristotelian-Thomistic Concept

25

objects close to sense, namely singular material objects,
are prior to and more known than universals. It is through
the senses that our intellect comes to know universal es­
sences. We work up from the bottom of the cognitional
scale, from the material toward the immaterial.70 The nat­
ural hierarchy of knowable objects, beginning with those
that are prior and more known secundum naturam, is just
the opposite. Since immateriality is the formal constitutive
of knowledge, the more known objects are those that are
more immaterial, more actual, more perfect. Strict scien­
tific knowledge proceeds from cause to effect. The cause
has more actuality, more perfection, more being than the
effect. Hence, the cause in itself has more knowability
than the effect, so that the premisses in which the cause is
known are more known than the conclusion in which the
effect is known.
What, then, will be the nature and extent of the fore­
knowledge we need in order to have a strict demonstration?
Demonstration, it has been remarked, is a reasoning
process, pertaining to the third act of the mind. It pre­
supposes simple apprehensions and definition of the terms
involved, namely, the subject, predicate and middle term.
It requires also two immediate judgments, whereby the sub­
ject and predicate are seen to be essentially related to the
middle term.71 The definitions and propositions that are
the premisses of demonstration are called its principles,
that is, its άρχαί, its beginnings, sources or points of
origin.72 One must also know, as a preliminary to demon­
70 Cf. Summa Theol., I, q. 85, a. 3; In I Physica, lect. 1, n. 7;
In I Post. Analyt., lect. 4, n. 15,16.
71 “Id cujus scientia per demonstrationem quaeritur est conclu­
sio aliqua in qua propria passio de subiecto aliquo praedicatur: quae
quidem conclusio ex aliquibus principiis infertur. Et quia cognitio
simplicium praecedit cognitionem compositorum, necesse est quod,
antequam habeatur cognitio conclusionis, cognoscatur aliquo modo
subjectum et passio. Et similiter oportet quod praecognoscatur princi­
pium, ex quo conclusio infertur, cum ex cognitione principii conclusio
innotescat.” (In I Post. Analyt., lect. 2, n. 2.)
l/ 72 “Principium syllogismi dici potest non solum propositio, sed etiam

26

Demonstrating in Natural Philosophy

strafing, the basic principle of the formal inference, name­
ly the principle of non-contradiction. However, this is spon­
taneously known by all and may therefore be passed over
here.
There are two ways of knowing anything: to know that
it exists (quia est) and to know what it is (quid est). In
order to know anything, we must first know that it exists,
either in the mind or in reality; for what does not exist
does not have any being whatever and is therefore unknow­
able. When we ask about a proposition the question an sit,
we are inquiring whether it has the being proper to a prop­
osition: does the predicate inhere in the subject? in other
words, is the proposition true? Once we know the exist­
ence of a thing, we inquire its nature: quid sit, that it, we
seek a definition of it, either of its essence (quid rei) or of
its name (quid nominis). Obviously we cannot have a defi­
nition of a proposition, for definition pertains to essences
known through simple apprehension, not to judgment.
Regarding the subject of a scientific conclusion we must
know its existence and its real definition, which we predi­
cate of it in the minor proposition. For the definition of
the subject is the middle term in our demonstration. Of
the attribute, however, we cannot have foreknowledge of
its existence, for its existence in the subject is what we
want to demonstrate. Neither, than, can we know its es­
sence, “for before we know whether a thing exists, we can­
not properly know what it is : non-beings do not have déli­
tions.”73 Besides, the proper subject enters into the defini­
tion of the attribute. Hence, we must be satisfied with a
nominal definition of the attribute?3
.definitio.” “Principium demonstrationis sit propositio immediata.”
(Ibid., lect. 5, η. 9, η. 1.)
73 St. Thomas* doctrine is given in the following text: “Horum
autem trium, scilicet, principii, subiecti et passionis est duplex modus
praecognitionis, scilicet, quia est et quid· est. Ostensum est autem
in VII Metaphysicae quod complexa non definiuntur. Hominis enim
albi non est aliqua definitio et multo minus enunciationis alicuius.
Unde cum principium sit enunciatio quaedam, non potest de ipso
praecognosci quid est, sed solum quia verum est. De passione autem

The Aristotelian-Thomistic Concept

27

The doctrine we have explained thus far by commenting
on each element of the two definitions of demonstration
applies properly to demonstration propter quid, or as Aris­
totle’s Oxford translator aptly renders it, “knowledge of
the reasoned fact.”74 It will help us to an accurate under­
standing of scientific demonstration if we contrast it with
other forms of proof.75
First, there is a distinction between demonstratio uni­
versalis, or the perfect type where there is commensurate
universality between subject and predicate, and demonstra^
tio particularis, where an attribute is predicated of a partic­
ular subject through a middle term which is the proper
and commensurate subject of the attribute; for example,
an isosceles has three angles equal to two right angles be­
cause it is a triangle.754 In this type of demonstration, even
though the attribute in the conclusion is not commensurate
with the subject, yet it is shown to belong to it because of
its participation in the nature of the proper subject: the
attribute belongs to the particular subject not by reason
potest de ipso quidem sciri quid est, quia, ut in eodem libro ostenditur,
accidentia quodammodo definitionem habent. Passionis autem esse et
cuiuslibet accidentis est inesse subiecto: quod quidem demonstratione
concluditur. Non ergo de passione praecognoscitur quia est, sed quid
est solum.—Subiectum autem et definitionem habet et eius esse a
passione non dependet; sed suum esse proprium praeintelligitur ipsi
esse passionis in eo. Et ideo de subiecto oportet praecognoscere et
quid est et quia est·, praesertim cum ex definitione subiecti et pas­
sionis sumatur medium demonstrationis....
“Alia vero sunt, de quibus oportet praeintelligere quid est quod
dicitur, idest quid significatur per nomen, scilicet de passionibus.
Et non dicit quid est simpliciter, sed quid est quod dicitur, quia
antequam sciatur de aliquo an sit, non potest sciri proprie de eo quid
est: non entium enim non sunt definitiones. Unde quaestio, an est,
praecedit quaestionem, quid est. Sed non potest ostendi de aliquo an
sit, nisi prius intelligatur quid significatur per nomen.” (In I Post.
Analyt., fect. 2, n. 3, n. 5.)
74 Post. Analyt., Bk. 1, Chap. 13, 78a 22.
75 Cf. the schema of types of demonstration given in the Leonine
Edition of the Commentary on the Post. Analyt., p. 239.
754 Cf. In I Post. Analyt., lect. 37 and 38, esp. note a, p. 291. See
also the opusculum De Demonstratione.

If·'-

28

Demonstrating in Natural Philosophy

of its specific nature, but by reason of its proximate genus.
Hence, the particular demonstration partakes of the perfec­
tion of propter quid demonstration, although not fully. The
cause assigned is an actual and proximate cause of the attri­
bute, not a remote or radical cause that needs a specific
difference which would assign the reason of the attribute.
Such would be the case if we said that an isosceles has three
angles equal to two right angles because it is a plane figure.
This particular demonstration is of great value, especially
when it occurs in conjunction with a universal demon­
stration as applying the universal conclusion to a less universai case.
A demonstration propter quid may be of two kinds from
the point of view of what is proved. This division is only
implicit in Aristotle, and was explicitly made by Averroes.
An effect may be already known, for instance, we may see
an eclipse of the moon, and a demonstration of that effect
will make known its cause. This Averroes called demon­
stratio propter quid tantum. Or we may deduce the very
existence of the effect and then we would have a demon­
stration of the proper cause and the being of the effect,
which Averroes called propter quid et absoluta.™
Demonstration quia,77 the kind of proof that establishes
the existence or truth of a fact without telling the proper
reason or cause of the fact, is univocally a type of demon­
stration, for it gives us certain and evident knowledge.
But it imperfectly participates the nature of science, which
sees the proper causes of attributes in the essence of their
subjects.78 There are degrees of demonstration quia. It
may be a posteriori, through effects that are convertible and
adequate with their hidden causes, which are thus made
known. Then we can come to a knowledge of the essence
of the cause. Or it may be through effects not adequate
78 Schema of demonstration, Illa (Cf. note 75 supra.) Cf. St.
Thomas, In II Post. Analyt., lect. 7, n. 5.
w Cf. Summa Theol., I, q. 2, a. 2.
Cf. John of St. Thomas, op. cit., p. 788.

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The Aristotelian-Thomistic Concept

29

to their cause, and then we arrive at only the existence of
the cause.
Some things are knowable to us through them­
selves; and in bringing such things to light the
speculative sciences use their definitions to demon­
strate their properties, as happens in the sciences
which demonstrate propter quid. There are other
things which are not knowable to us through
themselves but through their effects. And if in­
deed the effect is adequate to the cause, we take
the quiddity itself of the effect as our starting
point to prove that the cause exists and to investi­
gate its quiddity, from which in turn its properties
are made evident. But if the effect is not adequate
to the cause, then we take the effect only as the
starting point to prove the existence of the cause
and some of its conditions, although the quiddity
of the cause is always unknown.79
Demonstration quia occurs also when we have reasoning
from cause to effect, but the cause is remote and non-con­
vertible with its effect. Aristotle gives as one example that
a wall does not breathe because it is not an animal.80 This
is only a remote cause and is not convertible, or adequately
universal, with the effect, because there are some animals,
fishes, that do not breathe. The proper cause of not breath­
ing is the absence of lungs. Such demonstrations are useful
and yield certainty of fact when they are negative. But
often, to demonstrate from a non-convertible cause, says
Aristotle, is “like far-fetched explanations, which precise­
ly consist in making the cause too remote, as in Anacharsis’
79In De Trin., q. 6, a. 4, ad 2. Cf. In II Post. Analyt., lect. 13 . When
an a posteriori demonstration has led us to a proper and commensurate
cause, we can turn around and demonstrate the effect a priori. This
does not constitute a circular demonstration. There is a circular
demonstration when the conclusion is deduced a priori from the
premisses, and then the premisses are deduced a priori from the
conclusion. In such a case, the premisses are more known and less
known at the same time. Cf. St. Thomas, In I Post. Analyt., lect.
8, and note b of Card. Zigliara (Leonine ed.)
80 Post. Analyt., Bk. I, Chap. 13, 78b 15.

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Demonstrating in Natural Philosophy

account of why the Scythians have no flute-players, namely
because they have no vines.”81
Demonstration can also be indirect, or negative. It can
show that it is impossible or absurd that a certain attribute
should inhere in a certain subject. Such demonstration
can be both propter quid or quia. This type is not to be
contemned, for sometimes we must be satisfied to know
what a thing is not; at other times, when we are able to
set up a complete disjunction, then by showing that a thing
is not one member of the disjunction, we by that very fact
show that it is the other.
In the beginning of this chapter we spoke of the process
of understanding whereby we grasp the principles of dem­
onstration : the definitions and immediate propositions that
make up a syllogism. Understanding and scientific demonstration give us true knowledge of a necessary object or
fact. But there are also facts that are true, though not nec­
essary; they are contingent. They obviously cannot be the
object of science, which by its very nature concerns neces­
sary matters. The act of the mind that apprehends the
contingent is called opinion.82 Aristotle defines it as: “the
grasp of a premiss which is immediate but not necessary.”83
It may be an immediate and necessary proposition, but
thought to be contingent; or it may be itself contingent.
If there is some mediate contingent proposition,
it has to be reduced to some immediate propositions. But it is not reduced to necessary immediate
propositions, because necessary principles are not
the proper principles of contingent things, nor can
contingent things be concluded from necessary
things. Hence there must be some contingent im­
mediate proposition. For instance, the man is not
running is mediate ; it can be proven through this
middle: the man is not moving, which is a contingent, but immediate proposition. The knowledge of such contingent immediate propositions is
opinion : but this does not exclude the acceptance
« Ibid., 29-31.
82 Cf. In I Post. Analyt., lect. 44.
63 Post. Analyt., Bk. 1, Chap. 33, 89a 4.

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The Aristotelian-Thoinistic Concept

31

of a mediate contingent proposition from being
opinion.84
Thus we have opinion considered subjectively, or the assent
given to any proposition with some fear that it may not be
true; and opinion considered objectively, or the assent to
a proposition concerning contingent matter, whether the
proposition be actually true or false.85 Opinion can yield
us factual certitude regarding contingent things, but as
scientific explanation it cannot surpass the status of proba­
bility. A syllogism that concludes only an opinion or non­
necessary knowledge is called a dialectical syllogism.
It is to be noted that the reason for contingency is mat­
ter. It is by reason of form that things have 'the character
of necessity, and since form is the determinant of cogni­
tion, things are the more knowable the more necessary they
are. Matter is the principle of contingency, for matter in­
troduces into a being the potentiality to be otherwise than
it is. Thus, the contingent, being more immersed in matter,
is by that very fact less knowable, for a thing is knowable
in proportion to its immateriality. So we can have science
of the necessary, but only opinion of the contingent.88
84 “Si igitur sit aliqua propositio contingens mediata, oportet quod
reducatur ad aliquas immediatas. Non autem reducitur ad immedia­
tas necessarias, quia necessaria non sunt propria principia contingen­
tium, neque ex necessariis potest concludi contingens. Unde relinqui­
tur quod sit aliqua propositio immediata contingens. Sicut, homo non
currit, est mediata; potest enim probari per hoc medium, homo non
movetur, quae etiam est contingens, sed immediata. Existimatio ergo
talium propositionum contingentium immediatarum est opinio: sed
per hoc non excluditur quin etiam acceptio propositionis contingentis
mediatae sit opinio.” (In I Post. Analyt., lect. 44, n. 5.)
85 There is a broad and generic use of the word “opinion,” meaning
any knowledge with assent, e.g., St. Thomas’ opinion on the eternity
of the world. In this sense, understanding and science can also be
called opinion.
88 This is not meant to rule out the certainty of things known by
faith or history. The authority of another can give us certain and
necessary knowledge of a nature, such as the nature of the sacra­
ments. A trustworthy eye witness gives certitude of the contingent
facts of history; this is a certitude of existence or fact, not of essence,
and hence is of no concern to us in this discussion of science.

32

Demonstrating in Natural Philosophy

Moreover, since matter is the principle of individuation,
we immediately see that singular things are contingent—
singular things, the knowledge of which belongs properly
to sense, and only indirectly to the intellect.87 This knowl­
edge of singular contingent things as contingent is really
not an intellectual knowledge at all. It belongs rather to
the sense faculties, especially to the cogitative power. This
distinction is so important that it deserves to be corro­
borated by a pertinent quotation from St. Thomas.
Contingent things can be known in two ways. In
one way, according to their universal reasons ; in
another way, in their particularity. The universal
reasons of contingent things are immutable, and
from this aspect there can be demonstrations about
them and the knowledge of them pertains to dem­
onstrative sciences. For natural science does not
deal only with necessary and incorruptible things,
but also with corruptible and contingent things.
Hence, contingent things so considered clearly be­
long to the same part of the intellective soul as do
necessary things. This the Philosopher calls sci­
entific. __ Contingent things can be considered in
another way, in their particularity: thus they are
variable and are known by the intellect only
through the medium of the sensitive powers. Hence
among the sensitive parts of the soul there is a
faculty that is called particular reason or vis cogitativa, which collates particular intentions.88
87 “Est autem unumquodque contingens ex parte materiae, quia
contingens est quod potest esse et non esse; potentia autem pertinet
ad materiam. Necessitas autem consequitur rationem formae, quia ea
quae consequuntur ad formam, ex necessitate insunt. Materia autem
est individuationis principium; ratio autem universalis accipitur
secundum abstractionem formae a materia particulari. Dictum autem
est supra quod per se et directe intellectus est universalium; sensus
autem singularium, quorum etiam indirecte quodammodo est intel­
lectus, ut supra dictum est. Sic igitur contingentia, prout sunt con­
tingentia, cognoscuntur directe quidem sensu, indirecte autem ab intel­
lectu; rationes autem universales et necessariae contingentium cognos­
cuntur per intellectum.” (Summa Theol., I, q. 86, a. 3.)
88 "Contingentia dupliciter cognosci possunt. Uno modo secundum
rationes universales; alio modo secundum quod in particulari. Univer-

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The Aristotelian-Thomistic Concept

33

We wished to emphasize this matter of opinionative
knowledge of contingent objects, because positive science
deals with contingent objects, at least insofar as it does
not arrive at a grasp of their essences whereby necessary
knowledge is attained. Hence, de facto, positive science,
in as far as it is physical rather than mathematical, seems
to remain on the level of the cogitative power, and so is not
science at all in the Aristotelian sense. Its “concepts” are
not true universals, but the quasi-universals or generalized
sense images of the cogitative. We will have to come back
to this point presently. First, we wish to discuss opinion
in the domain of necessary matter, of conclusions which
in themselves are scientific, but which are not grasped as
such by a particular person—opinion, that is, considered
subjectively rather than objectively.
A man may have only opinion of a conclusion that is
objectively a scientific and necessary proposition. One may
see the proposition as impossible to be otherwise, and thus
have science. Another may think it possible to be other­
wise. The root of his difficulty is in the understanding of
the immediate propositions. The first man sees them as
immediate; the other cannot see them as such, so he is
barred from scientific knowledge of the conclusion. A corol­
lary to this possibility of a scientific demonstration being
known only opinionatively is the need to understand demon­
strative theory, and this especially for beginners in philos-

f

,

sales quidem igitur rationes contingentium immutabiles sunt, et secun­
dum hoc de his demonstrationes dantur et ad scientias demonstrativas
pertinet eorum cognitio. Non enim scientia naturalis solum est de
rebus necessariis et incorruptibilibus, sed etiam de rebus corruptibili­
bus et contingentibus. Unde patet quod contingentia sic considerata
ad eamdem partem animae intellectivae pertinent ad quam et neces­
saria, quam Philosophus vocat hic scientificum.... Alio modo possunt
accipi contingentia secundum quod sunt in particulari: et sic var­
iabilia sunt nec cadit supra ea intellectus nisi mediantibus potentiis
sensitivis. Unde et inter partes animae sensitavas ponitur una potentia
quae dicitur ratio particularis, sive vis cogitativa, quae est collativa
intentionum particularium.” {In VI Ethicorum, lect. 1, n. 1123. Cf.
De Anima, a. 12, c., De Ver., q. 15, a. 2, ad 3.)

34

Demonstrating in Natural Philosophy

ophy. If one does not understand the process of demon­
stration, he will indeed learn philosophy : he will know the
doctrines of Thomism and perhaps even teach them. But
if he does not recognize and understand the demonstra­
tions, his knowledge will not be scientific, but opinionative
and always vacillating and unstable/9 He will therefore
be tempted to look around for novel opinions, or to confine
'•himself to the historical approach to philosophy, or to be­
come a mere cataloguer of opinions.
Opinion, as an inferior type of knowledge, is character­
ized by uncertainty on the scientific level. St Thomas com­
pares it with natural processes that do not always and of
necessity produce their effects.90 Its essential weakness is
also apparent from the fact that we do not acquire an opin­
ion ordinarily from a single probable argument, but prefer
to multiply arguments and count the authorities favoring
the opinion.91 So when philosophy becomes a listing of
89 “To have knowledge, if it be not accidental knowledge of things
which are demonstrable, means precisely to have a demonstration of
them.” (Post. Analyt., Bk. 1, Chap. 2, 71b 28.)—Common sense
knowledge can in some cases be certain and necessary, and thus parti­
cipates the nature of science. Yet, because it is confused and uncriti­
cal, it falls short of the perfection of science.
"“Attendendum est autem quod actus rationis similes sunt,
quantum ad aliquid, actibus naturae. Unde et ars imitatur naturam
in quantum potest. In actibus autem naturae invenitur triplex
diversitas. In quibusdam enim natura ex necessitate agit, ita quod
non potest deficere. In quibusdam vero natura ut frequentius operatur,
licet quandoque possit deficere a propria actu. Unde in his necesse est
esse duplicem actum; unum, qui sit ut in pluribus, sicut cum ex semine
generatur animal perfectum; alium vero quando natura deficit ab eo
quod est sibi conveniens, sicut cum ex semine generatur aliquod mon­
strum propter corruptionem alicuius principii. Et haec etiam tria
inveniuntur in actibus rationis. Est enim aliquis rationis processus
necessitatem inducens, in quo non est possibile esse veritatis defectum;
et perhuiusmodi rationis processum scientiae certitudo acquiritur:
Est autem alius rationis processus, in quo ut in pluribus verum
concluditur, non tamen necessitatem habens. Tertius vero rationis
processus est, in quo ratio a vero deficit propter alicuius principii
defectum." (In I Post. Analyt., lect. 1, n. 5.)
81 “Quando actio agentis est efficacior, tanto velocius inducit formam;

'I

.1

rt

The Aristotelian-Thomistic Concept

35

opinions, it is actually in a weakened and degenerate state.
However, we do not wish to imply that opinion has no
place in the genesis of science. To begin with, the essen­
tial limitation of our minds does not permit us to have cer­
tainty about everything. There are some matters about
which we must be content to have only probability. Then,
there are many minds that cannot grasp demonstrations,
and so find satisfaction on the more superficial level of com­
mon opinion. But the most important function of dialectics
is its methodological character; it is a preparation for, a
clearing of the way for, and the first gropings toward true
scientific demonstration. “Dialectic is a process of criti­
cism wherein lies the path to the principles of all in­
quiries.”92 “Moreover, as contributing to knowledge and to
philosophic wisdom the power of discerning and holding in
one view the results of either of two hypotheses is no mean
instrument, for it then only remains to make a right choice
of one of them.”92 As St. Thomas puts it:
Sometimes the investigation of reason cannot ar­
rive at the ultimate end, but stops in the investiga­
tion itself, that is to say, when two possible solu­
tions still remain open to the investigator. And
this happens when we proceed by means of prob­
able arguments, which are suited to produce opin­
ion or belief, but not science. In this sense, ra­
tional method is contradistinguished to demonstra­
tive method. And we can proceed rationally in
all the sciences in this way, preparing the way for
necessary proofs by probable arguments.94
It is important to note the difference between demon­
stration and the so-called "scientific” method. This latter
et ideo videmus in intellectualibus, quod per unam demonstrationem,
quae est efficax, causatur in nobis scientia; opinio autem, licet sit
minor scientia, non causatur in nobis per unum syllogismum dialec­
ticum; sed requiruntur plures propter eorum debilitatem.” (De
Virtutibus in Communi, a. 9, ad 11.)
92 Topics, Bk. 1, Chap. 2, 101b 3-4. On this whole matter of opinion,
cf., L.—M. Regis, O.P., L’Opinion selon Aristote.
«Ζόάί, Bk. 8, Chap. 14, 163b 9-11.
84 In De Trin., q. 6, a. 1, c.

36

Demonstrating in Natural Philosophy

is not a species of demonstration, but rather a process of
discovery. It is more closely related to the search for defini­
tions and to induction, than to demonstration. Induction
is the progression of the mind from a sufficient enumera­
tion of singular instances to the universal implicit in them.
It takes its origin in the experience of the senses through
the mediation of the vis cogitativa, from whose generalized
image the intellect abstracts a universal essence, or in in­
ductive argumentation, infers the universal.95 It is to be
noted that induction does not necessarily give us a knowl­
edge of an essence down to its last specific difference at the
outset of our investigation. But it does yield us a general
definition; it gives us some knowledge of an essence, a
knowledge that we can further divide and specify in the
course of our sciences.

As we come down to the particular aspects of material
beings, we find their specific natures impervious to our in­
tellectual intuition. Their very materiality dims their intellibility. At this level we must often substitute an un­
known x, a conjecture or a hypothetical construction, espe­
cially of a mathematical kind, for the essence.9* In this
we touch upon the core of the experimental method. A
large number of facts are carefully observed, ordinarily by
measuring instruments, for example, the rectilinear propa­
gation of light, its reflection from a smooth surface, its
angle of refraction at the surface of a body of water, and
the transmission of energy by light. From the constant
recurrence of these phenomena we come to suspect that
they are properties of light. But we cannot demonstrate
95 Cf. In I Post. Analyt., lect 30, n. 4-6; II, lect. 20.
98 “Sunt autem quaedam in quibus non est possibile talem resolu­
tionem facere ut perveniatur usque ad quod quid est, et hoc propter
incertitudinem sui esse; sicut in contingentibus in quantum con­
tingentia sunt: unde talia non cognoscuntur per quod quid est,
quod erat proprium objectum intellectus, sed per alium modum, scilicet
per quamdam conjecturam de rebus illis de quibus plena certitudo
haberi non potest.” (De Ver., q. 15, a. 2, ad 3. Cf. Summa Theol.,
I, q. 32, a. 1, ad 2.)

1
,

/

;

The Aristotelian-Thomistic Concept

37

them as such, because we do not know the essence of light.
Essence is the middle term of a demonstrative syllogism,
and is the foundation of the necessity of the scientific con­
clusion. However, as a hypothesis, light was for many
centuries considered to be the emission of corpuscules shoot­
ing out from a luminous source. Taking such a provisional
definition of light as a middle term, scientists thought that
the attributes were shown to follow as properties. But nat­
urally, the whole demonstration did not surpass the level
of probability.
Thus we have two steps: observation and hypothesis.
Now, if the hypothesis is true, it will not only explain all
the observed facts in question, but it will also serve for
the deduction of new facts. Thus, the third step of the ex­
perimental method is that of verification : deduction of new
facts and the construction of a “crucial” experiment to test
the deduction.
Even when a hypothesis is “verified” by deduction of new
phenomena, no matter how startling they may be—even
then we do not enjoy necessary and scientific knowledge.
The fact could be otherwise, since we do not have an intel­
lectual intuition of the essence, but know it only by con­
jecture. Thus, there have been a succession of theories
regarding the nature of light: the corpuscular, the wave,
the electromagnetic and finally the quantum theory. The
atomic theory, the Copernican theory of the heavenly bodies,
the Freudian theory of the psyche, in fact, a large part of
Newtonian physics—all are merely probable explanations,
not in the realm of demonstration, but rather of inductive
attempts to reach a definition.97 In this respect we must
87 It would be better to say that the theories of experimental
science are working hypotheses for the discovery of new facts and
practical applications. Scientists are not so much interested in
essential as in functional and metrical definitions which will suggest
further research. As Vincent E. Smith says: “Discovery, not proof,
is the goal of empiriological physics. From Georges Sorel, one may
borrow the term systematic and some of its meaning. Empiriological
physics makes a system or catalogue of facts for the engineers. It

38

Demonstrating in Natural Philosophy

remember St. Thomas’ remark regarding the Ptolemaic sys­
tem of astronomy:
Reasoning may be brought forward for anything
in a twofold way: firstly, for the purpose of fur­
nishing sufficient proof of some principle, as in
natural science, where sufficient proof can be
brought to show that the movement of the heavens
is always of a uniform velocity. Reasoning is em­
ployed in another way, not as furnishing a suffi­
cient proof of a principle, but as showing how the
remaining effects are in harmony with an already
posited principle; as in astronomy the theory of
eccentrics and epicycles is considered as estab­
lished, because thereby the sensible appearances of
the heavenly movements can be explained; not
however, as if this proof were sufficient, since
some other theory might explain them.98
This method of the experimental sciences is called by
some “systematic explanation” and is merely a substitute
for demonstration.99 It can be used whenever we do not
have a definition of our subject. It is used in theology, as
for instance in the distinction of the angels into hierarchies
and orders.190 This method consists essentially in using a
logical, and very often mathematical, construct in place of
an essential definition. In this way congruous premisses
can be established from which a certainly known conclusion
is seen logically to follow. However, there is no question
of a connection of the conclusion with real and necessary
multiplies data by schemes that are not explanations and are not
ultimate. The ultimate in the empiriological order is the practical and
the factual of experience.” (Philosophical Physics, p. 174.)
98 Summa Theol., I, q. 32, a. 1, ad 2; cf. In II De Coelo, lect. 17, n. 2.
" Cf. tiie excellent treatinent of Owen Bennett, O.M.C., The Nature
of Demonstrative Proof, Chap. VI, “Systematic Explanation, the
Substitute fo Demonstrative Proof” and Chap. VII, “The Use and In­
terpretation of Systematic Explanation,” pp. 68-85. Our description of
the experimental method has been confined to the explanatory aspect,
the search for causes. There is another aspect to the method, the
search for physical laws or relations between phenomena. Cf. P.
Coffey, The Science of Logic, Vol. II, pp. 120-127.
loo Cf. Summa Theol., I, q. 108, a. 1-6.

The Aristotelian-Thomistic Concept

39

principles. The experimental method cannot directly and
immediately yield science in the strict Aristotelian sense of
the word.
As a final remark, we may say that where a definition of
a subject is available, particularly in the sciences of man,
whose specific definition we know, we should use the demon­
strative method, otherwise we close the door to a rich
harvest of truth and doom ourselves to roam in the stubblefield of uncertainty. We will return to this subject again
and again. For the present we may quote a few sentences
of Father Bennett, at the conclusion of his valuable study
of systematic explanation.
It would be foolish, indeed, to contemn such an in­
strument. But it would be more foolish to use it
or seek to use it when a more perfect instrument
is at hand and can be employed. Let man, rather,
prove what he can prove, and explain by system
what he cannot prove.101
ιοί Op· cit., p. 91.

CHAPTER II

THE SUBJECT OF NATURAL PHILOSOPHY
A science is a body of truths about some subject, varying!
in their degrees of certitude, but all essentially orientated
toward and leading to strict propter quid demonstrations.
We have seen that before we can demonstrate we have to
know the existence and nature of our subject, for the defini­
tion of the subject is the middle term in a demonstration,
and in the light of it we prove the proper attributes. The
knowledge of the subject is attained either through sensory
experience or is supplied from a higher science, for no sci­
ence can prove its own subject, but rather proves the attri­
butes by means of the subject.1
Sciences are distinguished from one another by reason of
their subjects, that is, according to the manner in which the
subjects are defined, for the definition of the subject as>
used for the middle term is the principle of intelligibility!
of all that is attained in a science.12 In order, then, to deter­
1 “Ipsum autem quod quid est sui subjecti aliae scientiae faciunt
esse manifestum persensum; sicut scientia, quae est de animalibus,
accipit quid est animal per id quod ‘apparet sensui,’ idest per sensum
et motum, quibus animal a non animali discernitur. Aliae vero
scientiae accipiunt quod quid est sui subjecti, per suppositionem ab
aliqua alia scientia, sicut geometria accipit quid est magnitudo a
philosopho primo. Et sic ex ipso quod quid est noto per sensum vel
per suppositionem, demonstrant scientiae proprias passiones, quae
secundum se insunt generi subjecto, circa quod sunt. Nam definitio
est medium in demonstratione propter quid.” (In VI Meta., lect. 1,
n. 1149. Cf. In II Post. Analyt., lect. 8, n. 1.)
2 “Ad cognoscendum differentiam scientiarum speculativarum ad in­
vicem, oportet non latere quidditatem rei, et ‘rationem’ idest defini­
tionem significantem ipsam, quomodo est assignanda in unaquaque
scientia. Quaerere enim differentiam praedictam, ‘sine hoc,’ idest
sine cognitione modi definiendi, nihil facere est. Cum enim definitio
sit medium demonstrationis, et per consequens principium sciendi,
oportet quod ad diversum modum definiendi, sequatur diversitas in
scientiis speculativis.” (Ibid., n. 1156.)
40

The Subject of Natural Philosophy

41

mine the nature of natural philosophy, we must first in­
vestigate the requirements and characteristics of the sub­
ject of a science.
There is a difference of terminology and viewpoint among
the scholastics regarding the subject of a science. This can
be confusing, especially when we are reading the text of
St. Thomas and paralleling his doctrine with that of his
commentators. In the following discussion we have adopted
the divisions and terminology of John of St. Thomas in
his Cursus Theologicus3 as being more in harmony with
the usage of St. Thomas. The terminology of Cajetan,4
which most authors follow, seems deficient in that it does
not explicitly distinguish between the subject of a science
and the object of the habit of science.
“In each science,” says John of St. Thomas, “subject and
object differ; and in each we can find something formal
and something material.”5* When St. Thomas speaks of sci­
ence in the sense of the .scientific process, he uses the term:
“subject” or “subject-genus” of the science. It is that of
which we are seeking knowledge: “A subject in a science·
is that whose causes and properties we are seeking.”*7
Whereas, when he speaks of science in the sense of an in­
tellectual habit, he refers to the object of science. Subject
and object are not identical, though there is an analogy
between them.7 It is to be noted that the object of the habit
of science is not a subsisting thing, as the subject is; it is
rather the scientific process itself, the demonstrations given
3 Cursus Theologicus, In Q. 1, Primae partis, Disp. 2, Art. 11, Vol.
I, p. 402.
4 Commentaria in la, q. 1, a. 3.
5 “In qualibet scientia differunt subjectum et objectum, et in
utroque potest invenire id quod est formale, et quod est materiale.”
(Ibid.)
* “Hoc enim est subjectum in scientia, cujus causas et passiones
quaerimus.” (In Meta., Proem.) Cf. “... genus subjectum, cuius
proprias passiones et per se accidentia demonstratio ostendit.” (In I
Post. Analyt., lect. 15, n. 3.)
■ 7 “Sic enim se habet subiectum ad scientiam, sicut obiectum ad
potentiam vel habitum.” (Summa Theol., I, q. 1, a. 7.)

42

Demonstrating in Natural Philosophy

in the science. John of St. Thomas calls it: "something
complex, namely that which is made known by the science
as inferred and proved.”8 That which specifies the habit
of science is not the subject known, but the scientific knowl­
edge of that subject, the scientific conclusions about that
subject.
The subject is both material and formal. The mate­
rial subject (or subject matter) is the thing or things to
be studied in the science, apart from the consideration of
the mind ; for instance, man, animals, vegetables, minerals,
etc., as they exist entitatively. It embraces everything that
can be the subject of a conclusion in the science. The formal
subject is the particular aspect from which the material
subject is to be considered, that aspect, namely whereby
the material thing is the proper and commensurate sub­
ject of the attributes to be demonstrated of it.
The material object of the habit of science is all the sci­
entific conclusions about the subject. The formal object is
the reason under which and through which the conclusions
are made known scientifically.9 We saw in the preceding
chapter that it is the middle term, as the definition of the
subject, that is the cause of the scientific intelligibility of
the conclusion. This is clear in the following passage of St.
Thomas:
The object of every cognitive habit includes two
things : first, that which is known materially, and
is the material object, so to speak, and secondly,
that whereby it is known, which is the formal
•“Objectum scientiae est aliquid complexum, scilicet id quod per
scientiam manifestatur tamquam illatum et probatum, scilicet con­
clusiones, ut docet S. Thomas (Π-ΙΙ, q. 1, a. 1) : scientia enim non
cognoscit, nisi probando et inferendo. Quod autem infertur et pro­
batur, est conclusio illata: conclusio autem est aliquid complexum,
in quo aliquod praedicatum dicitur de aliquo subjecto; et illa propo­
sitio seu conclusio illata dicitur objectum scibile, id est, id quod scitur
et infertur in aliqua scientia.” {Ibid, Cf. Summa Theolo., I-Π q. 57,
a. 2, ad 2.)
» "Formale vero est ratio illa sub qua, et per quam illustratur et
manifestatur talis conclusio.” (John of St. Thomas, Ibid.)

Λ

The Subject of Natural Philosophy

43

aspect of the object. Thus, in the science of geom­
etry, the conclusions are what is known materially,
while the formal aspect of the science consists in
the means (.media) of demonstration, through
which the conclusions are known.10
The formal object, then, is the middle term as it is the defi-J
nition of the formal subject. This middle term is a defini-]
tion by the first principles or component parts of the formal]
subject, and in the light of these first principles, the con-1
elusions are deduced.
We must investigate further into the nature and require­
ments of the object of a science. St. Thomas says:
Now we must understand that when habits or
powers are distinguished according to their ob­
jects, they are not distinguished according to just
any difference of objects, but according to those
which essentially characterize the objects as ob­
jects. For instance, to be either animal or plant is
accidental to a sensible thing as sensible; and so
the distinction of the senses is not taken from this
difference, but rather from the difference of color
and sound. Consequently, the speculative sciences
must be distinguished according to the differences
among objects of speculation precisely as objects
of speculation.11
In other words, although things may be specifically distinct
in their entitative being, such as men or brutes, they may
be united into one object of speculation, if there is a single
knowable aspect in them all, and if they can be made ob­
jects of knowledge by being defined with the same first
principles. As St. Thomas says in another place:
In order for a science to be simply one there is re­
quired unity of both subject and principles.... It
is not to be understood that for the unity of a sci­
ence it is sufficient to have unity of first principles
simply, but rather, unity of first principles in
some scientific genus (genere scibili). For sci™ Summa Theol., II-II, q. 1, a. 1.
» In De Trim, q. 5, a. 1. Cf. Summa Theol., I, q. 77, a. 3; Ι-Π,
q. 54, a. 2; In I Post. Analyt., lect. 41, n. 11.

44

Demonstrating in Natural Philosophy

entific genera are distinguished according to the
different manner of knowing.12
An object of the habit of science (i.e. a scientific demon­
stration) must have two characteristics, one on the part of
the intellect and another on the part of the habit of sci­
ence. John of St. Thomas remarks:
To be knowable scientifically adds to mere intel­
ligibility a special manner of knowledge, namely,
that something be known not in a simple manner,
but in an inferential manner by proceeding from
causes, or premisses, to conclusions; for to know
scientifically is to know the cause why a thing
is.13
A thing is intelligible according to its degree of immate-j
riality; but a thing is scientifically intelligible insofar as j
an attribute is seen to inhere necessarily in a necessary |
subject.14
Immateriality and necessity, then, arp^the two notes of '
the scientific object. The middle termis the cause of the J
necessity of the conclusion and must therefore itself be

•
!
;
I

1
j

12 "Ad hoc autem quod sit una scientia simpliciter utrumque re­
quiritur et unitas subiecti et unitas principiorum.... Nec tamen
intelligendum est quod sufficiat ad unitatem scientiae unitas princi­
piorum primorum simpliciter, sed unitas principiorum primorum in
aliquo genere scibili. Distinguuntur autem genera scibilium secundum
diversum modum cognoscendi.” (In I Post. Analyt., lect. 41, n. 12.)
13 "Esse scibile addit supra esse intelligibile talem modum cognoscendi, scilicet quod aliquid intelligatur non simplici modo, sed modo
illativo, ex causis seu praemissis procedendo ad conclusiones; scire
enim est cognoscere causam, ob quam res est, etc.” (John of St.
Thomas, Cursus Phil., I, p. 823 a).
14 “Speculabili autem, quod est objectum speculativae potentiae,
aliquid competit ex parte intellectivae potentiae et aliquid ex parte
habitus scientiae, quo intellectus perficitur. Ex parte siquidem in­
tellectus competit ei quod sit immateriale, quia et ipse intellectus
immaterialis est; ex parte vero scientiae competit ei quod sit neces­
sarium, quia scientia de necessariis est.... Omne autem necessarium,
in quantum hujusmodi est immobile, quia omne quod movetur in
quantum hujusmodi est possibile esse et non esse vel simpliciter vel
secundum quid.... Sic ergo speculabili quod est objectum scientiae
speculativae per se competit separatio et a materia et a motu, vel
applicatio ad ea.” (In De Trin., q. 5, a. 1.)

The Subject of Natural Philosophy

45

necessary in some way, as we shall see in Chapter III. The
intelligibility of the middle term—and therefore also of
the conclusion, which must be of commensurate universal­
ity—depends on the degree of removal from matter. These
two characteristics coalesce, in that the more immaterial a
thing is, the more necessary it is, for potentiality is equally
the principle of materiality and contingency.
There are some things that are so dependent on matter
that they can neither be nor be defined without matter.
Such, we shall see, are the objects of natural science, or
physics, which are abstracted only from individual matter,
but are essentially involved in sensible matter. Other ob­
jects of knowledge abstract from sensible matter in their
definition, such as straight or curved and other mathe­
matical entities; they depend on matter, however, as to
their existence, for they cannot exist apart from matter.
At the highest degree, there are objects of knowledge that
completely prescind from matter, both as to definition or
concept and as to existence, such as substance, actuality,
causality and being. These are the objects considered in
metaphysics. They are independent of matter in their con­
cept, and though they are jisually found in matter and it
is from their material existence that we learn of them,
yet they are verified even in immaterial existence, as in
God and separated souls. It is according to these three de­
grees of removal from matter that we have subjects given
us of the three sciences of physics, mathematics15*and meta­
physics.
We can now easily reconcile the apparently different
ways in which St. Thomas distinguishes the various sci­
ences. Sometimes he says that sciences differ according to
the different degrees in which their objects are abstracted
from matter.1® At other times he seeks the reason in the
15 There are two distinct mathematical sciences, arithmetic and
geometry.
le In De Trin., q. 5, a. 1; In I Phys., lect. 1, n. 2; Summa Theol.,
I, q. 85 a. 1, ad 3 ; De Sensu. Prol.

46

Demonstrating in Natural Philosophy

diversity of middle term.17 Again he appeals to the man­
ner of defining or the difference of first principles.18 Sci­
ences are distinguished, then, according to the degree of λ
immateriality whereby the formal subject is defined in the
middle term: namely, whether it be by physical, mathe­
matical or metaphysical principles. The same real thing
may be the subject in all three types of science.
We are now in a position to begin our determination of
the subject of natural philosophy. What is to be our pro­
cedure? How are we to begin a philosophy of nature, a sci­
ence of the material universe around us? Aristotle gives us
at the beginning a rule that flows from the very nature of
our knowledge. This is the supreme principle of procedure
throughout natural philosophy ; in fact, it covers the whole
of philosophy and all other disciplines as well. “We must
advance from generalities to particulars.”19
In our human type of knowledge we must advance from
what we know to what we do not know, and from what
we know better to what we know less. So we begin with
sense knowledge and then proceed on slowly and arduously
to the higher realms of intellectual attainment, gradually
extending, clarifying and systematizing our knowledge.
In philosophical terms, we say that our knowledge is a
development of the intellect from potency to act. On the
day of our birth our intellect is in a state of complete poten­
cy, a tabula rasa. On its first awakening to actuality our
mind conceives being: id quod primo cadit in intellectu
est ens,20 not indeed being as the metaphysician studies it,
but a most confused concept of something existing, the most
imperfect concept, almost completely enveloped in potency
17 Summa Theol., Π-Π, q. 1, a. 1 ; I-Π, q. 54, a. 2, ad 2.
™ In I Post. Analyt., lect. 41, n. 9-13; In VI Meta., lect 1, n. 1156,
1157.
19 Physics, Bk. 1, Chap. 1, 184a 24.
30 Summa Theol., I-Π, q. 55, a. 4, ad 1. Cf. Owen Bennett, O.F.M.
Conv., “Existence and the First Principles According to St. Thomas
Aquinas,” Philosophical Studies in honor of the Very Reverend
Ignatius Smith, OR., J. K. Ryan, editor, pp. 165-178.

π

The Subject of Natural Philosophy
47
Ί
and with the minimum of act'. The life-long intellectual
adventure consists of adding determinations to the poten­
tialities of the mind, of proceeding from potency to inter­
mediate act, and from that on toward perfect act.
Knowledge that has a large admixture of potentiality is
confused knowledge; clarification and distinction move in
the direction of actuality. We first know things in a gen­
eral way, as being, as body, as living; but as we add deter­
minations we clear up the confusion and make our ideas
specific and precise. So what we know first is a whole, such
as the universal whole, which contains its inferiors in po­
tency: we know animal before we know rational animal,
kudu, ferret or brant. Even the integral whole, for exampie a house, whose parts are actual, is first known as a ·
whole, before our attention focusses on the parts to dis­
tinguish them. When the intellect knows something only
in general, it is still in potency to know that which distin­
guishes the parts from the whole and from one another.
This progress of knowledge becomes clear in the light
of the fundamental principle that the formal constitutive
of knowledge is immateriality: a thing is knowable and
is cognitive according to the degree of removal from mate­
riality, or potentiality. A thing is more knowable insofar
as it has more being; but a thing has more being in pro­
portion as it is removed from potentiality and possesses
actuality. Likewise, knowledge is the perfection of being,
and the more actual and less material or potential a being
is, the more cognitive it is. Thus, God Himself, Pure Act,
is at the summit of cognition, and His essence is the most
knowable thing there is.21
Our knowledge, then, begins in the darkness and mate­
riality of the senses and spirals upward toward the pure
dazzling intelligibility of God’s Being.
21 On immateriality as the root of cognition, cf., Summa Theol.,
I, q. 14, a. 1; De Ver., q. 2, a. 2. On the progress of knowledge from
general to particular, cf., In I Phys., lect. 1, n. 6-11 and Summa Theol.,
q. 85, a. 3.

48

Demonstrating in Natural Philosophy

In accordance with the nature of our intellectual knowl­
edge our first science will be that of the sensible world, of
that which is most material and least knowable, of that,
namely, which has the most of potentiality and the mini­
mum of actuality whereby it is knowable. The first step
of this science will be to consider all sensible things in gen­
eral, or according to the aspects they have in common, and
then to descend to particular sensible beings and to their
proper characteristics. We must begin our science with a
subject-genus. In this way we follow the natural mode of
human knowledge even within a science, for the knowledge
of things in general is more confused, more potential, than
the knowledge of things with their particular determina­
tions
, The material subject of natural philosophy is all sensible
'and material being, thé whole world upon which our senses
feed. What will our formal subject be? To establish it we
must find some common aspect of all sensible beings, some
characteristic in which they all share, which will serve to
unify material being and to furnish a key whereby we can
penetrate to the general nature of it. For this common
characteristic must needs be a property of material being
as such, and by this property we will be able to define the
nature of the sensible world on the most general level.
Whatever common property we find will be a wedge where­
by we pry open the shell of physical being and get our first
look at the nature crouching within.
What is this common aspect? To find it was no difficulty
for Aristotle, nor need it be for us. The one facet of reality
that had puzzled philosophers from the beginning is that
all things are changing, or are in motion. The mark of
change is unmistakeably evident in all sensible things. “We
physicists,” says Aristotle, “must take for granted that the
things that exist by nature are, either all or some of them,
in motion—which is indeed made plain by induction.”22
Notice that he does not say absolutely “all of them,” but
22 Physics, Bk. 1, Chap. 2, 185a 13-15.

The Subject of Natural Philosophy

49

leaves open the possibility that there may be some beings
unknown to us that do not change. If we find that to be
true, then we will have to devise another science to study
them.23 But for the present it seems that the aspect of mo­
tion or change is a universal aspect of sensible being, and
in the light of change we can set up a science of nature.
Note that we do not mean any kind of motion without
restriction. There are some motions that are the result of
violence and others that issue from mere chance conjunc­
tions of causal actions. Moreover, there are motions that
are attributable to an artificial arrangement of matter, as
in a machine. Such motions are not essential, but only
contingent, and as such can in no way lead us to a knowl­
edge of essences and essential attributes. Therefore, they
cannot serve as the means of establishing a subject-genus
of scientific demonstration. We can take into consideration |
only motions that flow from an intrinsic principle, motions
that we qualify as “natural.” So the typical operations of an­
imals, plants and simple elementary bodies are evidently nat­
ural, as issuing from a commensurate interior principle. In >
this they are distinguished" from the operation of artificial
things whose principle is merely per accidens and imposed
from without. It is natural motions in which we are inter- )
ested, those that flow from a nature or intrinsic principle.
Let us pause here for a moment and ask just why we
should choose motion as the unifying aspect of all mate­
rial things. Would it not be possible to find some other
aspect of material reality as the basis for natural philoso23 As a matter of fact, the science of physics does lead us to im­
material beings not subject to sensory motion: to the First Unmoved
Mover and to the separated human soul. (Aristotle thought also that
he found in nature evidences of the causality of “separated sub­
stances,” which the Scholastics identified with the angels.) At once it
becomes evident that the concepts of substance, act, causality, even
being itself are not commensurate with material, mobile being, the
subject of physics. These concepts extend to immaterial beings also.
Hence, we need a new science, a “metaphysics,” to study them. Cf.
our article, “The Formal Subject of Metaphysics,” The Thomist, XIX
r (1956), pp. 59-74.

50

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Demonstrating in Natural Philosophy

phy? Why should we not study the material universe as
being, rather than as mobile?
We cannot study material things as being, because they
are not first presented to our knowledge as being. We become aware of material things through our sensory ex­
perience. What the senses testify to is a constant flux:
things are ever changing, they come and go, they are here
today and gone tomorrow. It was this dynamic aspect of
things given in sense knowledge that aroused the wonder
of the first philosophers and gave birth to scientific thought.
It was this continual flux of sensible things that made
Heraclitus proclaim: All things are changing, nothing re­
mains; we cannot bathe in the same river twice! There
can be no static universal knowledge of things that are
ever changing.
Parmenides tried to grasp nature as being, rather than
becoming. His celebrated dilemma forced him to admit only
one, eternal, immoblile reality. His grasp of the being of
things with its intelligibile stability and necessity was such
as could satisfy the intellect in its yearning for its proper
formal object, but it was a scandal to the senses; and he
could silence their violent protest only by denouncing them
as illusory. This was not the right approach. The human
mind had to face becoming and reconcile it with being.
This is the most basic problem of all natural philosophy:
nothing can be more general or more fundamental than
the question of being, not-being and becoming.
It may be added that the aspect of being is not a proper
I formal aspect under which to study material things as
' such, because being is not commensurate with material
things, but transcends matter. One might ask, however,
whether from our early contact with material beings we
can isolate the transcendental perfection of existence immanent in material things and thus begin philosophy with
an ontology. But the goncfiptjrf existence as found in material beings, is proportioned to material essences and extends
no further than they. Only when the existence of immata-

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The Subject of Natural Philosophy

51

rial beings has been demonstrated can our idea of existence
and being be scientifically extended beyond material things.
Ontology must follow philosophy of nature.23*
Sensible change, or becoming, we conclude, is the first
unifying aspect of all material beings, for it spontaneously
asserts itself to our attention at our first contacts with ma­
terial beings.
We are now in a position to determine the formal object !
of natural philosophy. The formal object, it will be remem-.
bered, is the definition of the formal subject and is the*
middle term in demonstration. No science can get started '
without such a definition. “Now in any science the things
that must first be known are its subject and the medium by
which it demonstrates.”24 We already have a nominal and
descriptive definition of our subject, being that changes, or
mobile being. There is no hope of getting a definition at
this stage through genus and specific difference, as our
genus could be nothing but being itself; but being tran­
scends all genera. Therefore, we must try to define our i
subject through its first or fundamental constituent physi-i
cal principles. We want to know the first principles, or in-!
trinsic causes, of mobile being as such.25
/?
As we well know,-these first principles of mobile being
are prime matter and substantial form. Mobile being as
such is defined as “being composed of prime matter and
substantial form.” With this definition we have a starting
point for the philosophy of nature, for in the light of it
we can proceed to demonstrate the properties commen­
surate with it. The following quotation from St. Thomas
23»Cf. G. Klubertanz, S.J., “The Teaching of Thomistic Meta­
physics,” Gregorianum, XXX (1954), pp. 187-205, for views differing
from those we have expressed.
24 “Ea autem quae primo oportet cognoscere in aliqua scientia,
sunt subiectum ipsius, et medium per quod demonstrat” (In II Phys.,
lect 1, n. 1.)
25 “Quaelibet scientia debet inquirere principia et causas sui sub­
jecti, quae sunt ejus inquantum hujusmodi.” (In VI Meta., lect 1,
n. 1145.)

52

Demonstrating in Natural Philosophy

is most important, not only as confinning what we have
just said, but as giving us a glimpse of the whole process
of natural philosophy.
The subject of any science can have two kinds of
parts, namely, the primary component parts, that
is, the principles of the subject, and the subjective
parts.... In every science there are certain prin­
ciples of the subject, which we must consider first,
for instance, in natural science, matter and form;
and in grammar, letters. There is also in every
science something ultimate at which the consider­
ation of the science terminates, that is, the mani­
festation of the properties.2’
Aristotle’s search for the first principles of mobile being
occupies the whole first book of the Physics. We do not
intend to make a detailed analysis of the process. The treat­
ment is given in its historical setting, and it strikingly ex­
hibits the logical acumen and high genius of its author.
We may remark that Aristotle first examines the require? ments of motion in general, without any distinction as to
the various kinds of motion, whether artificial or natural,
substantial or accidental. He proceeds from the kind that
is more known to us, namely, accidental change, and he
gives some easy examples from artificial motions, such as
making a statue out of bronze or a bed out of wood. So he
is able to establish that change as such requires a subject
that is permanent throughout the process of change, the
“Subiectum alicuius scientiae duplices partes habere potest,
scilicet partes ex quibus componitur sicut ex primis, ut dictum est,
idest ipsa principia subiecti, et partes subiectivas.... In qualibet
enim scientia sunt quaedam principia subiecti, de quibus est prima
consideratio; sicut in scientia naturali de materia et forma, et in
grammatica de literis. Est etiam in qualibet scientia aliquid ultimum
ad quod terminatur consideratio scientiae, ut scilicet passiones subiecti
manifestentur.” (In I Post. Analyt., lect. 41, n. 9.) The principies
of the subject also define the limits of the science·. “Consideratio
speculativae scientiae non se extendit ultra virtutem principiorum
illius scientiae, quia in principiis scientiae virtualiter tota scientia
continetur.” (Summa Theol., I-Π, q. 3, a. 6. Cf. I, q. 1, a. 7; II-II,
q. 4, a. 1.)

The Subject of Natural Philosophy

53

privation in the subject of the new status to be acquired,
and at the completion of the change, a new determination
or form in the subject. The investigation is pursued to the
point where it is seen that in the most fundamental sort of
change, where one thing becomes simply another thing, as )
when a living being becomes a dead being, there must be
a subject that is entirely devoid of any determinations, a
primary substratum, to which is given the name prime
matter. Correlative to this is a principle of determination
that is called substantial form.
At the beginning of the second book of Physics Aristotle
returns to the consideration of the principles of mobile
being, this time as nature. This added treatment can cause
us some confusion, and we ask with John of St. Thomas,
“Why/does the Philosopher treat the principles of natural
things in the first book, and again in this second treat of
nature as the principles of natural things?’’27
St. Thomas says that in the first book Aristotle had treat­
ed the principles of natural things, whereas in the second
book he determines the principles of natural science.28
This is certainly true, as the Stagirite goes on to establish
the special postulates and the manner of demonstrating in
the science in subsequent chapters of this same book. We
(may add that this discussion of the first principles as na­
ture is a further precision of the subject of our science. It
eliminates all artificial changes, and also the changes due
~tp violence, chance and fortune. In this science we are con-j
cerned only with things that have natures, that is, intrinsic/
principles of motion and rest,29 things whose prime matter!
27 “Cur ergo Philosophus egit de principiis rei naturalis in primo
libro, et iterum in hoc secundo agit de natura pro principiis rei
naturalis....” (Cursus Phil., II, p. 171. Cf. Celestin Taylor, O.P.,
“The Relation Between Book I and II of the Physics,” Laval Theologique et Philosophique, VII (1951), pp. 150-158.)
28 Il Phys., lect. 1, n. 1.
29 “Nature is a source or cause of being moved and of being at i
rest in that to which it belongs primarily, in virtue of itself and not 1
in virtue of a concomitant attribute.” (Physics, Bk. 2, Chap. 1, *
192b 23.)

54

Demonstrating in Natural Philosophy

and substantial form are the root sources of their typical P
characteristics and manifestations. Whereas the first book I
of Physics had discussed all types of change as a help to
establish the hylemorphic constitution of matter, now there
is a further refinement made to exclude certain of those
types from natural science.
The concept of prime matter and substantial form as
nature adds a dynamic connotation to these first principles
of material being.30 Every particular type of mobile being <
has its own characteristic properties and operations. These
are discovered by the regularity of their occurrence. What-1
ever happens with a significant frequency, either always
or almost always, cannot be the result of chance, but must
have some corresponding regular cause. The measurable!
regularities, whose discovery and formulation allow mod­
ern science to bear such fruitful results, reveal that there;
is a cause of this regularity in the very essence of the thing!,
concerned. The constancy of qualitative manifestations, such']
as typical structure and operations, are effects of some-;
thing in the heart of a being; they flow from the thing’s I
essence, and the principles of the being are also the prin-1
ciples of its properties and operations.
Matter in a mobile being is the principle of potentiality
and receptivity; form is the principle of actuality. Quan­
tity, then, is said to follow upon matter, and quality, upon
form.
.
Only a thing that is per se subsistent can act. So |
«/J
it is neither matter nor form, but the composite,
that acts. But it does not act by reason of matter,
but by reason of form, which is act and the prin-

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30 “Hic autem de principiis rei naturalis seu de natura agit sub
habitudine et respectu ad motum. Sic enim induit rationem naturae, in
quantum est principium motus, sive active sive passive, atque ita in
primo libro considerantur principia ut constituentia ens naturale, sive
in fieri sive in facto esse, ibique non tam considerantur principium
ut activum et passivum quam ut materiale et formale. In praesenti
vero considerantur principia non ut constituentia ens naturale, sed
ut principiantia motum, et ita consideratur principium ut activum vel
passivum.” (John of St. Thomas, ibid.)

The Subject of Natural Philosophy

55

ciple of action. And because quantity follows upon
matter and quality upon form, therefore quantity
does not act except by means of quality, which is
of itself a principle of action.31
It is not our duty here to study this important concept
of nature. It is vital, if we wish to attain an understand­
ing of the material world.32 For the present, we may well
quote a clarification given by John of St. Thomas, which
will preclude any misunderstanding. It is the composite
that is the subject of accidents, but matter is the subject
quo, that by which the composite is receptive.
That matter is the subject quo, or the principle
of receiving, is certain, for matter is the first root
of potentiality and reception in the composite,
since it is pure potency and is first in the order
of receiving. Hence, whatever is received in the
composite has matter as principle quo and first
root of receiving. Likewise, substantial form is
the first root and principle of actuality and being;
it is the principle of esse simpliciter, or substantial
being, which is given by form. If being simpliciter
comes from substantial form, a fortiori being se­
cundum quid depends on it. Therefore, matter and
form are only principles quo, because they are
constitutive of the subject on which accident de­
pends: the characteristic of potentiality comes
through matter, and of actuality, through form.33
31 “Agere non est nisi rei per se subsistentis. Et ideo neque materia
agit neque forma, sed compositum: quod tamen non agit ratione
materiae, sed ratione formae quae est actus et actionis principium.
Et quia quantitas se tenet ex parte materiae et qualitas ex parte
formae, ideo quantitas non agit nisi mediante qualitate quae est per
se actionis principium." (In IV Sent., d. 12, q. 1, art. 2, resp. ad la
quaest. Cf. De Pot., q. 9, a. 7; De Ente et Ess., Chap. 6; De Prin­
cipiis Naturae, n. 16; Summa Theol., I, q. 3, a. 4, c; Contra Gen.,
Bk. 3, Chap. 97.)
32 A recent study of “nature” has been made by James A. Weisheipl, O.P., “The Concept of Nature,” The New Scholasticism, ~KX.N1TL
(October, 1954), pp. 377-408.
33 “Quod materia sit subiectum quo seu principium recipiendi,
constat, quia materia est prima radix potentialitatis et receptionis
in composito, cum sit pura potentia et primum in genere recipiendi.

56

Demonstrating in Natural Philosophy

The starting point of Aristotelian natural science, it must
be noted, is the fact of natural motion, which is evident to
the senses. There is no need to prove the existence of our
formal subject. The physicist is justified in accepting the
testimony of the senses. It is not his domain to investigate
and defend the validity of sense knowledge: that belongs
to the metaphysician. Nor does he, strictly speaking, have
to refute Monism, which is also a metaphysical aberration.
If incidentally, however, a physicist’s audience has been
influenced by metaphysical errors that concern the prin­
ciples of natural science and thus block the very beginning
of it, he will have to settle the metaphysical issue before
getting started in his own science. Thus, Aristotle was
forced as a practical exigency to take up the arguments of
Melissus and Parmenides at the beginning of his Physics;
and likewise, the neo-Thomists at the beginning of this cen­
tury had to face the epistemological problem posed by Kan­
tianism. But it must always be kept clear that these tracts
are borrowed from metaphysics and do not belong per se
to natural philosophy.34 They can be treated here only
Unde quidquid in composito recipitur, habet pro principio quo et
prima radice recipiendi ipsam materiam, similiter forma substantialis
est prima radix et principium actualitatis et esse, siquidem est prin­
cipium ipsius esse simpliciter seu esse substantialis quod datur per
formam. Unde autem oritur esse simpliciter a fortiori dependet esse
secundum quid. Ergo materia et forma solum se habent ut principium
quo, quia sunt constitutiva ipsius subiecti, a quo dependet accidens
quantum ad rationem potentialitatis per materiam, et actualitatis
per formam.” (John of St. Thomas, ibid, p. 758; cf. 755-764. St.
Thomas, In VII Meta., lect. 2, n. 1285, 1286.)
31 We wish to call attention to the following warning of Father
Fernandez-Alonso, O.P.: “Sane modemi in naturali philosophia
quaestiones plurimas exponunt quae, sicut creatio, miraculi possibilitas,
pantheism! refutatio, obiectiva sensibilis mundi exsistentia, tractatus
de causis, de aeternitate, etc., sunt vere metaphysicae vel theologicae.
Sed est error absolute reprobandus. Horum enim scibilitas, utpote
ab omni materia abstrahens, est omnino distincta a scibilitate eorum,
quae, ut ultima corporum constitutio, naturae motus, spatii, temporis,
vitae, animae humanae, etc., sunt in primo gradu abstractionis.
Haec duo genera quaestionum, ad philosophiam sensu hodierno accep­
tam pertinentia, nequent sine errore, tanquam partes eiusdem scientiae

The Subject of Natural Philosophy

57

dialectically.35
The first part of natural philosophy deals with mobile
being in general. It formulates a general definition of mo­
tion; demonstrates its proper subject; treatsTtsTntrinsic
>
concomitants, action, passion and the infinite; anditsmeas- >
ures, place and time.3® It divides motion into its various "j£V
species37 and into its quantitative parts, under which comes
the consideration of the continuum.38 It also investigates
the efficient cause of motion38 and culminates by tracing
motion back to a First Unmoved Mover.40
With this, general physics has run its course. At this~l
point mobile being and the common properties commen­
surate with it will have been thoroughly investigated. The
next step is to divide our subject-genus into its subjective
parts or species, and to study each species as determina­
tions of the general principles already established. We di­
vide the subject-genus according to its formal aspect and
demonstrate the properties commensurate to the various
subjects obtained by division. Then we subdivide and again
demonstrate commensurate properties at the lower specific
levels.41 As we proceed toward the mysterious core of maconsiderari. Et si aliquando de illis in philosophia naturali est agendum
proper rationes extrinsecas, hoc explicite notandum est, ut faciunt
Aristoteles et S. Albertus ne ulla sit aequivocatio.” “Scientiae et philo­
sophia secundum S. Albertum Magnum,” Angelicum, XII (1936), pp.
30-31.
35 Note that when Aristotle (Physics, Bk. 1, Chap. 2, 185a 15-20)
decides to “spend a few words” on the opinions of Melissus and
Parmenides, he uses the term &ια\εγθηναι.
33 Physics, Bks. 1-4.
33 Ibid., Bk. 5.
38 Ibid., Bk. 6.
33 Ibid., Bk. 7.
*3 Ibid., Bks. 7 and 8.
41 “Sicut in rebus naturalibus nihil est perfectum dum est in poten­
tia, sed solum tunc simpliciter perfectum est, quando est in ultimo
actu; quando,vero medio modo se habens fuerit inter puram potentiam
et purum actum, tunc est quidem secundum quid perfectum, non tamen
simpliciter; sic et circa scientiam accidit. Scientia autem quae
habetur de re tantum in universali, non est scientia completa secundum

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Demonstrating in Natural Philosophy

terial beings, we have difficulty dividing our subjects into
their ultimate species, because we cannot know their spe­
cific differences. Hence, at that level we must make use
of descriptive definitions or of conjectures and hypotheses
in place of definitions.
ύ
In making our first divisions, we must note that, contrary
to the practice of some modern scholastics, it is not correct
to divide mobile being into that which is anorganic and
that which is organic; such is to divide the material sub­
ject, rather than the formal subject. The formal aspect
of the material world that has specified our science is mobility; therefore, the first divisions of our science will be
divisions of mobility, the three kinds of motion : locomotion, qualitative motion and quantitative motion.42 The first
two kinds are general and are common to all mobile beings ;
the third kind is proper only to corporeal living beings:;
augmentative^ghange is the one type of motion common to*
all organisms and proper only to them.
It is on the level of these first special divisions of natural
science that philosophy of nature and experimental science
ultimum actum, sed est medio modo se habens inter puram potentiam
et ultimum actum. Nam aliquis sciens aliquid in universali, scit
quidem aliquid eorum actu quae sunt in propria ratione eius : alia
vero sciens in universali non scit actu, sed solum in potentia. Puta,
qui cognoscit hominem solum secundum quod est animal, solum scit
sic partem definitionis hominis in actu, scilicet genus eius: differen­
tias autem constitutivas speciei nondum scit actu, sed potentia tantum.
Unde manifestum est quod complementum scientiae requirit quod non
sistatur in communibus, sed procedatur usque ad species: individua
enim non cadunt sub consideratione artis; non enim eorum est
intellectus, sed sensus.” (In I Meteor., lect. 1, n. 1. Cf. R. J. Nogar,
O.P., “Cosmology Without a Cosmos,” From an Abundant Spring,
pp. 363-392.)
’
42 “Res autem quas considerat Naturalis, sunt motus et mobile:
dicit enim Philosophus in II Physic, quod quaecumque mota movent,
sunt physicae speculationis. Et ideo oportet quod secundum differen­
tiam motuum et mobilium, distinguantur et ordinentur partes scientiae
naturalis. Primus autem motuum est motus localis, qui est perfectior
ceteris, et communis omnibus corporibus naturalibus.” (In De Gen.
et Cor., Proem., n. 1. Cf. In I Phys., lect. 1, n. 4.)

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The Subject of Natural Philosophy

59

can and must be integrated.43 For these divisions corre­
spond almost exactly to the sciences of Physics (locomo­
tion) , Chemistry (qualitative motion), and Biology, (quan­
titative motion). But it is to be noted that natural phi­
losophy does not absorb these experimental sciences, for
insofar as at least Physics and Chemistry are highly mathematized, they constitute autonomous sciences of the type
called medial by the ancients. Their demonstrations pro­
ceed from mathematical principles ; they do not give physi­
cal explanations. It is for the natural philosopher to take
the physical data furnished so abundantly by the experi­
mental sciences and to integrate it into his own explana­
tion of the physical universe. In fact, only the philosopher
can raise the factual findings of modem science to the level
of true science in the Aristotelian sense. It can be said,
then, that even the mathematical-physical sciences belong
reductively to philosophy of nature.
At each stage of . natural philosophy we first treat our
subjects in general and then in particular, in keeping with
our natural manner of proceeding from the potential or con­
fused to what is more actual. St. Thomas is acutely aware
of these methodological principles and he prefaces each of
his commentaries with a review of what has been accom­
plished so far and of how the same principles are to be
applied in the tract in hand.
By this method of proceeding from general to partic­
ular through progressive division of mobile being, the for­
mal subject of our science, we not only satisfy the natural
manner of our growth in knowledge, but we also provide
ourselves at each stage of natural science with a defini­
tion of our subject, in the light of which we can demon­
strate its commensurate attributes. This is the only way
in which we can construct a true science of nature, for with43 For an account of the studies made on the possibility of integra­
tion by the Albertus Magnus Lyceum for Natural Science, see Kane
et al., Science in Synthesis, p. 219sq. Cf. also W. H. Kane, O.P., “The
Nature and Extent of Philosophy of Nature,” The Thomist, VII
(1944), p. 231.

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Demonstrating in Natural Philosophy

out a definition of our subject we cannot have demonstra­
tion; but “the most convenient way to find definitions is
through divisions.”44
To a modem mind there arises a stubborn difficulty con/ cerning the whole principle of proceeding from the general
/ to the particular. How can we know general things about
all mobile being without having first studied the particular
' types of mobile being? Would it not be more natural to
study first the particular beings and on the basis of our
findings to form generalizations? Is it not the grossest a
priorism to form a general concept on the basis of a few
common sense observations and to extend it “sight unseen”
; ' to all material beings, in fact to make it the principle of
interpretation of all material beings? Such an_objection is
really a veiled attack upon the ability of our minds to know
^ 'abstract natures. It is the whole epistemological question
brought "back to us in a particularized form. It involves
a basic misunderstanding of the nature of induction, of
abstraction and of the formation of definitions. To answer
all this is out of the ambit of our present study. But it may
be answered indirectly in what we consider the unsur­
passed words of a modem Aristotelian, words which focus
for us the ultimate difference of the scholastic approach and
that of the modem scientist:
This whole argument toward the primacy of the
general in human knowledge and, in the limit, to­
ward the idea of being as the first of man’s intel­
lectual achievements can be put in another and
perhaps even more forceful form. If intellectual
knowledge had to begin by grasping the individual,
then it would have to be radically inductive, and
if it is radically inductive, it never begins with
the individual because it could never begin at all.
If a so-called individual is given in experience,
how can the knower be sure that it is truly an
individual unit? On radically inductive premises,
he cannot. Thus he splits the ‘individual,’ say a
« “Via ad inveniendum definitiones convenientïssima est per divis­
iones.” (In III Phys., lect. 1, n. 5.)

The Subject of Natural Philosophy

61

molecule, into atoms. But uncertain whether the
atom is an individual, he charges into it with his
particle guns and breaks the atom into neutrons,
protons, electrons, and other microscopic entities.
Radically inductive and compelled to begin with
the individual, he cannot logically even accept
these subatomic entities as realities that are ulti­
mate and given. So his process of division goes
on and on ad infinitum. His empiriological phys­
ics becomes an eternal quest after premises, a
constant effort to begin.45
There is one last point to occupy us momentarily in pass­
ing. The first divisions of our subject^genus are easy to
make, because they are still at the level of generalities and
of relatively indistinct knowledge. But as our scientific
invasion proceeds into the lush and fertile jungle of spe­
cific essences, we find that attainment of distinct knowl­
edge is hindered by the undergrowth of matter, which, is
of.itself impervious to scientific investigation. These es­
sences are by nature involved in matter and thus share the
obscurity of matter. What is the specific difference between
a lamb and wolf, between a rose and a tomato? Our intel­
lectual insight is dimmed in this dusky realm of limited
intellibility.4® Is it possible to make some inroad into the
45 V. E. Smith, Philosophical Physics, p. 24.
4< “Under the sensible clarity of phenomena, of the visible and
tangible, there is the obscurity of matter, which by its indétermina­
tion, its poverty and its instability remains beyond the grasp of the
intellect. Thus, there is nothing more clear empirically than the dif­
ference which distinguishes the two animal species, the eagle and the
lion, or the two vegetable species, the oak and the spruce. But how
can these species be defined otherwise than in a descriptive, empirical
fashion? How can these species be rendered intelligible? Only their
generic characteristics: corporal substance, alive, endowed or not
endowed with sensation, can be grasped by the intellect. The specific
difference of oak, of spruce, of eagle or of lion remains hidden from
us. It is impossible for us to have a distinct intellectual under­
standing of these species, from which we can deduce what is proper to
their natures, as we may do with regard to triangle or circle. Why
is this? Because their specific or substantial form, remains as if
buried, immerged in matter. Consequently the human idea of eagle or

62

Demonstrating in Natural Philosophy

interior of material species, to acquire some knowledge of
these specific essences, in order thereby to demonstrate the
properties commensurate with them?
There are three ways of getting some understanding of
particular essences : through descriptive definition, through
/ extrinsic causes, and through systematic explanation or
/ conjecture.
(1) When we do not know the specific difference of a
thing, we can often compose a definition from a proximate
genus and a property in place of a specific difference. Such
is a descriptive definition, that is, one that defines a thing
in terms of proper or common accidents, of sensible qualities and operations. “Since we do not know essential differ­
ences, sometimes we use accidents and effects in their
place.”47
. Since we do not know the substantial differences
lion is like a cone whose summit is lit up and whose base remains in
the shade. Eagle and lion are clearly intelligible for us in that they
are beings, substances, corporal substance, endowed with life and sen­
sation, but what formally constitutes the eagle, as eagle, or the lion,
as lion, remains intellectually very obscure. We can hardly go beyond
a descriptive or empirical definition. Thus St. Thomas notes often
that the specific differences of sensible beings are often left un­
named. There is a penury of terms because there is a penury of dis­
tinct ideas.” (R. Garrigou-Lagrange, Le Sens du Mystere, pp. 11-13;
cited by Owen Bennett, O.M.C., The Nature of Demonstrative Proof, p.
B9.) As St. Thomas puts it: “Cognitio nostra est adeo debilis quod
nullus philosophus potuit unquam perfecte investigare naturam unius
muscae: unde legitur, quod unus philosophus fuit trigenta annis in
solitudine, ut cognosceret naturam apis.” (In symbol, ap., art. 1.)
47 Quia differentiae essentiales sunt nobis ignotae, quandoque utimur
accidentibus vel effectis loco earum.” (De Ver., q. 4, a. 1, ad 8.
Cf. In I Post. Analyt., lect. 4, n. 16: “Quandoque id quod est notius
quoad nos non est notius simpliciter, sicut accidit in naturalibus, in
quibus essentiae et virtutes rerum, propter hoc quod in materia sunt,
sunt occultae, sed innotescunt nobis perea, quae exterius de ipsis
apparent. Unde in talibus fiunt demonstrationes ut plurimum per
effectus, qui sunt notiores quoad nos, et non simpliciter.” Here St.
.( Thomas is speaking of a demonstration a posteriori; from such a
v demonstration the essence of the cause becomes known and can then
be used in a demonstration a priori.

i

>

The Subject of Natural Philosophy

63

of things, those who make definitions sometimes
use accidental differences because they indicate
or afford knowledge οΐ the essence as the proper
effects afford knowledge of a cause. Therefore,-'
when sensible is given as the constitutive differ­
ence of animal, it is not derived from the sensepower, but the essence of the soul from which that;
power comes.4S
The proper qualities and proper motions of natural things i
must have their proper causes, which are ultimately the
specific essence. Hence, from the constancy of proper ac­
cidents known inductively we can construct a vague defini­
tion of the essence of their subject.48
49 Even from the con-'
stancy of a certain pattern of common accidents we can
get some idea of the nature that is the root of them.
(2) “In the case of natural science, in which demonstra­
tion takes place through extrinsic causes, something is
proved of one thing through another thing entirely exter­
nal to it.”50 We may define a thing in terms of its efficient
cause, for example that an acorn is a seed produced by an
oak tree or that a sun tan is the result of exposure to the
sun. It is especially by defining in terms of final cause
that we get to know something of natural things, but to
discuss this further would bring us into matter that must
be reserved for later chapters.
(3) Finally, there are many cases where we have to try
a systematic explanation, as discussed in our last chapter.
We reason that if such and such is the nature of a thing,
then its various manifestations or empirical properties
would follow. We are in the realm now of hypothesis, and
our knowledge of material things at this lowest' frontier
of intelligibility scarcely surpasses probability and opinion.
48 De Ver., q. 10, a. 1, ad 6. Cf. In VII Meta., lect. 12, n. 1551-1552;
Summa Theol., I, q. 29, a. 1, ad 3; In I De Gen. et Cor., lect. 8, n. 5;
In II Post. Analyt., lect 13-16; De Ente et Ess., Chap. 5, n. 25.
40 Cf. V. E. Smith, “Definitions,” From an Abundant Spring, pp.
343-344; Card. Zigliara, Leonine ed. of Commentary on Post. Analyt.,
note E, pp. 374-375.
50 In De Trin., q. 6, a. 1, c.

64

Demonstrating in Natural Philosophy

We are here undoubtedly in the field of the positive sciences
of nature, those which usually claim to profess no interest
in the intrinsic natures of things, but only in their sensible
manifestations. Whatever the nature and extent of the
positive sciences may be, we can state for certain that they
are at the lowest level of the study of nature. However, we
can see that they do fit in: insofar as they are physical
rather than mathematical, they are at least a continuation
(/ at the dialectical level of the philosophy of nature, as is
held by one of the Thomist theories of positive science.61
The methodological difference between natural philoso­
phy and positive science is that the latter starts from the
bottom and tries to work upward; it begins by trying to
understand the individual and to generalize on the basis of
the individuals known. But individuum est ineffabile; the
individual escapes the grasp of the intellect and yields it­
self only to the senses. Thus, positivistic knowledge is re­
stricted to the sensible and the dialectical. On the other
hand, true science begins with the general and defines its
subjects downward by progressive division,62 attaining a
51 Cf. C. De Koninck, “Introduction à L’Étude de L’Âme,” preface
to Précis de psychologie thomiste, S. Cantin, Ixxv-lxxxi; Most Rev. J.
M. Marling, C.PP.S., "The Dialectical Character of Scientific Knowl­
edge,” Philosophical Studies in Honor of the Very Reverend Ignatius
Smith, O.P., pp. 3-13. Our own study will make it clear that even
more than a dialectical understanding is sometimes possible at the
specific level.
52 “Oportet enim definitionum cognitionem, sicut et demonstrati­
onum, ex aliqua praeexistenti cognitione initium sumere.” (In De
Trin., q. 6, a. 3.) “In scientiis speculativis semper ex aliquo prius noto
proceditur tam in demonstrationibus propositionum quam etiam in
inventionibus definitionum. Sicut enim ex propositionibus praecognitis
aliquis devenit in cognitionem conclusionis, ita ex conceptone generis
et differentiae et causarum rei aliquis devenit in cognitionem speciet
Hic autem non est possibile in infinitum procedere, quia sic omnis
scientia periret et quantum ad demonstrationes et quantum ad defin­
itiones, cum infinita non sit pertransire. Unde omnis consideratio
scientiarum speculativarum reducitur in aliqua prima, quae quidem
homo non habet necesse addiscere aut invenire, ne oporteat in infinitum
procedere, sed eorum notitiam naturaliter habet...et etiam primae

The Subject of Natural Philosophy

65

much more perfect knowledge even of the same entities
against which the positivistic scientist hurls his forces in
vain. The demonstrative approach to nature can reveal na­
ture to the intellect; it can unlock the intelligible reason
stored away in the black cellar of matter. The method of
doing this is the concern of the present study.
To summarize briefly:—We need a definition of the sub­
ject of our science in order to demonstrate, as the subject
is the middle term of a demonstrative syllogism. Since we
cannot know a thing at once in all its virtuality, we must
take it from some particular aspect whereby it is know­
able. The science of nature studies material being from the
aspect of mutability. It defines its subject in terms of the
physical principles of its mobility, first in general and then
by division and concretion down to the lowest species. At
the lower levels the definitions are in relation to properties
and effects, through extrinsic causes, or by the systematic
method of conjecture. The last mentioned kind of defini­
tion is dialectical and yields us probable knowledge. The
other two kinds give us middle terms whereby we can at­
tain certain and necessary truths about things of the mate­
rial world about us.
conceptiones intellectus, ut entis et unius et hujusmodi, in quae oportet
reducere omnes definitiones scientiarum praedictarum.” (In De Trin.,
q. 6, a. 4. Cf. De Ver., q. 1, a. 1. )

CHAPTER III
CERTITUDE AND NECESSITY IN NATURAL
PHILOSOPHY
We have claimed that the demonstrative method can yield
us certain and necessary truth about things of the material
world. But how can this be? The formal subject of natural
science and the matter treated in the light of the subject
are so involved in sensible matter as to require it in their
very definition. Yet matter is the principle of uncertainty
and contingency. Where can we find the certainty and
necessity that are indispensable if we are to attain to
a strict demonstrative and propter quid science?
First let us note that the concept of a certain and neces­
sary objective truth about nature is unthinkable to the
modern mind.
The idea that thought is the measure of all things,
that there is such a thing as utter logical rigor,
that conclusions can be drawn endowed with an
inescapable necessity... these are not the ideas of
a modest animal.1
The proud self-assurance of the nineteenth century scientist
has collapsed along with the mechanical theory of nature
and in the face of the theoretical dilemmas with which the
present-day scientist is faced.
To Aristotle, however, there was no doubt about the mat­
ter. He does not hesitate to apply to his physical science
that technical term έπιστήμη that characterizes the ex­
alted type of demonstrative knowledge outlined in the Pos1P. W. Bridgman, The Nature of Physical Theory, (Princeton:
Princeton University Press, 1936), p. 135; cited by Owen Bennett,
O.M.C., The Nature of Demonstrative Proof, p. 1. Cf. Kane, et al.,
Science in Synthesis, p. 41; W. Agar, The Dilemma of Science, p.
101-105; AJ. Mc Nicholl, O.P., “The Uneasiness of Science,” The
New Scholasticism, XXIV (January, 1950), pp. 57-68.
66

Certitude and Necessity

61

terior Analytics.2 Moreover, in the exposition of his theory
of science in the Posterior Analytics he uses, along with
mathematical examples, a notable number of physical ex­
amples, which we will study in later chapters.3 He does
not, of course, consider that everything in physical science,
nor in any science, for that matter, is strictly demonstra­
tive. There will always be a substantial amount of dia­
lectical material and other matter preparing for propter
quid demonstrations or proved by lesser types of demon­
stration. In fact, strict demonstrations are the culmina­
tion of knowledge on any particular subject, and we must
not be disappointed if they are not as plenteous as we would
like them to be.
The question of certitude and necessity in science are
closely bound together, for it is the intellectual grasp of
necessity that yields the certitude characteristic of science.
But for the purpose of analysis we will investigate them
separately.
In the Nicomachean Ethics1 Aristotle lays down a gen­
eral principle, whose capital importance has been well illus­
trated by the history of philosophy.
Our discussion will be adequate if it has as much
clearness as the subject-matter admits of, for pre­
cision is not to be sought for alike in all discus­
sions, any more than in all the products of the
crafts.... For it is the mark of an educated man
to look for precision in each class of things just
so far as the nature of the subject admits; it is
evidently equally foolish to accept probable reason­
ing from a mathematician and to demand from a
rhetorician scientific proofs.
2 τη<! rrepi φύσΐως επιστήμης. Physics, Bk. 1, Chap. 1, 184a 14.
Cf. Ibid., Bk. 3, Chap. 4, 202b 30; On the Heavens, Bk. 1, Chap. 1,
268a 1; Bk. 3, Chap. 7, 306a 17; Parts of Animals, Bk. 1, Chap. 1,
641a 35; Metaphysics, Bk. 6, Chap. 1, 1025b 19; Bk. 11, Chap. 7,1064a
17; b 2.
s A list of them is given by A. Mansion, Introduction a la Physique
Aristotélicienne, p. 214, note 13.
* Bk. 1, Chap. 2,1094b 13-15, 24-28.

68

Demonstrating in Natural Philosophy

St. Thomas adds that a person ought not to require a great­
er certitude than his subject-matter affords, nor ought he
to be content with less.5
The same thing is touched upon in the Second Book of
the Metaphysics* from a slightly different angle. St. Thom­
as’ commentary on this is especially interesting and gives
us a good insight into the Angelic Doctor’s mastery of the
art of exegesis, as he elaborates the pithy sentences of the
Stagirite. In seeking truth men are impelled by the meth­
ods to which they have become accustomed. Those, for in­
stance, who have been brought up in mathematics are un­
willing to accept anything as true unless it is presented
with mathematical rigor and precision. In this Aristotle
and St. Thomas had the example of Plato, but they seem
almost to be prophesying about the dreams of Descartes
and the myopia of certain modern mathematical-physicists.7
Other persons who have a strong sensitivity but weak in­
tellects will assent only to what is given in sensible exam­
ples, that is, to that which can have some imaginative and
emotional appeal. Others must hide behind the authority
5 “Et ideo auditor bene disciplinatus, non debet majorem certi­
tudinem requirere, nec minori esse contentus, quam sit conveniens rei
de qua agitur.” In I Eth., lect. 3, n. 36.
« Chap. 3, 994b 33—995a 20. Cf. St. Thomas, In II Meta., lect.
5, n. 331-337.
’ Descartes wrote: “I was especially delighted with the Mathe­
matics, on account of the certitude and evidence of their reasonings:
but I had not as yet a precise knowledge of their true use; and think­
ing that they but contributed to the advancement of the mechanical
arts, I was astonished that foundations, so strong and solid, should
have had no loftier superstructure reared on them.... I reserved
some hours from time to time which I expressly devoted to the employ­
ment of the Method in the solution of Mathematical difficulties, or even
in the solution likewise of some questions belonging to other Sciences,
but which, by my having detached them from such principles of these
Sciences as were of inadequate certainty, were rendered almost Mathe­
matical.” (Discourse on Method, Harvard Classics, Vol. 34, pp. 9,26.)
Cf. F. J. Sheen, Philosophy of Science, “The Mathematical Theory,”
pp. 18-21 for some of the modern opinions on the primacy of the
mathematical description of natural phenomena.

Certitude and Necessity

69

of some noted author. Some minds are annoyed by an in­
sistence on certitude, especially when this involves hard
reasoning and a certain amount of detailed work, a charge
that can be made against many modern philosophers, who
have tried to oversimplify philosophy. Actually, however,
each discipline has its own method corresponding to its
own subject matter. Therefore:
That method which is without qualification the
best ought not to be looked for in every science.
“Acribology,” that is, the minute accuracy of
mathematics is not to be demanded in all cases
where there is scientific knowledge, but only as re­
gards those objects that are without matter. For
those that have matter are subject to motion and
variation, and so we cannot have perfect certitude
about them all. Wg.inquire about them not what_
is always and necessarilyZsb.'but what is so .in
^inost instances. Things that are immaterial are of
themselves most certain, because unchangeable.
However, such things that are immaterial of their
own nature, for instance, the separated substances,
are not certain to us, because of the imperfection
of our intellect, as we have mentioned above.
Mathematical entities are abstracted from matter,
and yet they do not exceed our intellect; so in
them the most certain method is required. Now,
because all nature is concerned with matter, this
method of greatest certainty does not belong to
' the natural philosopher.8
8 “Hie modus, qui est simpliciter optimus, non debet in omnibus
quaeri; dicens quod “acribologia” idest diligens et certa ratio, sicut
est in mathematicis, non debet requiri in omnibus rebus, de quibus
sunt scientiae; sed debet solum requiri in his, quae non habent
materiam. Ea enim quae habent materiam, subjecta sunt motui et
variationi: et ideo non potest in eis omnibus omnimoda certitudo
haberi. Quaeritur enim in eis non quid semper sit, et ex necessitate;
sed quid sit ut in pluribus. Immaterialia vero secundum seipsa sunt
certissima, quia sunt immobilia. Sed illa quae in sui natura sunt
immaterialis, non sunt certa nobis propter defectum intellectus nostri,
ut praedictum est. Hujusmodi autem sunt substantiae separatae. Sed
mathematica sunt abstracta a materia, et tamen non sunt excedentia
intellectum nostrum: et ideo in eis est requirenda certissima ratio.
Et quia tota natura est circa materiam, ideo iste modus certissimae

70

Demonstrating in Natural Philosophy

It is matter that limits the certitude of natural science.®
We must state precisely to what extent it does so and how
there can be true science of material objects. For since
matter is the principle of individuation and no science
treats of individuals, but only of universals, it would seem
that we cannot have any science of material things. More­
over, the intellect, to which the habit of science belongs,
knows only by abstracting from matter and the conditions
of matter; and therefore it seems that we cannot have a
science of what is not abstracted from matter.10
The answer to these objections must obviously involve an
explanation of physical abstraction. Assuredly, we have
to abstract from the determined dimensions whereby mat­
ter is the principle of individuation. The individual as
such is knowable, not to the intellect, but to the senses. Yet
we do not abstract from matter entirely when we know a
thing with the universality characteristic of intellectual
knowledge. We know essences; but the essences of mate­
rial things contain matter in their concept ; it is impossible,
rationis non pertinet ad naturalem philosophum.” (In III Meta., lect.
5, n. 336.) Cf. In I Meteor., lect. 11, n. 1, where we are told that in
some matters, e.g., the cause of the appearance of comments, we must
he satisfied with a mere possible solution.
8 Natural science is also less certain because of the many elements
that enter into it. “Ex hoc autem quod consideratio naturalis est
circa materiam, eis cognitio a pluribus dependet, scilicet a consider­
atione materiae ipsius et formae et dispositionum materialium et
proprietatum, quae consequuntur formam in materia. Ubicumque
autem ad aliquid cognoscendum oportet plura considerare, est diffici­
lior cognitio. Unde in I Posteriorum dicitur quod minus certa scien­
tia est, quae est ex additione, ut geometria arithmetica. Ex hoc vero
quod eius consideratio est circa res mobiles et quae non uniformiter
se habent, eius cognitio est minus firma, quia eius demonstrationes
frequenter procedunt ut in maiori parte ex hoc, quod contingit ali­
quando aliter se habere. Et ideo etiam quanto aliqua scientia magis
appropinquat ad singularia, sicut scientiae operativae, ut medicina,
alchimia et moralis, minus possunt habere de certitudine propter mul­
titudinem eorum, quae consideranda sunt in talibus scientiis, quorum
quodlibet si omittatur, sequetur error, et propter eorum variabilitatem.” (In De Trin., q. 6, a. 1, ad q. 2, c.)
10 In De Trin., q. 5, a. 2, obj. 1 & 2.

Certitude and Necessity

71

for instance, to conceive of man without body. However,
we include only that matter common to the whole essence,
such as flesh and bones, not the particular matter of in­
dividuals, this flesh and these bones.11
Thus, there is abstraction from matter sufficient to make
natural things intelligible in their universal aspects. Yet
there is sufficient relation to matter in the abstract, uni­
versal concept to make it represent the essence of material
beings. That is why “we do not call this simply nn abstraction of form from matter, but of the universal from the
particular.”12 However, because science is concerned with
universal· natures, it does not follow that it gives us no
knowledge of singular existing things. The universal be­
comes a means through which we know the particular.12
In order further to determine the degree of certitude
attainable in natural science, we must consider the kind of
necessity to be found in material things.14
But is there, indeed, anything necessary about natural
things? All material beings, by reason of possessing mat­
ter, the principle of change, are contingent, whereas the
necessary is unchangeable. Is it not a contradiction to ex­
pect science, that is, necessary knowledge, about contingent
things? This is the difficulty that drove Plato to seek the
reason for universal and necessary knowledge outside sen­
sible things in a separate world of ideal substances, and
to concede only contingent knowledge, that is, opinion, of
material things.15
11 Ibid., a. 2, c and ad 1 & 2; a. 3, c. Cf. Summa Theol., I, q. 85,
a. 1, ad 1 & 2; DeEnte et Ess., Chap. 2, n. 6.
12 “Ideo praedicta abstractio non dicitur formae a materia absolute,
sed universalis a particulari.” (In De Trin., q. 5, a. 2, c.)
12 Ibid., ad 4.
14 Cf. J. Maritata, “Reflections on Necessity and Contingency,”
Essays in Thomism, R. Brennan, editor, pp. 27-37 ; A. Mansion, Intro­
duction a la Physique Aristotélicienne, Chap. 8, n. 1, pp. 282-292;
W. H. Kane, O.P., “Comment on Father Nogar’s Paper” (“Nature:
Deterministic or Indeterministic?”), Proceedings of the American
Catholic Philosophical Association, XXVII (1953), pp. 104-109.
15 Cf. Summa Theol., I, q. 84, a. 1.

72

Demonstrating in Natural Philosophy

Following Aristotle, St. Thomas1® makes a profound meta­
physical analysis of the concept that is abstracted from
individual matter. A sensible substance existing in reality
is a composite whole, including the designated matter that
is the principle of individuality. Now the mind can prescind
from the individual notes of this material being and con­
sider only what is essential to it. The ensuing concept is a
form with respect to the whole individual ; for the individ­
ual participates in the species, receiving it and limiting
it as potency receives act.11 Yet this is not the substantial
form, for substantial form is not the whole essence, but
only a part of it. This form abstracted from the deter­
mined dimensions of matter includes that matter that is
essential to the nature, common matter, and excludes only
that matter that is accidental to the nature, the individual
determinations of matter. Hence, this form representing
the whole essence (substantial form and common matter)
is called the form of the whole.18 It does not change in the
process of substantial change; it is the individual that
changes. The nature itself, considered in precision from
the individual determinations is unchangeable and hence
necessary. The constitutive notes of a nature can never
be other than what they are.
For further clarity we may quote the words of St.
Thomas :
18 In De Trin., q. 5, a. 2, c.
17 “In definitione speciei non ponitur materia individualis, sed
materia communis; sicut in definitione hominis ponuntur cames et
ossa, non autem hae carnes et haec ossa. Natura igitur speciei con­
stituta ex forma et materia communi, se habet ut formalis respectu
individui quod participat talem naturam; et pro tanto hic dicitur quod
partes quae ponuntur in definitione, pertinent ad causam formalem.”
(In II Phys., lect. 5, n. 4.)
18 The substantial form is the forma partis, that is, the form of
the essence, which is itself the formal part of the whole. Cf. Summa
Theol., I, q. 3, a. 3; Suppl., q 79, a. 2, ad 2. There is an inadequate
real distinction between the individual and its nature, as betwen the
whole and the part. There is an adequate real distinction between
the substantial form and prime matter.

Certitude and Necessity

73

Now, as is shown in the Metaphysics, we find in a
sensible substance both the whole or the composite
itself, and also the nature {ratio), that is, its
form; and it is the composite which is essentiallygenerated and corrupted and not the nature or
form except accidentally. As the Metaphysics says,
x “It is not house that comes into existence, but this
I house.” Now anything can be considered apart
' from whatever is not essentially related to it.
Consequently, the forms and natures of things,
though they be forms and natures of things exist­
ing in motion, are without motion according as
they are considered in themselves. Therefore, as
the philosopher says, they can be the objects of sci­
ence and definitions.... Therefore, natures of this
sort, by reason of which there can be sciences of
mobile things, must be considered without deter­
mined matter and everything consequent upon
matter, but not without undetermined matter, be­
cause the notion of the form which determines
matter to itself depends on this notion of undeter­
mined matter.19
In investigating this matter of necessity and contingency
we must be careful to keep our point of view in mind., A
metaphysician will speak differently of necessity than, will
ajnatural philosopher. The metaphysician is interested in
the necessity and contingency of being and the reasons for
such. He speaks of an absolute necessity founded upon es­
sence or the intrinsic causes and made known to us when­
ever a predicate forms part of the definition of a subject.
Essences cannot be otherwise than they are, for any new
essential principle would destroy an essence and create a
new one. The metaphysician pushes forward his search
for the ultimate reason of the necessity and immutability of
essences to the mind of God wherein are contained the ex­
emplary ideas of all possible participations of the divine
Being.
Furthermore, the metaphysician speaks of a hypothetical
19 In De Trin., q. 5, a. 2, c. Cf. De Ente et Ess., Chap. 2, n. 11-12;
Contra. Gent., Bk. 4, Chap. 80-81; In VI Ethic., lect. 1, n. 1123;
Summa Theol., q. 85, a. 1.

Demonstrating in Natural Philosophy

necessity, or a necessity following upon existence. This falls
short of absolute necessity: only God’s existence is abso­
lutely necessary, because it pertains to His essence. But
given the existence of other things, it is necessary that
they exist when they exist, in virtue of the principle of non­
contradiction. Likewise, given the fact that Socrates is
seated, it is necessary that he be sitting while he is seated.20
Thus, both esse simpliciter and esse tale are hypothetically
necessary when they are posited.21 The metaphysician seeks
the reason for this necessity of existence and finds it again
in God. God wills all things other than Himself inasmuch
as He ordains them to His own goodness as to an end, that
is, as means of manifesting His goodness. He does this not
with any absolute necessity, but freely: His goodness is
already perfect without creatures. Creation is an overflow
of His goodness. But granting creation and the existence
of material things, they are necessary because God wills
them and cannot not-will them. His will is immutable.22
The will of God and final causality are the reason for the
hypothetical necessity of the whole physical order of exist20 "Omne quod est necesse est esse quando est, et omne quod non
est necesse est non esse quando non est. Et haec necessitas fundatur
super hoc principium: Impossible est simul esse et non esse: si enim
aliquid est, impossible est illud simul non esse; ergo necesse est time
illud esse.... Et ideo manifeste verum est quod omne quod est necesse
est non esse pro illo tempore quando non est: et haec est necessitas
non absoluta, sed ex suppositione. Unde non potest simpliciter et
absolute dici quod omne quod est, necesse est esse, et omne quod
non est, necesse est non esse: quia non idem significant quod omne
ens, quando est, sit ex necessitate, et quod omne ens simpliciter sit ex
necessitate; nam primum significat necessitatem ex suppositione,
secundum autem necessitatem absolutam.” (In I Periherm., lect. 15,
n. 2.)
21 St. Thomas also speaks of things whose existence God has made
absolutely necessary, insofar as there is no potency in them to non­
existence. Cf. Contra Gent., Bk. 2, Chap. 30.
22 “Unde cum bonitas Dei sit perfecta, et esse possit sine aliis,
cum nihil ei perfectionis ex aliis accrescat; sequitur quod alia a se
eum velle, non sit necessarium absolute. Et tamen necessarium est ex
suppositione; supposito enim quod velit, non potest non velle, quia
non potest voluntas eius mutari.” (Summa Theol., I, q. 19, a. 3.)

Certitude and Necessity

75

ence, just as the intellect of God and exemplary causality
are the reason for the absolute necessity of the metaphysical
order of essence.
The natural philosopher, on the other hand, does not
worry about the necessity of existence as such. He accepts
the existence of the material world as given in experience.
Likewise, he does not seek the ultimate reason for the im­
mutability of essences, but takes them for immutable and
necessary because they transcend the process of natural
change. His problem is different. To begin with, he does
not properly speak of essences at all, but rather of natures.
! Essences are of the static order of being; natures are of
jthe dynamic order of becoming, the proper domain of the
/ physicist. He observes the phenomena of nature, its changes,
and inquires about the proper causes without which these
V changes could not have come about. He begins with a
change or motion as already achieved and seeks everything
that was ordained to that change, every proper cause with­
out which that motion could not have been produced.23
There is true necessity between a natural change and
its causes when we view the matter a posteriori. The change
could not have been produced without the causes. But the
change itself is not at all necessary nor is the being or state
of being produced by the change. The change and the end
of the change, the terminus ad quern, the being produced
by the change, are posited or supposed : they are given in
experience. It is not the end or achievement of a change,
the intrinsic final cause of a change, that is necessary, for
it is contingent and presupposed. It is rather the connec­
tion between this posited end and its causes that is neces­
sary. Such necessity is hypothetical. It binds all the other
causes of a thing to the final cause.
Since this matter is so important, let us comment briefly
on St. Thomas’ Commentary to Book Two, Chapter Nine
of Aristotle’s Physics.2*
23 Parts of Animals, Bk. 1, Chap. 1, 640a 12-18.
24 Leet. 15. This chapter is Aristotle’s main treatment of necessity

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St. Thomas begins by inquiring whether in natural things
there is a simple and absolute necessity, or a conditional
and hypothetical necessity. He had defined his meaning of
necessity a few lessons back.
Some have defined the necessary as that which
does not have an impediment and the contingent
as what happens frequently but which can be im­
peded in a few cases. But this is irrational, be­
cause that is said to be necessary which in its na­
ture cannot not-be; but the contingent which
happens frequently is that which can not-be.25
In his commentary on the Perihermeneias2* he had shown
two erroneous definitions: that the necessary is what will
always be and that it is what cannot be kept from being
true. The first definition is a posteriori; it is an effect of
necessity rather than necessity itself. The second is from
an extrinsic condition: “A thing is not necessary because
it does not have an impediment, but rather because it is
necessary it cannot have an impediment."21 Therefore, he
defines the necessary as : “that which in its nature has been
determined only to existence.”28 This definition is fully veri­
fied only of absolute necessity; for hypothetical necessity
is such only in a qualified sense.29
Absolute necessity, says St. Thomas,30 is that which de­
in physics. He comes back to the subject in summary form in his
methodological treatise at the beginning of On the Parts of Animals,
Bk. 1, Chap. 1, 639b 21—640a 10; 642a 1-36. He devotes a chapter
to it in his metaphysical lexicon, Metaphysics, Bk. 5, Chap. 5, 1015a
20—b 15; St. Thomas’ Commentary, lect. 6, n. 827-841.
2S “Quidam definierunt esse necessarium, quod non habet impedi­
mentum; contingens vero sicut frequenter, quod potest impediri in
paucioribus. Sed hoc irrationabile est. Necessarium enim dicitur,
quod in sui natura habet quod non possit non esse: contingens autem
ut frequenter, quod possit non esse.” (In II Phys., lect. 8, n. 4.)
28 In I Periherm., lect. 14, n. 8.
22 “Non enim ideo aliquid est necessarium, quia non habet im­
pedimentum, sed quia est necessarium, ideo impedimentum habere non
potest.” (Ibid.)
28 “Quod in sua natura determinatum est solum ad esse.” (Ibid.)
22 In V Meta., lect. 6, n. 833-834.
80 In II Phys., lect. 15, n. 2. In De Principiis Naturae, n. 33, he

Hi

HL

Certitude and Necessity

77

pends on prior causes: matter, form and agent. For in­
stance, matter is the necessary cause of corruptibility, and
man’s rationality and the properties of mathematical figures
flow with absolute necessity from formal cause. Likewise,
“that which has necessity from the efficient cause is abso­
lutely necessary; for example, because of the motion of
the sun it is necessary that day and night alternate.’’’1
Again, because of the contraction of the lungs it is neces­
sary that the air in them be expelled.
Whatever has necessity from what is posterior in exist­
ence, namely end or form insofar as it is the end of gener­
ation, is conditionally or hypothetically necessary. “There­
fore,” St. Thomas says ,“to ask whether there is necessity
simply or from supposition in natural things is the same
as to ask whether the necessity in natural things is found
from the end or from matter.”32
In the pre-Aristotelian tradition, as well as in the modern
mechanist tradition, thinkers tried to explain the gener­
ation of natural things from the brute necessity of matter
and cosmic agents, without any recourse to design or final­
ity. Things have come into existence simply because of the
blind interplay of material and efficient causes.” With
Aristotle and St. Thomas, however, nature is strictly teleo­
logical. The marvelous disposition of matter cannot be
accounted for unless all the causes involved are predeter­
mined in the direction of the end to be realized, of the be­
ing to be produced. The intricate structures and coordina­
tions of the eye or ear, for instance, cannot be due to the
chance interactions of evolving matter; the matter had to
be given an intrinsic ordination to the production of eye
or ear, and this in view of the function of the eye or ear.
This does not deny, but rather implies, the absolute necescalls the form necessary by hypothetical necessity, in that it is the
end of generation.
31 In II Phys., lect. 15, n. 2.
“Ibid.
33 Cf. examples given by Aristotle in Parts of Animals, Bk. 1, Chap.
1, 640a 18—b 29.

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Demonstrating in Natural Philosophy

sity flowing from the essences of material beings ; each na­
ture necessarily has its own specific properties.34 But these
are all ordered and organized in the process of natural gen­
eration by the end, or specific nature, to be achieved.
The parts of a house are so disposed because of
the end, which is to shelter and protect men from
wind and rain. Also, just as it is with the house,
so it is in all other things where there is action
for the sake of something: for in all these the
dispositions of the things generated or made do
not follow without the material principles which
have the necessary matter whereby they are nat­
urally designed to be so disposed. But the things
made or generated are not so disposed because the
material principles are such, except insofar as the
because means the material cause; rather they
are so disposed because of some end, and the mate­
rial principles are sought that are apt for this
disposition that the end requires. This is plain
as regards the saw. Because the saw is such,
i.e. it is of such disposition or form; therefore it
should be of such, i.e. it should have such matter;
and it is such, i.e. it is of such disposition or form,
because of this, i.e. because of some end. How­
ever, this end, which is sawing, could not come
about unless it were made of iron. Therefore, the
saw must necessarily be of iron, if it is going to
be a saw and if its end is going to be achieved—
that is, its work. It is clear, then, that in natural
things there is necessity from supposition, just
as in artificial things. But this is not in such a
way that what is necessary is the end. What is
necessary is posited on the part of matter, but the
reason for the necessity is posited on the part of
the end. We do not say that it is necessary that
there be such an end because matter is such ;
rather the opposite: because such an end and
form is going to exist, it is necessary that such
â4 There are some events that are due to the absolute necessity of
matter without the intervention and direction of finality. These are
due to chance conjunctions of causes acting for other ends. These
events are all per accidens and contingent, so that they are outside
the scope of science. Cf. A. Mansion, op. cit., “Le hasard,” pp. 292314.

Certitude and Necessity

79

matter exist. Thus the necessity is placed in the
matter, but the reason for the necessity is placed
in the end.35
It follows that whenever we can arrive at a formal defi­
nition, either of a complete being or of a motion, we know
that such a definition is identical with the intrinsic final
cause of the production of that being or motion. Therefore,
from the point of view of necessity, we can demonstrate
the other causes of the subject in question. They are ren­
dered hypothetically necessary by the given end.
The following example given by Aristotle will clarify
the place of the two types of necessity in physical demon­
stration.
Of the method itself the following is an example.
In dealing with respiration we must show that it
takes place for such or such a final object; and
we must also show that this and that part of the
process is necessitated by this and that other stage
ss “Partes domus sic sunt dispositae propter finem, qui est co­
operire et salvare homines a caumate et pluviis. Et sicuti est in domo,
similiter est in omnibus aliis, in quibuscumque contingit agere propter
aliquid: in omnibus enim huiusmodi non consequuntur dispositiones
generatorum aut factorum sine principiis materialibus quae habent
necessariam materiam, per quam apta nata sunt sic disponi. Non tamen
res factae aut generatae sic disponuntur propter hoc, quod principia
materialia sunt talia, nisi sicut ly propter dicit causam materialem;
sed sic disponuntur propter aliquem finem, et principia materialia
quaeruntur ut sint apta huic dispositioni, quam requirit finis, ut patet
in serra. Est enim serra huiusmodi, idest talis dispositionis aut
formae; quare oportet quod sit talis dispositionis aut formae, propter
hoc, idest proter aliquem finem. Sed tamen iste finis, qui est sectio,
non posset provenire nisi esset ferrea: necessarium est ergo serram
esse ferream, si debeat esse serra, et si debeat esse eius finis, quod
est opus ipsius. Sic igitur patet quod in rebus naturalibus est
necessarium ex suppositione, sicut et in rebus artificialibus: sed
non ita quod id quod est necessarium, sit sicut finis; quia id quod
necessarium est, ponitur ex parte materiae; sed ex parte finis ponitur
ratio necessitatis. Non enim dicimus quod necessarum sit esse talem
finem, quia materia talis est; sed potius e converso, quia finis et forma
talis futura est, necesse est materiam talem esse. Et sic necessitas
ponitur ad materiam, sed ratio necessitatis ad finem.” (In II Phys.,
lect. 15, n. 4. [our trans.]).

80

Demonstrating in Natural Philosophy

of it. By necessity we shall sometimes mean hypo­
thetical necessity, the necessity, that is, that the
requisite antecedents shall be there, if the final end
is to be reached ; and sometimes absolute necessity,
such necessity as that which connects substances
and their inherent properties and characters. For
the alternate discharge and re-entrance of heat
and the inflow of air are necessary if we are to
live. Here we have at once a necessity in the for­
mer of the two senses. But the alteration of heat
and refrigeration produces of necessity an alter­
nate admission and discharge of the outer air, and
this is a necessity of the second kind.3®
Therefore, whenever a final cause is influencing a process,
the necessity ultimately comes from this final cause, rather
than from the absolute necessity of the prior causes. This
absolute necessity is indeed present in natural changes, but
the reason for the necessity is the end to be realized. This
is the case in natural as well as artificial changes. Chance
occurrences, on the other hand, are attributable to the neces­
sity of efficient and material causes.
We have seen that there is a special and limited kind
of certitude attainable in natural science, because there is
a special and limited kind of necessity between natural
things and their causes. We cannot expect the rigorous
and exact certainty of mathematics in the science of na­
ture. In mathematics there is a perfect intuition of es­
sences and deduction of properties through the medium
of formal causality. Hence, mathematics, which does not
transcend the realm of formal cause, yields the perfect
certitude that flows from absolute necessity.37 In natural
a® Parts of Animals, Bk. 1, Chap. 1, 642a 31-37.
aT Mathematical-physical sciences proceed according to middle
terms that are mathematical, non physical. These sciences participate
in the certainty of mathematics, but it is a certainty of mathematical
relation. Mathematical-physical sciences cannot demonstrate physical
necessity, but only mathematical necessity. Hence, its laws are physi­
cally only quia or factual. Physical necessity can be shown only by
the connection of properties with essence defined in terms of their
physical causes. Mathematical-physics does not attain physical es­
sences as such. Cf. In De Trin., q. 5, a. 3, ad 6 & 7.

Certitude and Necessity

81

science there is not a perfect intuition of essences or causes
from which properties and effects are rigorously deduced.
Rather, the properties and effects are discovered in con­
tingent matter, and the causes or essences are inferred
from their effects. Natural science, unlike mathematics,
cannot proceed a priori with rigorous certitude. All the
effects of natural causes can be impeded, for they are real­
ized in contingent matter which can be indisposed to re­
ceive the action of the cause. Once, however, we are given
an effect, we can proceed a posteriori to the proper causes.
There is a hypothetical necessity between a given effect and
its causes. But there is no necessity between any natural
cause and its future effect, unless we assume the necessity
by positing the production of the effect. We can do this
by abstracting from the contingent conditions of individual
matter and considering the cause-effect relationship in its
universal aspect.38
Experience apprises us of contingent facts. But among
these contingent facts we note a constancy of certain occur­
rences or phenomena. The judgment of this regularity pre­
supposes, of course, a thorough acquaintance with the case
in question and a critical investigation into the phenomena.
Some things always happen, such as the succession of day
and night. Others occur most of the time, as the genera38 “Est autem considerandum quod de his quidem quae sunt sicut
frequenter, continget esse demonstrationem, in quantum in eis est
aliquid necessitatis. Necessarium autem, ut dicitur in II Physicorum,
aliter est in naturalibus, quae sunt vera ut frequenter, et deficiunt
in minori parte; et aliter in disciplinis, idest in mathematicis, quae
sunt semper vera. Nam in disciplinis est necessitas a priori; in
naturalibus autem a posteriori (quae tamen est prius secundum
naturam), scilicet a fine et forma. Unde sic docet ibi Aristoteles
ostendere propter quid, ut si hoc debeat esse, puta quod oliva generetur,
necesse est hoc praeexistere, scilicet semen olivae; non autem ex
semine olivae generatur oliva ex necessitate, quia potest impediri gen­
eratio per aliquam corruptionem. Unde si fiat demonstratio ex eo
quod est prius in generatione, non concludet ex necessitate; nisi forte
accipiamus hoc ipsum esset necessarium, semen olivae ut frequenter
esse generativum olivae, quia hoc facit secundum proprietatem suae
naturae, nisi impediatur.” (In I Post. Analyt., lect. 42, n. 3.)

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Demonstrating in Natural Philosophy

tion of an integral human being rather than a monster.
When something seldom happens, it can be explained by
the contingencies of chance or coincidence. But when a
regularity or frequency of occurrence is evident, there must
be some cause of the regularity or frequency. A constant
effect denotes a corresponding constant cause. When we
consider only the constant effect and its proper and proxi­
mate cause, abstracting from the contingencies that can
hinder the effect in individual cases, then we have a neces­
sary relation: it cannot be otherwise but that such an ef­
fect follow from such a proper and proximate cause of it.
Universal aspects of contingent things are necessary, for
the universal is formed from the regularities noted by sen­
sory experience. Therefore, of the universal we can have
science and demonstration.38
39 But as soon as we begin to
apply our conclusions to individual instances, we are back
in contingency ; our conclusions will hold only for the most
38 “Ostendit quomodo eorum, quae sunt ut frequenter, possit esse
demonstratio, dicens: quod eorum quae saepe fiunt, sunt etiam
demonstrationes et scientiae: sicut de defectu lunae, qui tamen non
semper est. Non enim luna semper deficit, sed aliquando. Haec autem
quae sunt frequenter, secundum quod huiusmodi sunt, idest secundum
quod de eis demonstrationes dantur, sunt semper: sed secundum quod
non sunt semper, sunt particularia. De particularibus autem non
potest esse demonstratio, ut ostensum est, sed solum de universalibus.
Unde patet quod huiusmodi, secundum quod de eis est demonstratio,
sunt semper. Et sicut est de defectu lunae, ita est de omnibus aliis
similibus. Consideranda tamen est differentia inter ea. Quaedam
enim non sunt semper secundum tempus, sunt autem semper per
comparationem ad causam: quia nunquam deficit, quin posita tali
causa, sequatur effectus; sicut est de defectu lunae. Nunquam enim
deficit, quin semper sit lunae eclypsis, quandocunque terra diametraliter interponitur inter solem et lunam. In quibusdam vero contingit
quod non semper sunt, etiam per comparationem ad causam: quia
videlicet causae impediri possunt. Non enim semper ex semine hominis
generatur homo habens duas manus; sed quandoque fit defectus vel
propter impedimentum causae agentis vel materiae. In utrisque autem
sic ordinandae sunt demonstrationes, ut ex universalibus propositioni­
bus inferatur universalis conclusio, removendo illa, in quibus potest
esse defectus vel ex parte temporis tantum vel etiam ex parte causae.”
(In I Post. Analyt., lect. 16, n. 8.)

Certitude and Necessity

83

part, for their necessity is only hypothetical.
It is possible, then, to have true science of natural things,
because in their universal aspects there is a sufficient neces­
sity, a necessity discovered along with the universal na­
ture itself in the contingent individuals given in frequent
sensory experience.
We are now in a position to study the manner of demon­
strating in natural science.

CHAPTER IV
THE MANNER OF DEMONSTRATING
IN NATURAL PHILOSOPHY

In our treatment of the kind of certitude and necessity
to be found in natural science, we have virtually estab­
lished the manner of demonstrating in it. There is no neces­
sity of natural things a priori, that is, in the downward
direction from cause to effect. But there is hypothetical
necessity a posteriori, in the ascending direction from effect
to cause. Therefore, natural science must start with experi­
ence and proceed from it to essences and causes. It remains
for us to clarify this concept and establish it more firmly.
Perhaps, one of the most persistent calumnies leveled at
Aristotle is that his natural science is a priori, that it is
insufficiently founded in critical experience. As a result,
he is said to have come up with a kind of scientific mon­
ster purporting to be an explanation of nature. This Aris­
totelian science is thought to have been unmasked, discredit­
ed and definitively repudiated by the renaissance physicists
and their successors for all times.
The question is not as simple as that. Modern researches
into the nature of the experimental sciences are beginning
to show up a decided a priori element in them, whereas
Aristotelian studies are proving how the peripatetic sci­
ence is a picture much closer to physical reality.1 It is not
our duty here to delve into the content of Aristotelian sci­
ence and philosophy. We are at present interested only
in the methodology of the Stagirite, and that in principle,
rather than in application. In other words, we intend at
present to investigate his rules of procedure, abstracting
1Cf. Gavin Ardley, Aquinas and Kant, the Foundations of the
Modern Sciences.
84

The Manner of Demonstrating

85

for the moment from the question whether he sufficiently
put them into practice in his own physical studies.
We must begin by showing the fundamental role given
by Aristotle to observation and experience.2
Aristotle holds that a young man cannot be either a mor­
alist or a physicist, though he can be a mathematician. The
reason is that the objects of mathematics are abstract,
though not so abstract as not to be imaginable, whereas
natural and moral science require a great deal of experience,
which takes a long time to acquire.3 Moreover, the Philos­
opher shows a great respect for the opinions of elderly
people, especially in moral matters, so that “we ought to
attend to the undemonstrated sayings, and opinions of ex­
perienced and older people or of people of practical wisdom
not less than to demonstrations; for because experience has
given them an eye they see aright.”4
According to Aristotelian demonstrative theory, all dem­
onstrations proceed from foreknowledge which ultimately
comes from sense perception.
Now induction is the starting-point which knowl­
edge even of the universal presupposes, while syl­
logism proceeds from universals. There are there­
fore starting-points from which syllogism pro­
ceeds, which are not reached by syllogism; it is
therefore by induction that they are acquired.5*
Here are a few examples of inductions that Aristotle makes.
“We physicists must take for granted that the things that
exist by nature are, either all or some of them, in motion—
which is indeed made plain by induction.”® Nothing is con­
tained locally in itself: “Thus if we look at the matter
inductively we do not find anything to be ‘in’ itself in any
2 Cf. J. M. Le Blond, Logique et Méthode chez Aristote, Part 2,
Chap. 2, “L’experience,” pp. 222-268; A. Mansion, Introduction a la
Physique Aristotélicienne, Chap. 6, “La méthode aristotélicienne en
physique,” pp. 206-225.
3 Nicomachean Ethics, Bk. 6, Chap. 8,1142a 12-20.
*Ibid., Chap. 11, 1143b 11-13.
5 Ibid., Chap 3,1139b 27-30.
• Physics, Bk. 1, Chap. 2, 185a 13-14.

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Demonstrating in Natural Philosophy

of the senses that have been distinguished; and it can be
seen by argument that it is impossible.”7 “Change which
is not accidental on the other hand is not to be found in
everything, but only in contraries, in things intermediate
between contraries, and in contradictories, as may be proved
by induction.”8* Frequently throughout his treatises we find
an explicit appeal to induction as the source of his data.
Other times he uses induction, but does not explicitly in­
form us of it. “It is clear,” he says in the last paragraph
of the Posterior Analytics, “that we must get to know the
primary premisses by induction; for the method by which
even sense-perception implants the universal is inductive.”*
This induction must be established upon careful observa­
tion and experience. There is a capital text which must be
kept in mind:
Lack of experience diminishes our power of tak­
ing a comprehensive view of the admitted facts.
Hence those who dwell in intimate association with
nature and its phenomena grow more and more
able to formulate, as the foundations of their the­
ories, principles such as to admit of a wide and
coherent development : while those whom devotion
to abstract discussions has rendered unobservant
of the facts are too ready to dogmatize on the basis
of a few observations.10
Unbiased scholars know well how intimate was Aris­
totle’s association with nature and its phenomena. In his
treatise On the Parts of Animals he shows how we have
scanty enough evidence of the imperishable and eternal
things that we desire to know,
... whereas respecting perishable plants and ani­
mals we have abundant information, living as we
do in their midst, and ample data may be collected
7 Ibid., Bk. 4, Chap. 2, 210b 8-10.
8 Ibid., Bk. 5, Chap 1, 224b 28-30. Cf. Parts of Animals, Bk. 2,
Chap. 1, 646a 24-30. References to more specialized physical induc­
tions are given by Λ. Mansion, op. cit., p. 220.
* Post. Analyt., Bk. 2, Chap. 19, 100b 3-5.
10 On Generation, Bk. 1, Chap. 2, 316a 5-10. (Italics ours.)

The Manner of Demonstrating

87

concerning all their various kinds, if only we are
willing to take sufficient pains.11
Faithful to this principle, Aristotle made some rather amaz­
ing observations. He established that air has weight, that
a vessel breaks from the pressure of expanding vapors,
that “that which does not twinkle is near—we must take
this truth as having been reached by induction or sense­
perception.”11
12 It is well recognized that the Fourth Book
of Meteors is characterized by “its extraordinary richness
of precise observations,”1314so much so that scholars find
in it “a proof of the progress of Aristotle in precision of
research and a confirmation at the same time, if such is
needed, of the relatively late date of the Meteors.”11
Aristotle was not satisfied only with observation. He
practiced some rudimentary experiments, such as blinding
young swallows to see if their eyes would be regenerated.15
He says: “The following experiment makes the necessity
of a medium clear. If what has color is placed in immedi­
ate contact with the eye, it cannot be seen.”1® He speaks
of a kind of imaginary experiment : “If you planted a bed
11 Parts of Animals, Bk. 1, Chap. 5, 644b 26-31. (Italics ours.)
12 On the Heavens, Bk. 4, Chap. 4, 311b 9-11; ibid., Bk. 3, Chap. 7,
305b 9; Post. Analyt., Bk. 1, Chap. 13, 78a 33-35. Cf. Le Blond,
op. cit., pp. 233, 237, 238 and passim.
13 “On a depuis longtemps remarqué son extraordinaire richesse
en observations précises.” (Le Blond, op. cit., p. 237.)
14 “Leur richesse d’observation apporte par là une preuve du pro­
grès d’Aristote dans la précision de la recherche et confirmerait en
même temps, s’il était nécessaire, la date relativement tardive des
Météores.” (Ibid., p. 238-239.) It seems to us that this opinion does
not take sufficiently into account the Aristotelian methodology of pro­
ceeding from general to particular. At the more general levels, which
in present times is said to be the realm of philosophy as opposed to
science, there is less need of the minute and precise observation re­
quired at the lowest specific levels. Therefore, there is no point in
saying: “Il est certain par exemple que les traités sur les Parties des
Animaux et la Génération des Animaux, qui sont sûrement tardifs,
sont beaucoup plus riches en details que les Physiques.” (Ibid., p. 236.)
15 Generation of Animals, Bk. 4, Chap. 6, 774b 31-34.
« On the Soul, Bk. 2, Chap. 7, 419a 13.

I
88

Demonstrating in Natural Philosophy

and the rotting wood acquired the power of sending up a
shoot, it would not be a bed that would come up, but wood—
which shows that the arrangement in accordance with the
rules of the art is merely an incidental attribute.”17 We
know that he practiced dissection of animals, and some
authors think that he refers to a book of his : On Dissec­
tions, which do not have.18 He tried blowing into the wind­
pipe of an animal and thought that he saw the air enter
the heart.19 He cut insects in two, in order to learn if the
parts lived on.20 He gives a simple experiment purporting
to prove that the cicada has weak eyesight.21 A mere casual
paging through the works of Aristotle will convince us of
his esteem for the observation of facts. Only biased scholar­
ship or lack of scholarship could accuse him of a priorism.
We should not reproach Aristotle for the mistakes of
observation that he made. After all, he was a pioneer sci­
entist, and we would do well to look at his marvelous ac­
complishments, rather than to harp upon his errors. Like­
wise, we must not expect the precise observations and ex­
periments of a modern scientific laboratory from Aristotle.
He did not have to make such exact measurements, because
his science is not quantitative, but qualitative, a distinction
that many of his critics do not understand or keep in mind.
Aristotle studies the real world from the aspect of essences
and essential attributes, not from that of quantitative re­
lations. Finally, it is sometimes noted that the majority
of Aristotle’s observations appear in the biological treatises,
and that the observations of inanimate beings are less spec­
tacular.22 This is easily explained by the fact that he was
17 Physics, Bk. 2, Chap. 1, 193a 13-15.
18 Cf. On Respiration, Chap. 14, 474b 9 and footnote in Ross ed.
19 History of Animals, Bk. 1, Chap. 16, 495b 14.
20 Ibid., Bk. 4, Chap. 7, 531b 30.
21 Ibid., Bk. 5, Chap. 30, 556b 17-21.
22 Le Blond, op. cit., p. 228, says: “On a remarqué que les exemples
précédents sont empruntés aux traités biologiques: la physique des
inanimés manifeste moins vivement cette curiosité exigeante et cet
esprit d’observation scientifique: Aristote n’y fait était que d’un

The Manner of Demonstrating

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a specialist in biology and because living beings were more
numerous and accessible and more stimulating to scientific
curiosity.23 Living beings, moreover, because of their mani­
fest typical operations, are easier to study in a qualitative
manner. Even if it is true, however, that his observations
are relatively meager in the study of inanimate beings,
yet we must admit his inexorable demands that all natural
science take its origin in experience.
He found the Platonic theory of elements in the Timaeus
untenable because it broke against experience. “Anyone
who insists upon an exact statement of this kind of theory,
instead of assenting after a passing glance at it, will see
that it removes generation from the world,”24 which, of
course, is evident to experience. He finds Atomism unac­
ceptable because it cannot explain alteration, growth and
diminution, which also are evident to sensory experience.25
He asserts his principle vigorously against those who come
with a pre-conceived theory to the study of the generation
of elements one from the other.
nombre assez restreint de faits et c’est sur cette base un peu étroite
qu’il s’efforce d’édifier ses théories.”
23 It is interesting to note the reaction of Charles Darwin to
Aristotle’s biological studies. He wrote the following letter to Wm.
Ogle, upon receiving a copy of the latter’s translation of Parts of
Animals; ‘"“You must let me thank you for the pleasure which the
introduction to the Aristotle book has given me. I have rarely read
anything which has interested me more, though I have not read as yet
more than a quarter of the book proper. From the quotations which
I have seen, I had a high notion of Aristotle’s merits, but I had not
the most remote notion what a wonderful man he was. Linnaeus and
Cuvier have been my two gods, though in very different ways, but
they were mere schoolboys to old Aristotle. How very curious, also,
his ignorance on some points, as on muscles as the means of movement.
I am glad that you have explained in so probable a manner some of
the grossest mistakes attributed to him. I never realized, before
reading your book, to what an enormous summation of labour we owe
even our common knowledge.” Charles Darwin to W. Ogle, Feb. 22,
1882. Lafe and Letters of Charles Darwin, ed. by his son Francis
Darwin, Vol. I, p. 371.
24 On the Heavens, Bk. 3, Chap. 8, 306b 27-29.
25 On Generation and Corruption, Bk. 1, Chap. 9, 327a 16-25.

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It is absurd, because it is unreasonable that one
element alone should have no part in the trans­
formations, and also contrary to the observed data
of sense, according to which all alike change into
one another. In fact their explanation of the ob­
servations is not consistent with the observations.
And the reason is that their ultimate principles
are wrongly assumed: they had certain predeter­
mined views, and were resolved to bring every­
thing into line with them. It seems that percep­
tible things require perceptible principles, eternal
things eternal principles, corruptible things cor­
ruptible principles; and, in general, every subject
matter principles homogeneous with itself. But
they, owing to their love for their principles, fall
into the attitude of men who undertake the de­
fence of a position in argument. In the confidence
that the principles are true they are ready to ac­
cept any consequence of their application. As
though some principles did not require to be
judged from their results, and particularly from
their final issue ! And that issue, which in the case
of productive knowledge is the product, in the
knowledge of nature is the unimpeachable evidence
of the senses as to each fact.2*
It is quite significant that Aristotle did not limit the
amassing of experience to his personal activity. He looks
to the experience of others. He examines the writings and
uses many of the facts observed by others, sometimes nam­
ing his sources,27 more often not.28 He never accepts data
blindly and without criticism, even though his sources did
occasionally lead him into error. He knows and reports the
interpretations that his predecessors put upon their facts.
He shows deference for authorities, especially for the com­
mon accord of all philosophers. He was the first to study
the history of thought, its development and vicissitudes at
the hands of philosophers who had gone before. “Let us
28 On the Heavens, Bk. 3, Chap. 7, 306a 4-18. (Italics outs.)
27 Cf. T. W. Organ, An Index to Aristotle, “Anaxagoras,” "Demo­
critus,” “Diogenes of Apollonia,” “Empedocles,” “Heraclitus,” “Par­
menides,” “Pythagoreans.”
28 Cf. Le Blond, op. cit., p. 253; W. D. Ross, Aristotle, p. 113.

The Manner of Demonstrating

91

remember,” he wrote in regard to political wisdom, “that
we should not disregard the experience of ages; in the mul­
titude of years these things, if they were good, would cer­
tainly not have been unknown.”29 Again, “We should there­
fore make the best use of what has been already discovered,
and try to supply defects.”30 He is looking for the perennial
stream of truth, contributed to in greater or lesser degree,
by his predecessors: “the experience of the eternal man,
more complete and more imposing still than that of the
elderly individual man.”31
Aristotle showed an extraordinary reverence toward the
simultaneous experience of the multitude of people, as trust­
ing the judgment of the many more than of the individual.32
He does not disdain to study myths, common beliefs and
superstitions, proverbs, poetry and dreams as indications
of common experience.33 In all this he endeavored to ex­
tend his personal experience in time as well as in space by
recourse to the experience of others.
After the physicist has completed his observation of facts,\
he is ready to proceed to theory, to an understanding and
/
unification of his facts by means of the demonstrative proc­
ess. “The course of exposition must be first to state the
attributes common to whole groups of animals, and then
to attempt to give their explanation.”34 In the treatise On
the Parts of Animals, in which Aristotle is so thoroughly
conscious of methodological principles, he says:
The nature and the numbers of the parts of which
'animals are severally composed are matters which
have already been set forth in detail in the books
of Researches about Animals. We have now to
29 Politics, Bk. 2, Chap. 5, 1264a 1-3.
30 Ibid., Bk. 7, Chap. 10, 1329b 35. Cf. On the Soul, Bk. 1, Chap. 2,
403b 20-25; Metaphysics, Bk. 1, Chap. 3, 983b 1-6.
31 “... expérience de l’homme éternel, plus complète encore et plus
imposante que celle du vieillard.” (Le Blond, op. cit., p. 262.)
32 Cf. Polities, Bk. 3, Chap. 11,1281a 40—b 10.
33 Cf. Metaphysics, Bk. 12, Chap. 8, 1074b 1-15; Organ, op. cit.,
“Proverbs”; On Prophesying by Dreams, Ch. 1, 462b 13-20.
34 On the Parts of Animals, Bk. 1, Chap. 5, 645b 1-3.

SUM!

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Demonstrating in Natural Philosophy

inquire what are the causes that in each case have
determined this composition, a subject quite dis­
tinct from that dealt with in the Researches.35
The whole process of proof in natural science is well sum­
marized in the following passage from the Prior Analytics.
It is the business of experience to give the prin­
ciples which belong to each subject. I mean for
example that astronomical experience supplies the
principles of astronomical science; for once the
phenomena were adequately apprehended, the dem­
onstrations of astronomy were discovered. Sim­
ilarly with any other art or science. Consequently,
if the attributes of the thing are apprehended,
our business will then be to exhibit readily the
demonstrations. For if none of the true attributes
of things had been omitted in the historical sur­
vey, we should be able to discover the proof and
demonstrate everything which admitted of proof,
and to make that clear, whose nature does not
admit of proof.3®
St. Thomas is no less demanding of sensory experience
in the philosophy of nature. All our intellectual knowl­
edge takes its origin in the senses. The experience of the
senses is prior in our knowledge, and it is more known as
regards us. From this sensory experience we can abstract
mathematical entities, and because we know the whole es­
sence of these, we can rigorously deduce a perfect science
from them. The knowledge of these mathematical essences
is prior in us to the knowledge of their properties. There­
fore, we proceed from these principles to demonstrate. We
have seen in the .last chapter how St. Thomas excludes this
procedure in natural science, because we do not have a per­
fect intuition of material essences. Therefore, the direc­
tion of our demonstrations at the outset cannot be from
them, but must rather be toward them.
Some things are knowable to us through them­
selves; and in bringing such things to light the
speculative sciences use their definitions to demon­
’s Ibid., Bk. 2, Chap. 1, 646a 8-12.
” Prior Analytics, Bk. 1, Chap. 30, 46a 17-29.

The Manner of Demonstrating

93

strate their properties, as happens in the sciences
which demonstrate propter quid. There are other
things which are not knowable to us through them­
selves but through their effects. And if indeed the
effect is adequate to the cause, we take the quid­
dity itself of the effect as our starting point to
prove that the cause exists and to investigate its
quiddity, from which in turn its properties are
made evident.37
Again and again St. Thomas emphasizes that natural
science must start with the senses. “Physics gets its data
from the senses.” “As a starting-point for natural science,
we must take what appears sensibly.” “Natural principles
are taken from the experience of sensible things.” “We
should learn natural science after mathematics because the
extensive data it is grounded upon require experience."3*
He sees this fidelity to sensory experience as the distinctive
feature of Aristotle’s philosophy.39 He willingly concurs in
Aristotle’s criticism of Platonic procedure49 and even elab­
orates it:
He assigns the reason why Plato was more in er­
ror than Democritus was on this matter (i.e.
whether bodies are ultimately composed of indi­
visible planes: Plato). He says that the reason
why Plato was less able to see admitted facts, that
is, things that were manifest to everyone, was
inexperience. He was so intent on intelligible
ST In De Trin., q. 6, a. 4, ad. 2. Cf. In I Ethic., lect. 4, n. 51-52;
In II De Anima, lect. 3, n. 245.
38 “Modus physicae... secundum quod a sensu accipit.” (In De
Trin., q. 6, a. 1, ad q. 2, ad 4.) “Oportet autem id quod sensibiliter
apparet, accipere ut principium in scientia naturali.” (In 1 De Gen.
et Cor., lect. 12, n. 3.) “... in principiis naturalibus quae ex sen­
sibilium experimento accipiuntur.” (In VIII Phys. lect. 3, n. 4.)
“Naturalis post mathematicam addiscenda occurat, eo quod universalia
ipsius documenta indigent experimento et tempore.” (In De Trin.,
q. 5, a. 1, ad 10.)
39 “Quidam ad inquirendam veritatem de natura rerum, processerunt
ex rationibus intelligibilibus; et hoc fuit proprium Platonicorum;
quidam vero ex rebus sensibilibus ; et hoc fuit proprium Philosophiae
Aristotelis.” (De Spir. Creaturis, a. 3.)
40 The passage from Aristotle is quoted above, Chap. IV, note 10.

ΜΜΗΜΜΜ

94

Demonstrating in Natural Philosophy

things that he paid no attention to sensible things
with which experience deals. So those philoso­
phers who cared more for sensible and natural
things were more able to find the kind of princi­
ples to which they could adapt many sensible
facts. But the Platonists, who were unobservant
of existing things, that is, of natural and sensory
beings, regarded only a few sensory objects that
presented themselves ; and then, by many abstract
discussions and reasons, that is from many things
considered by the mind on a universal level, they
dogmatised, that is, they formed an opinion about
sensible matters without careful observation.41
In his well known tract on the division and methods of
the sciences, St. Thomas gives ample statement of the prin­
ciples of procedure whereby the science of nature is un­
folded. There are two passages that are of special interest
to us at present.
In question six, article one of his commentary on the De
Trinitate of Boethius, St. Thomas is inquiring whether the
mode of procedure in natural science can be characterized
as rational (rationabiliter), as distinguished from the mode
of learning (disciplinabiliter) in mathematics and the mode
of intellect (intellectualiter) in metaphysics. He answers
that a method can be called rational in three ways. In the
first two ways a method is called rational because it belongs
to rational science, or logic, either by using logical inten( tions as principles or by proceeding with probable argu41 “Assignat rationem quare circa hoc magis defecit Plato quam
Democritus. Et dicit quod causa huius quod Plato minus potuit videre
confessa, idest ea quae sunt omnibus manifesta, fuit inexperientia:
quia scilicet, circa intelligibilia intentus, sensibilibus non intendebat,
circa quae est experientia. Et ideo illi philosophi qui magis studuerunt
circa res sensibiles et naturales, magis potuerunt adinvenire talia
principia, quibus possent multa sensibilia adaptare. Sed Platonici,
qui erant indocti existentium, idest circa entia naturalia et sensibilia,
respicientes ad pauca sensibilium quae eis occurrebant, ex multis ser­
monibus vel rationibus, idest ex multis quae in universali rationaliter
considerabant, de facili enuntiant, idest absque diligenti perscruta­
tione sententiam proferunt de rebus sensibilibus.” (In I De Gen.
et Cor., lect. 3, n. 8.)

The Manner of Demonstrating

95

ments; in these two ways the rational method belongs to
the dialectician, not to the scientist.42
In a third way, the way proper to natural science, a meth­
od is called rational because it corresponds to the typical
manner in which the rational soul operates. “For in its
procedures natural science keeps the characteristic method
of the rational soul.”43 Just as the rational soul receives
its intelligible species from sensible things, so also does
natural science, which “proceeds from what is more known
relatively to us and less known in its own nature,”43 and
which makes use of “demonstration by means of a sign or
an effect.”43 The method of natural science has, like rea­
son itself, the characteristic of moving from knowledge
of one thing to knowledge of another thing really distinct
from the first: “In the case of natural science, in which
demonstration takes place through extrinsic causes, some­
thing is proved of one thing through another thing en­
tirely external to it.”43 Therefore, the method used by
natural science especially (though not only by natural sci­
ence) is most in conformity with the natural operation of
the human mind, which derives its data from the senses
and then elaborates it by judgment and reasoning.
In the next article St. Thomas shows explicitly that nat­
ural science begins in the sense and terminates in the sense.
It begins in sensory experience as does all intellectual knowl­
edge. It terminates in the sense, that is, it verifies its con­
clusions in the light of sensory experience. “Sometimes the
properties and accidents of a thing revealed by the sense
adequately manifest its nature,”44 as for instance the mani­
festations of nourishment, growth, reproduction and cog­
nition point to the nature of a living being. If we try to
demonstrate attributes of such a being merely in terms of
physics and chemistry, we would be doing violence to the
facts. “The intellect’s judgment of the thing’s nature must
42 Cf. In I Post. Analyt., lect, 20, n. 5; In IV Meta., lect 4, n.
572-574.
^In De Trin., q. 6, a. 1, c.
44 In De Trin,, q. 6, a. 2.

96

IJ
I
5
!
?
Î!
I

I
I
I

j
I

X

Demonstrating in Natural Philosophy

conform to what the sense reveals about it.”44 “The unim­
peachable evidence of the senses as to each fact,”4546
as Aris­
totle says in a passage to which St. Thomas alludes, is the
ultimate judge of our philosophical theories. “The person
who neglects the senses in regard to natural things falls
into error.”**
We see, then, that according to both Aristotle and St.
Thomas the method to be followed in the science of natural
things is the careful observation of natural phenomena,
even to the point of omitting none of the attributes of our
subject,45 then the demonstration of these attributes by discovering their causes and understanding the necessary re­
lation between cause and attributes—but ever with an eye
to sensory experience, which is the final arbiter of our
philosophical explanations. In other words, in natural sci­
ence we begin by observing sensory phenomena, then pro­
ceed by demonstration quia to discover the cause, from
which, by demonstration propter quid we can proceed to
a^more perfect knowledge of the observed properties.
f~"· There is no question in this Aristotelian-Thomistic nat/ tural science of deducing new facts. That is an achieve/ ment that becomes possible when an a priori discipline such
> as mathematics is applied to natural things; this is the
/ glory of mathematical physics. But a purely physical sci/
ence of nature, such as Aristotle envisioned, must start with
I
the facts already gathered. The method of demonstration
i
^s n°t a method of discovery, but of explanation. The work
!
of a qualitative natural science is not to deduce the prop' > erties of a being, but rather to understand a being and its
observed properties by seeing them in .the. light of their
first^nnm^^j^'jpropei^cajmjes. The philosophical sci< encehf nature is strictly an experimental science, a science
■ of observation of material beings and their properties from
the most general down to the most specific. At the most
general level, the observations will be those of ordinary,
45 On the Heavens, Bk. 3, Chap. 7, 306a 16. Quoted above, note 26.
46 Cf. text quoted above, note 36.

The Manner of Demonstrating

97

though not uncritical, common sense and consequently easi­
ly accessible. At the level of the ultimate species we must
make use of the most refined instruments of observation
and of facts borrowed from the higher mathematical-phys ­
ical sciences. At every stage natural science must keep it­
self solidly anchored in the unimpeachable evidence of sen­
sory experience.·"
It was this healthy empiricism of peripatetic philosophy
that St. Thomas, under the inspiration of St. Albert, found
so convincing and attractive. Because of this he was will­
ing to champion that philosophy and fight for it in a cul­
tural milieu that was aggressively Augustinian and that
looked upon Aristotle as an Averroist heresiarch. As an
illustrious religious brother of St. Thomas has remarked:
In his rallying to the doctrine of Aristotle, St.
Thomas was led less by the contested authority of
the Master than by the incontestable value of his
experimental method.... In this constant fidelity
to a rational method based upon experience con­
sists the true originality of St. Thomas in philos­
ophy—an originality more uncommon than is gen­
erally thought—which consists less in producing
truth than in discovering it; less in constructing
an abstract system out of all its fragments than
in finding solid and stable bases for it in living
and concrete reality. It is for having followed
this method, for having been constantly faithful
to it even in theology when he had to treat purely
philosophical problems that St. Thomas merits the
name of a philosopher. Accordingly, we have no
right to assert that he approached philosophy only
as a theologian and with a method proper to the­
ology.47
48.
47 Cf. W. H. Kane, O.P., “Comment on Dr. Foley’s Paper,” Pro­
ceedings of the American Catholic Philosophical Association, XXVI
(1952), pp. 140-146.
48 “C’est que, dans ce ralliement à la doctrine d’Aristote, St,
Thomas fut moins séduit par l’autorité contestée du Maître, que par la
valeur incontestable de sa méthode expérimentale.... En celà, c’est
à dire dans sa fidélité constanteà une méthode rationelle baseé sur
^expérience, consiste la véritable originalité de St. Thomas en philo-

98

Demonstrating in Natural Philosophy

The method of natural science, we have seen, is that
typically human process of seeing facts and asking the rea­
son why. There remains a further question : in what sense
does the physicist ask the question why; by what causes,
in other words, does the physicist demonstrate? Our an­
swer can be given in a proposition taken verbatim from
Aristotle.
Now, the causes being four, it is the business of
the physicist to know about them all, and if he re­
fers his problems back to all of them, he will
assign the ‘why’ in the way proper to his science—
the matter, the form, the mover, ‘that for the
sake of which.’49
The natural scientist must answer the question propter quid
in terms of all four causes, for his science is that of natural
motion. He studies subjects that are intrinsically mobile.
It is impossible for him to understand his subject until
he assigns all the causes that in any way contribute to the
changes he observes in natural being.
f Obviously, the physicist is concerned with the intrinsic
causes, matter and form, for they are "nature”; they are
/ the first principles of his science, without which he could
] know nothing scientifically about his subject. But no mo' tion can come about without an efficient cause, and no ef­
ficient cause can operate except for some end. So natural
science must consider also the extrinsic causes, agent and
end. The physicist is also interested in these extrinsic causes
Sophie, originalité plus rare qu’on ne le pense généralement, et qui
consiste moins à inventer la vérité qu’à la découvrir; à construire
de toutes pièces une système, dans l’abstrait, qu’à lui trouver des
bases solides et stables dans la réalité vivante et concrète. C’est donc
pour avoir suivi cette method; c’est pour y avoir été constamment
fidèle même en théologie, lorsqu’il eut à y traiter des problèmes pro­
prement philosophiques, que St. Thomas mérite le nom de philosophe,
et qu’on n'a pas le doit de soutenir qu’il n’a abordé la philosophie qu'on
théologien et avec un méthode propre a la théologie.” F. M. S. Gillet,
O.P., “La méthode philosophique de SL Thomas et l’expérience,"
Angelicum, Nil (1930), pp. 150-151.
*e Physics, Bk. 2, Chap. 7, 198a 23-25.

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because he is not satisfied to see changeable beings in isola­
tion, but wants to know their relation to all other beings:
what initiated their changes and to what goal are they
moving?
It will be our task in the remaining chapters to show how
natural science demonstrates from each of the causes. For
the present, we must delimit the application of two of the
causes, the form and the agent. The natural philosopher
is not interested in form as such, but in form as it is a
principle of motion in matter, for his science is restricted
to beings that are defined with sensible matter. He con­
siders the forms of all material beings, including the hu­
man soul as existing in the body. But this is the limit of
his science. When it comes to the question of the soul’s
existence apart from the body, the first principles of mo­
tion are of no more use for demonstrating. The physicist
yields the problem to the metaphysician, whose domain is
that of immaterial existents.50 The questions, therefore, of
the manner of existence and operation of souls after death
belongs to metaphysics.51 They can at best be treated only
dialectically in natural science. Such things cannot be
known through the principles of natural motion. They are
rather a part of the science of being as such.
As regards efficient causes, natural philosophy extends
to all mobile efficient causes, to all those which, though
they move others, are yet moved themselves by another.
In studying natural movers, the physicist discovers that
there has to be a First Mover that transcends the whole
order of mobility : one that moves others, but is in no way
moved itself. Again physics has reached the end of its
vision. It cannot investigate immobile being with princi50 Cf. In II Phys., lect 4, η. 10; In VI Meta., lect. 1, n. 1159. In the
first lesson of De Sensu et Sensato, St Thomas says: “Praeter librum
De anima Aristoteles non fecit librum de intellectu et intelligibili:
vel si fecisset, non pertineret ad scientiam Naturalem, sed magis ad
Metaphysician, cujus est considerare de substantiis separatis.”
01 Note that the question of the origin of the human soul also
belongs to metaphysics: creation is not motion.

dHÜ

100

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Demonstrating in Natural Philosophy

pies of mobility. There is need of a higher science to study
the first efficient cause of all natural motions.52 The phys­
icist merely retires at this point in order to study in greater
detail the effects of the First Mover in nature.
There will hardly be any objection to the Aristotelian
principles of demonstration at the general level of what is
currently called philosophy of nature. It seems unanimous­
ly admitted among Thomists that natural philosophy de­
rives its data from sensory experience and elaborates this
data by causal explanation. But many will disagree with
the attempt to extend this method to the level of the ulti-—
mâtë~~speciës. Aristotle, St. Thomas and thé scholastics
thought that we could get a certain amount of strict sci■ entitle knowledge of specific essences and their properties.
\ln fact, they held that science lacked its full perfection if
iit remained in generalities.53 There is no doubt that the
human mind seeks a knowledge of specific essences, and
(many experimental scientists are attempting to learn the
i natures of material things. Moreover, in at least one case
philosophy of nature does extend down to the ultimate spe­
cies, namely, in the case of man, whose nature we know
and whose properties we can demonstrate through the defi­
nition of his nature.
Many who object to the integral Aristotelian concept
of natural science as starting with general principles and
extending to the ultimate differences, may be thinking in
terms of mathematicized science. In passing, we may re­
mark that the exact nature and noetic value of mathemat­
ical physics is one of the thorniest epistemological problems
52 “Sunt enim principia moventia dupliciter, scilicet mota et non
mota: quorum id quod non movetur non est naturale, quia non habet
in se principium motus. Et taie est principium movens quod est
penitus immobile et primum omnium.... Rerum enim quaedam sunt
immobilia, et circa hoc est unum studium philosophiae; aliud vero
studium eius est circa ea quae sunt mobilia.... Et primum quidem
negotium pertinet ad metaphysicam; alia vero... ad scientiam
naturalem.” (In II Phys., lect. 11, n. 5, n. 3.)
53 In I Meteor., lect. 1, n. 1. Quoted above, Chap. II, note 41.

The Manner of Demonstrating

101

being discussed at the present time. The pendulumhas
gone full swing from the claim that this type of metrical
science gives an exact picture of nature Lo. the.,charge that^_
it in no way depicts reality, but is rather an a priori con­
structionthat deforms reality.
The Aristotelian natural science is strictly qualitative
and causal. It claims that the specific stratum of nature
is scientifically knowable only in the light of the general
principles and causes of mobile being. A property cannot
be known as such unless the definition of the subject is
known. Aristotelian science defines subjects, not by quan­
titative principles, but by purely physical or qualitative
principles. In the light of these, it proceeds to give causal
demonstrations of natural phenomena at every level.
! The most serious hurdle which the modern physI ical theorist has when he is confronted with Aris/ totelian cosmology is understanding that the physI ical theory of matter-form and its entire elaboraI tion in organizing the several branches of science
is a purely physical theory.54
A qualitative physical science proceeding according to
Aristotelian demonstrative method would in no way sup­
plant or absorb the mathematicized sciences. They would
remain specifically different, as being at different levels of
abstraction. But the Aristotelian natural science would
supplement its mathematical counterpart and submit the
discoveries of the latter to the demonstrative process where­
by they would attain the full status of scientific truth.
An integral natural science such as Aristotle envisioned
has yet to be developed. Gavin Ardly writes :
The new physics of Galileo and his contemporaries
ousted the real physics of the ancient and medieval
period. The latter has made no progress since the
close of the Middle Ages. Let us hope that now
the situation has become clearer the pursuit of a
54 R. J. Nogar, O.P., “Toward a Physical Theory,” The New
Scholasticism, XXV (October, 1951), pp. 397-438. This article gives
an excellent survey of attempts to achieve a satisfactory theory of
science and of the need for a truly physical theory.

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Demonstrating in Natural Philosophy

neo-Aristotelian physics will be resumed parallel
to the pursuit of Galilean physics.85
It is well to observe that the method of demonstrating in
natural science is not proper to just one particular part, as |
though Aristotle extended the method of biology to all of .'~ ’
natural science. The methodological principles are estab­
lished at the generic level of the science, in fact, immedi­
ately after the subject-genus is determined and according
to the exigencies of the subject. The method is commen­
surate with the subject-genus, and therefore applies to all
the divisions of the subject. For the subject-genus is uni­
vocal in ratione scibilitatis; the divisions, though different
essentially in their real existence, are united by the same
first principles and are thereby knowable in the same way.
The Aristotelian demonstrative method, we have seen, is
solidly rooted in sensory experience, which must be varied
and sure. From observation of constantly recurring phe­
nomena we are led to discover their proper and adequate
cause, whose essence is made known to us through its ef­
fects. In the light of this essence, defined in terms of all
four causes, we can demonstrate and understand the prop­
erties and their necessary connection with their subject
With this method we can develop a qualitative science, a
philosophical physics, that extends down to the lowest spe­
cific difference.
It remains for us to see this method at work.
05 Aquinas and Kant, p. 156.

CHAPTER V
DEMONSTRATION THROUGH FORMAL CAUSE

The mqst_diffi^cult^eature_of._the._demonstratiye theory
is tcTpuT it into practice. Aristotle and St. Thomas have
the theory constantly in mind and use it implicitly, with­
out always casting their demonstrations into strict syl­
logistic form.1 But their successors have not been faithful
to this method in natural philosophy, with the result that
it is hard to find strict propter quid demonstrations given
in modem manuals of philosophy. Still more, it is hope­
less to find them developed at the level of the ultimate spe­
cies, as the philosophers have abandoned that sphere to the
positive sciences.
We will give a few random examples of demonstrations,
using each of the causes in turn as middle terms. Most of
our examples will be taken from the Posterior Analytics,
because Aristotle cites them precisely as instances illus­
trating his demonstrative theory. Many of these examples
are outmoded as science. They depend on defective observa­
tions or incorrect theories, such as the ancient theory of
the elements. The conclusion of a demonstration shares
the noetic status of the premisses, for the premisses cause
the conclusion and can produce no more certainty than
they have themselves. Yet these examples from the Pos­
terior Analytics are valuable : they indicate how Aristotle
intended his demonstrative theory to be applied. The task
1 “Si quis recte consideret, omnia ex quibus fides potest definiri
in praedicta descriptione tanguntur, licet verba non ordinentur sub
forma definitionis; sicut etiam apud philosophos praetermissa syl­
logistica forma syllogismorum principia tanguntur.” (Summa Theol.,
Π-Π, q. 4, a. 1.) “Quandoque enim ipsis philosophis sufficit tangere
principia syllogismorum et definitionum, quibus habitis, non est
difficile in formas reducere secundum artis doctrinam.” (De Ver.,
q. 14, a. 2.)
103

104

Demonstrating in Natural Philosophy

lies ahead of modern natural philosophers to organize their
science according to the exigencies of this method of demon­
stration and to present demonstrations of those matters that
are susceptible of demonstration.
We must first consider demonstration through formal
cause. For St. Thomas himself tells us :
Whatever must be considered about generation
must be considered by the philosopher of nature.
But in generation we must consider form, matter
and the mover, because whoever wants to consider
generation as to its causes considers it in this
way: first what is that which comes to be after
something, for example fire comes to be after air
when fire is generated from air, and in this one
considers the form through which what is gener­
ated is what it is. Likewise one considers what it
is that first did this, i.e. what first moved this to
generation, and this is the mover. Again one con­
siders what it is that sustains this, and this is the
subject and matter.__ The philosopher of nature
also considers the end.2
It must be remembered that the formal cause is the end
of generation; it is that which the process of generation
is ordained to produce in a given matter. Therefore, in
generation formal and final cause coincide.8 Hie process
of demonstration is simple in this case:
We should proceed in demonstration as follows:
If this is to come to be, this and this are required;
for example, if man is to be generated, it is neces­
sary that there be human seed acting in genera­
tion. ... But that which should come to be, i.e.
that in which generation is terminated, wag. that
which was to be, i.e. the form, according to-what
was said before. Thus it is clear that when we
demonstrate according to this mode, if this is to
come to be, we demonstrate by the formal cause.4
2 In II Phys., lect. 11, n. 5 and 6.
3 “In generatione autem, forma non habet causalitatem, nisi per
modum finis. Finis enim et forma in generatione incidunt in idem
numero." (In VI Meta., lect. 3, n. 1202. Cf. In II Phys., lect 4, n. 8.)
4 In II Phys., lect. 11, n. 8.

Demonstration Through Formal Cause

105

The formal cause—as final cause of generation—is not
demonstrated, but must be attained by intellectual intui­
tion through experience and the process of definition. But
once given, it necessitates the other causes and the proper­
ties and can be the medium of demonstrating them.
We must call attention to the fact that the whole defini­
tion of a nature, that is, the essential definition, when taken
in abstraction from the individuals in which it is realized,
pertains to formal cause. St. Thomas says:
To this mode of cause all the parts which are
placed in the definition are reduced because the
parts of the species and not the parts of matter
are placed in the definition, as is said in the sev­
enth book of the Metaphysics. Nor is this contrary
to the statement above that matter is placed in the
definition of natural things, because it is not in­
dividual matter which is placed in the definition of
the species but common matter; for example in
the definition of man we posit flesh and bones,
but not this flesh and these bones. Therefore the
nature of the species constituted of form and com­
mon matter is formal with respect to the individ­
ual which participates in such nature ; to this ex­
tent we say here that the parts which are placed
in the definition pertain to the formal cause.5
The most fertile field for demonstration through formal
cause is at the generic levels of natural science, that which
modem scholastics regard as natural philosophy. For at
the generic level formal definitions are relatively easy to
obtain. Thus, the logic texts dole out such stock examples
as: “Every rational animal is capable of science; man is
a rational animal. Therefore man is capable of science.”
Such examples are easy and obvious. The use of the demon­
strative method in natural philosophy takes us into more
complicated cases.
There is one demonstration of natural science which we
feel ought to be incorporated into this study, the demonstra­
tion, namely, of motion, the first property of mobile being.
8 In II Phys., lec. 5, n. 4.

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Demonstrating in Natural Philosophy

We will use St. Thomas’ ex professo treatment of the sub­
ject, the fourth lesson on the third book of Physics.
He introduces the subject as follows:
After the Philosopher has defined motion, he here
shows whose act motion is, namely, whether it be­
longs to the mobile or to the mover. It can be said
that here he lays down another definition of mo­
tion, which is related to the foregoing as material
to formal and as conclusion to principle. This is
the definition: motion is the act of the mobile
insofar as it is mobile: motus est actus mobilis
inquantum est mobile.6
This definition of motion through its material cause, or
proper subject, is the conclusion of a demonstration which,
as we shall see, is a posteriori. In the three lessons preced­
ing the one we are now considering St. Thomas, following
Aristotle, has gone through the process of finding the for­
mal definition of motion, which serves as the principle and
middle term for demonstrating the further definition. Mo­
tion is, namely, the act of a being in potency as such : actus
existentis in potentia secundum quod huiusmodi.7 St. Thom­
as gives the demonstration in the following words:
Motion is the act of what exists in potency as
such; but what exists in potency as such is the
mobile, not the mover, for the mover as such is
a being in act. It follows that motion is the act
of the mobile as such?
The reason for this demonstration centers about the
major premiss: “what exists in potency as such is the
mobile, not the mover.” A doubt could arise about the
• “Postquam Philosophus definivit motum, hic ostendit cuius actus
sit motus, utrum scilicet mobilis vel moventis. Et potest dici quod
hic ponit aliam definitionem motus, quae se habet ad praemissam ut
materialis ad formalem, et conclusio ad principium. Et haec est defin­
itio: motus est actus mobilis inquantum est mobile.” (Ibid., n. 1.)
7 Ibid., lect 2, n. 3.
•“Motus est actus existentis in potentia inquantum huiusmodi;
existons autem in potentia inquantum huiusmodi, est mobile, non
autem movens, quia movens inquantum huiusmodi est ens in actu;
sequitur quod motus sit actus mobilis inquantum huiusmodi.’’ (Ibid.,
lect 4, n. 1.)

Demonstration Through Formal Cause

107

proper subject of motion, since we see that the mover it­
self passes from potency to act, and thus is moved. The
doubt is solved by observing that the mover is itself moved
insofar as it passes from potency to act; but precisely as
mover, it is in act and communicates act to the thing being
moved. Another consideration is the following:
Every agent moves according to its form. Since
every agent acts insofar as it is in act,... and
since each thing is in act through a form, it fol­
lows that form is the moving principle. And so
a thing moves insofar as it has a form through
which it is in act. Hence, since motion is the act
of a being in potency, it follows that motion does
not belong to anything precisely as moving, but
as mobile. Therefore, it is laid down in the defini­
tion of motion that it is the act of the mobile
insofar as it is mobile: inquantum est mobile.9
We have in the above proof a demonstration quia, or
certitude of fact, which proceeds a posteriori, since the
middle term is the definition of the effect or property, and
through this definition the proper subject is predicated of
the property in the conclusion. At this stage we ought to
construct a propter quid demonstration linking up motion
with the definition of mobile being and thereby showing
the proper reason why motion is a property of the mobile.
“For it is manifest,” says St. Thomas, “that the properties
are caused by the principles (ex principiis) of the sub­
ject, which are matter and form.”10
Actually, the demonstration given above can be under9 “Omne agens moveat secundum formam. Omne enim agens agit
inquantum est actu,... unde, cum unumquodque sit actu per formam,
sequitur quod forma sit principium movens. Et sic movere competit
alicui inquantum habet formam, per quam est in actu. Unde, cum
motus sit actus existentis in potentia, sequitur quod motus non sit
alicuius inquantum est movens, sed inquantum est mobile: et ideo in
definitione motus positum est quod est actus mobilis inquantum est
mobile. (In III Phys., lect. 4, n. 6.)
10 “Manifestum est enim quod propriae passiones causantur ex
principiis subiecti, quae sunt materia et forma.” (In V Phys., lect. 3,
n. 4.)

108

V,

8

»!
c1
Si

Î
i

Demonstrating in Natural Philosophy

stood as a priori and propter quid by inverting the terms.
The syllogism then reads :
A being in potency as such is the subject of motion.
But the mobile is a being in potency as such.
Therefore, the mobile is the subject of motion.
In the minor premiss when we speak of the mobile, we
mean mobile being only potentially moved. If it were actu­
ally moved or moving another, it would have to have some
form whereby it was moved or moving, for the substance
of mobile being is not immediately operative, but must have
some proximate principle of operation.” Since the first
principles of mobile being are established at the begin­
ning of the science, mobile being, or a being in potency
as such, means a being composed of prime matter and sub­
stantial form.
The major premiss is already evident from the hunt
which Aristotle and St. Thomas had made for the defini­
tion of motion, for motion has thereby been defined as the
act of a being in potency as such. But a deeper insight
can be gained by taking each part of the definition of mo­
tion and showing that it flows from the first principles of
mobile being, taken either together or separately.
Motion is an act. We find in the heart of mobile being a
first principle of act, substantial form. This is the source
of the substantial actuality of material beings, and thus also
of all the actuality of the derived properties.
Motion is the act of a being (existentis). The proper
subject of motion is something existing, that is, a sub­
stance. It must be a material substance, because the mo­
tion we are considering is sensory motion. Prime matter11
11 Cf. Summa Theol., I, q. 77, a. 1, c. “Actio est compositi, sicut et
esse; existentis enim est agere. Compositum autem per formam
substantialem habet esse substantialiter; per virtutem autem quae
consequitur formam substantialem, operatur. Unde sic se habet
forma accidentalis activa ad formam substantialem agentis,... sicut
se habet potentia animae ad animam.” (Ibid., ad 3.) “Dicendum quod
hoc ipsum quod forma accidentalis est actionis principium, habet a
forma substantiali. Et ideo forma substantialis est primum actionis
principium, sed non proximum.” (Ibid., ad 4.)

Demonstration Through Formal Cause

109

and substantial form compose such a substance. It is to
be noted that motion differs from mutatio, or substantial
change, whose subject is a being only potentially existing,
prime matter.12
The proper subject of motion is a being in potency. The
mobile substance, composed of prime matter and substan­
tial form, is in potency to all its properties, for accidents
are distinct from substance and related to it as act to po­
tency. The potency included in the definition of motion is
a passive, not an active potency.13 Hereby the subject of
motion is distinguished from the subject of operations,
which is an active potency, namely, some form in addition
to prime matter and substantial form.14
Finally, motion is the act of a being in potency as such
(in quantum huiusmodi). This particle designates the
specific difference of motion. It does not seem necessary
12 “Quandoque ergo contingit quod utrique mutationis termino est
unum commune subiectum actu existens; et tunc proprie est motus;
sicut accidit in alteratione et augmento et diminutione et loci mutatione.
Nam in omnibus his motibus subiectum unum et idem actu existens,
de opposito in oppositum mutatur. Quandoque vero est idem commune
subiectum utrique termino, non quidem ens actu, sed ens in potentia
tantum, sicut accidit in generatione et corruptione simpliciter. Formae
enim substantialis et privationis subiectum est materia prima, quae
non est ens actu: unde nec generatio nec corruptio proprie dicuntur
motus, sed mutationes quaedam.” (De Pot., q. 3, a. 2. Cf. In V Phys.,
lect. 2, n. 8-11 ; lect. 3, n. 5.)
13 “Potentia igitur, secundum quod est principium motus in eo in
quo est, non comprehenditur sub potentia activa, sed magis sub
passiva.” (In V Metaph., lect. 14, n. 955.) “Potentia enim passiva
est in patiente, quia patiens patitur propter aliquod principium in
ipso existens, et huiusmodi est materia.” (In IX Metaph., lect 1,
n. 1782.)
14 “Licet motus sit actus imperfecti, scilicet existentis in potentia
... actio est actus perfecti, idest existentis in actu.” (Summa Theol.,
I, q. 18, a. 3, ad 1.) “Si largo modo accipiamus motum pro qualibet
operatione, sicut Philosophus accipit in III de Anima ubi dicitur,
quod sentire et intelligere sunt motus quidam, non quidem motus qui
est actus imperfecti, ut definitur III Phys., sed motus qui est actus
perfecti, sic proprium videtur esse viventis, et in hoc ratio videtur
consistere, quod aliquid sit movens se ipsum.” (De Pot., q. 10, a. 1.)

110

Demonstrating in Natural Philosophy

to correlate this particle with the definition of mobile be­
ing, for the purpose of this is to differentiate motion from
the other properties of mobile being, such as extension,
which would share in the characteristic of an act of a be­
ing in potency. However, even this particle points up the
depths of potentiality in material being by reason of prime
matter and thereby links up motion even more closely as
the fundamental property of the mobile. Nothing else, not
even sensation in animals, shows such deep roots in prime
matter, for sensation proceeds from an active principle,
and so follows more upon substantial form as the act of
a being in first act.
Thus we have a propter quid demonstration of the first
property of mobile being. Because motion is a property
following so closely on prime matter, it is well to quote in
clarification one of those valuable physical obiter dicta
of St. Thomas from the Summa Theologiae, in which he
shows in what sense motion is a property of material things.
In the case of natural things, that which is nat­
ural, as a result of form only, is always in them
actually, as heat is in fire. But that which is nat­
ural as a result of matter, is not always in them
actually, but sometimes only in potentiality: be­
cause form is act, whereas matter is potentiality.
Now movement is the act of that which is in
potentiality. Wherefore that which belongs to,
or results from movement, in regard to natural
things, is not always in them. Thus fire does not
always move upwards, but only when it is out­
side its own place.15
Let us consider another example, this time one from
psychology.
All motions and operations are defined by their termina­
tions. In the case of physical things, we speak of defini­
tion by the intrinsic final cause of motion.15 As regards the
15 Summa Theol., I-II, q. 10, a. 1, ad 2.
“ Cf. B. Ashley, O.P., “Research into the Intrinsic Final Causes
of Physical Things,” Proceedings of the American Catholic Phil­
osophical Association, XXVI (1952), pp. 185-194.

'l*j*3

Demonstration Through Formal Cause

111

potencies of the soul we say that they are specified by their
acts and ultimately by their formal objects. Thus, by refer­
ence to its object, we find that man has a kind of knowl­
edge that is independent of matter in varying degrees.
Therefore, by a posteriori reasoning we can demonstrate:
A being that performs immaterial cognitive acts is
a being that has a corresponding immaterial
cognitive faculty or potency.
But man performs immaterial cognitive acts.
Therefore, man has an immaterial cognitive fac­
ulty.
Moreover, whatever has an immaterial cognitive
faculty has a correspondingly immaterial sub­
stance in which the faculty is subjected.
But man has an immaterial cognitive faculty, his
intellect.
Therefore, man has an immaterial substance which
is the subject of his intellect. This obviously is
not his body, therefore it is the other co-principle of his being, his soul.
The soul, then, is a spiritual substance.

These two demonstrations are a posteriori. They go from
effect to proper and commensurate cause. Given the com­
mensurate cause, intellect, as made known in the first dem­
onstration, we can proceed deductively to demonstrate the
property known from experience, i.e. immaterial cognition.
This demonstration will be of the cause of the effect, but
not of our knowledge of the existence of the effect, which
is known by experience.17 Likewise, because the cause was
made known a posteriori, there will be no circle in demon­
stration.
Whatever being has an immaterial cognitive fac­
ulty can perform immaterial acts of knowledge.
But man has an immaterial cognitive faculty, or
intellect.
Therefore, man can perform immaterial acts of
knowledge.
37 Cf. Card. Zigliara, note t, Illa in the Leonine edition of the
Commentary on the Post. Analyt., p. 239. See our summary of this
point, Chap. I, p. 28.

112

Demonstrating in Natural Philosophy

The middle term is a formal cause. In passing, we should
note that this demonstration can be accepted as strictly
propter quid by the natural philosopher, even though actu­
ally the predicate is more extensive than the subject, for
God and the angels have intellectual knowledge. But the
natural philosopher as such knows nothing about the nature
of God, only His existence and immateriality. And it re­
mains for the theologian to consider the angels. The demon­
stration would be strictly applicable to man if it were in
terms of rational operations and a rational cognitive fac­
ulty.
We have established the spirituality of the soul a poste­
riori, as the subject of the intellect. As we attain a deeper
understanding of intellectual cognition, we find that its
formal reason is immateriality and that consequently any­
thing immaterial is by that very fact intellective. There­
fore, we can set out the following demonstration:
Every spiritual substance is intellective.
But man’s soul is a spiritual substance.
Therefore, man’s soul is intellective.
This demonstration proceeds through formal cause. The
major premiss is in the fourth mode of essential predica­
tion, because the spirituality of a substance is the cause
of the attribute, for all properties emanate from the nature
of their proper subject. The minor premiss contains a
definition. However, as we pointed out above, this defini­
tion is not fully commensurate, as there are other spiritual
substances besides man’s soul. Of itself, this demonstration
lacks the perfection of propter quid knowledge. It is rather
the next best thing, a demonstratio particularis.
The proof for the freedom of the will gives us a good
example of the demonstrative method. St. Thomas gives
the proof in various places ;18 for our purpose we can take
the treatment of the Summa Theologiae. In one sentence
he shows how the existence of the fact is established by
the universal experience of the human race. “Man has free
™Swnma Theol., I, q. 83, a. 1; De Malo, q. 6, a. 1; De Ver. q. 24,
a. 2.

Demonstration Through Formal Cause

113

choice, or otherwise counsels, exhortations, commands, pro­
hibitions, rewards and punishments would be vain.”1’ It
was not necessary for St. Thomas to defend this common
experience of freedom from philosophical prejudices, as we
are forced to do. He proceeds immediately to establish the
propter quid reason for man’s freedom. He finds it in the
indifference or indetermination of our judgment in the face
of particular and contingent goods.
In order to make this evident, we must observe
that some things act without judgment, as a stone
moves downwards; and in like manner all things
which lack knowledge. And some act from judg­
ment, but not a free judgment ; as brute animals.
For the sheep, seeing the wolf, judges it a thing
to be shunned from a natural, and not a free judg­
ment; because it judges, not from deliberation,
but from natural instinct. And the same thing
is to be said of any judgment in brute animals.
But man acts from judgment, because by his ap­
prehensive power he judges that something should
be avoided or sought. But because this judgment,
in the case of some particular act, is not from a
natural instinct, but from some act of comparison
in the reason, therefore he acts from free judg­
ment and retains the power of being inclined to
various things. For reason in contingent matters
may follow opposite courses, as we see in dialecti­
cal syllogisms and rhetorical arguments. Now par­
ticular operations are contingent, and therefore in
such matters the judgment of reason may follow
opposite courses, and is not determinate to one.
And in that man is rational, it is necessary that
he have free choice.20
As usual, the demonstration contained in the above para­
graph is not put into strict form. The medieval mind was
so well trained in logic that it could see the syllogisms im­
plicit in a discursive exposition. For us it is desirable that
the demonstrations be given in form.
An appetitive faculty that follows a judgment not
determined by nature is a faculty that has free
18 Summa Theol., I, q. 83, a. 1.

114

Demonstrating in Natural Philosophy

dominion over the judgment whereby it is spe­
cified.
But the will is a faculty that follows a judgment
not determined by nature.
Therefore, the will is free, that is, it has dominion
over the practical judgment whereby it is spe­
cified.
The middle term in the major premiss is a definition of the
will through a property and is a formal definition. This
puts the premiss in the fourth mode of essential predica­
tion. The minor premiss is in the first mode of essential
predication (i.e. definition), and the conclusion is in the
second mode (i.e. property). The premisses are per se
evident after an explanation of the terms. Therefore, we
have fulfilled all the requirements of a strict, propter quid
demonstration.
We may take a couple of examples from the science of
acoustics. Two of the properties of musical tones are in­
tensity and pitch. Both can be demonstrated propter quid
as properties.
We know through experiment that sound is the vibra­
tion of air and that a tone, as distinguished from mere
noise, is a regular vibration or wave. The intensity of sound
is due to the energy of the sound. This is determined ex­
perimentally, hence, a posteriori. The intensity of sound
diminishes when the distance from the source is increased
and also when the density of the air diminishes. The in­
tensity can also be measured by a sound-level meter. Hence
it can be easily seen that intensity or loudness is a property
, x of sound because the definition of sound is included in the
definition of loudness. It will be well to formalize the dem'
onstration. _
_______ ___ -—-The energy of sound produces intensity of sounds
r fl
as is evident from experimentation.
. · i But sound is the vibration of air, i.e. air in motion
5
or energized.
j
Therefore, sound has the property of intensity.
The definition of sound, air waves, air in motion or ener­

Demonstration Through Formal Cause

115

gized, is through both material and formal causes, but the
present demonstration flows from the formal cause.
The demonstration of pitch is similar to that of intensity.
It can be shown a posteriori through experiment that the
pitch of a note depends on the frequency of vibrations per
second. If we hold a card against the teeth of a revolving
gear, we find that the pitch of the sound produced rises as
the revolution of the wheel is accelerated. This is also veri­
fied by using a siren disk, a metal disk with evenly spaced
holes around the edge, and able to be rotated at varying
speeds. When a current of air is directed through a tube
against the row of holes, there is a regular succession of
puffs, and a musical tone is produced. As the velocity of
the wheel is increased, the tone becomes higher. The fre­
quency of the tone can thus be measured by multiplying
the number of holes by the number of revolutions of the
wheel per second. Given this definition of pitch, determined
a posteriori, we easily link it up with the nature of sound
and get a propter quid demonstration. In form, it would
read:
Frequency of vibrations produces the phenomen
of pitch, as determined a posteriori by experi­
ment.
But a musical tone is a regular vibration of air.
Implicit in the idea of vibration is a number or
frequency of vibrations.
Therefore, a musical tone has the property of
pitch.
One of Aristotle’s own examples of his demonstrative
theory is that of the non-twinkling of the planets. He gives
it to illustrate the difference between knowledge of the fact
(quia) and knowledge of the reasoned fact (propter quid).
When a cause and effect are convertible, or commensurate,
we usually find that the effect is more known to us because
it is closer to sense. From this effect we can demonstrate
the nature of the cause.21 For instance:
You might prove as follows that the planets are
21 Cf. St. Thomas’ comment, In I Post., lect. 23, n. 4.

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near because they do not twinkle: let C be the
planets, B not-twinkling, A proximity. Then B
is predicable of C ; for the planets do not twinkle.
But A is also predicable of B, since that which
does not twinkle is near—we must take this truth
as having· been reached by induction, or sense­
perception. Therefore A is a necessary predicate
of C ; so that we have demonstrated that the plan­
ets are near.22
In form, the demonstration reads:
B, Any heavenly body that does not twinkle is A,
near.
C, The planets are B, heavenly bodies that do not
twinkle.
Therefore, the planets are near.
Regarding the major, it is taken as being evident by in­
duction from sense perception that the near stars do not
twinkle. Aristotle’s reason for saying this was that our
vision trembles at looking such a great distance, as it sim­
ilarly trembles when looking at the sun, because of its great
brilliance.23 The minor premiss contains a descriptive defi­
nition of the minor term. It is to be noted that the middle
term in the major premiss is not a cause of the major ex­
treme, but rather an effect of it. Therefore, the demon­
stration is a posteriori and quia. “This syllogism, then,
proves not the reasoned fact but only the fact ; since they
are not near because they do not twinkle, but, because they
are near, do not twinkle.”24 The middle term is a cause
in cognoscendo, not in essendo.
Since the cause and effect are convertible, we can change
around the major and middle terms of the proof and get
a demonstration propter quid.
22 Post. Analyt., Bk. 1, Chap. 13, 78a 30-36.
23 “Our sight, when used at long range, becomes weak and unsteady.
This is possibly the reason also why the fixed stars appear to twinkle
but the planets do not. The planets are near, so that our vision
reaches them with its powers unimpaired; but in reaching to the fixed
stars it is extended too far, and the distance causes it to waver.”
(On the Heavens, Bk. 2, Chap. 8, 290a 18-23.)
24 Post. Analyt., ibid., 36-38.

Demonstration Through Formal Cause

117

Thus: let C be the planets, B proximity, A not
twinkling. Then B is an attribute of C, and A—
not twinkling—of B. Consequently A is predicable
of C, and the syllogism proves the reasoned fact,
since the middle term is the proximate cause.25
In syllogistic form we have:
B, whatever heavenly body is near, is A, does not
twinkle.
C, The planets are B, heavenly bodies that are
near.
Therefore, the planets do not twinkle.
The major premiss is just reversed from that of the pre­
ceding demonstration; it is in the fourth mode of essen­
tial predication : B is the cause of A. What kind of cause
is B in relation to A? It is a formal definition given in
terms of the property of nearness. It does not make any
difference that A is negative, since non-twinkling is equiva­
lent to “steady light.” In the minor premiss we have a
descriptive definition of planets, through their property
of nearness. The example, then, fulfills all the theoretical
requirements of a demonstration.
Another interesting example is the demonstration that
ice is water in a solid state.
Take a second example: assuming that the defini­
tion of ice is solidified water, let C be water, solidi­
fied, B the middle, which is the cause, namely total
failure of heat. Then B is attributed to C, and A,
solidification, to B: ice forms when B is occur­
ring, has formed when B has occurred, and will
form when B shall occur.2®
Let us put this demonstration into form, before we dis­
cuss it.
A liquid that loses the heat required for its liquid
state becomes solidified.
But water is a liquid that loses the heat required
for its liquid state.
Therefore, water solidifies, or becomes ice.
The major premiss is immediately evident by induction, for
25 Ibid., 78b 1-3.
2*Ibid., Bk. 2, Chap. 12, 95a 17-21.

ssii

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Demonstrating in Natural Philosophy

we know that at temperatures proportioned to their spe­
cific densities, fluids become solid. Aristotle’s understand­
ing of the cause of solidification was incorrect, because it
was linked up with his concept of the elements.27 But his
demonstration as given above is valid when we understand
the major according to our own scientific information. The
middle term is a formal definition through a property.
Hence, the major premiss is in the fourth mode of essen­
tial predication, the minor in the first mode, and the con­
clusion in the second. The demonstration is propter quid,
but since water and liquid are not commensurately univer­
sal, the proof is a demonstratio particularis.
2T Cf. Meteorologies, Bk. 4, Chap. 7-8, 383b 17—385b 6.

CHAPTER VI

DEMONSTRATION THROUGH EFFICIENT CAUSE

Demonstration through efficient cause is characteristic
of natural science. The physicist is interested in efficient
causes, because they enter into the process of natural gen­
eration.1 But his use of them is somewhat circumscribed.
The cause that, serves as middle term in demonstration
must necessitate the effect. However, “not from every agent
cause does the effect follow of necessity.”1
2 Therefore, we
must investigate under what conditions we can demonstrate
through this cause.
It will be well to consider first Aristotle’s treatment of
the question in the Second Book of the Posterior Analytics,
where he is treating it ex professo. He mentions all four
causes and concludes that “each of these can be the mid­
dle term of a proof.”3 Then he gives the following example:
“Why did the Athenians become involved in the
Persian war?” means “What cause originated the
waging of war against the Athenians?” and the
answer is, “Because they raided Sardis with the
Eretrians,” since this originated the war. Let A
be the war, B unprovoked raiding, C the Athe­
nians. Then B, unprovoked raiding, is true of C,
the Athenians, and A is true of B, since men make
war on the unjust aggressor. So A, having war
waged upon them, is true of B, the initial aggres­
sors. Hence here too the cause—in this case the
efficient cause—is the middle term.4
This is not a perfect example from the aspect of scientific
knowledge, because it deals with a particular instance,
1 Cf. In II Phys., lect. 11, n. 5; In De Trin., q. 6, a. 1.
2 “Non enim ex omni causa agente sequitur ex necessitate effectus.”
(In II Post. Analyt., lect. 7, n. 2.)
5 Post. Analyt., Bk. 2, Chap. 11, 94a 20-24.
*Ibid., 94a 36—b 8.
119

120

Si
=91

$
■ lij
■it:
■

Demonstrating in Natural Philosophy

rather than with the universal, and because the necessary
bond between cause (raid) and effect (war) is a moral
necessity. The conclusion, however, is true and valid with
a moral necessity.
A few lines later5 Aristotle adds in his characteristic
pithy style that in nature some things come about for an
end and some by necessity. St. Thomas’ remarks on this
will bring out its significance.
Many things of this kind, those namely that are
of necessity and come about for an end, are found
especially in things that subsist by nature and are
constructed by nature. For nature does some
things for an end, but others from the necessity
of prior causes. This latter can be of two kinds:
one according to nature, that is, according to the
condition of matter; the other according to the
moving cause: for instance, a rock is sometimes
moved upward by necessity and sometimes down­
ward, but not because of the same kind of neces­
sity; it is moved downward because of the neces­
sity of nature, but upward because of the necessity
of the mover or projector.6
Since in natural science we wish to demonstrate natural
motions and their causes, it is obvious that we will exclude
proof through coercive efficient causality, or violence. It is
to be noted, however, that in generation the action of the
efficient cause, though natural as regards the form to be
acquired, is coercive in respect to the form that is lost.
In the second Book of Physics the problem of demons Ibid., 94b 35—95a 3.
6 “Plurima huiusmodi, quae scilicet sunt ex necessitate et fiunt
propter finem, maxime inveniuntur in his quae subsistunt a natura,
et in his quae sunt per naturam constructa. Natura enim quaedam
facit propter finem, quaedam vero facit ex necessitate priorum caus­
arum. Quae quidem est duplex: una secundum naturam, quae est
secundum conditionem materiae; alia secundum causam moventem:
sicut lapis movetur quidem ex necessitate quandoque sursum, quand­
oque deorsum, sed non propter idem genus necessitatis; sed deorsum
movetur propter necessitatem naturae, sursum autem propter neces­
sitatem moventis, idest proiicientis.” (In II Post. Analyt., lect. 9, n.
12.)

Demonstration Through Efficient Cause

121

strating by efficient causality is taken up again, this time
explicitly in reference to natural science. We are told
there7 that the efficient cause of generation is often spe­
cifically identical with the form and the end. St. Thomas
asserts that
This is true chiefly in univocal agents in which
the agent makes something like himself in species,
as man generates man. In these the form of the
generator which is the principle of generation is
the same in species as the form of what is gener­
ated which is the end of generation. But in non­
univocal agents it is different because in these
the things which come to be cannot extend so far
that they follow the form of the generator accord­
ing to the same reason of species, rather they par­
ticipate in a similitude of it according as they can,
as is plain in those which are generated by the
sun. Therefore not every agent is the same in spe­
cies as the form which is the end of generation,
nor again is every end the form.®
When he comes to show how we actually demonstrate
from the prior causes, matter and agent, Aristotle puts it
concisely: “We must explain the ‘why* in all the senses
of the term, namely, (1) that from this that will necessarily
result (‘from this’ either without qualification or in most
cases) ; (2) that ‘this must be so if that is to be so.’..
When placing the prior causes necessitates the effect, there
can be a demonstration by means of them; for instance,
the movement of the earth with respect to the sun neces­
sarily determines the length of our daylight. However,
effects do not always follow with necessity from efficient
causes; in fact, most efficient causes produce their effects
only for the most part or frequently.10 This places a limita­
tion upon the use of efficient causes as middle terms.
It should be noted that when something follows
necessarily from causes prior in generation, name’ Physics, Bk. 2, Chap. 7, 198a 27.
8 In II Phys., lect. 11, n. 2.
8 Physics, ibid., 198b 5-8.
10 Cf. In II Phys., lect. 11, n. 7.

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ly from matter and the mover, the demonstration
can be taken from these, as was said above; but
not when something frequently follows. In the
latter case the demonstration should be taken from
that which is posterior in generation because some­
thing necessarily follows from this just as the
conclusion follows from the propositions of the
demonstration. Thus we should proceed in demon­
stration as follows : If this is to come to be, this
and this are required; for example, if man is to
be generated, it is necessary that there be human
seed acting in generation. But, if we were to pro­
ceed conversely, from the proposition, there is hu­
man seed acting in generation, the proposition,
therefore man will be generated, does not follow
as the conclusion follows from the premisses.11
Demonstration, then, through final cause is more conatural
to physical science; but there are cases where efficient
causes can be used as middle terms. At the level of ulti­
mate species, where formal definitions are hard to come
by, demonstration takes place frequently through efficient
cause.12 For if we cannot know what a thing is, at least
knowledge of its proper and proximate efficient cause gives
us some insight into its nature. Things are what their
causes make them to be. And efficient causes produce ef­
fects like to themselves : omnes agens agit sibi simile. Many
of the examples that Aristotle gives to clarify the theory
of the Posterior Analytics are demonstrations having effi­
cient causes for middle terms.
A good example of the demonstrative method is that of
the waxing of the moon.
Another example is the inference that the moon
is spherical from its manner of waxing. Thus:
since that which so waxes is spherical, and since
the moon so waxes, clearly the moon is spherical.
Put in this form, the syllogism turns out to be
proof of the fact.13
The middle term of this syllogism is an effect: “so waxWbid., n. 8.
12 Cf. In De Trin., q. 6, a. 1.
is Post. Analyt., Bk. 1, Chap. 13, 78b 3-7.

Demonstration Through Efficient Cause

123

es,” and it concludes to the cause, “spherical.” The basis
of this argument is the observation that the moon waxes
and wanes in a crescent shape. Only a spherical body could
present this phenomenon, by reason of the sun’s light strik­
ing only a part of it.14 This is, therefore, a demonstration
quia, proceeding a posteriori. Once the cause is discovered,
we can demonstrate the attribute propter quid. As Aris­
totle says :
Put in this form, the syllogism turns out to be
proof of the fact, but if the middle and major be
reversed it is proof of the reasoned fact; since the
moon is not spherical because it waxes in a certain
manner, but waxes in such a manner because it is
spherical. (Let C be the moon, B spherical, and A
waxing.)15
We must construct a syllogism in which B will be the
middle term.
B, A body of spherical shape is A, a body that wax­
es in such a manner.
C, the moon is B, a body of spherical shape.
Therefore, the moon so waxes.
In the major premiss A is a proper effect of B. The prop­
osition is in the fourth mode of essential predication (i.e.
contains a cause). B, the spherical shape, is the efficient
cause of the manner of waxing and waning in crescent
shape, a kind of instrument for so reflecting the sun light
as to produce the phenomenon we observe. As efficient cause
it acts in accord with its form, and so the effect is spe­
cifically identical with the cause in that aspect whereby
it is cause; thus we could also consider this middle term
a formal cause. From another point of view we may con­
sider the spherical shape as a material cause receptive, ac­
cording to its own dispositions, of the sun’s light. In the
minor premiss the moon is defined by a formal cause, its
spherical shape, and hence the^premissjsjnJhejfirstjmode
of essential predication. The conclusion of the demonstra14 Aristotle’s ex professo treatment of this is in On the Heavens,
Bk. 2, Chap. 10, 291b 19-24. St. Thomas’ Commentary, lect. 16, n. 6-7.
15 Post. Analyt., ibid.

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Demonstrating in Natural Philosophy

tion enables us to understand the moon’s characteristic way
of waxing and waning in view of its spherical shape, the
cause of the phenomenon.
The eclipse of the moon is one of Aristotle’s favorite
examples. He returns to it repeatedly in the Posterior
Analytics, as exemplifying the various stages of the demon­
strative process. If we put these texts together, we will
have a quite complete demonstration, from start to finish.
We may wonder if strict demonstrative proof is possible
of such an occasional thing as an eclipse. Aristotle re­
assures us that, although “no attribute can be demonstrated
nor known by strictly scientific knowledge to inhere in
perishable things,” nevertheless, “demonstration and sci­
ence of merely frequent occurrences—e.g. of eclipse as hap­
pening to the moon—are, as such, clearly eternal.”1® The
meaning is made clear by St. Thomas in his commentary.11
The moon is not always in eclipse, but sometimes. Now
something that happens frequently or regularly can be
demonstrated from the aspect of the frequency or regu­
larity, because there has to be an enduring cause of the
regularity, to which the attribute in question has a constant
relation.
A demonstration, therefore, could not be given of an iso­
lated particular occurrence. Demonstration must deal with
universal aspects and commensurately universal causes.
Even if a cause should be clearly evident to sense percep­
tion, we do not thereby have scientific knowledge of the
effect.
So if we were on the moon, and saw the earth
shutting out the sun’s light, we should not know
the cause of the eclipse; we should perceive the
present fact of the eclipse, but not the reasoned
fact at all, since the act of perception is not of the
commensurate universal.18
We would not know the cause of the eclipse as proper and
1« Ibid., Bk. 1, Chap. 8, 75b 24, 33-36.
1T Leet. 16, n. 8. Cf. Chap. Ill supra·, note 39.
Post. Anaiyt., Bk. 1, Chap. 31, 87b 39—88a 2.

Demonstration Through Efficient Cause

125

commensurate cause; as far as sense perception goes, the
interposition of the earth between the sun and moon might
well be an accident or freak of nature, rather than a uni­
versal and necessary cause. Aristotle continues:
I do not, of course, deny that by watching the
frequent recurrence of this event we might, after
tracking the commensurate universal, possess a
demonstration, for the commensurate universal is
elicited from the several groups of singulars.18
The essential cause of eclipse must be universally the cause
of eclipse. Therefore, it cannot be known by a single act
of sense perception, but must be abstracted by the mind
from many sense perceptions.
The first stage in the demonstrative process in natural
science is to establish the existence of facts. These facts are
usually learned from sensory experience, but there is no
reason why facts should not be supplied by another science,
such as by the mathematical sciences. Aristotle describes
the beginning of the process, shifting us, however, from
the eclipse of the moon to that of the sun.
When our question concerns a complex of thing
and attribute and we ask whether the thing is thus
or otherwise qualified—whether, e.g., the sun suf­
fers eclipse or not—then we are asking as to the
fact of a connexion. That our inquiry ceases with
the discovery that the sun does suffer eclipse is
an indication of this; and if we know from the
start that the sun suffers eclipse, we do not inquire
whether it does so or not. On the other hand, when
we know the fact we ask the reason; as, for ex­
ample, when we know that the sun is being eclipsed19
19 Ibid., a. 3-4. St. Thomas says about this: “Ponamus ergo quod
aliquis esset in. ipsa luna, et sensu perciperet interpositionem terrae
per umbram ipsius: sensu quidem perciperet quod luna tunc deficeret
ex umbra terrae, sed non propter hoc sciret totaliter causam eclipsis.
Ulud enim est per se causa eclipsis, quod causât universaliter eclipsim. Universale autem non cognoscitur sensu; sed ex pluribus singu­
laribus visis, in quibus multoties consideratis invenitur idem accidere,
accipimus universalem cognitionem. Et sic per causam universalem
demonstramus aliquid in universali, de quo est scientia.” (In I Post.
Analyt., lect. 42, n. 7.)

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Demonstrating in Natural Philosophy

and that an earthquake is in progress, it is the
reason of eclipse or earthquake into which we
inquire.20
Sometimes the existence of the fact has to be proved.
Thus, we can give an a posteriori demonstration that the
moon suffers eclipse.
Let C be the moon, A eclipse, B the fact that the
moon fails to produce shadows though she is full
and though no visible body intervenes between us
and her. Then if B, failure to produce shadows in
spite of the absence of an intervening body, is
attributable to C, and A, eclipse, is attributable
to B, it is clear that the moon is eclipsed, but the
reason why is not yet clear, and we know that
eclipse exists, but we do not know what its essen­
tial nature is.21
Put in syllogistic form, the argument reads:
B,That which fails to produce shadows is A,
eclipsed.
But C, the moon, is B, that which fails to produce
shadows.
Therefore, C, the moon, is A, eclipsed.
The middle term, B, is an effect, rather than a cause of
eclipse, so the syllogism is a posteriori. But it gives us a
fact whose cause we search for in order to demonstrate the
fact.
To ask the reason or cause of a thing is equivalent to
asking about the middle term, for the middle term is the
cause according to its position and function in the demon­
strative syllogism.
In all our inquiries we are asking either whether
there is a ‘middle’ or what the ‘middle’ is: for
the ‘middle’ here is precisely the cause, and it is
the cause that we seek in all our inquiries. Thus,
‘Does the moon suffer eclipse?’ means ‘Is there or
is there not a cause producing eclipse of the
moon?’, and when we have learnt that there is,
our next question is, ‘What, then, is this cause?’22
«° Post. Analyt., Bk. 2, Chap. 1, 89b 26-31.
nlbid., Chap. 8, 93a 37—b 3.
Ibid., Chap. 2, 90a 5-9.

Demonstration Through Efficient Cause

127

In order to find the cause which is to be our middle term,
we have to define the attribute in question, for the defini­
tion of the attribute will point out its cause, which will be
one with the subject of the attribute.
The middle term is the cause of the unqualified
substance (as distinguished from this or that at­
tribute of it) and of an essential attribute or acci­
dent (as distinguished from the substance). I call
the unqualified substance the subject, such as
moon, earth, sun or triangle. By the latter (i.e.
the attributes) I mean eclipse, equality, inequality,
interposition or non-interposition. In all these it
is clear that the quid est is the same as the propter
quid.13
In other words, once we learn that a subject has a certain
attribute (e.g. the moon suffers eclipse) we know that there
is a cause of this fact. To ask what is the cause is equiva­
lent to asking why the attribute belongs to the subject. To
find the answer to both these questions, we seek a defini­
tion of the attribute. This definition will manifest the
cause; but since the subject is in some way the cause of
its essential attributes, the causal definition of the attri­
bute will be at least a descriptive definition of the subject.
Thus:
The quesion ‘What is eclipse?’ and its answer,
‘The privation of the moon’s light by the inter­
position of the earth’ are identical with the ques­
tion, ‘What is the reason of the eclipse?’ or ‘Why
does the moon suffer eclipse?’ and the reply, ‘Be­
cause of the failure of light through the earth’s
shutting it out.’24
23 Ibid., 90a 9-15. Because of the difficulties of the Oxford trans­
lation of this cumbersome passage, the above is our own translation.
We include here the Greek text.
To <γάρ αίτιον τοΰ είναι μη τοδί τοδί άλλ* απλώς την ουσίαν, ή τό
μη απλώς αΚλά τι των καθ' αυτό ή κατά συμβεβηκός, το μέσον εστίν.
Χεηω Sè το μέυ απλώς το υποκείμενον, οίον σελήνην ή γην ή ήλιον
ή τρίγωνον, το δ« τΐ εκλειφ·ιν, Ισότητα, ανισότητα, εΐ εν μέσω ή μη.
Έκ απασι γάρ ταύτοις φανερόν εστιν οτι το αυτό εστι το τί εστι κα\
Ζιά τίεστιν.
24 Ibid., 15-19.

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Demonstrating in Natural Philosophy

In a later chapter Aristotle sets forth the demonstration:
When it is clear that A (eclipse) is attributable
to C (moon) and we proceed to ask the reason of
this fact, we are inquiring what is the nature of
B (the cause) : is it the earth’s acting as a screen,
or the moon’s rotation or her extinction? But B is
the definition of the other term, viz., in these ex­
amples, of the major term A; for eclipse is con­
stituted by the earth acting as a screen.2526
The essence of the cause, B, is made known, then, when
we find the definition of the major extreme, A. Put in syl­
logistic form, the demonstration reads:
B, A heavenly body whose light is screened off by
the earth is a body in eclipse.
But C, the moon, is B, a heavenly body that has
its light screened off by the earth.
Therefore, the moon suffers eclipse.
In the major premiss B is the efficient cause of A.2e In the
minor premiss the moon is defined in terms of the proper­
ty of suffering loss of its light when the earth comes be­
tween it and the sun.
Aristotle gives an easy example of the demonstrative
process in the case of thunder. The first prerequisite for
a demonstration is to establish the existence of some fact.
“We are aware whether a thing exists or not sometimes
through apprehending an element in its character, and
sometimes accidentally, as for example, when we are aware
of thunder as a noise in the clouds.”22 We have, therefore,

)

I

ί

i

25 Ibid., Chap. 8, 93b 3-8.
26 “What is the cause of eclipse? What is its matter? There is
none; the moon is that which suffers eclipse. What is the moving
cause which extinguished the light? The earth. The final cause per­
haps does not exist. The formal principle is the definitory formula,
but this is obscure if it does not include the cause. E.g., what is
eclipse? Deprivation of light. But if we add ‘by the earth’s coming
in between,’ this is the formula which includes the cause.” (Meta­
physics, Bk. 8, Chap. 4, 1044b 10-15.)
21 Post. Analyt., Bk. 2, Chap. 8, 93a 21-23. St. Thomas comments:
"Oportet autem quod qui cognoscit aliquam rem esse, per aliquid rei
illud cognoscat: et hoc vel est aliquid praeter essentiam rei, vel
aliquid de essentia ipsius. Et de hoc ponit exemplum, puta si cognos-

Demonstration Through Efficient Cause

129

a certain knowledge of the existence of thunder when we
apprehend something of its essence, namely, a noise in the
clouds.
We know the fact, now, that there is such a phenomenon
as thunder. But our knowledge is not perfect until we have
demonstrated the fact, that is, until we have found the
reason of the fact. The reason for the fact will be the es­
sential nature of thunder, its definition.
Thus, (1) ‘What is thunder?’ ‘The quenching of
fire in cloud,’ and (2) ‘Why does it thunder?’ ‘Be­
cause fire is quenched in the clouds,’ are equiva­
lent. Let C be cloud, A thunder, B the quenching
of fire. Then B is attributable to C, cloud, since
fire is quenched in it; and A, noise, is attributable
to B ; and B is assuredly the definition of the major
term A. If there be a further mediating cause of
B, it will be one of the remaining partial defini­
tions of A.28
Let us put this argument into syllogistic form:
Every extinction of fire produces a sound.
But in the clouds there is extinction of fire.
Therefore, in the clouds there is the sound that we
call thunder.29
The major premiss is immediately evident from experi­
ence. The middle term, extinction of fire, is efficient cause
of the production of sound, hence the premiss is in the
fourth mode of essential predication. The act of extin­
guishing is an efficient cause, specified by its term or ob­
ject, fire. In the minor premiss the extinction of fire is given
as a property of clouds, and hence it is a descriptive definicamus tonitruum esse, propter hoc quia percipimus quemdam sonum
in nubibus: quod quidem pertinet ad essentiam tonitrui; non tamen
est tota tonitrui essentia, quia non omnis sonus nubium est tonitruum.”
(In II Post. Analyt., lect. 7, n. 6.)
28 Post. Analyt., ibid., 93b 7-14.
29 The syllogism is set out for us by St. Thomas : “In C est B,
idest in nube est extinctio ignis; sed omnis extinctio ignis est sonus;
ergo in nube est sonus tonitrui. Et sic patet quod accipiendo propter
quid, per demonstrationem accipimus quid est, quia ipsum medium
ostendens propter quid, est ratio definitiva primi termini, idest
maioris extremitatis.” (Ibid., n. 8.)

f

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Demonstrating in Natural Philosophy

tion. It is well to note here that this theory of thunder is
not Aristotle’s own, but that of Empedocles and Anaxa­
goras. Aristotle himself held that thunder is the sound of
the impact resulting when a dry exhalation from the earth
(wind) is projected into a moist exhalation (cloud).30 St
Thomas remarks: “He often uses the opinions of others
in his examples.”31 This gives us a good precedent for using
Aristotle’s examples in studying his demonstrative theory,
even though at our present stage of physical knowledge
we know that many of them are incorrect.
We have, therefore, demonstrated that there is thunder
in the clouds. As a result of this demonstration we have
a richer definition of thunder, namely, the noise of fire be­
ing quenched in the clouds. Such a definition is called a
“qwasi-demonstration of essential nature, differing from
demonstration in the arrangement of its terms.”32 This
is the richer and more perfect sort of definition that is ac­
quired at the end of a science, as compared with the imper­
fect definition that is a principle of demonstration.
It is not at all difficult to adapt this demonstration of
thunder to what we know now of this phenomenon.
Every violent disturbance of the air produces
noise.
But lightning causes a violent disturbance of the
air by the discharge of static electricity.
Therefore, lightning produces the noise that we
call thunder.
A more difficult case of demonstration is given in the
example of the falling of leaves. It is proposed as follows:
“Every broad-leaved plant is deciduous;
Every vine possesses broad leaves;
Every vine is deciduous.”33
The conclusion is in the second mode of essential predica­
tion (property), and the minor premiss in the first mode,
so Cf. Meteor., Bk. 2, Chap. 9, 369a 10—370a 32.
31 “Utitur autem multoties in exemplis opinionibus aliorum.” (Ibid.)
n Post. Analyt., Bk. 2, Chap. 10, 94a 2-3; cf. ibid., 1-13. St
Thomas, lect 8, nn. 8-9.
ο® Ibid., Bk. 2, Chap. 16, 98b 5-10.

Demonstration Through Efficient Cause

131

since its predicate is a descriptive definition. In order that
we may have a true demonstration, the major premiss must
be in the fourth mode of essential predication, in which the
middle term is shown to be the cause of the attribute.
Whether it is so or not in this case depends on the proof
which we give of the major; for since it is not immedi­
ately evident, it must itself be demonstrated.
As Aristotle says, “Deciduous is a universal attribute
of vine, and is at the same time of wider extent than vine;
and of fig, and is of wider extent than fig: but it is not
wider than but coextensive with the totality of the spe­
cies.”34 The question is : how are we to define the species,
or proper subject, to which deciduous belongs per se primo?
We approach our solution by noting a common character­
istic of all plants that are deciduous; we find that they
all have broad leaves. Therefore, we give a descriptive defi­
nition of the commensurate subject of deciduous, in terms
of the other characteristic of having broad leaves. This
common subject, thus vaguely defined, is the proximate
genus, of which all the types of deciduous plants are species.
We do not as yet have a cause as middle term and as the
subject of the major extreme. But in proving the major
premiss we can hope to find a cause. It will be a defini­
tion mediating between broad-leaved plant and deciduous.
As broad-leaved plant is a descriptive definition, we must
look to the definition of deciduous to discover a cause. It
is to be noted that the full definition of a property must
include its proper subject, for a property can neither be
nor be understood without its subject. Aristotle defines
deciduous in terms of efficient causality: “It is the coagu3*lbid., Chap. 17, 99a 23-25. Aristotle continues: “Then if you
take the middle which is proximate, it is a definition of deciduous. I
say that, because you will first reach a middle, next the subject, and a
premiss asserting it of the whole subject, and after that a middle—the
coagulation of sap or something of the sort—proving the connexion of
the first middle with the major: but it is the coagulation of sap at
the junction of leaf-stalk and stem which defines deciduous.” (find.,
25-30.)

LWIWMI

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lation of sap at the junction of leaf-stalk and stem -which
defines deciduous.”35 Thus we have found our cause, and
our demonstration is thereby achieved.
We can now put the syllogism into form:
Every broad-leaved plant is deciduous.
But, every vine possesses broad leaves.
Therefore, every vine is deciduous.
The minor is a descriptive definition arrived at through
sensory experience. The major must be proved.
Every plant that exhibits coagulation of sap at the
junction of leaf-stalk and stem is deciduous.
But, every broad-leaved plant exhibits coagulation
of sap, etc.
Therefore, every broad-leaved plant is deciduous.
The middle term in the major premiss is the efficient cause
of the attribute and is therefore in the fourth mode of es­
sential predication. The minor premiss shows the middle
term as a further descriptive definition of broad-leaved
plant.
Since the first middle term—coagulation—is the proper
cause of the attribute, we have a strict demonstration. It
proceeds through efficient causality: a proper activity of
the broad-leaved plant, i.e. coagulation of sap, causes its
leaves to dry up and fall. When the demonstration is
brought down to the level of the particular subject, vine,
it is of the type called particular demonstration, where the
predicate is not commensurate with the subject.
35 Cf. note 34. St. Thomas’ comment is: “Hoc enim quod est folio
fluere, consequitur ad vitem et excedit ipsam, quia est in pluribus;
consequitur etiam ad ficum et excedit eam : non tamen est excessivum
omnium quibus convenit, sed est eorum sicut aequalium. Si ergo
aliquis velit accipere id quod est primum medium respectu omnium,
erit haec definitio eius quod est folio fluere; quae quidem definitio
erit primum medium ad alia, eo quod omnia talia-sunt. Et iterum huius
accipietur aliquod aliud medium, puta quod succus densatur per
desiccationem, vel aliquod aliud huiusmodi. Unde si quaeratur quid
est folio fluere, dicemus quod nihil aliud est quam condensari succum
seminis in contactu, scilicet folii ad ramum.” {In II Post. Analyt.,
lect. 19, n. 4.)

ί

Demonstration Through Efficient Cause

133

A chapter of the Posterior Analytics26 shows how one
generic middle term may prove attributes of different spe­
cific subjects and how, on the other hand, several middle
terms may be subordinate one to the other.
As instances of the former, Aristotle says:
This class may be exemplified by the questions as
to the causes respectively of echo, of reflection,
and of the rainbow: the connexions to be proved
which these questions embody are identical gen­
erically, because all three are forms of repercus­
sion; but specifically they are different.37
Before we consider this demonstration, it will be helpful
to examine its premisses and to learn what Aristotle thought
of the phenomena in question. He conceived of echo and
reflection of light not as waves moving through the medi­
um, but as the medium moving and rebounding “like a ball
from a wall.”38
Regarding the rainbow, he has a lengthy account of it
running through the third book of the Meteorologica. A
few remarks on Aristotle’s procedure there will be of value.
He prefaces the second chapter with : “Let us now explain
the nature and cause of halo, rainbow, mock suns, and rods,
since the same account applies to them all. We must first
describe the phenomena and the circumstances in which
each of them occurs.”39 When he has given the data of ob­
servation, which, we again insist, is the prerequisite and
beginning of the demonstrative process, he continues:
These are the facts about each of these phenom­
ena: the cause of them all is the same, for they
are all reflections. But they are different varieties,
and are distinguished by the surface from which
and the way in which the reflection to the sun or
some other bright object takes place.·*9
Causal explanation, or demonstration proper, follows upon
observation of facts.
“ Post. Analyt., Bk. 2, Chap. 15, 98a 23-34.
3’ Ibid., 27-29.
»» On the Soul, Bk. 2, Chap. 8, 419b 28; cf. 25-33.
39 Meteorologica,, Bk. 3, Chap. 2, 371b 19-21.
<° Ibid., 372a 18-21.

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1

Demonstrating in Natural Philosophy

“We have already stated,’’ he says in Chapter Four,
“that the rainbow is a reflection: we have now to explain
what sort of reflection it is, to describe its various con­
comitants, and to assign their cause.’’·41 The investigation,
accordingly, has reached the stage of determining the spe­
cific cause of rainbow and of demonstrating its proper­
ties. By a posteriori reasoning he establishes that “the rain­
bow is a reflection of sight to the sun” by some substance
in the sky.42
Now that he has a definition of rainbow,43 he can go on
to demonstrate its properties. It always appears opposite
the sun.44 Its colors are red, green and purple: “The colors
of the rainbow are those we described, and how the other
colors come to appear in it will be clear from the follow­
ing considerations... .”45 In other words, he is now assign­
ing the cause, or demonstrating the facts that previously
he had observed: not only that there are such colors, but
why it should be so. “The same cause,” he goes on, “ex­
plains the double rainbow and the faintness of the colors
in the outer one and their inverted order.”44 Next, by a
41 Z5«Z., Chap. 4, 373a 33-34.
K Ibid., Chap. 4, 373b 33. “Alexander observes that the language
in which Aristotle speaks of vision in this book is not that of his
theory in the De Anima.” (Note 4, 372a 29 of the Oxford translator
of the Meteorologica.)
43 For Aristotle the definition would be in terms of efficient
cause. The vapor, or other substance, acting in accord with its parti­
cular nature, would be the agent cause of the phenomenon. We would
define a rainbow as a multicolored arc in the heavens (formal cause)
formed by the sun (efficient cause) whose rays are received into
moisture (material cause) in a diffracted condition (formal cause).
“■Ibid., Chap. 4, 373b 34ff.
43 Ibid., 374b 7-10. Aristotle’s reasons for the different colors are
of no concern to us. A sample of the following: “The rainbow is
distinguished by the variety of its colours. The reflection in the one
case is from water which is dark and from a distance; in the other
from air which is nearer and lighter in colour. While light through a
dark medium or on a dark surface (it makes no difference) looks
red....” (373b 34—374a 4.)
44 Ibid., 375a 30-35.

Demonstration Through Efficient Cause

135

mathematical demonstration he shows why the rainbow
can never be a circle nor a segment of a circle greater
than a semicircle.47 He completes his investigation by other
mathematical deductions relative to the time of day when
there can be a rainbow at the different seasons of the year.
Although much of Aristotle’s treatment of the rainbow
is outmoded, yet his method and procedure are noteworthy
as being able to provide us a means of systematizing and
understanding the immense body of factual knowledge we
have accumulated during the last few centuries.
Let us note that Aristotle has started, in accord with his
method, from the generic consideration, common to the
echo, reflection and luminous phenomena connected with
sunlight. Then he differentiated the latter by division to
halo, rainbow, mock suns, and rods. We followed him in
brief outline as he broke down rainbow to its nature and
attributes, even borrowing mathematical reasoning to com­
plete the picture.
Returning now to the demonstration at the begining of
this section, we can summarize it by a schema of subjects
and predicates, together with the generic middle term that
proves them all.45
Repercussion—echoes . Repercussion—reflection
Sound—repercussion
Light—repercussion
Sound—echoes
Light—reflection

Repercussion—rainbow
Sun-light—repercussion
Sun-light—rainbow.

In each instance the middle term is an efficient cause in the
major premiss. The middle term may seem to be not com­
mensurate with the attributes. But this is a case of a re­
mote cause being convertible with its effect because the
specification of the cause to its different subjects comes
"Ibid., Chap. 5, 375b 16 ff.
48 For the generic middle term, translated “repercussion” in the
Posterior Analytics (cf. supra, p. 133), Aristotle uses the word
άντιττερίστασκ. The attribute “reflection” attributed to light in
the second example is διά τΐ ΐμφαίυεται, translated in the Latin
text as “propter quid apparet,” to which St Thomas adds “in speculo."
(In II Post. Ancdyt., lect 17, n. 5.) When he speaks of the cause of
the rainbow in the Meteorologica, Aristotle uses the term ανάκΚασκ
which is translated “reflection.”

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Demonstrating in Natural Philosophy

about through a material condition, and not strictly through
a specific difference: the effect is formally attributable to
the generic aspect (repercussion)?9 In the minor premiss
the middle term defines sound, light and sun rays as that
which undergoes repercussion; it is a descriptive definition.
Besides having a generic middle term for several demon­
strations, as in the examples we have just discussed, we
can have instances where the middle term of one demon­
stration is subordinate to the middle term of a preceding.
Aristotle gives this example:
Why does the Nile rise towards the end of the
month? Because towards its close the month is
more stormy. Why is the month more stormy
towards its close? Because the moon is waning.50
If we put this demonstration in form, it will read:
The waning of the moon causes the end of the
lunar month.
But stormy weather follows upon the waning of
the moon.
Therefore, stormy weather comes toward the end
of the month.
But the rising of rivers follows upon stormy
weather.
Therefore, the rising of rivers occurs toward the
end of the month.
Rivers have the property of rising toward the end
of the month.
But the Nile is a river.
Therefore, the Nile rises toward the end of the
month.
In the first major premiss we show the waning of the
moon as the efficient cause of the end of the month, because
the lunar month is determined by the motion of the moon.
In the first minor the stormy weather is defined in terms
of its efficient cause. The reason why stormy weather fol­
lows upon the waning of the moon, according to St. Thom49 Cf. Zigliara, note T, p. 239 of the Leonine ed. of the Commentary
on Post Analyt. Cf. supra, Chap. 1, note 67.
™Post. Analyt., Bk. 2, Chap. 15, 98a 31-34.

Demonstration through Efficient Cause

137

as,51 is that the moon has dominion over the vapors of the
air, and when it is on the wane, they are more agitated, so
as to cause storms. The conclusion of the first syllogism
becomes the major of the second; and the subject of the
first, the middle term of the second. Consequently, the
proposition: “Stormy weather comes toward the end of
the month” is in the second mode of essential predication
(property) when considered as the conclusion of the first
syllogism, and in the fourth mode (cause), when considered
as the major of the second syllogism; it is not immediate­
ly in the fourth mode, because it does not immediately ex­
hibit the cause, but only by means of the demonstration
of which it is the conclusion. The second minor gives us a
definition of the rising of the rivers by reason of its effi­
cient cause, stormy weather. Therefore, the conclusion:
that the rising of rivers occurs toward the end of the month.
It remains merely to bring the demonstration down to
the particular instance of the Nile river. Since we have
connected the rising of rivers and the end of the month,
and since the rising of rivers is itself a property of rivers
(which the property contains in its own definition as proper
subject), we need only predicate the property “rising to­
wards the end of the month” with the universal notion of
river. Therefore, since the Nile too is a river, the Nile
then rises toward the end of the month. Note, however,
that in the last syllogism the premiss “Rivers have the.
property of rising toward the end of the month” does not
immediately exhibit the cause, but we have it from the
preceding demonstration: rivers are bodies of water af­
fected by the stormy weather at the end of the month. How­
ever, since in the conclusion Nile and rising at the end of
the month are not commensurate, but are proved through
the proper subject of the attribute as middle term, this is
not the perfect type of propter quid demonstration, but
rather a particular demonstration. It is of great value,
however, in showing that the attribute belongs to Nile, not
S1 In II Post. Analyt., lect. 17, n. 6.

ΗίΗΜβί

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Demonstrating in Natural Philosophy

by reason of anything proper to itself, but by reason of
its being a river.
We have in the above example two subordinate middle
terms, the waning of the moon and stormy weather. Al­
though the whole example is not true, because of the faulty
data of the first minor premiss, yet it gives us a good idea of
the kind of science Aristotle envisioned as attainable by the
demonstrative method.

CHAPTER VII

DEMONSTRATION THROUGH MATERIAL CAUSE
Intrinsic causes have absolute necessity.1 But this abso­
lute necessity is in the order of essence. From this aspect
the material cause has scientific value and can be the mid­
dle term of a demonstration.
It will be helpful first to determine just what we mean
by material cause, for the term is broader than we may
suspect at first sight. Aristotle, speaking of material cause,
says: “That out of which a thing comes to be and which
persists, is called ‘cause,’ e.g. the bronze of the statue, the
silver of the bowl, and the genera of which the bronze and
the silver are species,” i.e. metal.2 Later on in the same
chapter he adds:
The letters are the causes of the syllables, the
material of artificial products, fire, etc., of bodies,
the parts of the whole, and the premisses of the
conclusion, in the sense of ‘that from which.’ Of
these pairs the one set are causes in the sense of
substratum, e.g. the parts, the other set in the
sense of essence—the whole and the combination
and the form.3
With the help of St. Thomas’ Commentary we must clari­
fy and amplify the statements of the Stagirite. Aristotle
does not mention prime matter when speaking of material
cause in science. Prime matter must be properly disposed
in order to receive a form. This comes about—keeping
*“Alia autem est causa, qua posita necesse est causatum poni; et
haec est causa materialis, quia ea quae sequuntur ex necessitate
materiae sunt necessaria absolute.” (In II Post. Analyt., lect. 9, n. 2.)
3 Physics, Bk. 2, Chap. 3, 194b 23-25.
3 Ibid., 195a 15-21. Cf. St. Thomas’ Commentary, lect. 5, n. 3. In
another place Aristotle says : “The material of animals is their
parts—of the whole animal the non-homogeneous parts, of these again
the homogeneous, and of these last the so-called elements of all matter.”
(Generation of Animals, Bk. 1, Chap. 1, 715a 8-11.)
139

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Demonstrating in Natural Philosophy

in the same genus of cause—through the combination of
the elements and parts. To know the elements and parts
of anything is to know its material cause. Aristotle’s ex­
amples are of artificial things. He makes it clear that in
treating natural bodies, with which natural science is con­
cerned, we look for the natural elements.
The parts are in the order of material cause with re­
spect to the nature and definition. The parts of the defini­
tion are formal with respect to the subsisting individual
whole,4 but they are material in relation to the essential
whole. All the integral parts, such as the eyes and the
limbs, are material causes of the whole. As St. Thomas
comments :
He says that the parts are the material cause of
the whole while above he reduced the parts of the
definition to the formal cause. However, we can
say that he was speaking of the parts of the
species which fall in the definition of the whole,
while here he is speaking of the parts of matter
in whose definition the whole falls, just as the
circle falls in the definition of the semicircle. But
it would be better to say that although the parts
of the species which are posited in the definition
are compared to the suppositum of the nature in
the manner of a formal cause, still they are com­
pared to the nature itself of which they are parts,
as matter because all· parts are compared to the
whole as the imperfect to the perfect which is a
comparison of matter to form.5
In another sense, the subject of an attribute is related
to it as material cause, for substance is a material cause
in respect of the accidents that inhere in it. Therefore, if
the precise aspect of the middle term upon which we con­
centrate in any demonstration is its causality as proper
subject, then we would be demonstrating through a mate­
4 “Natura igitur species constituta ex forma et materia communi,
se habet ut formalis respectu individui quod participat talem naturam;
et pro tanto hic dicitur quod partes quae ponuntur in definitione, per­
tinent ad causam formalem.” (In II Phys., lect. 5, n. 4.)
5 In II Phys., lect. 5, n. 9.

Demonstration Through Material Cause

141

rial cause. The middle term always implicitly has this
function of subject, but most of the time we are more in­
terested in its definition through other causes?
Regarding the limitations on material cause as the mid­
dle term in a demonstration, we must quote St. Thomas’
expression verbatim:
He says first that an antecedent which necessitates
a consequent, namely, a material cause, cannot be
taken in such a way that of necessity something
follows from it if there is only one proposition.
There must be at least two propositions so con­
structed that they communicate in one middle
term. If therefore, there is one middle (a material
cause) in two propositions, the conclusion will
necessarily follow. For instance, if we say : What­
ever is composed of contraries is corruptible; a
rock is such; therefore, etc. There must be two
propositions, not only because the syllogistic form
demands them, but also because not all that is from
matter has necessity from matter, as is proved
in the Second Book of Physics. Therefore, be­
sides the proposition in which something is said
to have such a matter, there must be another
proposition, which declares that from such matter
something necessarily follows.7
e In the Summa Theologiae (I-Π, q. 55, a. 4) St. Thomas distinguish­
es materia ex qua, namely, the intrinsic constituent matter; materia
in qua, the subject; and materia circa quam, which corresponds to the
proper object, for instance, of a virtue or of a science.
7 “Dicit ergo primo quod illud, quo existente necesse est aliud
esse, scilicet causa materialis, non contingit accipi sic, ut ex neces­
sitate aliquid sequatur, si accipiatur una sola propositio; sed oportet
accipere ad minus duas hoc modo se habentes, quod communicent in
uno medio. Si ergo accipiatur in duabus propositionibus unum med­
ium, quod est causa materialis, ex necessitate sequitur conclusio: puta
si dicamus: omne compositum ex contrariis est corruptibile: lapis
est huiusmodi; ergo etc. Oportet autem accipere duas propositiones,
non solum propter exigentiam formae syllogisticae, sed etiam quia
non omnia quae sunt ex materia, habent exmateria necessitatem, ut
probatur in II Physic. Et ideo praeter propositionem in qua sumitur
hoc habere talem materiam, oportet quod sumatur alia propositio,
quae declaret quod ex tali materia aliquid ex necessitate sequatur.”
(In II Post. Analyt., lect. 9, n. 4.)

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Demonstrating in Natural Philosophy

When Aristotle is treating ex professo the manner of
demonstrating by the various causes,8 he gives, as an ex­
ample of demonstration through material cause, an argu­
ment from mathematics. We have so far avoided the mathe­
matical examples, because our interest is in physical demon­
strations. But this one is too important and enlightening
to pass over. St. Thomas’ introductory comment must be
given in full:
He then proposes a mathematical example. Nor
is this contrary to what he said in the third book
of Metaphysics, namely, that the mathematical sci­
ences do not demonstrate through material cause.
Mathematics, indeed, abstracts from sensible mat­
ter, but not from intelligible matter, as is said
in the sixth book of Metaphysics. Intelligible mat­
ter is considered as something divisible, whether
in regard to numbers or continua. Accordingly,
whenever in mathematics something is demon­
strated of the whole through its parts, it seems to
be a demonstration through material cause: for
the parts are as matter in relation to the whole,
according to the second book of Physics. How­
ever, because matter is more properly spoken of
in relation to sensible things, he does not want to
call it material cause, but the cause of necessity.®
St. Thomas now follows Aristotle10 as he developes a
8 Post. Analyt., Bk. 2, Chap. 11, 94a 20ff.
® “Deinde... proponit exemplum in mathematicis. Nec est contra
id quod dicitur in III Metaphys., quod mathematicae scientiae non de­
monstrant per causam materialem. Mathematica enim abstrahit
quidem a materia sensibili, non autem a materia intelligibili, ut
dictur in VI Metaphys.: quae quidem materia intelligibilis conside­
ratur secundum quod aliquid divisibile accipitur vel in numeris vel in
continuis. Et ideo quandocunque in mathematicis aliquid demonstratur
de toto per partes, videtur esse demonstratio per causam materialem:
partes enim se habent ad totum secundum rationem materiae, ut
habetur in II Physic. Et quia materia magis proprie dicitur in sen­
sibilibus, propter hoc noluit eam nominare causam materialem, sed
causam necessitatis.” (In II Post. Analyt., lect, 9, n. 5. Cf. In De
Trin., q. 5, a. 3, ad 4.)
10 Aristotle puts it tersely as follows: “Thus, let A be right angle,
B the half of two right angles, C the angle in the semicircle. Then

Demonstration Through Material Cause

143

demonstration of the proposition that the angle in a semicircle is a right angle. We must construct a semicircle
upon chord A C, which is the diameter of the full circle.
Upon point D, the center of the diameter and of the circle,
we erect a perpendicular line to point B on the circum­
ference. Then two lines are drawn from this point, one to
point A and another to point C. We have, therefore, two
right triangles ADB and CDB, because line DB is per­
pendicular to line AC. Now, angles DCB and DBC are
" b
equal to one right angle, because the angle at point D
/
/
x.
x.
is a right angle, and all three
f
/
X. \
angles of a triangle total up
//
X. \ to two right angles. Moreover, the two angles DCB and
abc
DBC are equal to one an­
other, since DB and DC are equal, both being radii of the
circle. Therefore, angle DBC is half of a right angle. By
the same process we find that angle ABD is half of a right
angle. Therefore, the whole angle ABC is half of two right
angles, that is, one right angle.
This demonstration, at the point where it interests us,
may be put into syllogistic form, using as middle term:
the half of two right angles.
The half of two right angles is a right angle.
But the angle in a semi-circle is the half of two
right angles..
Therefore, the angle in a semicircle is a right
angle.
In this way we can easily see that in the major premiss the
middle term expresses parts of the whole, that is, the two
halves. Therefore, it is a material cause. However, Aris­
totle and St. Thomas note that this middle term can also
pertain to formal cause, since it can be taken as a defini­
tion of a right angle ; but this must be in relation to a par­
ticular angle, as the parts of the definition are formal as
regards the supposit or individual participating the nature,
not as regards the nature itself. So we can say that the

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Demonstrating in Natural Philosophy

angle ABC shown in the drawing above can be defined as
the half of the two right angles, and this definition will
be formal: it will tell the whatness of that angle.11
It should be easier now for us to understand another ex­
ample that Aristotle gives. “Light shines through a lantern
because that which consists of relatively small particles
necessarily passes through pores larger than those particles
—assuming that light does issue by penetration.”11
12 Let
us put this into form:
What consists of relatively small particles is that
which will pass through the pores of a lantern
glass.
But light consists of relatively small particles.
Therefore, light shines through the lantern glass.
The middle term here exhibits the parts of which light is
composed. The property demonstrated of light belongs to
it precisely because of its material composition. Actually,
this definition of light is a hypothetical definition; it is not
Aristotle’s own opinion of the nature of light.13 The demon­
stration has no more validity than does the definition
in the middle term; for that definition is a principle
and cause of the demonstration. This shows us the es­
sential function of demonstration as a supplementation
11 The failure to grasp this distinction has led Le Blond, Logique et
Methode chez Aristote, pp. 94-95, to reject the above example as a
demonstration through material cause. He says it is really through
formal cause.
B is the cause in virtue of which A, right angle, is attributable to C,
the angle in a semicircle, since B = A and the other, viz., C, = B,
for C is half of two right angles. Therefore it is the assumption of
B, the half of two right angles, from which it follows that A is
attributable to C, i.e., that the angle in a semicircle is a right angle.”
(Z6id., 29-34.)
12 Post. Analyt., ibid., 94b 28-31.
13 “Light is neither fire nor any kind whatsoever of body nor an
efflux from any kind of body (if it were, it would again itself be a
kind of body)—it is the presence of fire or something resembling fire
in what is transparent. It is certainly not a body, for two bodies
cannot be present in the same place.” (On the Sold, Bk. 2, Chap. 7,
418b 14-17.)

Demonstration Through Material Cause

145

of the act of understanding and of defining. But the
example serves its purpose of illustrating the manner of
demonstrating through material cause.
While we are on the subject of light, it will be well to
mention a modern demonstration about the same. Newton,
experimenting with the refraction of light through a prism,
discovered the existence and shape of the spectrum. By
admitting the various bands of the spectrum to a second
refraction through another prism, he found that each color
has its proper degree of refractibility and that the pure
colors of the band could not be further refracted. Moreover, he found that the colors of the spectrum can, when
passed through a large lens, be again combined into white
light. The conclusion was inescapable that white light con­
sists of a composition of colored rays in a definite propor­
tion. The cause for the phenomenon of the spectrum is
precisely the composition of white light from heterogeneous
rays, each with its proper color and index of refractibility.
Given this cause, the phenomenon of the spectrum can be
demonstrated to be a property of white light.
A light composed of various colored rays each with
a different index of refractibility will produce
a band of colors when passed through a prism.
But, white light is so composed.
Therefore, a white light produces a band of colors
when passed through a prism.
In the major premiss the middle term is seen as the material cause of that which causes the phenomenon of the spectrum : i.e. because white light is so composed, it can be broken up into a band of its component parts. In the minor
premiss white light is defined by its material cause, and
this definition, it should be noted, has been acquired through
the a posteriori demonstration whereby Newton discovered
the composition. Therefore, the conclusion follows through
the medium of material cause.
Chemistry is that part of natural science par excellence
which makes use of definitions through material cause.
Chemical definitions, or formulae, quite evidently show the

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Demonstrating in Natural Philosophy

parts of which any given substance is composed such as
H2SO4, H2O, etc. A11/ properties that can be found to
flow from the material composition of a substance, e.g.
molecular weight, can be given propter quid demonstra­
tions in chemistry.14
A simple example can be given. Everyone knows from
ordinary experience that water extinguishes fire. But mere
knowledge of this fact is not scientific knowledge. Knowl­
edge of a fact is imperfect until we can assign the proper
reason Or cause why the fact is so and cannot be otherwise.
In the present example we assign incombustibility as a
property of water through the definitions of both the prop­
erty and of water. Combustion is defined as the process of
oxydation. Water is by definition an oxide of hydrogen.
Its chemical definition, H2O, a definition through material
cause or component parts. Water, then, is not combustible,
it cannot be oxydized, because by its very nature it is al­
ready oxydized. As it stands, this is what we call a partic­
ular demonstration. It lacks the full perfection of science,
because the property—incombustibility—is more extensive
than the subject water. The proper subject of incombusti­
bility is: any substance that cannot combine chemically
with oxygen. By an easy deduction we add : water is such
a substance; therefore, water is incombustible. Such a par­
ticular demonstration is but one easy step removed from
perfect demonstration and participates intimately in its sci­
entific. character.
At the beginning of the seventh book of Physics Aristotle
gives an interesting demonstration by material cause of the
principle: “Everything that is in motion must be moved
by something.”15 The argument here is quite difficult, but
we wish to discuss it because it is a valuable example for
our present concern and because St. Thomas, as against
14 Cf. Kane, et al., Science in Synthesis, p. 67ff. See ibid., p. 935
and 103ff for a famous demonstration through material causality
in biology, namely, Harvey’s demonstration of the circulation of the
blood.
15 Physics, Bk. 7, Chap. 1, 241b 24.

rtnra

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147

Averroes, explicitly contends that this is a propter quid
demonstration.16
There is no difficulty in seeing how there must be an
extrinsic mover to impart violent motion, such as to move
a stone upward through the air. The study, then, is limited
to those mobile beings that have an intrinsic source of mo­
tion, such as living beings and other natural beings. Now,
if something is moved of itself and not by another, that
thing must have motion essential to itself and in virtue of
its very self : per se et primo. If the mobile whole does not
have motion essential to it in virtue of itself, but in virtue
of its parts, it could not be moved per se primo: motion
could not be of its essence, and would thus have to come
from something outside its essence.
Aristotle first gives an indirect argument. Just because we
can perceive no external mover, he says, does not mean
that a thing has its motion essential to it; for one part of
the thing can be moving another part, as the soul moves
the body.
We have simplified the direct demonstration as much
as possible and put it into strict form. A deeper and more
complex consideration can be found in the treatment of
St. Thomas.
Whatever is in motion is divisible into parts on
which depends the motion of the whole.
But whatever is divisible into parts on which de­
pends the motion of the whole is something
moved, not per se primo, but by another.
Therefore, whatever is in motion is moved, not
per se primo, but by another.
Minor :
1. (Whatever is in motion is divisible into parts.)
Whatever is in motion passes from one state to
another, and so is partly in the terminus a quo
and partly in the terminus ad quern.
But whatever so passes from one state to an­
other is divisible.
i« In VII Phys., lect. 1, n. 6. St. Thomas gives the same demon­
stration in shorter form in Contra Gent., Bk. 1, Chap. 13.

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Demonstrating in Natural Philosophy

Minor: This is evident, for if something mobile
is in the terminus ad quern, then the motion has
ceased. If it is in the terminus a quo, then the
motion has not commenced. Therefore, while it
is moving, it must be partly in both.
Major : To be partly in one terminus and partly
in another is to be divisible: an indivisible
would be wholly in either terminus.
2. (... into parts on which depends the motion of
the whole.)
If the motion of the whole would cease by reason
of a part coming to rest, then the motion of the
whole depends on the motion of the part.
But the motion of the whole would truly cease if
a part came to rest.
Therefore, the motion of the whole depends on
the motion of the part.
The minor is evident, since the whole as such
cannot move unless the parts all move.
Major : When one thing cannot be without an­
other, then it depends on that other. But if the
motion of the whole cannot be without the mo­
tion of the parts, then it depends on them.

Major :
Every mobile being that comes to rest from its
motion byreason oftherestofsomethingelse
is moved not per se primo, but by another.
But whatever is divisible into parts on which de­
pends the motion of the whole is something that
comes to rest from its motion by reason of the
rest of something else, namely, the parts.
Therefore, whatever is divisible into parts on
which depends the motion of the whole is some­
thing moved, not per se primo, but by another.
Major: It is per se evident that such a mobile
being would not be moved per se primo, for to
be moved per se primo means that motion would
be of the essence of that being, and so it could
not come to rest. Therefore, if it is not moved
per se primo, it must, by complete disjunction,
be moved by another. Whatever is not of the
essence of a being comes to it from another.
The minor is evident.

Demonstration Through Material Cause

149

The middle term of this demonstration (whatever is divis­
ible into parts on which depends the motion of the whole)
is a material cause.· Therefore, as St. Thomas says, “it
seems we must say that this is not a demonstration quia,
but propter quid; for it contains the cause why it is im­
possible that anything mobile move itself.”17
There is a fascinating chapter in the Posterior Analytics1*
that will show us something of the building up of a demon­
stration from material cause in biology. Suppose that we
have an attribute to demonstrate of a particular subject,
without, however, knowing the commensurate subject. We
ask why this attribute inheres in this particular subject.
The answer will evidently be the definition of the proper
subject of the attribute. How do we go about identifying
that proper subject?
First, according to Aristotle, we must consider the vari­
ous divisions and subdivisions of a common genus, in an
attempt to find the subject that is commensurate with the
attribute in question. Suppose that we want to demonstrate
sleep of man. We note that sleep is an attribute also of bird
and horse. We select the genus common to all the particular
subjects in which we find the attribute of sleep, namely,
animal, and we also lay down the common properties of
animal as such. Then we proceed to the subdivisions with
their properties, in order to find out which sub-genus is
coextensive with sleep. In this case it is easy to see that
sleep belongs to man, bird and horse in virtue of their being
animals.18
Let us take a difficult example. Suppose we should ask
why certain animals, such as the cow and the stag, have
more than one stomach and have just a few or no teeth in
the upper jaw? Aristotle observes that there is no exist­
ing classification that will easily point out the proper sub11 “Videtur dicendum quod non sit demonstratio quia, sed propter
quid; continet enim causam quare impossibile est aliquod mobile
movere seipsum." (Ibid.)
»» Post. Analyt., Bk. 2, Chap. 14, 98a 1-23.
18 Cf. In II Post. Analyt., lect. 17, n. 2.

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Demonstrating in Natural Philosophy

ject of such qualities, but that we can hit upon a common
characteristic that will help us work toward a propter quid
demonstration. That characteristic is that all or most ani­
mals without teeth and with more than one stomach have
1
horns. Of course, it takes a goodly amount of observation
to establish this characteristic as being common to the ani­
mals with the attributes in question.
A descriptive definition of an unnamed and unclassified
proper subject will be our starting point. We will say that
the attributes of possessing more than one stomach and
only one row of teeth belong to cow and stag in virtue of
their being homed animals. Can we find in this descriptive
definition some cause of the attributes? We have an in­
dication, at least, in that the definition points to a mate­
rial cause : to prove something of the whole by one of the
material parts is to prove by material cause.
Aristotle at once thought that he saw a cause. According
to him, larger animals have more earthy matter in their
composition. This matter is that from which bone is
formed; from the same matter tusk and teeth and horns
are formed.
Thus it is that no animal that has horns has also
front teeth in both jaws, those in the upper jaw
being deficient. For nature by subtracting from
the teeth adds to the horns ; the nutriment
which in most animals goes to the former being
here spent on the augmentation of the latter.20
Therefore, the reason for the lack of upper teeth is the
possession of horns, as the matter that would have nour­
ished the growth of teeth has been used for horns. Aris­
totle sees this verified in that
... in other animals, where this material is not
secreted from the body in the shape of horns, it
is used to increase the size of the teeth; in some
cases of all the teeth, in others merely of the
tusks, which thus become so long as to resemble
horns projecting from the jaws.21
20 Parts of Animals, Bk. 3, Chap. 2, 663b 36—664a 3.
«i Ibid., 8-12.

Demonstration Through Material Cause

151

Accordingly, a demonstration can be made:
Animals in whom a limited amount of nutriment
that would have gone toward the formation of
teeth has been used for some other purpose are
animals that have few or no upper teeth.
But horned animals are such.
Therefore, horned animals have few or no upper
teeth.
But cows and stags are homed animals.
Therefore, cows and stags have no upper teeth.
The first major contains a material cause in the fourth
mode of essential predication. The first minor is a definition of homed animals by material cause. The second minor
is a definition of cows and stags through material cause,
that is, a descriptive definition through one of the integral
parts. It is material cause also from another aspect, that
of proper subject. The first demonstration is fully commensurate; the second is a particular demonstration, which
uses the proper subject as middle term.
It is quite easy to see now how Aristotle can demonstrate
the possession of more than one stomach of horned animals.
A... multiplicity of stomachs exists also in the
horned animals ; the reason being that horn-bearing animals have no front teeth in the upper
jaw.... For since the mouth, owing to its lack of
teeth, only imperfectly performs its office as regards the food, this multiplicity of stomachs is
intended to make up for its shortcomings....
For those horned animals that have no front teeth
in the upper jaw also ruminate.22
The demonstration reads as follows:
Animals that lack upper teeth must ruminate their
food.
But horned animals are animals that lack upper
teeth.
Therefore horned animals must ruminate their
food.
Whatever must ruminate its food needs several
stomachs for storage of food.
But horned animals must ruminate their food.
Bk. 3, Chap. 14, 674a 31-33; b 8-11; 675a 5-6.

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Demonstrating in Natural Philosophy

Therefore homed animals must have several stom­
achs.
In the major premiss of the first syllogism the middle
term is the cause of the rumination of food. It appears
to be a material cause, i.e. something is said of the whole
because of a part, in this case, the lack of a part. The minor
is a definition of homed animals, again in terms of a mate­
rial part. The major of the second demonstration shows the
final cause of having several stomachs. The minor is a defi­
nition of homed animals in terms of final cause. Therefore,
we have demonstrated that horned animals have several
stomachs because they must ruminate their food; they
must ruminate their food because they lack upper teeth;
they lack upper teeth because the nutriment that would
have formed teeth has gone into the formation of horns.
They have these properties, then, precisely because they are
horned animals.
This example shows us how high Aristotle aimed in find­
ing an intelligible explanation of the world of nature by
assigning the causes of each natural thing. Aristotle’s
ideal and method may well be a guide to us in achieving
true scientific knowledge of nature.

/7

CHAPTER VIII

DEMONSTRATION THROUGH FINAL CAUSE
“In natural, moral and artificial matters,” says St. Thom­
as, “demonstrations are taken especially from the end.”1
We have discussed the reason for this at some length in
Chapter Three. We do not start out natural science with a
perfect intuition of essences, from which we can deduce
their properties. The process is just the reverse: to ob­
serve the properties of natures through sensory experi­
ence and to let them lead us back to the natures that cause
them, from the knowledge of which we can demonstrate
and understand all the properties.
Not only does the final cause help us to demonstrate
properties, but it also enables us to demonstrate the other
causes. For final cause is first in intention: it moves the
efficient cause to unite the form and matter. Furthermore,
matter is ordained to form and form to operation, as is evi­
dent in the case of a saw, which is made of steel accord­
ing to a certain form for the purpose of cutting wood.
It is evident in things that have four causes that
one cause is in some way the cause of another.
Matter is because of form, and not the other way
around ; so the definition that is taken from formal
cause is the cause of the definition taken from the
material cause of the same thing. Likewise, be­
cause the thing generated attains its form through
the action of the generator, it follows that the
agent is in some way the cause of the form, and is
the definition of the definition. Furthermore, every
agent acts because of the end ; hence the definition
taken from the end is somehow the cause of the
definition taken from the agent cause. We cannot
1 “In naturalibus enim, et moralibus et artificialibus, praecipue
demonstrationes ex fine sumuntur.” (In V Meta., lect 1, n. 762,)
153

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Demonstrating in Natural Philosophy

proceed further in kinds of causes: hence it is
said that the end is the cause of causes.2
By final cause we mean that for the sake of which some­
thing is done : the goal or purpose of a being or an opera­
tion. Aristotle’s lively consciousness of teleology in nature
is well known ; we need not discuss it here at length.3 The
main reason he finds for finality in nature is the regularity
and intelligent design with which things come about
Such a regularity could not be due to chance, for
chance happenings occur only infrequently. Moreover, the
fittingness and purposiveness whereby all things are pat­
terned and ordered with such obvious perfection precludes
an origin from mere mechanical interactions of matter.
Things are and act in regular and typical pattern because
they are so determined by their natures. This determina­
tion of natural agencies to produce constant effects is what
we mean by finality in nature.
The existence of finality in nature is known to the phys­
icist from his wide experience of physical reality. He does
not demonstrate teleology: he sees it. All beings exhibit
to him a natural inclination to what is good for them: to
their conservation, their operations, their perfection. More­
2 “Manifestum est enim in rebus habentibus quatuor causas, quod
una causa est quodammodo causa alterius. Quia enim materia est
propter formam et non e converso, ut probatur in II Physic., definitio
quae sumitur ex causa formali, est causa definitionis, quae sumitur ex
causa materiali eiusdem rei. Et quia generatum consequitur formam
per actionem generantis, consequens est quod agens sit quodammodo
causa formae et definitio definitionis. Ulterius autem omne agens
agit propter finem; unde et definitio quae a fine sumitur, est quod­
ammodo causa definitionis quae sumitur a causa agente. Ulterius
autem non est procedere in generibus causarum: unde dicitur quod
finis est causa causarum.” (In II Post. Analyt., lect. 8, n. 3. Cf. In
V. Meta., lect. 3, n. 782; In II Phys., lect. 5, n. 11; De Principiis
Naturae, n. 10; etc.)
,
3 Aristotle’s best treatment of final cause in nature is given in
Physics, Bk. 2, Chap. 8, 198b 10—199b 33. St. Thomas' Commentary,
lessons 12-14, should be consulted. St. Thomas often returns to this
subject; he gives a good summary of it in De Veritate, q. 5, a. 2;
q. 22, a. 2.

Demonstration Through Final Cause

155

over, typical structures and organs are constructed not
only with a view to their function, but rather that their
function may be accomplished in a better and more fitting
way. For instance, the front teeth are sharp for the sake
of biting off our food, and the back teeth are broad for
the sake of better chewing the food. What a contrast are
natural parts and functions to their man-made substitutes,
such as artificial limbs and hearing aids.
The main thing that is of concern to us at present is the
various aspects of final causality that the natural philoso­
pher uses in demonstrating. We have already seen that the
form of a thing generated is identical with the final cause
of the whole generative process. But the being_generated_
Js ordained to a further end, which is^peration or the
thing attained by bperation^ The thing attained by opera­
tion is callëd'thé bbjective end, in distinction to the perfec­
tion acquired by the agent in attaining it; this latter is
the subjective end. Not only the ultimate end, subjective
or objective, has the nature of final cause, but all the inter­
mediate ends ordained as means to it.5 Likewise, all the
individual parts of the agent, its organs and faculties and
operations, are mutually coordinated, one being ordained
to the other.
The whole physical universe itself has an intrinsic final
cause, the perfect correlation of its parts, a bonum ordinis.
* “Natura rei, quae est finis generationis, ulterius etiam ordinatur
ad alium finem, qui vel est operatio, vel aliquod operatum, ad quod
quis pervenit per operationem.” (Summa Theol., I-II, q. 49, a. 3.)
“Sic igitur causam finalem per tria notificat; scilicet quia est
terminus motus, et per hoc opponitur principio motus, quod est causa
efficiens: et quia est primum in intentione, ratione cujus dicitur
cujus causa: et quia est per se appetibile, ratione cujus dicitur
bonum. Nam bonum est quod omni appetunt. Unde exponens quo
modo causa finalis efficienti opponatur, dicit quod est finis genera­
tionis et motus, quorum principium est causa efficiens. Per quae duo
videtur duplicem finem insinuare.” (In I Meta., lect 4, n. 71.)
5 "Per formam perficitur natura rei.... Ipsa tamen forma ordin­
atur ulterius ad operationem, quae est vel finis, vel via in finem.”
(Summa Theol., I-II, q. 49, a. 4, ad 1.)

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Demonstrating in Natural Philosophy

It has also an extrinsic final cause, which is the glory of
God. The final chapter of St. Thomas’ Commentary on the
Metaphysics of Aristotle is a magnificent Weltansicht, a
view of the universal teleological order of reality. The doc­
trine there is summarized with equal beauty in the Summa
Theologiae. It will be to our advantage to quote this latter
passage.
The entire universe is constituted by all creatures,
as a whole consists of its parts. Now if we wish
to assign an end to any whole, and to the parts
of that whole, we shall find, first, that each and
every part exists for the sake of its proper act, as
the eye for the act of seeing; secondly, that less
honorable parts exist for the more honorable, as
the senses for the intellect, the lungs for the heart;
and thirdly, that all parts are for the perfection
of the whole, just as matter is for form, since the
parts are, as it were, the matter of the whole.
Furthermore, the whole man is for the sake of an
extrinsic end, namely, the fruition of God.
So, even in the parts of the universe every crea­
ture exists for its own proper act and perfection,
and the less noble for the nobler, as those crea­
tures that are less noble than man exist for the
sake of man. Furthermore, each and every crea­
ture exists for the perfection of the entire uni­
verse. Further still, the entire universe, with all
its parts, is ordained towards God as its end, in­
asmuch as it imitates, as it were, and shows forth
the divine goodness to the glory of God. Reason­
able creatures, however, have in some special and
higher manner God as their end, since they can
attain to Him by their own operations, by know­
ing and loving Him. Thus it is plain that the di­
vine goodness is the end of all corporeal things.4
It is the duty of the natural philosopher to specify this
plan of the universal order. He has to determine the pur­
pose of every material being, from that of the lowest part
and function of the lowest natural unit up to the order of
the cosmos itself. He must link up all mobile beings into a
4 Summa Theol., I, q. 65, a. 2.

Demonstration Through Final Cause

157

teleological pattern by demonstrating of each one and of
each part their proper and proximate intrinsic and ex­
trinsic final causes. A momentous assignment and one not
likely ever to be fully accomplished—but it is imposed upon
the physicist by his own natural desire to understand the
world in which he lives.
There is one point at which the investigation of the nat­
ural philosopher must stop. He cannot, as a natural phi­
losopher and in virtue of the principles of his science, dis­
cover the extrinsic final cause of the universe. He is cap­
able of detecting finality in the structure and operations of
mobile being. He can demonstrate the causal interrelations
of mobile beings. But the proper principles of his science
are inadequate to explain the ultimate reason for finality
in nature and the ultimate extrinsic final cause of mobile
being. For the principles of mobility7 can take him no
further than to the existence of the First Unmoved Mover.
There is need of a science that treats of being as being to
give the definitive reason for the existence of finality and
of the natural inclinations of all beings. That answer is
the Creator, Who has called all things into existence for
His own glory and has planted in the natures of all a spon­
taneous tendency toward Himself, the Infinite Good.8

A demonstration of the active intellect can be made
7 “Consideratio speculativae scientiae non se extendit ultra virtutem
principiorum illius scientiae, quia in principiis scientiae virtualiter
tota scientia continetur.” (Ibid., I-II, q. 3, a. 6,. Cf. I, q. 1, a. 7.)
“Substanta enim solet dici prima inchoatio cuiuscumque rei, et maxime
quando tota res sequens continetur virtute in primo principio; puta
si dicamus quod prima principia indemonstrabilia sunt subiecta
scientiae, quia scilicet primum quod in nobis est de scientia sunt
huiusmodi principia, et in eis virtute continetur tota scientia.” (Ibid.,
Π-Π, q. 4, a. 1.)
8 Metaphysics treats of all things under the aspect of being, namely,
of essence having existence. The proper cause of esse as such is
God, the Creator and Subsistent Being. The ultimate final cause of
esse is the glory of God. This is commensurate with being as such, and
not with mobile being; hence, it cannot be attained through the prin­
ciples of mobile being.

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Demonstrating in Natural Philosophy

through final cause. St. Thomas treats this subject in a
number of places,9 and he developes proofs of it in various
ways. The proof in the Summa Theologiae, for instance,
seems to be quia, because it proceeds from the general prin­
ciple that the potential must be reduced to act by some­
thing already in act.
Since Aristotle did not allow that, the forms of
natural things exist apart from matter, and since
forms existing in matter are not actually intelli­
gible, it follows that the natures or forms of the
sensible things which we understand are not actu­
ally intelligible. Now nothing is reduced from
potentiality to act except by something in act;
as the senses are made actual by what is actually
sensible. We must therefore assign on the part of
the intellect some power to make things actually
intelligible, by the abstraction of the species from
material conditions. And such is the necessity for
positing an agent intellect.10
Here, as well as in other places, St. Thomas gives us the
matter for a strict demonstration, although he does not
put it into syllogistic form. He gives us a definition of the
active intellect in terms of its function, namely, a power or
agent that abstracts species from material conditions. A
definition through function is a definition through final
cause, for beings are ordained to operation as to an end.
With this definition, we can demonstrate the active intel­
lect. In skeletal form, it may be expressed as follows :
An intelligent being who receives intelligible spe­
cies from the phantasms of sense powers, where­
by the intellect is put into act, is a being en­
dowed with an active intellect.
But, man is such.
Therefore, man is a being endowed with an active
intellect.
9 Summa Theol., I, q. 79, a. 3; Sent., Π, d. 17, q. 2,a. 1; Contra
Gent., Bk. 2, Chap. 76 & 78; In HI De Anima, lect. 10, n. 728-739;
De Spir. Creat., a. 9; De Anima, a. 4; Compendium Theol., Chap. 83.
Cf. Gredt., Elementa Philosophiae Aristotelico-Thomisticae, I, n. 572,
who gives a good demonstration of the thesis.
10 Summa Theol., I, q. 79, a. 3.

Demonstration Through Final Cause

159

The minor premiss is established by experience. For
man realizes that his abstract intellectual knowledge takes
its rise from sensation, and this is verified by the fact that
the intellect’s function is impaired by weariness and by
injury to the organs of internal sensation. A rich status
quaestionis must show how this mode of operation follows
from the composite nature of man, who is both material
and spiritual, with his body being ordained to serve his
soul. In the major premiss the middle term is final cause,
or goal of operation. This premiss is made known by an
a posteriori demonstration, for since the senses of them­
selves cannot produce an intelligible species, there must be
an immaterial power to do it. In St. Thomas’ day it was
necessary to bolster this premiss with indirect demonstra­
tions proving, against the Arabian philosophers, that the
active intellect is a faculty in each individual soul, and not
a separated intellect. The premisses are all commensurately
universal, so it seems that we have here a true propter quid
demonstration.

In the chapter of the Posterior Analytics where Aristotle
is discussing the principle that we can demonstrate with
any of the four causes as middle terms, he gives this ex­
ample of a demonstration from final cause.
Why does one take a walk after supper? For the
sake of one’s health.... The end in view is...
health. To ask the reason why one must walk
after supper is precisely to ask to what end one
must do it. Let C be walking after supper, B the
non-regurgitation of food, A health. Then let
walking after supper possess the property of pre­
venting food from rising to the orifice of the stom­
ach, and let this condition be healthy; since it
seems that B, the non-regurgitation of food, is
attributable to C, taking a walk, and that A,
health, is attributable to B. What, then, is the
cause through which A, the final cause, inheres
in C? It is B, the non-regurgitation of food;
but B is a kind _ of definition of A, for A will
be explained by it. Why is B the cause of A’s

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belonging to C ? Because to be in a condition such
as B is to be in health.11
The example at first sight presents considerable diffi­
culty. As a help to understanding it, we must warn that as
it stands, it seems to be a demonstration through formal
causality. We will have to transpose the terms to make it
a demonstration through final causality, as Aristotle him­
self informs us: “The definitions must be transposed, and
then the detail will become clearer.”12 When the data given
above are put into form, the demonstration goes:
B, Good digestion of food is A, a healthy condition.
C, Walking after supper is that which causes B,
good digestion.
Therefore, walking after supper causes a healthy
condition.
In the major premiss B is a formal cause or definition
of A, which is the final cause. In the minor, C is the efficient
cause of B, which is also a final cause of C. In this premiss
we have a definition of C through its end, B. In the con­
clusion we see that since B is a formal cause of A and C
is for the sake of B and is an efficient cause of B, so then
C, walking after supper, is the efficient cause of A, good
health, and is for the sake of A, its end. B, the medium
of demonstration, is both an end and an effect of C and
a definition of A.
The syllogism proceeds according to the order of execu­
tion, and hence through what is first in becoming. If we
transpose the terms, we can make it prove through final
cause, or what is first in intention.
A, Health requires B, good digestion.
But C, walking after supper is A, for the sake of
health.
Therefore, C, walking after supper is for B, good
digestion.
In the major premiss A, the middle term, is the final cause
of B, good digestion. The minor premiss contains a defini­
tion of C by reason of its final cause, health. Therefore, C
11 Post. Analyt., Bk. 2, Chap. 11, 94b 8-21.
r2 Ibid., 22.

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is the subject and cause of B through the medium of the
final cause, A.13
Let us turn our attention to the field of biology where
finality and hence the ability to demonstrate are plentifully
evident.
In the first chapter of the little treatise De Sensu et Sensi­
bili Aristotle demonstrates the possession of the various
senses. “Touch and taste,” he says, “necessarily appertain
to all animals, touch for the reason given in the De Anima,
and taste, because of nutrition.”14 It is by taste that an
animal distinguishes savory substances, which are suitable
for food, from unsavory ones, which are not good. But
what is the proper reason for the higher senses of smelling,
hearing, and seeing? First of all, their proper subject
must be assigned. They are found in all animals that have
locomotion. Therefore, we may give a descriptive definition
of the proper subject : animals that have the faculty of loco­
motion. This definition of the commensurate subject gives
a clew to the final cause of these three senses:
The senses which operate through external media,
viz. smelling, hearing, seeing, are found in all ani­
mals which possess the faculty of locomotion. To
all that possess them they are a means of preserva­
tion; their final cause being that such creatures
may, guided by antecedent perception, both pur­
sue their food, and shun things that are bad or
destructive.15
If we wish to put this into syllogistic form, it would read:
Animals endowed with locomotion are animals
that must pursue their food and shun things
that are bad or destructive.
But in order to do so these animals must be able
to smell, hear, and see.
Therefore, animals endowed with locomotion are
animals that are able to smell, hear and see.
The connection between these faculties and their final
13 Cf. St. Thomas’ Commentary (Leonine ed.), lect. 9, n. 9 and
footnote k, where Card. Zigliara works out the above syllogisms.
14 De Sensu et Sensibili, Chap. 1, 436b 13-14.
33 Ibid., 18-22.

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cause is quite evident. An animal that moves around to
find its food must have some means of detecting that food
from a distance. The same applies to the avoidance of
dangers. The sense of smell, at least, is simply necessary;
the other senses are necessary for the more perfect attain­
ment of the end.
Aristotle adds that in animals with intelligence these
faculties serve a higher purpose. “They bring in tidings
of many distinctive qualities of things, from which the
knowledge of truth, speculative and practical, is generated
in the soul.”1® This constitutes another demonstration from
final cause, which can easily be put into form :
Animals with intelligence are animals that need
sensory data from which to abstract specula­
tive and practical truth.
But animals that need such sensory data are ani­
mals that have it supplied especially by the
senses of smelling, hearing and sight.
Therefore, animals with intelligence have the
senses of smelling, hearing and sight.
The need for sensory data from which to abstract intelli­
gible species is thus seen to be the final cause of man’s hav­
ing the higher senses.
Aristotle’s treatment of the eye is characteristic of his
method of demonstration by final cause. The eye is to be de­
fined in relation to its function.
What a thing is is always determined by its func­
tion : a thing really is itself when it can perform its
function; an eye, for instance, when it can see.
When a thing cannot do so, it is that thing only
in name, like a dead eye or one made of stone.1’
Given this definition through function, or final cause, Aris­
totle now seeks a demonstration of the material cause of
the eye, the matter from which it is constructed.
Some of Aristotle’s predecessors thought that the eye
437a 2-3.
17 Meteorologica, Bk. 4, Chap. 12, 390a 10-14. Cf. On the Soul,
Bk. 2, Chap. 2, 412b 19-23, where he shows that the faculty of vision
is the form of the visual organ.

Demonstration Through Final Cause

163

was composed from the element fire. Their main reason
for saying this was that “when the eye is pressed or moved,
fire appears to flash from it.”18* This was also consonant
with their theory of vision as an emanation of light from
the eye, as from a lantern. Aristotle shows the impossi­
bility of this opinion. Then he establishes his own, that the
eye is composed from the element water, because water
is translucent.1® The element air is also translucent, but
it is not as well adapted for the purposes of the eye.
“Water,” he says, “is more easily confined and more easily
condensed than air; wherefore it is that the pupil, i.e. the
eye proper, consists of water.”20 He shows that experi­
ence testifies that this is so, for water issues from a decom­
posing eye. He then gives his demonstration.
Accordingly, that the inner part of the eye con­
sists of water is easily intelligible, water being
translucent. Now, as vision outwardly is impos­
sible without light, so also it is impossible in­
wardly (without light within the organ). There
must, therefore, be some translucent medium
within the eye, and, as this is not air, it must
be water. The soul or its perceptive part is not
situated at the external surface of the eye, but
obviously somewhere within: whence the neces­
sity of the interior of the eye being translucent,
i.e. capable of admitting light. And that it is so
is plain from actual occurrences. It is matter of
experience that soldiers wounded in battle by a
sword slash on the temple so inflicted as to sever
the passages of (i.e. inward from) the eye, feel
a sudden onset of darkness, as if a lamp had gone
out; because what is called the pupil, i.e. the trans­
lucent, which is a sort of inner lamp, is then cut
off (from its connexion with the soul).21
This can be formalized as follows:
The eye is the organ of vision.
But the organ of vision must be composed from
18 De Sensu, Chap. 2, 437a 24.
“ Cf. ibid., 438a 13sq.
η Ibid., 15-16.
11 Ibid., 438b 5-15.

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a translucent element, as vision is not possible
without light.
Therefore, the eye is composed from a translucent
element, either air or water.
But air is not sufficiently adapted to this purpose.
Therefore, the eye is composed of water.
The major premiss (the organ of vision must be composed
from a translucent element) is made evident for Aristotle
because the visual faculty is seen to reside not on the sur­
face of the eye, but within; hence, light must be admitted.
This cursory glance at Aristotle’s demonstration of the
composition of the eye suggests the rich understanding we
can attain, in terms of final causality, of the structure of
the eye. We can demonstrate the reason why the cornea,
aqueous humor, lens and vitreous humor are transparent,
namely, in order to admit light stimuli to the retina. We
can also demonstrate that a more perfect and more adapt­
able vision requires an adjustable lens for focussing light
stimuli, and that such a lens must have a focussing mech­
anism, which is what the ciliary muscle is. We also know
that the choroid coat is highly pigmented in order to pre­
vent light from entering the eye except through the pupil.
Such properties as the enlarging or closing of the pupil
may be demonstrated to result from the increased or decreased light for the purpose of equalizing the stimuli on
the retina. All these are proper final causes and hence con­
stitute middle terms of demonstrations.
Since Aristotle gives the example of respiration in one
of his methodological tracts,82 it will be helpful to con­
sider it briefly. The little work De Respiratione is a signficant example of Aristotle’s method. Be begins by say­
ing:
A few of the previous physical philosophers have
spoken of respiration. The reason, however, why
it exists in animals they have either not declared,
or when they have, their statements are not cor­
rect and show a comparative lack of acquaintance
22 Parts of Animals, Bk. 1, Chap. 1, 642a 31—b 2. Cf. supra, Chap.
3, note 36 where the text is quoted.

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Demonstration Through Final Cause

165

with the facts. Moreover they assert that all ani­
mals respire—which is untrue. Hence these points
must first claim our attention, in order that we
may not be thought to make unsubstantiated
charges against authors no longer alive.23
This is a remarkable passage, showing Aristotle’s devotion
to observed facts, his demand for causal explanation, and
his intellectual honesty.
He first establishes the proper subject of respiration,
namely, animals that have lungs, especially those whose
lungs are charged with blood.24 He proceeds then to the
opinions of some of his predecessors, and concludes:
The main reason why these writers have not given
a good account of these facts is that they have
no acquaintance with the internal organs, and that
they did not accept the doctrine that there is a
final cause for whatever Nature does. If they had·
asked for what purpose respiration exists in ani­
mals, and had considered this with reference to
the organs, e.g. the gills and the lungs, they would
have discovered the reason more speedily.25
Aristotle now considers facts that throw light on the
purpose of respiration. He is particularly impressed by the
fact that in hot weather, when we grow warmer, respiration
is increased, whereas in cool weather breathing is retard­
ed.2® What we breathe out, moreover, is hot, whereas what
we breathe in is cold.27 He notices that some animals with
a spongy lung, little blood and low body heat have less need
for respiration ; they remain a long time under water.
Such are frogs, tortoises and the like.28 He finds it impos­
sible that fishes breathe at all.29 These facts seem to link
respiration to body heat. This is Aristotle’s approach to
building up his definition of respiration by function.
23 De Respiratione, Chap. 1, 470b 6-12.
2iIbid., 13, 24-26.
25 Ibid., Chap. 3, 471b 23-29. (Italics ours.)
28 Ibid., Chap. 4, 472a 29—b 4.
21 Ibid., 472b 35-473a 2.
28 Ibid., Chap. 1, 470b 13-20.
29 Ibid., Chap. 2, 470b 28-471b 30.

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All vital processes involve a certain heat The digestive
process does not occur “apart from soul and warmth, for
it is to fire that in all cases elaboration is due.”30 If this
heat becomes excessive, it will burn out the organism.
Hence it must be cooled.31 In a later chapter Aristotle says
that “The universal cause of the need which the animal
has for refrigeration, is the union of the soul with fire that
takes place in the heart.”32 Water animals and small blood­
less land animals can be adequately cooled by the surround­
ing medium. Some insects, such as bees, cockchafers and
crickets are wanper and require more refrigeration; this
is supplied by a deep indentation beneath the waist covered
with a thinner membrane.33 Animals with blood, heart and
lung require to be cooled by breathing in air.M Thus, res­
piration can be defined as the process of tempering the
heat of an organism. Such a definition is through final
cause.
Aristotle can now demonstrate “why animals with a fullblooded lung respire most.”35 We can formalize the core
of the argument:
The process of tempering the heat of an organism
by aerating the hot blood in the lungs is respi­
ration.
But animals with full-blooded lungs have greater
need to have their blood cooled, because they
cannot deviate much from normal temperature.
Therefore, animals with full-blooded lungs respire
most.30
It can be demonstrated on Aristotle’s principles why
more perfect animals have greater respiration. He holds
that “the higher animals have a greater proportion of heat,
for at the same time they must have been assigned a higher
30 Ibid., Chap. 8, 474a 26-28.
« Ibid., 474b 20-25.
33 Ibid., Chap. 16, 478a 28-29.
33 Ibid., Chap. 9, 474b 25-475b 14.
3‘ Ibid., Chap. 10, 475b 15-476a 15.
33 Ibid., Chap. 15, 478a 21.
33 Ibid., Chap. 15 gives the fuller development of this demonstration.

Demonstration Through Final Cause

167

soul and they have a higher nature than plants.”37 Plants
are cold, and the scale of life and the scale of natural heat
correspond. Therefore:
The more perfect animals are those with greater
heat.
But animals with great heat need a more perfect
process for tempering their heat.
Therefore, more perfect animals have a more per­
fect process for tempering their heat.
But the process of tempering natural heat is res­
piration.
Therefore, the more perfect animals have a more
perfect process of respiration.
The middle term in the first syllogism (animals with greater
heat) is a descriptive definition through a formal cause.
In the second, the middle term is a definition through final
cause. We could go on to demonstrate the correspondingly
perfect anatomy of the respiratory system in higher ani­
mals:
A more perfect process of respiration demands
more perfect lungs.
But higher animals need and have more perfect
respiration.
Therefore, higher animals need more perfect
lungs.
Aristotle’s doctrine on respiration is intimately connected
with his theory of the elements. That is why he was natur­
ally led to speak of the process in terms of heat and cool­
ing. Let us glance for a moment at what we moderns know
of respiration.
For us, respiration is defined in terms of oxygen needs
for cellular activity and of the discharge of waste products
in the form of carbon dioxide. Carbon dioxide is given off
by the tissues, is flushed out in the blood stream and re­
leased to the air in the lungs. Likewise, the aerated blood
in the alveoli of the lungs receives oxygen molecules and
carries them to the tissues throughout the body. Respira­
tion, then, can be defined as “the physiological process which
" Ibid., Chap. 13, 477a 16-19.

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Demonstrating in Natural Philosophy

is concerned in the intake of oxygen and the output of
carbon dioxide.”38 This is a definition by function or final
cause, for the process is a means to secure the end of oxygen
intake and carbon dioxide output. Taken in this general
sense, respiration can be demonstrated as belonging to every
\ living body.
^--^TEvery living body needs a normal oxygen supply
and must throw off cellular waste products.
But the physiological process which is concerned
in the intake of oxygen and the output of carbon
dioxide is respiration.
Therefore, every living body must have the process
of respiration.
In the minor premiss we have a definition of living things
in terms of a need or of an end to be attained. This need^,
is._evident from induction. This definition by final cause
corresponds to the definition of respiration by final cause.
Therefore, we see that respiration is coextensive with living
body./Taking material structure into account, i.e. the pos-'^
/ Session of lungs, blood, etc., we would demonstrate the J
negessityiof respiration by breathing_air into the lungs. - "^
When there is an increase of carbon dioxide in the alveo­
lar air, the blood becomes insufficiently aerated and the
arterial blood stream carries carbon dioxide to the respira­
tory center in the medulla. This sets to work a complicated
physiological mechanism that increases the rate of respi­
ration until the excess carbon dioxide is removed from the
blood and normalcy is restored.38 This is a mechanical ac­
tion, but a proper reason may be given for it in terms of
final causality, and so it can be demonstrated.
Restoration of a normal carbon dioxide content in
the blood is the purpose of the physiological
process whereby carbon dioxide in the arterial
blood stimulates the respiratory center in the
medulla and causes increased respiration.
38 J. S. Haldane, “Respiratory System,” Encyclopaedia Britannica,
(11th ed.), XXIII, 187.
38 On this complex process cf. J. S. Haldane, art. cit., 187-192;
E. S. Russell, The Directiveness of Organic Activities, 51-60.

Demonstration Through Final Cause

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But increased respiration in animals possessing
the anatomical structure corresponding to the
said physiological process is for the purpose of
restoring the normal carbon dioxide content in
the blood.
Therefore, increased respiration in these animals
is the result of the above-mentioned physiolog­
ical process.

Notice that the proper subject of the physiological process
is indicated in terms of animals having the corresponding
anatomical structure. If the proper subject were not thus
identified, there would not be a strict demonstration, for
the general subject “animal” is too broad.
Admittedly, the physiological process as described above
is over-simplified. But even in all its complexity, there are
demonstrations at every stage of the process. In such mat­
ters it would become cumbersome to formalize every dem­
onstration. Whenever there is a proper cause assigned for
any fact, however, the matter for a demonstration is present
and according to the rules of logic, it can be put into form.
The true scientific procedure is not just to accumulate facts,
but to assign the commensurate causes for facts.

It belongs to the natural philosopher to consider the final
end of man. Although modern scholastic manuals have
turned over this task to the moral philosopher, still it be­
longs by rights to the pyschologist, who must investigate
the causes and properties of his subject. In fact, this con­
sideration is most essential to natural philosophy. The tele­
ological ordination of all physical beings focusses upon
man. In the order of generation, prime matter tends to the
most perfect act that it can attain, namely, the human soul,
so that
... the last end of all generation is the human
soul, and to this does matter tend as its ultimate
form. Consequently, the elements are for the sake
of the mixed body, the mixed body for the sake of
living things, and of these plants are for the sake
of animals, and animals for the sake of man.

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Demonstrating in Natural Philosophy

Therefore man is the end of all generation.40
A similar order obtains in the preservation of beings.
Composite mineral bodies are preserved by the chemical
affinity of their elements ; plants are nourished on the min­
erals and provide protoplasm whereby animals are nour­
ished. All animals feed on plants, and the higher animals
on the lower. Man uses all: minerals, plants and animals.
As for man, he employs all kinds of things for
his own use : some for food, some for clothing....
Some things also he employs as a means of transit,
for he is inferior to many animals in swiftness and
endurance, as though other animals were furnished
for his needs.41
This ordination of things cannot be demonstrated direct­
ly, since the final cause is the first of causes. The order of
the world is a fact of observation. As St. Thomas says
vigorously in a parallel passage : “As anything acts in na­
ture, so it is natural for it to act.”42
All things are ordained to man in another and even more
perfect way. “Over and above this (i.e. that generation
and preservation are directed toward man), he employs
all sensible things for the perfection of his intellectual
knowledge.”43 The natural philosopher, therefore, will show
that the intrinsic final end of man in the natural order, his
highest perfection, is the highest activity of which he is
capable, namely, the contemplation of the speculative intel­
lect. To this all nature is ordained, as providing objects
of contemplation. In fact, St. Thomas holds that in the
state of innocence man did not need the animals for food,
clothing or transportation. “But man needed animals in
order to have experimental knowledge of their natures.”44
40 Contra Gent., Bk. 3, Chap. 22. Cf. In II De Anima, lect. 7„ n.
321-322.
41 Ibid.
42 “Secundum autem quod agitur unumquodque in rerum natura, ita
natum est agi.” (In II De Anima, lect. 7, n. 322.)
43 “Et super hoc omnibus sensibilibus ■ utitur ad intellectualis
cognitionis perfectionem.” (Contra. Gent., ibid. Our transi.)
“Summa Theol., I, q. 96, a. 1, ad 3.

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171

We thus see that man’s contemplation is the end of the
whole physical universe, as such a universe is necessary to
provide a rich treasury of species for contemplation.
The contemplation of the natural philosopher is limited.
He considers all the natures of his material universe, their
beauty and coordination. But it remains for the meta­
physician to show that all beings are reflections of the
grandeur of the Creator, and that all things are ordained to
man’s knowledge in order that through man all physical
creation may return to its Principle unto His glory and
the praise of His Goodness. Such a vision requires the light
of a higher science than that of natural philosophy.
We can now construct an easy demonstration that the
physical universe is ordained to man. We shall use a final
cause as middle term.
A composite spiritual-material being ordained to
contemplation is a being that needs a universe
of species for objects of contemplation.
But man is such.
Therefore, man is a being that needs a universe of
species for objects of contemplation.
The middle term is a formal cause with an added deter­
mination from final cause; hence, the proof proceeds espe­
cially from final cause. The major premiss is in the fourth
mode of essential predication, the minor is in the first, and
the conclusion is in the second. The terms are all commen­
surate. Therefore, we have manifested the propter quid
reason for the conclusion.

SUMMARY AND CONCLUSION
Logic is the general methodology of science; and all
logic is orientated toward a specific type of science, which
Aristotle called ίπιστήμη and the Scholastics name propter
quid. This is the kind of knowledge that the Scholastic
tradition identifies as science simply. It is the next most
perfect type of knowledge after the intellectual intuition
that we share with the angels. The instrument for attain­
ing this knowledge is the demonstrative syllogism, whose
nature and requirements we investigated at length in the
first chapter. It is by definition a syllogism productive of
scientific knowledge, that is, a syllogism which makes known
“the cause on which the fact depends, as the cause of that
fact and of no other, and further, that the fact could not
be other than it is.”1 From this Aristotle concluded an­
other definition, one by material cause: “The premisses
of demonstrated knowledge must be true, primary, im­
mediate, better known than and prior to the conclusion,
which is further related to them as effect to cause.”12
“To have knowledge, if it be not accidental knowledge,
of things which are demonstrable, means precisely to have
a demonstration of them."3 If we neglect the strictly dem­
onstrative process in building up and developing a science,
we will indeed attain much knowledge of the intuitive sort,
which issues in definition, and many proofs of the exist­
ence of facts. But there will be a hiatus in our science.
We shall not attain the fullness and perfection of knowl­
edge possible to us about the subject of our science.
We made mention of the lesser types of demonstration,
both a priori and a posteriori, down to the level of opinion
1Post. Analyt., Bk. 1, Chap. 2, 71b 9-12.
iIbid., 19-21.
3 Ibid., 27-29.
172

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Summary and Conclusion

173

and of systematic explanation. These are all situated in a
science with an essential orientation toward the perfect
kind of demonstrative syllogism. All the elements that
enter a science and all the moments and movements of the
science must be directed according to the exigencies of the
highest type of science, for it is the higher that orders the
lower.
In the second chapter we investigated the meaning and
requirements of the subject and object of a science and
applied our findings to determining the subject and object
of a science of the physical world. We saw how sensory
motion is the key that opens up nature to us and how the
science of nature proceeds, according to the mode of human
knowing, from general considerations toward ever further
specifications, attaining perfection only when it can arrive
at demonstrative knowledge of the lowest species.
A doubt suggested itself as to how we can have certain
and necessary knowledge about things essentially involved
in matter, the principle of uncertainty and of contingency.
In the third chapter we solved this difficulty by showing
that the certitude of natural science is not the purely de­
ductive certitude of mathematics, nor even the more per­
fect type of science attainable about the immaterial reali­
ties and formalities of metaphysics, but that on the uni­
versal level even mobile things have, by reason of their
natures that transcend motion, enough stability to furnish
a basis for science. Moreover, just as the certitude about
physical beings is of an inferior sort, so is their necessity.
The science of nature unfolds by reason, not of the abso­
lute necessity following upon essence, but of the hypotheti­
cal necessity following upon final cause, that is, upon the
existing nature and its proper motions manifested through
sensory experience. In this is verified the word of St. Thom­
as, “Nothing is so contingent as not to have some necessary
aspect to it.”4
4 “Nihil enim est adeo contingens, quin in se aliquid necessarium
habeat.” (Summa Theol., I, q. 86, a. 3. Our transi.)

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From this we saw spontaneously that natural science
is essentially experimental and inductive, that it seeks, not
to deduce facts, but to explain facts in the light of their
propter quid causes and of the principles of the subject
The fourth chapter, accordingly, discussed and explained
the manner of demonstrating in the philosophy of nature.
It showed how the physicist must answer the question why
in terms of all four proper and proximate causes of every
natural thing. The following chapters made a few refine­
ments of principles and gave illustrations of the demon­
strative process.
We have gained some insight into the kind of integral
natural science that Aristotle and St. Thomas were striving
for. And we came to see that the method of natural philos­
ophy according to Aristotle and St. Thomas cannot be
understood without their concept of the nature and extent
ôf the science. Is it extravagant to suggest that when men
threw out the outmoded special science of Aristotle and
philosophers retired into the ivory tower of generalities,
men destroyed too much, that they discarded the ideals and
the method that should be guiding us today to understand
the meaning of the world in which we live?
Our study has brought us to think that this is so.
As a final word, the author feels that he cannot express
himself better than did that great Thomist, Cardinal Cajetan, as he laid down his pen in completion of his commen­
tary on De Ente et Essentia-*
Ultimo epilogue fit eorum quae dicta sunt in quo­
rum explicatione meam opinionem ita prolatam
esse volo, ut ubi veritati consentanea inventa non
fuerit et ingenio et aetati venia detur: adolescen­
tium enim adhuc ago. Ubi autem veritatis trami­
tem secuta videbitur, gratiarum debitae actiones
divo Thomae habeantur a quo quidquid veri est
didici.
5 In De Ente et Essentia, n. 156.

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