THE THOMIST
A SPECULATIVE QUARTERLY REVIEW
OF THEOLOGY AND PHILOSOPHY

EDIToRs:

THE DoMINICAN FATHERS oF THE PROVINCE oF ST. JosEPH

Publishers:

VoL. XIX

The Thomist Press, Washington 17, D. C.

JULY, 1956

No.3

REFLECTIONS ON THE NATURE OF THE
AESTHETIC

I

N his " Sacre Creur de Mont-Martre " 1 Utrillo paints in
subdued colors. He uses reds high in tint but of meager
saturation. His blues and greens are neutral and his gently
moving brush accents the evanescent shapes in a black which
rises just above the threshhold of aesthetic perception. With
careful choice of local color and disciplined strokes-with these
deliberate elements-he achieves artistic impact.
In the eye of the observer the artistic impact so achieved
depends upon perception of the elements. One must see the
redness and the greenness in their peculiar shades and tints to
grasp the aesthetic whole. Yet if one were not to see them in
their artistic setting-to see them in isolation-they would not
evoke the same reaction. They would appear as severed mem1

William P. Seligman, Collecticm. (New York).

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KEVIN A. WALL

hers of a once living substance, not having lost their external
form but deprived of their underlying meaning. The colors,
lines and masses have significance for the eye in relation to the
whole so that in this dependence they are posterior to it in
perception. To the extent to which they are prior in perception
to the whole they do not stimulate the aesthetic sense nor evoke
an aesthetic reaction. Like separated members of a once living
substance they lack the vital principle which resides in every
part of the living being: the vital principle which is totally in
the whole and totally in every part.
It would be wrong to define the eye by its organic structure
without reference to the vitalizing principle. An eye lacking
animation is only equivocally an eye. 2 So it would be wrong
to define the work of art by the integration of the parts without
relation to the aesthetic whole. A work of art deprived of inner
meaning through the absence of the animating form is artistic
by equivocation. The observer viewing the " Evening Rain on
the Great Pine Tree at Karasaki " of Utagawa Hiroshige and
seeing only a juxtaposition of oriental shapes and colors without the immanent form does not " see " that matchless work
of art.
For this reason the attempt to reach aesthetic insight by
prior analytical consideration of the elements might seem to be
futile. Yet such is not the case. For in the course of running
the eye over the picture aesthetic insight is achieved. At a
certain point in the search the eye no longer sees the part in its
isolated quality but sees it fuse with the underlying form. The
part becomes for it truly a part in the perception of the vital
principle. The insight so achieved justifies the initial analytical
procedure.
Still one must exerci!ie caution not to confuse this initial
analytical procedure with that which occurs once the unifying
principle is grasped. Then the eye in virtue of its penetration
to form proceeds to absorb more and more the articulation of
the total work of art-to see the vital principle manifesting
• Aristotle, De Anima, II, 4Ub !lO.

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ON THE NATURE OF THE AESTHETIC

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itself in varied ways in the many parts. It focuses, point by
point, upon the distinct elements in order to see, in each one,
the peculiar revelation of the underlying form. The eye must
make the first analysis to have any grasp of form at all. But it
makes the second to reach profound understanding. And it
needs both to arrive at the goal of aesthetic insight.
Sometimes artists complain about critics who confuse the
initial process of analysis with the subsequent aesthetic process.
The critic can avoid the complaint only by clearly determining
his purpose. If he intends to lead the reader through the psychological steps necessary to apprehend the form of a work of
art he must exclude from his mode of conceiving and exposing
the subject anything which supposes aesthetic insight. If he
intends to unfold in a reader already possessed of the fundamental insight a deeper knowledge of the form in its varied
manifestations he must exclude anything which has no relation
to such an insight.
The artist complains about these analytical considerations of
his work when they are confused in the mind of a critic. But he
rarely complains about another form of aesthetic analysis which
is quite different from them in that it does not lead to aesthetic
insight of itself nor does it increase it when it has already been
achieved. This is the analysis proper to philosophy. Perhaps
its very remoteness from aesthetic experience is the reason for
the indifference of the artist. It cannot be related clearly to his
work and for that reason he can take no clear stand either for
it or against it. For the most part he feels that, since it does
not yield a practical aesthetic result, it is of no interest for him.
And yet, though the philosopher's analysis may not of itself
lead to aesthetic insight or intensify it once acquired, it has a
definite relationship to the aesthetic-one which should draw the
artist to philosophize about his art. For it reveals a truth about
the work of the artist which is not had in production and contemplation itself and this truth should attract him by reason of
the love he has for his work. He should be led by that love to
seek knowledge of his art wherever it is obtainable. The philosopher considers the problem of the nature of the aesthetic

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A. WALL

because it is a problem and he needs no other motive than the
natural desire to know.a But the artist should philosophize
about the aesthetic because he loves it and because that love
impels him to comprehend it. This is true not only of the active
artist but also of anyone with aesthetic insight-he should view
the philosophy of art as St. Augustine viewed theology of the
faith, as something to be pursued by the sheer pondus amoris,
the inertia of faith itself which once set in motion will not allow
the mind to rest; 4 the inertia of the aesthetic which will not
remain satisfied with partial knowledge.
The idea which I propose to sketch out in these few pages
seems to me to arise quite naturally from such an approach.
It implies the overflow of the experience into speculation, for
it deals with a quality which predominates in aesthetic experience itself, that is to say, the quality of beatitude. Like a lens
which is selective because of its peculiar refractive index, artistic
experience accentuates this aspect and leads the Thomist mind
naturally to consider the aesthetic as a kind of partial beatitude.
If we were to ask Utrillo to describe the mental processes
involved in the painting of the" Sacre Coeur de Mont-Martre,"
most probably he would speak of them as essentially nonintellectuaL At least that is the way he would describe them if
he were to look upon the creative activity as most artists do.
Artists tend to conceive their work by contrast to the plandrawing of the architect, who elaborates the finished work from
preliminary sketches, or by contrast to the geometrician, every
step of whose activity is predictable and rationaL Utrillo
would probably accentuate the unplanned and the unpredictable and the non-rational, if not the irrational. And all of these
traits, according to the vague intuition which he shares with
Nietzsche and the existentialists, seem to correspond to the
appetitive. For Utrillo, an artist who would proceed academically from the preliminary sketch to the finished work, without
allowing the process to spring from unplanned and unpredictable feeling, would be devoid of creativity.
3 Aristotle, Metaphysics, I, 980a !il!ie.
• }<:, Gilson, St. Augustin, In trod., Chap. II.

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ON THE NA'rURE

OF THE AESTHETIC

297

Of course, it is undeniable that the intellect enters into the
process. The rational predominates in such a detailed phase
of artistic growth as the gradual domination of the medium.
But it is one thing to admit its presence and another to pose
it as the substance of the process. It would seem truer to the
artist to affirm that creative activity consists of bursts of
rational control tied together by the continuity of the appetitive drive.
The artist inclines toward this view of things because of the
quality of aesthetic experience-the pleasure which is the fruit
of creativity, and which seems rather appetitive than rational.
He conceives of the contrary quality as existing in such a purely
intellectual activity as geometrical reasoning. Not that this is
a precise conception for him since he cannot so clearly focus
on the quality of aesthetic enjoyment as he can upon the quality
of geometrical reasoning. But nevertheless it seems more appetitive than intellectual as is confirmed by the accompanying
state of the emotions. The ecstasy of the artist and the vivid
emotions, sometimes rising to the point of the painful, make
aesthetic experience seem worlds apart from what he conceives
to be the experience-quality of geometrical reasoning.
The Thomist, even with this meager datum alone to go on,
cannot fail but be struck with the similarity of the problem to
the Thomistic analysis of ultimate beatitude. For in the problem of what constitutes ultimate happiness for man there exists
a similar difficulty in determining for this operation the exact
dosage of the intellectual and the appetitive. There exists also
the similar " natural " inclination to weight the response in
favor of the appetitive. The solution of St. Thomas, that ultimate beatitude is essentially an act of the intellect, brings out
this natural inclination by awakening a certain resistance in
the mind meeting it for the first time, just as the assertion that
aesthetic experience is essentially rational awakens resistance
in the mind of the artist.
Yet it is evident, once the problem is faced in its theoretical
purity, that the basic question, in both cases, concerns the
nature of the operation which attains the desired goal: in the

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KEVIN A. WALL

one case, the goal of moral activity; and in the other, the immediate goal of artistic activity. And the answer to this fundamental question in both cases is that the desired operation is
one which is possessive since it must seize upon the goal and
thereby make it present. To answer the question concerning
the ultimate goal of human life St. Thomas considers the natures
of the possible activities which might be thought to achieve
this end: the appetitive activity and the intellectual. He excludes appetitive activity from the field of possession, for appetitive activity has a twofold function: it has desire for an object
which is absent; and it takes delight in an object which is
present. But it has no intermediate activity which effects the
presence of the object. By elimination, therefore, the activity
of possession must pertain to the intellect. 5
In analyzing artistic activity we may use the same method.
We may begin by distinguishing the two facets of the movement toward the goal: the rational apprehension of the media
and the goal; and the appetitive drive which carries us on. To
which of these does it belong to achieve conjunction with the
goal? Certainly not to the appetitive drive for this either carries us toward the goal when we have not as yet achieved the
work of art; or it takes delight in the achieved goal-the completed work of art. But it has no intermediate action rendering
us in possession of the term. By elimination then we must conclude that the rational formally unites us to the desired end
and thereby constitutes the essence of the aesthetic.
Of course the factual unfolding of the creative process is more
complicated than this idealized analysis indicates. It involves
a continual partial realization and partial delight. And in not
reserving all the quality of achievement and delight for the
final termination of the movement it makes for a certain obscurity in the experience of the process. The subjective reaction
is not analyzable in the way which the theory indicates so that
from this point of view the rational does not seem to predominate. True as this may be, I am not concerned in this article
• Summa Thsol., I-11, q. 8, a. 4.

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299

with explaining the concrete situation of the artist but with
developing the aspect of the problem which is parallel to that
of ultimate beatitude. For it seems clear to me that the parallel
character of the two questions makes possible a methodological
shortening of the investigation. What has been discovered to
be true in one (the solution of the problem of ultimate beatitude by St. Thomas) must necessarily have analogous applications in the investigation of the other (the aesthetic experience).
St. Thomas maintains, in the famous position which Aristotle before him defended, that the ultimate happiness of man
consists essentially of an act of the intellect contemplating the
highest possible object. 6 Upon this act of the intellect follows
delight in the will which is brought to rest by the obtaining of
so great a good. St. Thomas holds that the quies of the will in
the possessed good of the intellect is not itself beatitude, nor a
part of the essence, but that it pertains to its integrity. Without quies (delight) the ultimate operation of man would lack
integrity (just as a man without an actual faculty of reason
would be essentially a man but would lack the integrity of
human nature). Nevertheless it is true by abstraction that
ultimate happiness would be possessed even if the act of delight
did not co-exist with the intuition of the intellect.
If the ultimate operation of human nature is essentially intellectual then those operations which fall short of the ultimate
but share its quality must likewise essentially be intellectual.
For such operations are participations of beatitude, occupying
a median position relative to it and as is true of all means partaking of the character of the ultimate term. However they
may appear to us subjectively they must be essentially intellectual since they are intermediate between total ignorance of
the ultimate and beatifying intuition into it. Moreover, since
they pertain to the order of the intellectual and are deficient in
this order their character of intermediacy must result from a
deficiency in the intellectual. For this reason if they are studied
• Ibid.

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KEVIN A. WALL

from the point of view of the possible ways in which they can be
deficient in the perfection of the intellectual intuition of the
ultimate their types and characteristics can be determined a
pr1or1.
Now Aristotle holds that ultimate beatitude is found in the
highest operation of the noblest faculty concerning the most
perfect object-or as St. Thomas presents the same, in the
perfect possession of the greatest good. 7 An operation which,
though short of such perfection, pertains to its line (that is,
partially realizes it) must be deficient either in the quality of
possession or in the perfection of the object possessed. Let us
first consider, then, an operation which is deficient in the quality
of possession.
An imperfect intellectual possession fails to attain the intelligibility of the object even relative to the capacity of the
one who knows it. Such a deficient possession would be found,
for example, in the student of geometry who fails to see the
evidence of the principles respecting a particular figure, or who,
though seeing the evidence of the principles, fails to see their
application in complicated figures. His possession is imperfect
for it only partially assimilates the intelligibility of the object
even though all of that intelligibility is within the power of his
mind.
Quite a different situation is encountered in the knowledge
of an object which is not within the power of the mind as is
the case in our knowledge of God. Obviously some knowledge
of God is natural to us for it is found at all stages of cultural
development and in an degrees of perfection culminating in the
natural order in the scientific insight of philosophy. Whatever
may be the level of sophistication and insight in this knowledge as a partial realization of ultimate beatitude (in the line
of knowledge, fo:r it should be clear that the line of appetite
and morality as such is being methodically excluded) , it must
cause a partial realization of the happiness found at the tenn.
It must cause a certain joy in the soul though not the full joy
of beatitude because of the imperfection of the possession.
7

Ibid., q. !i!, a. 8.

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ON THE NATURE OF THE AESTHETIC

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The imperfection of possession is particularly obvious in our
knowledge of God for so much of His intelligibility lies outside of our ken. Possession is perfect to the extent to which
it renders an object ours and it is imperfect to the extent to
which it leaves the object outside of our grasp. The imperfection of our knowledge of God lies in the infinity of knowability of the divine essence exceeding our understanding. We
both possess and do not possess Him. To the extent to which
we possess Him there is happiness and a partial realization of
beatitude; but to the extent to which He eludes us there is
unhappiness and a feeling of dissatisfaction.
The knowledge which we have of God is deficient in the ratio
of possession but not in the ratio of the object possessed. God
could not be greater nor could there be anything greater than
Him. But the knowledge which we have of objects lesser than
the divine nature can be deficient and is doubly deficient-both
in the ratio of possession and in the ratio of the object known.
The things of the world which surround us are infinitely below
the perfection of God and therefore knowing them, even perfectly, cannot give us ultimate beatitude. 8 Insight into the
material world and even insight into our own souis falls short
of beatitude in the imperfection of the object. Such insight, it
is true, since it belongs to the line of the intellectual and is a
partial realization of the final insight, gives joy to the mind.
But insofar as it is imperfect, it also gives sorrow or at least
dissatisfaction and the sense of the necessity to push on. The
dissatisfaction caused by defective insight co-exists with the
joy and is so commingled as to be experimentally inseparable. It
may even, perhaps, enjoy psychological predominance according to the general psychological tendency of the unpleasant to
prevail over the pleasant. But it is clear, at least for philosophical analysis, that the dissatisfaction is only a partial aspect
of :the total experience. And this gives rise to an interesting
question: is it possible to isolate some experience in which what
is theoretically true could be rendered sensible-in which the
• Ibid., q. 5, a. 5 c.

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KEVIN A. WALL

pleasant, though not completely overpowering the unpleasant,
might predominate over the latter?
-

EXPERIENCE

SATISFACTION

PREVAILS

-1-

ULTIMATE

BEATITUDE

-

?

-- PRESENT

KNoWLEDGE

-

-

DISSATISFACTION

PREVAILS

-1

,-

"

"

oF

Gon

"

'WoRLD AND SoUL

This question arises naturally from our considerations up to
the present. For our approach to the problem up to now has
revealed the presence of factors in the phenomenon of human
knowing which we might suppose to form combinations in
varying ways and varying intensities: the factor of possession
and the factor of the possessed object. We have considered
particular combinations in which there is imperfection in the
factor of possession together with perfection (the case of the
knowledge of God) or imperfection (the case of the knowledge
of the soul or of material things) in the factor of the object
possessed. Might we not now conceive of a combination in
which the factor of possession (that which most closely resembles the ultimate) would prevail? If such an experience were
possible it would create a striking sense of satisfaction and
would be marked out among other human operations not by
reason of an essential difference but because the quality of
beatitude found in all would predominate in this one.
Of course, I am not so humble as to pose a problem in the
course of an article which I do not think I can solve. It seems
dear to me that the desired combination is found in the aesthetic experience of the artist with its many variations. This experience takes a place of pre-eminence by the satisfaction it
causes and it seems richer than the experience we have in
knowing God or our own souls or the material world, where the
element of insufficiency and imperfection predominates and
where we are more impressed by the character of defect than
by the quality of possession.
It is true that the knowledge which we have of God, even

REFLECTIONS

ON THE NATURE OF THE AESTHETIC

303

on the natural order, sometimes provokes a powerful reaction.
And it might be thought that this should constitute the most
striking approach to the quality of beatitude in present experience. But it seems to me that this is not true, for "the
natural knowledge we have of God always involves consciousness of a great mystery lying beyond. We sense the tenuous
character of our grasp upon Him and so that knowledge never
rises to the acute level of subjective satisfaction found in the
contemplation of the aesthetic. I£ this be true of our knowledge of God it is even more true of our knowledge of ourselves
or of the world. There not only is the possession imperfect but
the object possessed is also defective.
The defective character of our possession of the material
world in knowledge is surely clear in the necessity which we
sense to grow in our understanding of it. We never feel that
we have done more than approach a little closer to a nearly
infinitely removed total knowledge, so much so that the growth
of our knowledge itself increases our sense of the remaining
infinity to be crossed and thereby accentuates our dissatisfaction. We know that we have not exhausted the object and we
know this by the very act of apprehending part of its intelligibility. By reason of this knowledge we are led to multiply
and organize our concepts indefinitely as if we were seeking a
term at the end of an infinite process in which we would totally
exhaust the intelligibility of the object in an infinite number
of concepts.
The movement and dynamism of thought are rendered sen-'
sible to us in this process of multiplying concepts. For the distinction of concepts leads to the judgment and we know, in the
act of judging itself, that the object is more than we apprehend
it to be under the conception of the predicate-not more in
reality (for the reality is grasped) but more in the knowability
of that reality. 9 In judging we have knowledge of a beyondness-the beyondness of the existentialist which is the logical
basis for our feeling of dissatisfaction and of longing for a goal
• Summa Theol., I, q. 14, aa. 7 and 14; and a. 1, ad !l.

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not yet achieved. Quite contrary to this phenomenon of elusiveness the knowledge of beatitude of its very nature excludes
the sense of beyondness for in it the object is totally within
our grasp.
The logically possible experience to which we have referred
is suggested by symmetry of division:
-

PERFECT OBJECT

Gon

IMPERFECT

SouL,

-DEFICIENT- 1
PossESSION

OBJECT

-

PERFECT

-1

-

PERFECT OBJECT

-

IMPERFECT

OBJECT

GoD

BEATITUDE

BEATITUDE

It is an experience in which possession is perfect though the
object be i.mperfecL We might surmise from what we have seen
that such an experience would form a vivid content for our
minds. The ratio of possession would predominate in it and
thus it would acutely mirror the quality of the ultimate operation. But do. we, for a fact, have such an experience? Do we
have a knowledge which gives the satisfaction of total possession and eliminates the dissatisfaction of beyondness? It seems
to me that we do both in the field of mathematics and in the
realm of artistic experience, and I want first of all to consider
the effect of mathematical knowledge.
It seems to me to be a matter of experience that the reasonings of mathematics, when the mind adequately grasps them,
awaken a far more vivid response than those of philosophy or of
purely empirical science. The mind feels a great joy in finding
a rigorous mathematical deduction exemplified in a sensible
object in the field of mathematical physics. 10 We express the
joy by speaking of the beauty of the :reasoning, the elegance of
the proofs and the perfection of treatment-so many aesthetic
predicates. No other field of knowledge awakens a comparable
response. There are other intense reactions, of course, of an
10 J. C. Duncan, Astronomy
(Harper Bros., 1935), p. 204, where mention is made
of Kepler's reaction to the discovery of the third law of planetary movementthe Harmonic Law.

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ON THE NATURE OF THE AESTHETIC

305

entirely different character. The moral reaction to ethical
reasoning, for example, may have a more profound effect upon
our lives than mathematical syllogizing but this reaction pertains to the order of appetite-to the moral order and not to the
line of the intellectual participation in beatitude. Moral reasonings may guide us more profoundly but they do not evoke
the response peculiarly found in mathematical reasoning. The
reaction of the metaphysician, seeing in the complexities of
human
an exemplification of the ontology of dependent
being, may be intense but again it has not the quality, the
pleasure and satisfaction, found in mathematical thought. He
always senses a beyondness in the object-something which
seems to remove it from his grasp, not only in the sense that
he has not yet achieved total knowledge, but in the sense that
total knowledge seems unattainable. His fundamental feeling
is one of melancholy and frustration in the pursuit of a science
which does not seem proportioned to his capacity. Aristotle
brings this out when he refers to metaphysics as a divine science
-the proper science of the gods rather than of men-whose
pursuit by man must be justified. 11 The metaphysician senses
that he is as one who holds a precious thing in a vessel hardly
suited to contain it-an object which is great in itself but
imperfect by reason of the mode of the container (like the
knowledge by intuition of essence in the separated state) .12 The
mathematician, on the other hand, knows no such frustration.
He pursues an object which he knows to be quite within his
capacity. His attitude is confident and bold whereas the attitude of the metaphysician is hesitant and timid. And it is this
attitude which indicates the quality of the experience. May we
not surmise, then, that in mathematics we see the quality of
beatitude present in a science whose possession of the object
is perfect?
The factor which renders mathematics such a pleasing experience, so delightful to the mind, is that of perfect possession.
11
12

Aristotle, Metaphysics, I, 98!!b SO.
Summa Theol., q. 89, a. 1 c.

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This factor is not found only in mathematics as can be indicated again by a preliminary logical construction. In mathematics we have perfect possession (actual or potential and
understood to be actualizable) of an object which exists fundamentally independently of our minds and which we know
through the action of the world upon us. Therefore, to put the
same idea in a simpler form, we have perfect possession of an
object which we do not make. We can conceive of another possibility symmetrical to this one: perfect possession of an object
which we do make.
PERFECT PossESSION

oF IMPERFECT

OBJECT -

WHICH WE DO NOT
MAKJl--?MATHEMATlCS

Let us consider this second possibility for a moment.
If we make an. object we must have knowledge of it.
knowledge is the principle which determines an agent to act.
Knowledge, or possession of. the singular term of the action,
is the fundamental postulate of all action. 13 The thing which
we make, therefore, is necessarily known to us. But again there
are two possibilities: either the thing which we make only
partially depends upon our causality and therefore is only partially known to us; or it is totally dependent upon our action
and therefore is exhaustively known.
OBJECT WHICH WE MAKE

-1

-

ToTALLY DEPENDENT UPON OUR

-

PARTIALLY DEPENDENT UPON OUR
UsEFUL--TooL,

MACIIINE, ETC.

H the thing which our knowledge determines us to make
depends upon our causality only for accidental formal modifications-as is the case in artificial products, such as a tool,
or a machine-then our knowledge of it will not be exhaustive
and we will not experience a strikingly different quality of
human satisfaction. For the object only partly depends upon
our causality and is, therefore, only partly possessed. Our
18

Ibid., I-ll, q. 1, a.

c.

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ON THE NATURE OF THE AESTHETIC

307

knowledge of the accidental modifications is complete but our
knowledge of the total object is incomplete for it is much more
than those accidental forms-it is the material itself and the
infinite possibilities of actualization of the material. These possibilities enter into our notion of the object-the definition of
a tool, or a machine or a bridge-and make us aware that the
object .itself indefinitely exceeds our grasp. Thus we are aware
of the mysterious beyondness which produces the feeling of
dissatisfaction.
If, on the other hand, the object is totally dependent upon
our causality it is therefore totally known to us and the possession is perfect. In such a case nothing of the object lies
outside of our grasp or of our action. If there were something
beyond both, by definition it would not pertain to the object.
In such an experience the dissatisfaction is eliminated by the
awareness of total possession-of total grasp-and it must
obviously create a striking human reaction, clearly mirroring
the quality of the ultimate. Such, it seems to me, is the aesthetic experience.
The aesthetic experience is a perfect possession of an imperfect object-an object short of the ultimate desirable good.
It is perfect in possession because the object is no more than
what it is seen to be. Nothing outside of the knowledge of the
artist pertains to it. It is the decoration, harmony or composition which is totally self-sufficient, into whose definition the
beyondness of the material substratum does not enter. Anything of the matter which is not assimilated into the object by
way of intelligent apprehension does not belong to it. And that
which is assimilated is brought in by way of intentionality
determining the active capacity to produce the singular effect.
The block of marble carved into a statue is aesthetic insofar as
it is a self-sufficient intelligible whole, completely understood,
at least by the artist. Whatever lies beyond such a grasp, the
infinite possibilities of actualization of the material principle,
lies also beyond the field of the art object as such. The indefinite and the mysterious, in this sense, do not pertain to it.
The imperfection of the object aesthetically intued takes, of

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KEVIN A. WALL

course, from the satisfaction of the experience, but not in such
a way as .to lower this experience to the common qualitative
level of other human reactions. The artist, sensing this imperfection together with the delight of the achieved result which
he so thoroughly understands, is impelled to perfect it ever
more. He submits himself to a dynamism whose force is supplied by a drive toward a higher and higher productive perfection, toward a greater work, so that the intelligibility of the
product approaches closer and closer to the ultimate intelligibility of beatitude. Of course the term of the movement is always infinitely removed from the ultimate but the sense of
the movement is toward it. When the artist paints a decoration,
a design whose total entity is self-contained, he achieves a satisfying work which he totally understands. But he could achieve
an even deeper insight if he were to produce a more articulated
product. He could produce an intued deeper intelligibility and
it is this possibility which drives him on, and supplies the
movement in art. The young Beethoven and the mature Beethoven may not differ in the ratio of aesthetic possession found
in their masterpieces but certainly they differ in the perfection
of the achieved work, in its integrated intelligibility. So a
decoration may not differ in the ratio of aesthetic possession
from an etching of Rembrandt but it certainly differs in the level
of intelligibility of the object possessed and the degree of this
difference is sensed in the greater intensity of the resultant
reaction.
The dynamism which drives the artist to more complicated
expressions of his capacity within the field of the aesthetic may
be compared to the ultimate in another interesting way. For
the artist by the complexity of his product mirrors an ever
greater manifestation of his full rational intelligibility. So in
his artistic activity he approaches step by step to a product
which would be the full projection of his rationality. And of
course such a projection would be a creation by means of which
the total rational nature would depend upon his action. That
would be obviously an impossible goal. The aesthetic and the
creative converge, in that sense, to the same term-one which

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ON THE NATURE

OF THE AESTHETIC

309

can never be reached by purely aesthetic productivity. It would
be the full penetration of the total intelligibility of his own
nature, which is necessary to the Creator in order to produce
it, and is necessary to the beatified to rest in it. On the natural
plane, then, which is the plane on which we must explain the
natural aspect of the aesthetic, the full intelligibility of rational
nature is possessed by the Creator as the presupposition to
action by means of which He produces the creature. Likewise
the full intelligibility of the rational is the term of the movement of -the artist,in his creative activity. And it is also the
term possessed by the beatified.
The quality of the ultimate operation of man, then, that it be
a perfect possession of a perfect object, is necessarily mirrored
in every other operation of the intellectual order short of the
goal. Every act of the intellect in some way reflects the perfection of the ultimate. But this perfection is manifested in
greater or lesser intensity in the various human experiences.
Both theoretically and by way of actual observation it is manifested most clearly (that is to say, as most noticeably differing
from other reactions) in those actions in which the deficiency is
rather from the side of the perfection of the object than from
the side of the perfection of the possession itself. So those
operations of the mind even so sublime as the natural knowledge of God fail to achieve this quality in a striking way because the possession is imperfect. Whereas those operations in
which the perfection of possession is not deficient (such as is
found in mathematical thinking, where the object is quite
within the grasp of the human mind) tend to give this ecstatic
impression in a noticeable way. That is why we refer to mathematics in terms which are properly aesthetic: that its reasoning
processes are beautiful, harmonious and elegant. But even
mathematics is not the highest realization of this reaction.
Hather its deepest exemplification is found in that operation
where perfection of possession is without defect (because the
total entity of the object is no more than it is conceived to be)
and the perfection of the object itself transcends the mathematical (in that it is a deeper manifestation of the intelligi2

KEVIN A. WALL

bility of human nature) . This is found in artistic activity in all
of its various forms and it is to this activity that we apply the
term "aesthetic" in a most proper sense.
The artist is not, then, a simple imitator of nature. He is
rather one who takes into himself the intelligible forms of reality
and constructs with them wholes which he totally understands.
He works the material slowly until its formal possibilities
emerge before his eyes-thereby coming to an understanding
of them-and creates with these forms a self-contained whole.
Whatever of the material lies outside of this whole does not
pertain to the work. He views a sunset, an object of natural
beauty, and allows his imagination and his mind to dwell upon
it until the intelligibility of its form becomes clear to him. Then
he "paints " the sunset, that is to say, he constructs an intelligible whole out of those of its forms which he has assimilated.
The " painting " of the sunset as an artistic whole is no more
than the integration of those forms. It is not the infinite unassimilated knowability of nature. So in viewing a great painting, such as Utrillo's "Sacre Coeur de Mont-Martre," or the
line drawings of Hokusai, we feel an entirely different reaction
from that which we feel when we view the natural subject itself.
We have a sense of understanding which progresses to the extent that we approach the understanding of the artist. We feel
that the object is self-contained and enclosed, whereas the
natural subject in its natural existence gives an impression of
mystery and infinite beyondness. VVe do not advance our
understanding of the work by comparing it with nature but by
gradually apprehending the vital whole-the formal principle
according to which the artist constructed it.
The aesthetic whole, therefore, cannot be defined without
reference to the vitalizing principle any more than the eye or
the body can be defined without reference to the soul. .But this
does not mean that it cannot be apprehended by a process
which supposes no preliminary knowledge of it. If this were
not the case the aesthetic whole would either be immediately
intued or lie forever beyond our grasp. Rather, the eye of the
observer wanders casually over the parts of the finished work,

REFLECTIONS

ON THE NATURE OF THE AESTHETIC

311

with no understanding of the true principle of life, whose knowledge guides the eye of the observer with insight, till suddenly
at a certain point in its movements it no longer rests materially
upon the parts as isolated qualities but sees them fuse together
in the unity of the formal principle. Then the eye has insight
and the great joy of aesthetic delight so that it senses, short of
beatitude, the quality found in an infinitely higher degree in the
ultimate operation of human nature.

KEviN A. WALL, 0. P.
St. Albert's College
Oakland, California

THE CONCEPT OF THE INFINITE IN THE
PHILOSOPHY OF ST. THOMAS AQUINAS

I

N his Summa Theologiae, in discussing the Infinity of God,
St. Thomas defines infinite thus: " a thing is said to be
infinite by reason of the fact that it is not limited." 1 Substantially the same definition occurs in the Quaestiones Quodlibetales: " Infinity ... is predicated by reason of the fact that
[something] is not limited"; 2 and in the De Potentia: "infinity
is predicated by a negation of limit." 3 Infinity, then, is predicated by a contradiction of finiteness, per remotionem finis; it
is said of that which is unending, unbounded, interminable.
SL Thomas undertakes, in the De V eritate, in an article on
the Divine Power, to analyze the concept of the infinite; he
writes:
... infinite is distinguished in two ways. In one way, it is distinguished according to potency and act. The potential infinite is
predicated of that which consists in an uninterrupted succession, for
example: the generation ofbodie:; and the division of a continuum;
in every such case there is a potency to infinity, one thing always
following another. Actual infinity, on the other hand, would involve
something like positing a line without end. In another way, the
infinite is distinguished as necessary and contingent; the reason for
this distinction may be shown in this wise: infinity, by its nature,
is proper to the order of quantity, but quantity is predicated primarily of discrete quantity rather than of a continuum. Consequently, to determine the distinction of the necessary and the
contingent infinite, it must be observed that a multitude may be
either necessarily such, or it may be so only contingently. A multitude is a necessary multitude, if, as for example in a series of
1 •••

infinitum dicitur aliquid ex eo quod non est finitum (Summa Theol., I, q. 7,

a. l c.).

Dicitur ... infinitum ex eo quod non finitur (Quodl. III, q.
• ... infinitum dicitur per remotionem finis (De Pot., q. 1, a.

2

ob. 8.).

CONCEPT OF INFINITE IN PHILOSOPHY

OF ST. THOMAS

318

subordinated causes and effects, each member has an essential
dependence on another: thus, the soul moves the natural heat, by
which are moved the nerves and muscles, which, in turn, move the
hands, which move a stick, by which a stone is moved; in this series,
each one of the subsequent members depends necessarily on one of
the preceding. On the other hand, a multitude is ·said to be contingent when all the members contained in the multitude can be
taken, as it were, as only one and are thus indifferently one, or
many, or several; take, for example, a builder who constructs a
house and uses up a number of saws successively in the process: a
multitude of saws is not required for the construction of the house,
except contingently by reason of the fact that no single saw can
last forever. Nor does it make any difference in the construction
how many saws are employed, wherefore no one of them has a
dependence on any other, as was the case in the necessary multitude. 4

We have here a double distinction: first, a distinction of
actual and potential infinites, and then of necessary and contingent infinites (infinitum per se, per accidens) . An actual
infinite is had when something is simply without limits, like
a line with no terminal points, or an unlimited multitude whose
members are co-existent: its characteristic is an esse totum
simul. A potential infinite, on the other hand, occurs only in
instances of a succession; it consists in a repetitive process of
some kind-generation, for example, or division of a wholewhich does not come to an end. Its potentiality is grounded
in the fact that each separate event, separately considered,
could be initial or intermediate or final, or even unique; or it
could be one in a series of similar events which is without beginning and without end. Characteristic of the potential infinite
is its esse unum post aliud.
St. Thomas introduces his second distinction, that between
the infinite as necessary and the infinite as contingent, with
the remark that infinity, by its nature, is proper to the order of
quantity (infiniti ratio quantitati congruit), an observation
which he takes from Aristotle 5 and which recurs again and
again in his treatment of the subject. He adds that quantity,
• De Verit., q. 2, a. 11 c.; cf. Quorll. IX, q. l c.
See, for example, Physics III, 6 · (206a9 ff.).

6

314

GEORGE F. J. LAMOUNTAIN

primarily (per prius), is predicated of discrete, rather than of
continuous, items. (Quantification, thus, will begin in a simple
process of numbering, of taking things unum post aliud; its
further elaboration in the measurement of continua will be
achieved only through a real, or simulated, division of the
latter into numerable parts. 6 )
A discrete quantity, multitudo, can result either from some
determinant which is intrinsic to it and which necessitates its
being such, or it may occur as the effect of some contingency.
As an example of a necessary multitudo, or plurality, Aquinas
cites a series of causes and effects so interrelated that each one
exhibits a dependence sine qua non on another, a dependence
which is essential to the causal esse of the dependent: a stone
is moved by a stick, which is moved by a pair of hands, which
are moved by the neuro-muscular structure, which is energized
by the Galenic calor naturalis, which is set in motion by the
soul. If the stone is to move, all of these successively ordinated
causes, in their plurality, must cooperate: it is not the case
merely that certain causes are independently necessary; it is
precisely the multitudo causarum that is required here. The
necessity involved resides in the plurality as such: we have a
multitudo per se. Obviously, a necessary infinite will be just
such a multitudo per se which will lead back, however, not to
some first thing (like the soul, in the present example), but
which will regress endlessly through cause after cause. This
necessary infinite, the infinite series of essentially subordinated
causes, is a concept of the highest importance in the philosophy
of St. Thomas (as it was also in the thought of Aristotle). The
impossibility of. its actual existence is crucial to the first two
of the quinque viae by which he proves the Existence of God
• Quantity is said, per prius, of discrete quantities; infinity, however, is predicated
primarily of magnitude (cf. XI Metaphys., lect. 10). Actual quantity is the effect
of an actuating form, and the individual quantity of each discrete material thing
is the first formal effect of the information of prime matter, determining something
to be hoc individuum. Infinity, on the other hand, is (as will be shown later) the
result of a lack, or privation, of a formal determination in material things. Consequently, infinity will be said primarily of an unterminated, all-extensive magnitude,
in potency to determination by some quantitative form.

CONCEPT OF INFINITE IN PHILOSOPHY

OF ST. THOMAS

315

in the first part of the Summa. We shall have to return to
further consideration of it later.
A contingent plurality, multitudo per accidens, exists, Aquinas says, in those cases where the several items constituting the
plurality are, effectively, the same as any one of them alone
(quasi loco lunius ponantur) ; he cites, as an example, a hypothetical case in which several, or many, saws are used in some
piece of work because the saws, one after another, wear out.
Clearly, such a plurality has no intrinsic necessity, it being a
matter of utter indifference in the production of the effect (a
house) whether one such tool be used, or many-or even (given
the requisite time) an infinite number. This plurality arises,
not from any necessity radicated in the effect or in the mode of
its production, but from an accidental quality of the saws, that
they are too brittle, for example, or are of faulty construction,
etc.
We might schematize the twofold distinction of the infinite,
presently under discussion, as follows:
actual
necessary (per se) . . . . . . . . . . {
.
potential
Infinite
actual
contingent (per accidens) ... {
potential

l

Mindful that the infinite is proper to the order of quantity
(infiniti ratio quantitati congruit), let us confine our attention,
for the moment, to that order and inquire further into the
various kinds of infinity, as diagrammed above. First, then,
can there be an actual necessary infinite (infinitum per se
actu)? This can only mean: Carr there be a plurality which is
an actual necessary infinite, there being, obviously, no infinite
magnitude? St. Thomas, commenting on the twelfth book of
Aristotle's Metaphysics, argues that there cannot:
... if, of three things (a first, an intermediate, and a last), we
must declare which one is the cause, we will, of necessity, say that
the cause is the one that is first. We cannot say that that which is

316

GEORGE F. J. LAMOUNTAIN

last is the cause of the series ... nor that which is intermediate.
And lest anyone take the position that the intermediate never has
following it any more than one thing, which one thing is the last
(a situation which only comes about when, between two extremes, a
single intermediate is given) -to meet such a position [Aristotle]
maintains that it makes no difference whether there be only one
intermediate or several: all must agree that several intermediates
are effectively the same as one inasmuch as they all share the charactristic of being intermediate. Likewise, it makes no difference
whether the intermediates be finite or infinite in number, because,
precisely as intermediate, they cannot be the first moving cause.
Now, inasmuch as, prior to every second moving cause, there is
required a first moving cause, there must be, prior to every intermediate cause, a cause which is first and which is in nowise intermediate, as having other causes prior to itself. If, however, moving
causes are posited as infinite in number, it follows that all the causes
are intermediate. . . . So it must be that, if moving causes are
posited as proceeding to infinity, no cause will be first: but the first
cause was the cause of the whole series; it must follow, then, that
there can be no causes here at all, for if a cause is removed, everything of which it is the cause is also removed. 7

For a plurality to constitute an actual necessary infinite, its
constituent individual members must coexist in an esse totum
simul, and there must be some essential interdependence among
them. Such interdependence implies, of necessity, causal relationship, since it involves an intrinsic need on the part of the
dependent for an extrinsic principle to effect its reduction to
act. (As an example of such a necessary infinite series, one
might take a man standing aboard a ship which is supported by
a sea which is held in position by the surrounding land which is
held in place by the gravitational pull of the earth which results
from the speed of rotation of the planet-and so on, per impossible, without end.) St. Thomas maintains, in the passage just
cited, that such an actual and necessary infinite causal series
cannot be. If there are only three things given, he says, a first,
an intermediate and a last, we can only posit the first as the
cause of the series, because, obviously enough, the last is not
causal at all, and the intermediate, as intermediate, and there• II Metaphys., lect. 8 a; cf. Aristotle, Metaphysics II, 9 (994al-b 80).

C'OXCEPT OF IXFIXITE IX PHILOSOPHY

OF ST. THOl\IAS

317

fore secondary, cannot be the cause of the first. If a series is
given with more than three constituent members, all save the
first and the last will be intermediate and will, consequently,
depend, together with the last, upon the first as upon the cause
of the whole series. If the series is given as infinite, then all
save the last are intermediate and secondary; there is no first
cause, and the series remains unexplained: sublata causa, tolluntur ea quorum est causa. As Father Garrigou-Lagrange has
written:
It is contrary to reason to say that an actually existing motion can
have its sufficient reason, its actualizing raison d'etre, in a series of
movers, each one of which is itself moved by
external cause.
If all the movers receive that impulse which they transmit, if there
is not a prime mover which imparts movement without receiving it,
then motion is out of the question, for it has no cause . . . To try
to dispense with the necessity of a source is the same as saying
that a watch can run without a spring, provided it has an infinite
number of wheels ... 8

The impossibility of an infinite series of essentially subordinated causes is crucial, as was remarked above, in the first two
" ways " by which St. Thomas proves the existence of God in
his Summa Theologiae. Garrigou-Lagrange summarizes the
prima via in the following propositions:
That there is motion in the world is a certainty attested by experience .... Now, everything which is in motion is moved by another.
. . . l\l[oreover, there cannot be an infinite series of movers essentially and actually subordinated one to another. . . . We must,
therefore, conclude that there is a prime mover, who is not himself
set in motion by a mover of a higher order, and whom we call God. 0

Clearly, the third proposition above is the crux of this argument: it is through it, so to speak, that one moves f:rom the
obvious fact of motion as proximately caused to the conclusion
that there is a Prime Mover. This is a perfect dilemma, one
• God: His Existence and His Nature, trans!. Dom Bede Rose, 0. S. B. (St. Louis:
Herder, 1934) I, 9!65. Italics in the original.
• Ibid., 381-8.

318

GEORGE F. J. LAMOUNTAIN

horn of which is the affirmation of a First Uncaused Cause, the
other the postulation of an endless series of intermediate causes
which are not intermediate.
A plurality which would be an actualJ'lecessary infinite,
therefore, cannot be. There is no infinite magnitude. Consequently, for St. Thomas, there is no actual necessary infinite
in the quantitative, and hence in the material, order.
A potential necessary infinite, qua potential, would be a series
characterized by an esse unurn post aliud (infinitum potentia
sernper in successione consistit); qua necessary, it would involve
the same intrinsic interdependence, the same causal relationship, among its constituent members, that we have just found
to be impossible in examining the problem of a simultaneous
infinite plurality. Consequently, there is no material infinite
per se potentia, and so no necessary infinite of any kind, in
the material universe.
The case is not the same with the quantitative contingent
infinite (infiniturn per accidens); St. Thornas considers the
problem in the first part of the Surnrna:
A contingent infinite multitude ... is predicated when such an infinity of plurality is not necessitated but merely happens to be so.
And this can be exemplified in the situation of a builder, where a
certain plurality is required necessarily: for instance, that the virtue
of art be in his soul, that his hands be moving, and that he have
a hammer; and if this plurality were multiplied to infinity, the
builder's work would never reach completion, because it would be
dependent upon an infinite number of causes. But a plurality of
hammers which comes about because each one breaks and is replaced by another is a contingent multitude; and it makes no difference whether the builder uses one hammer, or two, or many, or
even an infinite number, provided he has an infinite time in which
to work. In this way [certain men, like Ibn-Sina and Al-Ghazali]
thought it possible for thePe to be an actual contingent infinite multitude. But this is not possible, because every multitude must fall
under some species of multitude; but the species of multitude follow
the species of numbers. No species of number, however, is infinite,
because any number is a multitude measured by unity. Wherefore,
it is impossible for there to be an actual infinite multitude, either
contingently or necessarily. Again, any multitude existing in nature

COXCEP'l'

OF INFINITE

IN PHILOSOPHY

OF ST. THO::\IAS

319

is created, and every created thing is comprehended under some
specific intention of its creator, for no agent acts without a purpose.
It is, therefore, impossible for there to be an actual infinite multitude, even contingently! 0

A contingent infinite, we are told, is an unterminated plurality which is not intrinsically necessitated, but simply happens
to be such (accidit ita esse). An example is drawn from carpentry to distinguish sharply the necessary, from the contingent, infinite. The contingent infinite exemplified-an infinity
of hammers successively used as one after another is brokenobviously does not involve the difficulty inherent in an infinite
regress of subordinated causes: it does not involve any intrinsic
contradiction. Such considerations, it seems, prompted some
of the Islamic scholastics to affirm the possibility of an actual
contingent infinite (posuerunt quod possibile est esse actu multitudinem infinitam per accidens). St. Thomas advances two
arguments against this position.
He contends first that every multitude falls under some
species of multitude, which species are ordinated according to
the species of numbers (species multitudinis sunt secundum
species numerorum). No species of number, however, can be
infinite, for the reason that number is simply a multitude, or
plurality, measured or divided by unity. Consequently, an
actual infinite multitude is impossible, whether per se or per
accidens. The case seems clear enough: as soon as a plurality
is predicated as infinite in act, it is invested with an esse totum
simul, but any such plurality can be comprehended under some
specific numerical quantity and must, therefore, be limited.
(It might, perhaps, be noted in passing that St. Thomas' argument is only against the possibility of an actual contingent
infinite; it does not touch the example of the builder who uses,
or uses up, an infinite number of hammers: such an infinity is
not actual at all, but potential. As will be evident below, St.
Thomas admits the possibility of the potential contingent
infinite.)
10

Summa 'I'heol., I, q. 7, a. 4 c.

320

GEORGE

F. J. LA:\IOUNTAIN

The second argument brought against the possibility of an
infinitum per accidens actu declares that every plurality is a
creature (since multiplication of entities is one of the effects of
matter, and every material entity as such must be a creature);
every creature, however, is comprehended under some definite
intention of its Creator: non enirn in vanurn agens aliquod
operatur. An actually existing infinite, toturn sim,ul, would lack
such determination or specification; it would be quantitatively
formless, potential and unintelligible, and, consequently, it
could not be the end or purpose of any creative act: ornne agens
agit pmpter finem.
:::a the De Aeternitate 1.l:lundi contra JJ;Jurrnurantes, we find
what is, at first sight at least, a position which is the contradictory of this. In this opusculum, Saint Thomas is endeavoring
to establish that the eternity of the world, as a mere philosophical possibility, would not be repugnant to reason; to this
end he cites elaborate arguments brought forth by St. Augustine, St. Anselm, and other Christian theologians to refute the
position that the world is de facto eternaL The fact that such
elaboration of argument was felt to be necessary, Aquinas contends, is evidence that the eternity of the wo:rld is not simply
repugnant to :reason. Among these arguments of the theologians, he notes near the end of this short wo:rk, is one which
denies the eternity of the world on the grounds that such
eternity would involve an infinity of human souls in actual
existence. This argument is not cogent, however, he continues,
because the world might be eternal without the race's being so.
"And besides," he goes on to say, pertinently to our present
problem, " it has not been shown that God could not create
actual infinites." (Et praete1·ea adhuc non est demonstratum
quod Deus non possit facere ut sint infinita actu.)
There is, it would seem, no escaping the implied contradiction
between this position and that set forth above. Perhaps,
though, we may say that the present text, dealing ex profcsso
with the Divine Omnipotence and only indirectly with the
nature of infinity, cannot overthrow the doctrine of the Summa

CONCEPT OF INFINITE

IN PHILOSOPHY

OF S'l'. TH.OMAS

3Ql

Theologiae that every multitude falls under a species of number
and is comprehended under a definite creative intention.
A similar argument obviates the possibility of an actual contingent infinite in the order of magnitude. St. Thomas considers
this question also in the Summa Theologiae:
It must be observed ... that a body, which is a complete magnitude, can be considered in two ways: namely, mathematically as
when only its quantity is regarded, and naturally as when its matter
and form are taken into account. Now it is evident that a natural
body cannot be actually infinite, because every natural body has
some determinate substantial form; and, since accidents depend
upon the substantial form, it must be the case that upon a determinate substantial form determinate accidents will be found to be
dependent, and among them quantity. Therefore, every natural
body has a determinate quantity ... Consequently, it is impossible
that any natural body be infinite .... The same is true of a mathematical body. If we should imagine an actually existing mathematical body, we should have to imagine it under some form, because
nothing is in act except by virtue of its form. Now the form proper
to continuous quantity as such is figure; such a body, therefore,
would have to have some figure. Hence, it would be finite, for
figure is given in its limits or boundaries. 11

A natural body has a specific and determinate substantial
form upon which all the accidental modifications of that body
depend. St. Thomas argues that the accidents consequent upon
such a determinate form must themselves be determinate and
limited; among these accidents is quantity. Therefore, a natural
body will have a determinate and finite quantity by reason of
its determinate and finite substantial form. This argument
might give us pause. If infinity is a Temotio finis, a lack of
determination and specificity, a privation rather than a perfection, then why could not a finite substantial form be infinite
in quantity peT accidens, that is simply privately or negatively?
Why could it not simply lack any quantitative determination?
The answer, of course, is that the Temotio finis, considered in
itself, is indeed merely negative, but the effect of this negation
is a positive increase ad infinitum in the quantity of matter
11

Ibid., a. 3 c.

GEORGE F. J. LAMOUNTAIN

united to a given fonn. Moreover, the remotio finis and the
consequent quantitative infinity of the body flow from the substantial fonn as from their sufficient principle: the fonn, by its
positive infonning action, gives infinity to the matter; the fonn
is, in a strict sense, a principium infinitatis. Consequently, it
cannot be finite. (Operatio sequitur esse, et modus operandi
modum essendi.) Every natural body, however, has a substantial form which is finite (otherwise, it would not be infanning matter at all) ; therefore, no natural body can be
infinite. There is no infinity, even contingently and potentially,
in the order of physical magnitude.
Nor can a mathematical figure (corpus mathematicum) be
infinite. Any figure we imagine (or conceive of-the imaginemur must not be taken too literally here) will have some fonn
which is the ratio by which we are able to know it; in mathematical figures, such form is the shape (figura) . Shape, however, is given in the limits, the contour (termini, fines) of the
figure; the latter is, therefore, necessarily detenninate and finite.
There is, for St. Thomas, then, no infinite magnitude, actual or
potential, necessary or contingent.
Arguments such as the foregoing, however, do not tell against
a plurality which would be a potential contingent infinite (infinitum per accidens potentia). Since it has no esse totum
simul, it does not fall under a species of number: " an infinity
of multitude is not reduced to act all at once, but successively,
because plurality can follow plurality to infinity." 12 Similarly,
since its infinity is merely accidental or incidental, no problem
arises, it would seem, by reason of its indetennination. St.
Thomas can, therefore, write:
. . . it is not deemed impossible to proceed to infinity merely contingently in a series of efficient causes, as, for example, where all
the causes multiplied to infinity are effectively the same as one
cause, their multiplication being contingent, as in the case of a
12 " ••• infinitum
multitudinis non reducitur
successive, quia post quamlibet multitudinem
infinitum." (Ibid., a. 4, ad 1).

in actum ut tatum simul, sed
potest sumi alia multitudo in

CONCEPT 0:1<' INFINITE

IN PHILOSOPHY

OF ST. THOMAS

323

workman who, contingently, uses many hammers, because, one
after another, they are broken. It is, therefore, purely accidental
to this hammer that it is used subsequently to some other hammer.
It is, in the same way, merely accidental to this man in generating
that he was himself generated by another; he generates as man, not
as the son of some other man. All men, as generating, are effectively
the same as one particular generator in the order of efficient causes.
Hence, it is not impossible for man to be generated by man unto
infinityY
The possibility of a potential contingent infinite (as has
been noted already .in passing) lies precisely in this that the
constituent members of the infinite plurality are individually
dispensable (non tenent ordinem nisi unius causae); there is no
relation of necessity among them at all, nor is there any necessity even that they be a plurality. As far as any effect of the
series is concerned, the individual causes antecedent to it might
be indifferently one or several, few or many, finite or infinite
in number. And the reason thereof is quite clear: none of the
causes in this infinite series is dependent on a preceding cause
for its causal esse. The preceding cause did, of course, effect
the coming-to-be of the subsequent cause, as an extrinsic principle of action. But that action reached its term at the instant
that the subsequent cause became an actual entity; thereafter,
the subsequent cause, however much dependent on the preceding for its fieri, is quite independent of it in its esse and,
consequently, in its esse causa: operatio sequitur esse, et modus
operandi modum essendi.
St. Thomas concedes, then, the possibility of a contingent
potential infinite in the order of quantity. (He does not, of
course, admit the actual existence of such an infinite series; to
do so would require the postulation of an eternity in which such
a series might run and would, therefore, contradict the revealed
doctrine of the creation of the world in finite time. 14 All that
he argues is the objective possibility of an infinitum per accidens potentia: such a thing could have been, although in fact
13 Ibid., q. 46, a. !'l, ad 7.
"Cf. ibid., a. !'l: "Utrum mundum incoepisse sit articulus fidei."

GEORGE

F. J. LAJ\'IOUNTAIN

it is not; its non-existence does not flow from an intrinsic impossibility rooted in an essential contradiction, as is the case
with the infinite series of essentially subordinated causes; rather,
it is radicated in a free decision of the Divine Creative WilL)
It may be well briefly to recapitulate here what has been said
of infinity in the order of quantity:
1. There cannot be an actual necessary infinite, because such a

thing would have to be an infinite multitude, or plurality,
which, qua necessary, would have to be an infinite series of
essentially subordinated causes-a series which would lack
any sufficient reason.
There cannot be a potential necessary infinite, because such
would be, again, an infinite series of subordinated causes,
existing unum post aliud, however, rather than totum simul;
it would equally lack any sufficient reason for being.
3. There cannot be an actual contingent infinite, because every
multitude falls under a determinate species of number and
every magnitude has determinate quantity as a result of
having a determinate actuating form.
4. Only the potential contingent infinite is possible in the order
of quantity, in the material order. It would involve no
intrinsic necessity, and hence no inner contradiction, in regressing ad infinitum; and it has no esse totum simul which
would confine it to a specific number.

There can, then, be no material infinite which is either actual
or necessary; only an infinite which is both contingent and
potential (infinitum per accidens potentia) is objectively possible in the order of quantity and of matter.
Before quitting this discussion of material infinity, there is a
passage of considerable length in St. Thomas' commentary on
Aristotle's Physics which ought to be noted. The passage,
which contains a comparison of infinity and perfection in the
material order, reads, in part, as follows:
[Aristotle] says ... that infinite ought to be defined otherwise than
some have proposed. Some have maintained that the infinite is
that outside of which there is nothing; it ought rather be said that
the infinite is that of which something always remains over ....
" That outside of which there is nothing " is the definition of the

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perfect and the whole, which is demonstrated by the fact that a
thing is defined as a whole when it is not lacking anything .... But
the whole and the perfect are either fundamentally the same or
closely similar in nature ... wherefore it is clear that the perfect is
that of which nothing lies outside. But nothing which is umbounded
is perfect (because the boundary is the perfection of a thing) . The
boundary, however, is the limit of that of which it is the boundary;
nothing unbounded (infinitum) or unlimited, therefore, is perfect.
It follows that the definition of the perfect does not apply to the
infinite, viz., "that outside of which there is nothing," ... dearly,
since it belongs to the whole to contain and to matter to be contained, the infinite of this [material] kind does not contain but is
contained, insofar as whatever of the infinite is in act is always
contained in something greater, because something can always be
conceived as lying beyond it. From this, however, that it is like
being in potency, not only does it follow that the infinite is contained and not containing, but two further conclusions follow also.
Of these, the first is that the infinite of this kind is unknown, because it is like matter, lacking any species or form ... ; matter,
however, is known only through form. The other conclusion, which
arises from the same premise, is that the infinite has rather the
nature of a part than of a whole, because matter is related to a
whole as part. Rightly, therefore, is the infinite taken as part, since
only some part of it, which is in act, can be known. 15
Here St. Thomas approvingly follows Aristotle in rejecting as
a definition of the material infinite " that outside of which there
is nothing" (extra quod nihil est). This definition, clearly
intended to designate material infinity, since it involves the
notion of parts, confounds the infinite with perfection and
totality. That outside of which there is nothing is a totality, a
whole, the latter being precisely that which is not deficient or
lacking in anything properly intrinsic to it. Totality, therefore,
is, or at least approximates, perfection. But a material thing
which lacks a determination (finis) in quantity is, by that very
fact, imperfect in its material nature, quantity being the first
formal effect of matter. Consequently, infinity is not a perfection in material things, nor is it susceptible of being defined
15

In VIII Libras Physicorum Aristotelis, III, 10; cf. Summa Theol., I, q.

3

a. 1,

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GEORGE F. J. LAMOUNTAIN

as " that outside of which there is nothing." On the contrary,
the material infinite is "that of which something always remains over" (cuius est semper aliquid extra). It is exactly
this inexhaustibility, this continuing unbounded residuum,
which, just because it has no term or limit, cannot be got
through, that characterizes the very essence of the infinite in
the order of quantity and matter.
Upon this definition of the infinite as "that of which something always remains over," there follows at once the fact that
the material infinite is contained rather than containing; this,
in turn, yields two further conclusions: (a) that a material
infinite could not be known, because it is always incomplete
and therefore in potency only, lacking the form needed to render it both existent and intelligible in act; and (b) that such
an infinite, because it is actualizable only unum post aliud, has
rather the nature of a part than of a whole or totality.

*

*

*

In article two, question twenty-five of the first part of the
Summa, " Whether the Power of God is infinite," the first
objection is put as follows:
Every ... infinite is imperfect, according to the Philosopher in the
third book of the Physics. But the Power of God is not imperfect.
Therefore, it is not infinite.16
The objector formulates in his major premise the Greek
cosmological concept of the infinite as the undetermined, the
incomplete, the imperfect (the concept just noted above in the
citation from St. Thomas' commentary on the Physics), and
this he opposes to the Christian theological notion of infinity
as absolute perfection. St. Thomas replies to the objection, as
follows:
It must be said that the Philosopher is speaking here of the infinite

as found in matter unspecified by any form; such is the infinite
•• Omne . . . infinitum est imperfectum, secundum Philosophum in III Phy:t.
Sed potentia Dei non est imperfecta. Ergo non est infinita (Summa Theol., I,
q.
2).

CONCEPT OF INFINITE IN PHILOSOPHY

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827

which is proper to the order of quantity. The Divine Essence is not
infinite in this manner, however, ... nor, consequently, is the Divine
Power. Whence it does not follow that the Divine Power would
be imperfect.H

St. Thomas himself has said, as we saw before, that infinity,
by its nature, is proper to the order of quantity (infiniti ratio
quantitati congruit) . And so, indeed, it is; it is to the quantitative, the extended or the multiple-to magnitude or multitude-that, in the first instance, we apply the notion of finis,
of bounds or limits (the last point or line or plane, the last
numbered item); it is in this order that, originally, we employ
the notion of being-bounded (finitum) or of being-unbounded
(infinitum). Equally evident is it that such an infinity is a
mark of imperfection, simply because it is in potency to actualization under an accidental quantitative fomi-so much we
have seen already. Sic autem non est infinita divina essentia:
the Infinity of God is a Divine Perfection.
If the infinite in matter is a sign of potency and of imperfection, while the Divine Infinity is contrariwise a perfection,
simply and absolutely, then, clearly, we have to do with an
analogical predication. The intrinsic nature of being-infinite is
simply different, according as the various kinds of infinite
beings, actual or possible, are, qua beings, simply different. We
have already encountered the analogical character of the predicate infinite in comparing magnitudes and multitudes: the same
infinite
kind of infinity simpliciter cannot be predicated of
body and of an infinite series. But here, in this objection and
its reply, we have a much more profound differentiation, a much
greater sweep of analogy, a distinction whereby infinity spells
entitative perfection or ilnperfection, according as it is said of
God or of material things. St. Thomas analyzes this analogy
in the first part of the Summa:
.. Dicendum quod Philosophus loquitur de infinito quod est ex parte materiae
non terminatae per formam, cuiusmodi est infinitum quod congruit quantitati. Sic
autem non est infinita divina essentia . . . et per consequens nee eius potentia.
Unde non sequitur quod sit imperfecta. (Ibid., ad i).

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GEORGE F. J. LAMOUNTAIN

a thing is said to be infinite by reason of the fact that it is not
limited. Now, matter is limited in a certain way by form, and form
by matter. Matter, indeed, is limited by form, inasmuch as matter,
prior to receiving a form, is in potency to many forms; when, however, it receives a form, it is limited by ito ]i'orm, on the other hand,
is limited by matter, since form, considered in itself, is common to
many things; by the fact, however, of being received in matter, it
becomes, determinately, the form of this thing. But matter is perfected by the form by which it is limited; and so the infinite, as
attributed to matter, has the natm:e of an imperfection, for it is, so
to speak, unformed matter. Form, however, is not perfected by
matter; its amplitude is, rather, contracted by the matter; hence,
the infinite, as related to for.l;ll not determined by matter, has the
character of a perfection. 18

That is infinite which is not bounded (infinitum dicitur aliquid ex eo quod non est finitum). Consequently, the intrinsic
character of infinity as such, and thereby the ontological value
of being-infinite (ens et bonum convertuntur), will depend on
the nature and the value of the entity of which it has to be
predicated. If a being is essentially actual and, therefore, a
perfection in itself, then to be infinite will be for it a further
perfection-a crowning perfection, so to say-because such a
being-infinite will mean this that no term or limit, no finis, is
set to its entitative perfection: by reason of its infinity it will
be a perfection simply and absolutely. On the other hand, in
the case of a being which is essentially and by nature imperfect
and potential, infinity spells the removal of any limit to such
imperfection; the being is, as it were, irremediably confirmed in
its essential lack of value; its purely passive capacity for becoming some value, howsoever slight, is unredeemed. There is
in such an infinite thing no shadow of concretization, formalization, or value, only an unbounded inertness, one might say by
way of figure, a gaping abyss of perfectibility in which no trace
of actual perfection is to be found.
Finitur autem quodammodo et materia per formam et forma
18 Ibid., q. 7, a. 1 c. For the analogical application of this distinction in the order
of intelligence, see ibid.,
q. 86, a. 8; I-ll, q. 80, a. 4, ad. !i!; de Verit., q. !i!,
a. !i!, ad 5,

CONCEPT OF INFINITE IN PHILOSOPHY

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:329

per materiam: form and matter can limit each other (quodammodo, it is said, because the intrinsic nature of this reciprocal
limitation is simpliciter different in either case). Matter, prior
to its information, is in potency to many forms: it is actually
nothing, potentially it can be anything material. Here is a true
infinity, a remotio finis: there is no limit to what material
determination unformed matter can have. This is, to be sure,
no quantitative infinity, such as we were considering above;
there is no question of number or shape, multitude or magnitude, at stake here; it is even irrelevant whether the number of
forms to which matter is in potency be few or many, finite or
infinite. This is a case of essential or quidditative infinity: in
the natme of unformed matter, there is no limit to its capacity
for material forms, however many, objectively, the latter may
be. In other words, so destitute of the most elementary entitative perfection is such matter, that its openness to information is simply boundless. Matter without form has an essential
infinity of imperfection; it is nothing, actually; it can become
anything, without limitation, in the order of material things.
The case is just the contrary with form. Any form is an
actuality and a principle of actuality. Those forms which are
destined for union with matter (formae 1·eceptae), if they are
considered in themselves, prescinding from their material correlative, are actualizing principles common to whole species;
they are, as it were, full and unrestricted expressions of specific
natures. They have, it is true, the capacity to inform any given
quantum of matter; this, however, is not a potency in the form,
but an aspect of its full actuality. So rich an expression of a
determinate reality is the form, so pure is it as an exemplar of
a specific nature, that it can communicate an existenial perfection to any unformed matter. The form is, therefore, a term
and goal of that potency common to all matter into which it
can be received: forma communis ad multa. Only when it has
been received in matter, when its actualizing power is united
with its correlative potency, is the form limited and bounded
in its perfection: antecedently the full and true expression of
a species as such, it becomes subsequently the form of this one

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GEORGE F. J. LAMOUNTAIN

individu,al subsumed under that species; it is contracted from
being or expressing a simple nature to actualizing an individual
thing participating that nature: forma ... communis ad multa
... per materiam ... contrahitur.
This being so, consider the character of those unreceived
forms, perfect in themselves, not ordinated to the information
of matter. Here is simple essential perfection, pure actuality,
unreceived and, therefore, unbounded by any principle of potency extrinsic to them. Matter apart from form, pure matter,
we found to be characterized by an infinity of imperfection, an
infinite capacity with no shadow of realization. But these pure
forms, being, each of them, a complete and unlimited expression, in existential act, of some possible nature, an utterance,
so to say, of a Divine Idea, whole in the fulness of its truth,
unlimited in any way in the plenitude of its specific perfectionthese forms have an intrinsic infinity of actuality. They are
radiant realizations of possible modes of reflecting the Divine
Nature Itself-each one of them perfectly and completely imaging a perfection of God to such a decree of fulness and exhaustiveness that the same image could never be repeated.
Infinity is being-unlimited, and the intrinsic character of a
mode of infinity is determined by what it is that has no limits.
In matter, it is mere potency that is unlimited an infinity; in
forms, it is actual being that has no term or bound: the former
is an infinity of imperfection, the latter an infinity of perfection
(infinitum secundum quod attribuitur materiae habet rationem
impetfecti; secundum quod se tenet ex parte forowe habet
rationem perfecti).
Can we relate this quidditative infinity with the infinity in
the order of quantity which we considered before? An actual
quantity of any kind results from the actualization of a potency
in a material thing by an accidental quantitative form. Quantitative infinity, then, must be either formal or material in
essence. It is the infinity of pure matter, the infinity of imperfection, which underlies the potential contingent infinitethe infinite process of generation, for example, or the infinite
series of divisions in a continuum: these are consequences of

CONCEPT OF INFINITE IN PHILOSOPHY

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331

the potency to many forms inherent in matter. Therein lies the
fundamental reason why such non-actual, non-necessary infinite series are held not to be intrinsically impossible. On the
other hand, where the possibility of an infinite which is actual
or necessary in the material order is denied, the denial strikes
at the possibility of a formal quantitative infinity, because the
principle of actuality or of necessity could only be the form,
never the matter. The function of a quantitative form is precisely to determine the potency of matter to be a specific shape
or number; to postulate a quantitative form which would actualize an unlimited multitude or an unbounded magnitude is to
affirm a contradiction. St. Thomas calls attention to the ontological basis of material infinity in several places:
. . . the infinite which is proper to the order of quantity is on the
part of matter. By division of a whole, we approach to matter, for
parts arise from the nature of matter; by addition, however, we
approach the whole, which has the character of form. And for this
reason, the infinite is not found in the addition of magnitudes, but
in division only.19
. . . as the infinite is found in potency in the division of a continuum, because it is in the direction of the matter ... so likewise
is the infinite found in potency in the addition of a multitude, for
the same reason. 20
Only that infinity which is rooted in the formal indifference
of prime matter (potentia ad multas formas) is intrinsically
possible in the universe of material things.
Let us return to the consideration of infinity ex parte fo1'mae.
St. Thomas concludes the passage on the analogical character of
material and formal infinity, quoted above, 21 as follows:
That ... which, of aU things, is most formal is being itself
Since, therefore, the Divine Being is not received in anything, but
Summa Theol., I, q. 7, a. 8, ad 8.
sicut infinitum invenitur in potentia in divisione continui, quia proceditur
ad materiam ... eadem ratione etiam infinitum invenitur in potentia in additione
multitudinis" (Ibid., a. 4 c.; see also a., 2, ad 8).
21 Supra, footnote 18.
19

20 •••

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GEORGE F. J. LAMOUNTAIN

He is His own subsistent Being ... it is evident that God Himself
is Infinite and Perfect. 22
The infinity of form is an infinity of perfection, because it is
an unboundedness of actual being. If this be true of forms in
general, it is a fortiori the case with that most formal of all
entities, that lpsum Esse, with Him Who commanded that He
be identified as Yahweh: Est qui est. God's Actuality is
utterly unreceived: not only is there no composition with
matter in His Divine Nature, there is no composition, either, of
essence with existence. His Essence is His Existence, or rather
He is His own Being. If there is no aspect of reception into a
limiting potency of any kind discernible in God's Being, then,
indeed, His Existence is a pure infinity of actuality. He is His
own limitless, unfathomable act of Existence, and He is likewise, simple, absolute Perfection.
From this simple and periect Infinity of God flows the necessity of His Unicity:
. . . God comprises, in Himself, the whole perfection of being.
Were there, then, several gods, they would have to differ among
themselves. Something, therefore, would be proper to one and not
to another. Thus, that one in whom the privation was found,
would not be simply perfect; were this itself a perfection, then it
would be lacking to some other of them. Consequently, it is impossible that there should be several gods. Wherefore, the ancient
philosophers, as if compelled by truth itself, when they posited an
infinite principle, posited only one such principle.23
There is a subtle psychological block to a clear and compelling
vision of formal unicity, be it the essential unicity of the angelic
species or the absolute Existential Unicity of God Himself,
which has its source in the connatural ordination of the human
intellect to material natures multiplied within the same species.
We are too accustomed to seeing the same nature repeated and
too apt to forget that it is matter which accounts for this
situation.
•• IUud . . . quod est maxime fonnale omnium est ipsum esse . . , Cum igitur
esse divinum non sit esse receptum in aliquo, sed ipse sit suum esse subsistens ...
manifestum est quod ipse Deus sit infinitus et perfectus (Summa Theol., I, q. 7,
a, l c).
•• ibid., q. 11, a. 3 c.

COKCEPT OF INFINITE IX PHILOSOPHY

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333

Two separate forms, however, can only differ in a formal
manner. If they a:re not to be unum idemque, there must
be in one fonn some quality not to be found in the other. If,
per impossibile, one were to imagine two gods, they would, to
be different deities, have to be distinguished by this that one
had a formal quality and perfection not to be found in the
other. But this immediately vitiates the possibility that the
supposed being characterized by the lack, privative or negative,
could be divine, inasmuch as such a privation per se argues a
limitation intrinsic to that being's nature and an essential composition which must deprive it of that simple and unbounded
act of existence which is God. (Such a composition, also, would
demand a ratio essendi extrinsic to the being itself, which would,
at once, mark it as a creature.) God's Infinity, as such, is the
ground of His Divine Uniqueness.
A necessary consequence of this fact is that there will be no
simple and absolute infinity outside of God: only God Himself
could be His own Infinity, just as God Himself is His own
unique Existence .
. . . a thing other than God may be infinite relatively, but not
absolutely. Thus, if we consider the infinite as it pertains to matter,
it is dear that every existing thing has some form, and the matter
is determined by that form. Since, however, the matter, according
as it is under some one substantial form, still stands in potency to
many accidental forms, that which is simply finite can be relatively
infinite; thus, wood is finite from the standpoint of its substantial
form, but it is, nonetheless, infinite, :relatively speaking, since it is
in potency to an unlimited number of shapes. Now, if we consider
the infinite as it pertains to form, it is quite evident that those
things, the forms of which are in matter, are simply finite and in no
way infinite. But if there are some created forms, not received in
matter but self-subsisting, as some hold with regard to the angels,
then such forms will be relatively infinite, inasmuch as they are not
terminated or contracted by matter. Since, however, a created form
thus subsisting has existence, and is not its own existence, it follows
that its act of existence is received and contracted to a determinate
nature. Hence, it cannot be simply infinite. 24
"Ibid., q. 7, a. !'l c.

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GEORGE :F'. J. LAMOUNTAIN

God is infinite absolutely; any other infinite can only be such
relatively. Everything existing outside of God has an intrinsic
composition in its being, whether of essence-existence and matter-form, or of essence-existence only. Entitative composition
is, in either case, the limitation of an active formal principle by
a receptive potency: such limitation :removes the possibility of
simple infinity. Thus every material fo:rm is contracted to this
individual thing, leaving only the inert and imperfect infinity of
matter ad multas formas. So also, the intrinsically unlimited
perfection of the separate angelic form, within its essential
order, is terminated in the fact that such formal infinity does
not necessitate the angel to be per se. God alone is simply and
utterly infinite; other beings, His creatures, may be relative
infinites-either potentially and contingently, as matter could
be, or actually and per se, as are the angelic spirits.
God's simple and uniquely Infinite Being is, of course, the
ground (or, more precisely, it is identical with) His infinite
Active Power: secundum hoc'potentia activa invenitur in Deo,
secundum quod ipse actu est. 25 An interesting observation on
the Infinite Divine Power is made by St. Thomas in replying to
an objection that God creates no infinites:
. . . the power of a univocal agent is completely manifested in its
effect; thus, the generative power in man can only produce another
man. But the power of an agent which is not univocal is not completely manifested in the production of its effect; the power of the
sun, for example, is not completely manifested in the production of
some animal generated by putrefaction. God is clearly not a univocal agent, for nothing else agrees with Him, either in species or
in genus.... Whence it follows that the effect produced is always
less than God's Power. But it is not necessary that the Infinite
Power of God be manifested in His producing an infinite effect.
Indeed, even were He to produce no effect at all, God's Power
would not be in vain; and the reason is that what is vain is what
is ordinated to an end which it does not attain; God's Power, however, is not ordinated to its e:ffect as to its end, rather the Power
is the end of the effect.26
26
26

Ibid., q. 25, a. !il c.
Ibid., ad !il.

CONCEPT OF INFINITE

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335

Operatio sequitur esse: as God is His Nature and His Existence, so is He His unreceived, and consequently unlimited,
Divine Power. But God is not a univocal agent; the term of
His Action is not the production of another Being. 21 The reason
why God's creative Power is not univocal is simply that, as has
been argued just above, there cannot be two simple infinite
beings per se. Consequently, His Power can never be equalled
by its effect. It is, therefore, no valid objection to the thesis
that God's Power is infinite that He creates no infinite effects.
Nor could the Infinity of His Power be called in question, or
held to be in vain, were It to have produced no effect at all.
God's Active Power, unlike all created power, is not ordinated
to any end beyond Itself, as to Its ratio; it is rather the case
that the Divine Power, Which is one with God's Being, is the
end and the reason of every effect of His Action.
As God's Being and Power are infinite, so is His Divine
Knowledge, in which he apprehends Himself. St. Thomas writes
in the De V eritate:
. . . God knows and understands and comprehends Himself, although, simply speaking, He is infinite. For God is not infinite
privatively, like the infinite which is proper to the order of quantity
and which has part beyond part unto infinity. In such a case, the
infinite, if it had to be apprehended precisely as it was infinite, so
that part was known after part, simply could not be grasped: there
would never be an end to the process of knowing. God, however, is
said to be infinite negatively, by reason of the fact that His Essence
is not limited by anything. Every form received in something is
limited according to the mode of the thing receiving it; wherefore,
since the Divine Existence is not received in anything, because He
is His own Existence, that Existence is not finite; and for the same
reason, Gbd's Essence is infinite.... Since God's cognitive Power
is infinite in the same manner as is the Divine Essence, His Knowledge is equal to his Essence, and so He attains to a perfect knowledge of Himself. For this reason is God said to comprehend Himself: not that there is any limit to what is known in comprehend21 We are speaking exclusively here of the Divine Operations ad extra; the possible bearing of. the question of univocal agency on God's Operations ad intra
exceeds the abilities of the present writer.

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GEORGE F. J. LA MOUNTAIN

ing, but b{.cause of the perfection of that Knowledge, to which
nothing is wanting. 28
God's Knowledge, being identical with His Being, is completely unreceived, and therefore unlimited and infinite. What
is more (and this, at first sight, presents a problem, at least
terminologically) God's Knowledge comprises (comprehendit,
cum, prehendere: takes in, encompasses) His Infinite Being.
Comprehensive, or exhaustive, knowledge, by a created intellect, necessarily indicates an intrinsic finiteness in the object of
such knowledge; the fact that such a thing can be got through,
can be encompassed, in a cognitive act, indicates its essential
limitation in being. On the other hand, a material infinite, an
infinity of part after part, could never be comprehended, secundum rationem suae infinitatis, simply because there is no end or
term to the parts (infinitum est cuius est semper aliquid extra).
In God's Knowledge of Himself, however, where there is, of
course, no extension, and where both Knowledge and Known
are infinite (and, indeed, identical) , the comprehensio involved
does not argue any limitation in What is known, but only a
perfect understanding, cui nihil deest-an adequation, as St.
Thomas explains elsewhere:
Transition implies a certain succession of parts; consequently, the
infinite cannot be traversed, by anything finite or infinite. Adequation, however, suffices to the ends of comprehension, for that is
said to be comprehended, no part of which is outside of the one
comprehending. "lt is not, therefore, contrary to the nature of the
infinite that it should be comprehended by an infinite. And so what
is, in itself, infinite can be said to be finite to God's Knowledge, as
comprehended, not however as traversable. 29
God alone is infinite in Being and Power and Knowledgeindeed, in all of His Divine Attributes, for the reason that He is
His Being, and all of His Attributes, distinguishable quoad nos,
are per se identical with His Being, which is, uniquely, Infinitum simpliciter. Other beings, however, can be infinite secun28 De Verit., q.
a. 2, ad 5; on God's Knowledge of infinites outside Himself,
see Summa Theol., I, q. 14, a. 12.
20 Summa Theol., I, q. 14, a.
ad

CONCEPT OF INFINITE

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dum quid-relatively,

as we saw above. In a passage parallel
to that in which the distinction between absolute and relative
infinity was made, St. Thomas says:
Every creature is finite, simply speaking, inasmuch as its act of
existence is not absolutely subsistent but is terminated in some
nature to which it is communicated. Nothing, however, prevents
some creature from being infinite relatively. Material creatures
have an infinity on the side of the matter, but they are finite on
the part of the form, which is limited by the matter in which it is
received. But created immaterial substances are finite according to
their act of existence, but infinite in that their forms are not
received in anything. Thus, we might speak of whiteness, existing
separately, as infinite precisely as white, because it would not be
contracted to any subject; its act of existence, however, would be
finite, because it would be determined to a certain specific nature. 30
The finiteness of the creature is the mark of non-necessity:
be its essence ever so exalted, and its essential perfection completely unbounded, that essence does not necessitate the creature's existence. Actual existence is a further perfection, extrinsic to, and limited, by the essence. Infinite in its proper
essential order a creature may be; it will, nonetheless, be finite
in the act of existence received into (as into a potency), and
bounded by, that essence. Such are the angelic forms, infinite
in their unreceived and therefore unlimited essences-perfect
intellectual natures, without blemish or bound; finite in their
received and bounded acts of existence.

*

*

*

In conclusion, we may resurvey briefly the concept of the
infinite as we have found it in the philosophy of St. Thomas
Aquinas. The infinite is that which is not limited, not finite.
A necessary infinite is a being which is necessarily determined to
be unlimited in some perfection by its formal nature. God, the
unique Absolute Infinite, is the perfect example of such a necessary infinite. Examples of relative necessary infinites are, in
the immaterial order, the separate angelic forms, and, in the
30

Ibid., q. 50, a. 2, ad 4.

338

GEORGE F. J. LAMOUNTAIN

material order, the impossible infinite series of subordinated
causes. An actual necessary infinite is a necessary infinite in
esse totum simul (such is God, an actual angel, or, per impossible, an infinite series of subordinated and coexistent causes).
A potential necessary infinite is an infinity radicated in the
potentiality of matter to many forms, since it involves an esse
unum post aliud; an example would be any successive series
ad infinitum.
The contingent infinite is also radicated in potency, a fact
evidenced by its intrinsic accidental character. In the material
order, an actual contingent infinite would be an actual infinite
magnitude or multitude. A potential contingent infinite would
be a non-necessary, non-simultaneous series of material beings.
GEORGE

Aquinas College,
Grand Rapids, Michigan

F. J. LAMOUNTAIN

RATIO INFERIOR AND RATIO SUPERIOR IN
ST. ALBERT AND ST. THOMAS

T

HE history of philosophy in the thirteenth century is
in part the history of a gigantic effort of constructive
assimilation. Yet the great geniuses of this period
made the assimilation with such tranquil assurance that unless
one is familiar with the sources of their writings and the often
vastly different ideas which these men reconciled, the magnitude of their accomplishment can neither be adequately understood nor fully appreciated.
A case which well illustrates the mediaeval achievement of
assimilating the wisdom of the past is the history of the theory
of ratio inferior and ratio superior-a theory which M. D.
Chenu, 0. P., considers to have been "one of the pillars of the
noetic common to all the masters of the thirteenth century.
Derived ostensibly by the mediaevals from the De
• • ." 1
Trinitate of St. Augustine, the theory seems to have had a much
older and much more complicated history. St. Augustine's own
source was very likely the Enneads of Plotinus; and from this
one source of the Enneads at least two lines of tradition can be
projected: one passing through the De Trinitate of St. Augustine and the Augustinian schools of the early middle ages;
another passing through the neo-Platonic Arabian schools represented by the Theologia of pseudo-Aristotle, the De anima of
Avicenna, and the Liber philosophiae of AlgazeL Both lines
converged momentarily but significantly-before
continuing
their separate paths to the intellectual centers of mediaeval
France,-in the writings of the eminent translator of Toledo,
1 M. D. Chenu, 0. P., "Ratio 11Uperior et inferiOT: un cas de philosophie chretienne," Laval theologique et philosophique, I (1!145), l!i!l: "En verite, nous
sommes Ia devant l'un des piliers de la noetique commune a tous les maitres du
XIII• siecle .... "

339

340

R. W. MULLIGAN

Dominicus Gundissalinus, whose own writings include a modified version of the Arabian theory of duae facies animae in
terms that clearly echo the teaching of St. Augustine on ratio
superior and ratio inferior.2
In the twelfth and early thirteenth centuries, morever, the
theory was freighted with such extrinsic problems as that of
delectatio morosa by Peter Lombard and that of synderesis by
William of Auxerre and Richard Fishacre until it almost entirely lost its original meaning. 3 The purpose of the present
essay is to trace its subsequent history in the works of St. Albert
the Great and St. Thomas Aquinas. After briefly reviewing the
theory as it is found in the writings of St. Augustine, we will
follow its development in the works of St. Albert and then its
evolution and ultimate assimilation in the writings of St.
Thomas Aquinas.
II

The human mind, St. Augustine writes in the De Trinitate/
has two principal functions: it contemplates the eternal reasons
-the universal natures that give meaning to experience-and
it guides man through the vicissitudes of life. Consequently, it
may be said to have two parts, a higher part whose object is
the eternal reasons, and a lower part whose object is corporeal
things} These "parts" are not to be understood in a material
• Cf. Dominicus Gundissalinus, De immortalitate animae, edited by Georg Billow,
Beitriige zur Geschichte der Philosophie des Mittelalters, Band II, Heft III (1897),
p. 19: 1\:Ianifestum est virtutem istam nobilem aut esse duarum facierum, quarum
altera illuminabilis est desuper, a rebus scilicet nobilibus, incorporalibus, scilicet
spoliatis a materia et ab appendiciis ipsius, altera illuminabilis a parte inferiori,
videlicet corporalium et sensibilium; aut eadem est virtus et eadem facies, sed
liberum habens vertere se in quam partem voluerit. . . .. St. Augustine uses the
term facies to describe the upper part of the reason in De diversis quaestionibus
LXXXIII, xlvi (PL 40: 80) and in his De Trinitate, XV, 7 (PL
1065).
• For a fuller treatment of the history of this theory, see author's" Ratio Superior
and Ratio Inferior: The Historical Background," The New Scholasticism, XXIX
(1955).
• St. Augustine, De Trinitate, XU, 8 (PL
999).
• It seems that St. Augustine never used the precise terms ratio inferior and ratio
superior. This terminology was introduced
Ordinarily he simply refers to
the two parts of the mind or of the reason, e. g., Ibid. XII, 7 (PL
1008); ibid.,
XII, 12 (Pf.
1007).

" RATIO

INFERIOR "

AND " RATIO SUPERIOR "

341

sense, as though they were actual divisions of the mind. 6 The
mind simply has two distinct functions; and so closely integrated are these two functions that any universal, necessary
judgment we make about any corporeal reality is the result of
their cooperation, i. e., of the lower part of the mind presenting
data to the upper part, which then judges the data according
to the eternal norms that are its own proper object. 7
The lower part of the mind or reason, he continues, is engaged
in action, which is necessarily singular, and there is always present a distinct danger that it fall victim to the appetite unless it
constantly follow the norms presented to it by the upper part of
the :reason.8 This duality in the human reason suggests to him
the duality in the human race: man, the head of the family and
the source of the general principles that are to orientate its life,
and woman, engaged in the practical details of daily life, intent
upon immediate objectives, but prone to lose sight of the universal significance of action unless properly guided. 9 However,
when the lower part of the reason submits to the rule and wisdom of the upper part, then the entire reason becomes a living
image of God. The lower part of the reason acquires the virtue
of prudence, which St. Augustine calls science, and the higher
part of the reason, transformed by its contemplation of the
eternal reasons, acquires the virtue of wisdom, the habitual
knowledge of " those things which neither have been nor will be,
but are .... " 10
• Ibid., XII, 4 (PL
1000): Cum igitur disserimus de natura mentis humanae,
de una quadem re disserimus, nee earn in haec duo quae commemoravi, nisi per
officia geminamus.
• Ibid., XII,
(PL
999): Judicamus autem de corporalibus ex ratione dimensionum atque figuramm, quam incommntabiliter manere Jr1lens novit.
1004).
• Ibid., XU, 7 (PL
• An interesting parallel is to be found in the writings of Freud: " This passage
from the mother to the father ... marks a victory of spirituality over sensuality,
and consequently a progress in civilization," Gesammelte Werke, XIV, p.
cited by L. Beirnaert in his review of M. Choisy's Le scandale de l'amour, Etudes,
CCLXXXI (1954),
(Translation ours). Beirnaert himself, loc. cit., writes as
follows concerning the role of man and woman in marriage: "Le premier pour
l'universaliser et en faire un facteur de civilisation; Ia seconde pour lui donner son
poids de matiere et sa palpitation cosmique."
10 De Trinitate, XII, l4 (PL
1010): Ea quae nee fuerunt, nee futura sunt,
sed sunt ....

4

34£

R. W. MULLIGAN

When Peter Lombard came to treat sensuality in his Sentences, he seized upon the texts of St. Augustine cited above. 11
While mentioning only briefly the contemplative function of
the upper part of the reason, he suggested that when the sacred
scriptures speak of sensuality what is often signified is the lower
part of man's reason. Again, when the problem of synderesis
arose,"2 mediaeval writers such as William of Auxerre 13 and
Richard Fishacre 14 identified synderesis with the higher part of
man's reason. The strange but brilliant genius, John of La
Rochelle, even fused the Augustinian theory of the higher and
lower powers of reason with the Avicennan doctrine of the two
visaged soul (duplex facies animae): the upper visage of the
soul is turned towards the First Truth, the lower visage, towards the objects of the senses.15
These were merely some of the teachings into which St.
Augustine's original theory had been incorporated by the middle of the thirteenth century when St. Albert the Great and St.
Thomas Aquinas began to teach and write.
11

Peter Lombard, Libri IV Sententiarnm, Il, d. 24, e. 5 (Quaraechi edition: l,

422).
10 The problem of synderesis seems to have arisen from an error made by
mediaeval copyist when transcribing St. Jerome's commentary on the Book of
Ezechiel. For a full account, see J. De Blic, S. J., "Synderese ou conscience?"
Revue d'ascetique et de mystique, XXV (1949), 146-157.
10 William of Auxerre, Summa a urea: Nobis videtur sine praeiudicio quod sinderesis est superior pars rationis et ipsa aliquando peccat. . . . Cum enim ratio inferior
per errorem decipitur, si sinderesis consulat primam formam, statim corrigit inferiorem partem rationis. Cited by 0. LoUin, 0. S. B., Psychologie et morale aux rii•
et riii• siecles, tome
(part 1), (Gembloux, 1942), p. "H!5, f. n. L
u Richard Fishacre, In 11 Sent., d. 24: Dico ergo quod sinderesis est animlll vel
mentis aspectus intuens regulas veritatis in Deo. . . . Igitur in nostro superiori
rationis sunt duo, scilicet sinderesis et conscientia. . . . Cited by 0. Lottin, 0. S. B.,
ibid., p. 808. The dispute over whether or not synderesis was distinct from the
upper part of the reason or identical with it seems to have been the origin of the
later disputes over the nature of synde:resis, i. e., is it a power .or a habit? See St.
Thomas, De Veritate, q. 16, a. l.
•• John of La Rochelle, Summa de anima, I, 48: [Solvuntnr obiectiones contra
immortalitatem] distinguendo faciem virtutis intellectivae duplicem, sci., inferiorem
et superiorem, inferiorem quae illuminatur et perficitur per comparationem ad sensibilia. . . . [Superior] illuminatur a prima veritate .. Cited by J. Rohmer, "Sur Ia
doctrine franciscaine des deux faces de l'il.me," Archives d'histoire doctrinale et
litwraire du moyen age, II (19fl7), 74.

" RATIO INFERIOR

AND " RATIO SUPERIOR"

343

III
Although the dates of all of St. Albert's writings have not
been determined with any great accuracy, it is generally agreed
that his Summa de creaturis was written around the years 12401243, his commentary on the Sentences seems to have taken
final form between 1244 and 1249, his De anima belongs to his
"Aristotelian" period (1254-1270), and his Summa theologiae,
never completed, occupied the last ten years of his life, 12701280.16 Since it is in these works that the most important texts
on ratio superior and ratio inferior occur, the dates, general as
they are, will help us to study St. Albert's theory as it developed.
The Summa de creaturis, probably a compilation of questions
given by St. Albert when he was a master of theology in Paris/ 1
contains a very interesting treatment of the two parts of the
human reason-which, incidentally, St. Albert usually designates as portio superior and portio inferior. The two "portions " of reason, St. Albert teaches here in this early work, are
simply terms used to describe two habits of the practical reason:
the term portio superior signifies the habit of wisdom, which
aids a man to act in conformity with the divine law, the term
portio inferior signifies the habit of science, which aids a man
to act in conformity with human law.18 It is for this reason,
he adds, that St. Augustine spoke of the lower part of the reason
as symbolizing woman and of the higher part as symbolizing
man; for the higher part of the reason has for its object the
unchangeable, certain principles of divine law, whereas the
lower part has for its object merely human positive law, which
changes as times change. Now, because of the superior qualities of divine law, it is naturally the norm and the guide of
human positive law, just as man, because of his superior quali16 F. Van Steenberghen,
"Les grandes syntheses doctrinales de 1!!!50 a l!!!'l"i',"
Le mouvement doctrinal du ix• au xiv• mcle, chapter 4, book
pp. !!!87-88. Vol.
XIII of Histoire de l'Eglise, directed by A. Fliche and V. Martin (Paris, 1951).
17 0. Lottin, 0. S. B., "Problemes concernant Ia Summa de creaturis," Recherches
de theologie ancienne et medicvale, XVII (1!150), 328.
18 St. Albert, Summa de creaturis, I, tr. 4, q. 69, a. 8, p. 3 (Borgnet
edition:
XXXIV, 70S).

344

R. W. MULLIGAN

ties, is the natural guide for woman. Yet, St. Albert adds, when
reason is transformed by grace, its parts are no longer merely a
symbol of man and woman; they are instead, a single image of
God Himsel£.19
The most striking feature of St. Albert's treatment of the
theory in the Summa de creaturis is that he considers the lower
and ·higher parts of reason exclusively in their practical functions. The virtue of wisdom, proper to the higher part of
reason, is a practical virtue: " Wisdom as taken here means
knowledge of divine justice, which persuades men to dispose
even temporal things according to divine, eternal reasons." 20
No mention is made of the speculative function of the higher
part of reason. And yet, strangely enough-especially in view
of the close association which had been made by many of his
contemporaries between the higher part of reason and synderesis-when he comes to treat synderesis in the present work,
he mentions the portio superior only in passing. 21 In the question concerning conscience, neither portio is mentioned at all.22
In his commentary on the Sentences of Peter Lombard,
written several years later, St. Albert is even more explicit in
his interpretation of St. Augustine's theory as being one concerned only with practical activity:
I say, without prejudice, that it seems to me that we must concede
that when St. Augustine divides the reason here he is simply speaking of the whole which perfects the movement of the rational part
of the soul-the movement of the practical reason and the appetite
of the will, but primarily that of the practical reason .... 23
'"Ibid.
•• Ibid., "ad id quod obiicitur de muliere," (Borgnet edition: XXXIV, 708) :
Dicitur hie sapientia cognitio iustitiae divinae, quae per rationes divinas et aeternas
suadet etiam temporalia disponere.
21 Ibid., II, q. 71, a. 1 (Borgnet edition: XXXV, H98).
•• Ibid., II, q. 70, aa. 1-8. (Borgnet edition: XXXV, 590 seq.).
•• In II Sent., d. 24, F, a. 10, sol. (Borgnet edition: XXVII, 408): Sine praeiudicio videtur mihi esse concedendum quod ratio quae hie dividitur ab Augustino
dicit totum quo perficitur motus ex parte animae rationalis secundum rationem
practicam et appetitum voluntatis, sed ta:nen principaliter quoad rationem
practicam ... ,

"RATIO

INlfERIOR"

AND "RATIO SUPERIOR!!

345

It is difficult to determine what actually brought St. Albert to
take this position whereby he practically ignored the speculative aspect of St. Augustine's original theory. The most plausible reason seems to be that he was influenced by his contemporaries who ordinarily treated the higher part of reason
only in its relation with synderesis.
When St. Albert comes to treat synderesis and conscience in
the present work, he departs considerably from the lines he
had laid down previously in the Summa de creaturis. Whereas
he had made little or no use of the higher or lower reason in
these questions in the Summa de creaturis, he now uses the
higher reason somewhat as Aristotle had used the particular
reason. Both the higher part of reason and synderesis are
related to the divine law, he writes, but synderesis, a "special
power," has for its object the knowledge of universal principles
of morality, whereas the higher part of reason has for its object
simply the knowledge of how these universal principles should
be applied to particular cases. Erroneous judgments of conscience arise when the higher part of reason applies the general
rules of morality incorrectly because of its own fallibility or
because the case in question is extremely complicated and thus
difficult to solve.24 The lower part of reason is simply a term
used to designate the reason together with a special habit
formed by the knowedge of the intrinsic goodness or evil of an
act, as well as by the knowledge of the relation of that act to
the common good of the state. 25 These are the only sections in
this work where he speaks of the lower and higher parts of
reason at any length, and no indication is given of the principles which made him modify his earlier teaching.
In the third work in which there is to be found discussion of
the two parts of reason, the De anima, written, it seems between 1254 and 1270, St. Albert takes a position quite similar
to that taken in the Summa de creaturis. He now holds that
"'Ibid., d. 24, F, a. 14, sol. (Borgnet edition: XXVII, 414).
•• Ibid., d. 24, L, a. 16, sol. (Borgnet edition: XXVII, 421): Ipsa est operans
circa particularia sensibilia . . . licet disponat ea ·secundum rationes non sensibiles
sed abstractas, quae sunt rationes honesti et boni civilis.

346

R. lV. 1\IUI ..LIGAN

there are three types of habitual knowledge orientated towards
action, namely, synderems, portio superior, and portio inferior.
Synderems is the dynamic possession of such general principles
of morality as " It is wrong to steal," and " I must not do to
another what I would not have him do to me." Portio superior
is a term that describes man's reason as charged or informed
with knowledge of the divine law, a knowledge which enables
man to apply with ease and assurance the principles of divine
justice to his daily life. Portio inferior designates the reason
when it possesses a thorough knowledge of the principles of
human positive law that are sanctioned and enforced by the
weight of custom-a knowledge that is essential to the formation of a good citizen. 26
The theory as found in the De anima, described above, was
altered only slightly in the Summa theologiae, a work which St.
Albert never lived to finish. The changes, however, are interesting and significant. First of all, he no longer insists upon the
exclusive practical function of the virtues of wisdom and science
described by St. Augustine as the virtues proper to the higher
and lower parts of the reason. He now admits that the portio
superior plays a role in the life of contemplation/ 7 and its wisdom is both speculative and practical. 28 The science characteristic of the portio inferior has a mixed nature too, but, as he
points out correctly, the science which St. Augustine speaks of
as being the virtue proper to the lower part of reason is totally
different from the kind of science described by Aristotle. Sci•• De anima, III, tr. 4, c. 10 (Borgnet edition: V, 409).
Summa theologiae, II, tr. 15, q. 98, m. S, sol. (Borgnet edition: XXXIII,
204) : Dicendum ergo est, quod portio superior dicitur propter officium ilia pars
mentis superior, quae extenditur ad contemplandum Deum, et rationes iustitiae
divinae quibus homo regitur secundum totum ordinem vitae suae ad formam
iustitiae divinae. Et ideo dicit Augustinus quod contemplandis et consulendis
rationibus aeternis inhaerescit. Hoc enim est officium superioris partis mentis iu
qua impressa est homini imago creationis, signata lumine vultus Dei per exemplum
iustitiae aeternae, quae est lumen sapientiae divinae.
•• Ibid., ad 8 (Borgnet edition: XXXIII, 204): Superior portio deputatur
sapientiae secundum quod sapientia dicitur scientia per altissimas causas. . . .
Scientia vero dicitur habitus intellectualis acceptus per causam et medium naturae
inferioris. Et ideo licet utraque sit virtus intellectualis, non tamen eodem modo,
nee per idem medium accepta. . . .
£T

" RATIO

I:SFERIOH " A:SD "RATIO

15CPEHIOR "

:3-47

ence as conceived by Aristotle consists in the habitual knowledge of conclusions drawn from first principles, whereas the
science spoken of by St. Augustine consists primarily in the
knowledge of human la\v, which is subject to change, involves
individual cases, and cannot be reduced to any uniform rule
from which deductions can be made-a technique essential to
the Aristotelian notion of science."9
Secondly, when SL Albert discusses synderesis and conscience
in this work, he does not assign to the portio superior the important role it had in the De anima. Moreover, the portio
inferior begins to look suspiciously like the particular reason
of Aristotle, whose function is to apply the general rules of
conduct to particular cases. He writes,
Synderesis ... has two relations. It is related to what is above
it and to what is below it. Ruled by what is above it, it rules
what is below it. From its relation to what is above, it attains
the habit of the natural law .... It is also related to the lower
reason, which treats particular cases, and, in treating them, because
of a defect of reason, will, and free judgment, it sometimes acts
precipitately. 30
•• Ibid., m. 4, ad l (Borgnet edition: XXXIII, 205); Scientia iuris humani, quae
casibus et mutationibus permixta est . . . tota die variatur, et ad uullam uniformem regulam redigi potest; ibid., ad 2: Aristoteles loquitur de scientia secundum
quod est ex primis, veris, et immediatis; et hoc modo non loquitur Augustinus de
scientia, sed secundum quod est ex coniecturis humanorum ad guberuationem vitae
humanae pertinentium. For St. Augustine, any code of ethics whose norms were
directly related to space and time would fall under the classification of science.
Thus the lives of great men would be science. See De 'l'rinitate, XII, 14 (PL 4!il:
1010): Quidquid propter exempla vel cavenda vel imitanda, et propter quarumque
rerum quae nostris accommodata sunt usibus necessaria documenta, historica cognitione colligimus. Consequently, the life of Christ (both written and as lived in
time) is the object of scientia, whereas His divine person is an object of sapientia;
and just as science should lead us to wisdom, so does our knowledge of the life
of Christ on earth lead us to the wisdom of contemplating His person now in
timeless glory. See ibid., XIII, 19 (PL 42: 1083-84).
30 St. Albert,
Summa theologiae, II, tr. 16, q. 99, m. 3, a. 2, sol. (Borgnet
edition XXXIII, 244): Duo tamen habet in se synderesis per duplicem respectum:
unum ad superius, et alterum ad inferius. A superiori regitur, inferius regit. Et per
respectum ad superius attingit habitum legis naturalis, . . . Alterum habet respectum ad rationem inferiorem quae disponit particularia: et in his propter
defectum rationis et voluntatis et liberi arbitrii aliquando praecipitatur ....

348

H.. W. MULLIGAN

Reviewing the general lines of this theory as it developed in
the writings of St. Albert, we find that in the earlier writings
there was a decided tendency to reduce St. Augustine's theory
of the lower and higher parts of reason to a very minor :role in
his own broader theory of practical activity. It was only towards the end of his life that he began to admit that the knowledge proper to the two parts of reason had a speculative-practical character. Secondly, it is clear that the hesitations and
changes in his teaching on this point over the years indicate the
genuine difficulty he felt when he tried to incorporate an Augustinian doctrine into his philosophical system, which grew more
and more Aristotelian as time went on. 31

IV
St. Thomas' treatment of the theory of the higher and lower
parts of reason (to which he usually refers as ratio superior and
ratio inferior) is even more striking evidence of the many problems faced by the great mediaeval thinkers who wanted to
assimilate the wisdom of the past.
St. Thomas first refers to the higher and lower reason in his
commentary on the Sentences, written during 1254-1257. 32
Largely because he was commenting on a section in the Sentences in which Peter Lombard had cited St. Augustine's text
on the two parts of the reason in connection with the sin of
sensuality, and also, perhaps, because of the influence of St.
Albert the Great, St. Thomas discusses here the ratio superior
and ratio inferior primarily in their relation to the appetite. 33
31 It is interesting to note that in the loagoge in libros de anima, long ascribed to
St. Albert but probably the work of one of his commentators, the portio superior
becomes the intellectus agens, and the portio inferior becomes the intellectus possibilis. See lsagoge in libros de anima, ch. 31 (Borgnet edition: V, 534). St. Thomas
refers to this teaching in his commentary on the II Sentences, d. 24, q. 2, a. 2, ad I
(Mandonnet-Moos edition U, 606): Ratio superior et inferior non differunt sicut
agens et possibile ....
32 M. Grabmann, Die Werke des hl. Thomas von Aquin.
Beitriige zur Geschichte
der Philosophie und Theologie des Mittelalters, Band XXII, Heft I/U (1949), p.
287.
•• 11 Sent., d. 24, q. 2, a. 2, sol. (Mandonnet-Moos edition: II, 605): Ratio hie
accipitur quae hoc modo se habet ad voluntatem et liberum arbitrium.

"RATIO

IJSFERIOR"

AXD "RATIO

SUPERIOR"

349

There is a hierarchy of values implied in the things that reason
considers, St. Tho:Q:laS writes, for some of the things we know
are eternal and necessary, whereas others are temporal and contingent. Since what is eternal and necessary is the cause of
what is temporal and contingent, it follows that ultimately all
our values and directive norms for action are derived from
eternal and necessary principles. As a consequence, the mind
may be said to have two kinds of knowledge of eternal things,
one practical, the other speculative. "Reason can dwell upon
eternal things in two ways: it can consider them in themselves
or it can consider them as they are rules for temporal things
that we are to dispose or carry out. The first type of consideration is within the limits of the speculative reason; the second,
however, belongs to the genus of practical reason." 34 The term
ratio superior, St. Thomas continues, simply designates the
reason as it consults "eternal and divine reasons " for counsel,
whereas the term ratio inferior designates the reason as it draws
its counsel from the created principles of morality which are
treated in moral philosophy. There is no question of the two
ratio's being separate powers. If a distinction is to be made, it
is to be made on the basis of the intellectual habits proper to
each: the higher reason is perfected by wisdom, the lower by
science. 85
Two things should be noted in this important section: first
of all, what St. Thomas means by our knowledge of the " eternal
and divine reasons," and, secondly, what St. Thomas means
by the wisdom which he speaks of as perfecting the higher
reason. With respect to the first, it is clear that when St.
Thomas speaks of the intellect's knowledge of the eternal
reason, he is referring only to that knowledge of God which we
have through discursive reasoning. There is no mention of
•• Ibid.: Ratio aeternis dupliciter inhaerere potest: vel considerando ipsa in se, vel
considerando ipsa secundum quod sunt regula temporalium per nos disponendorum
et agendorum: et prima consideratio non exit limites specuiativae rationis; secunda
autem ad genus practicae rationis pertinet.
•• Ibid.: Ratio superior et inferior non distinguuntur sicut diversae potentiae, sed
magis secundum habitum, vel quem iam actu habet, vel ad quem naturaliter ordinatur: ratio enim superior perficitur sapientia, sed inferior scientia.

350

U. W. MULLIGAN

faith, illumination, or any kind of privileged knowledge of God.
As a matter of fact, St. Thomas explicitly describes man's
knowledge of values as a knowledge that is obtained " Tl}rough
a kind of investigation and comparison"; and shortly after he
speaks of the object of the ratio superior as being " Eternal
and necessary things "-terms that would be surprisingly vague
were they supposed to describe the truths of faith. 36
The wisdom which St. Thomas asserts to be proper to the
ratio superior also deserves note, for, whereas he ordinarily
speaks of natural wisdom as a purely speculative virtue, the
wisdom described here is both speculative and practical, inasmuch as the "eternal reasons" which are the object of the
higher reason are not only the object of contemplation but also
norms and rules of action. All of our ultimate practical judgments are made by the higher reason, he writes later, and
precisely as it is perfected by this virtue of practical wisdom.37
Hence, the sapientia of which St. Thomas speaks in this section
is to be understood in a far wider sense than it usually is; and,
of course, it is far closer to the sapientia described by St. Augustine than it is to the sapientia described by Aristotle. 38
When St. Thomas comes to discuss syndereais in the Sentences, the echoes of tradition are even clearer. The very wording of the question," Is synderesis a habit or a power?" recalls
the position of William of Auxerre, who taught that syndereais
was to be identified with the mtio superior and hence was a
power. 39 St. Thomas, of course, refused to identify the two:
to him synderesis was a special habitus arising from the knowl•• lb·id.: In rebus autem quas ratio considerat, talis invenitur distinctio et ordo,
ut quaedam aeterna et necessaria, a temporalibus discreta, eis proponantur ....
•• Ibid., d. 24, q. S, a. 1, ad 5: Dico quod rationi superiori reservatur indicium
respectu ultimi, quod est executio operis: et ideo attribuitur sibi consensus in opus.
38 The sapientia of St. Augustine, though primarily speculative, directs our entire
life. See De Trinitate, XII, cc. S-4 (PL 42: 999-1000). St. Thomas himself writes
in Ill Sent., d. 85, q. 1, a. S, sol. 2: Sed tamen cognito contemplativa aeternorum
aliquando pertinet ad activam vitam, non quod sit de essentia eius, sed quia
praeexigitur ad ipsam sicut causa, dum rationes vivendi ex contemplatione aeternorum sumuntur.
•• II Sent., d. !i!4, q. !i!, a. 8.

" RATIO

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851

edge of self-evident principles in the practical ordero It is not
possible that synderesis be the same as reason, he points out,
for the knowledge proper to it is had intuitively, whereas the
operations of reason are all discursive. 40 Yet in this stage of
his development, St. Thomas did not entirely dissociate synderesis from the ratio superior and ratio inferior. In the practical syllogism that terminates in a judgment of conscience, he
writes, synderesis proposes as the major premise some general
principle such as "Whatever is evil is to be avoided." The
minor premise is supplied by the ratio superior or ratio inferior:
by the former if the particular type of act in question is forbidden by the divine law, by the latter if the particular type of
act is contrary to the created principles of justice" For example, the ratio superior will affirm that adultery is evil because
forbidden by God, and the ratio inferior will affirm that it is evil
because it is a violation of justiceo41 Synderesis, St. Thomas
adds, can never err, for it consists primarily in the habitual
knowledge of the general self-evident principles of the practical
order-the conditions of the very possibility of intelligent
action. 42 The ratio superior and ratio inferior, however, can and
do err, either because a faulty step is made in the construction
of the practical syllogism or because of ignorance as to how
certain acts are related to divine or human law. 43
The same general ideas are repeated in a later article interestingly entitled, " Can the higher spark of reason be extinguished? "-the "higher spark" being synderesis, and its
name, superior scintilla, undoubtedly derived from the earlier
doctrine that had identified synderesis with the ratio superior. 44
When St. Thomas comes to discuss the relation of reason to
•• Ibid., sol.
"Ibid., d. 24, q. 2, a. 4, sol.: Verbi gratia, synderesis hanc proponit: omne malum
est vitandum; ratio superior hanc assumit: adulterium est malum, quia lege Dei
prohibitum; sive ratio inferior assumeret illarn, quia est malum, quia iniustum,
sive inhonestum; conclusio autem, quae est adultcrium hoc esse vitandum, ad conscien tiam pertinet. . . .
c.
' 2 Summa Theol., I, q. 79, a.
"11 Sent .• d.
q. 2, a. 4, sol.
"Ibid., d. 89, q. S, a. l.

R. "\\'. MULLIGAN

the movements of sensuality, he is faithful to the tradition
established by Peter Lombard, and treats the problem almost
exclusively with reference to the higher and lower reason. 45 The
object of the higher reason, he asserts, is man's final end; hence,
it is the higher reason that passes final judgment on what is
ultimate in the practical order, namely, the act itself. Consent
to the act is, consequently, to be attributed to the ratio
superior. On the other hand, since the lower reason is not
concerned with man's final end, its primary relation is to the
means whereby some work can be carried out; and its consent
is not to the act but to the pleasure which it sees involved in
the means· towards the act. St. Thomas coordinates the two
consents, however, by pointing out that the same quality of
judgment can be made about an operation and the pleasure
involved in its execution. 46
In a later article, St. Thomas discusses the condition of the
higher reason as it is in itself and as it is when elevated by
faith. 47 He begins by pointing out that, when it is possible for
a potency to be elevated in some way to a level higher than its
own proper level, two motions are to be found in that potency
after its elevation: a sudden motion to its own proper object,
and another, distinct motion to its new object. For example, in
the sensible appetite as found in man there is a sudden connatural motion towards sensible objects; but, when the sensible
appetite is, as it were, raised from its level of a mere sense power
to a higher level through being habitually controlled by reason
and the virtues, it has a new motion, one that follows the
guidance of the intellect. In a like manner, when the higher
reason is elevated by faith and given an object essentially
higher than its own connatural object, it has a new motion
towards this object-a motion directed by faith-but nevertheless it still retains in some measure its former spontaneous,
natural motion. Hence, the ratio superior, even when informed
'"See Th. Deman, 0. P., "Le Peche de senaualite," Melanges Mandonnet,
(Paris, 1930) , 264-283.
•• I1 Sent., d. 24, q. 3, a. 1, sol. & ad 5. See also ibid., d. 24, q. 3, a. 4, sol.
•• Ibid., d. 24, q. 8, a. 5, sol.

I

"RATIO

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AND "RATIO

SUPERIOR"

353

by faith, may suddenly and, as it were, instinctively recoil
from accepting a truth of faith. When it does so, the offense is
real but not grievous. However, if after the force of faith has
made itself felt and the ratio superior still refuses to accept a
revealed truth, the offense is serious. 48
A study of the texts on ratio superior and ratio inferior in
the Sentences reveals a very significant fact: St. Thomas rarely
makes use of the theory except when his contemporaries or
predecessors had done so when commenting on the same texts
of Peter Lombard. Moreover, on several occasions when St.
Thomas might easily have had recourse to the theory, he fails
to do so. For example, when he treats the active and contemplative life, he makes no mention at all of the ratio inferior and
ratio superior. As a matter of fact, St. Thomas's deepest debt
in the articles on contemplation seems to be to Aristotle, whom
he quotes twenty-nine times, whereas he refers to St. Augustine
only four times. 49 Again, while discussing the gifts of the Holy
Spirit and especially the nature of the gift of wisdom, St.
Thomas refers to Aristotle eleven times but not at all to St.
Augustine. It is only when treating the gift of science that he
briefly mentions the ratio superior and ratio inferior, asserting
that the former is perfected by the gift of wisdom, the latter by
the gift of science. 50 In view of these facts, it seems clear that
at this stage of his development St. Thomas did not consider
the theory to be essentiaL
•• This notion of a double movement in the higher reason seems to have been
current in St. Thomas's time. St. Bonaventure rejects the idea in his commentary
on the Sentences. See his In ll Sent., d. 39, a. Q, q. S, ad 2 (Quaracchi edition:
II, 915).

•• 111 Sent., d. 35, q. 1, aa. 1-4. In this section, St. Thomas quotes St. Gregory
the Great fourteen times, Isidore of Seville four times, St. Bernard four times,
Richard of St. Victor three times, and Proclus, Averroes, Cicero, Pseudo-Dionysius,
St. Anselm once only.
50 Ibid., d.
q. Q, a. 3, sol. 2: Unde et inferior ratio quae et speculativa et
practica potest esse, perficitur dono scientiae quantum ad operahilia, scientiis vero
speculativis inquantum est speculativa. Sapientia autem rationem superiorem
quantum ad utrumque perflcit; quia superiores rationes quibus contemplandis
sapientia inhaeret, etiam operationum nostrarum regulae sunt. Uncle secundum
quod assumit eas ut regulas operabilium, sic in praxim extenditur.

354

R. W. MULLIGAN

The principal article in the De Veritate (1256-59) concerning
the ratio inferior and ratio superior is far richer in content than
any of the articles on the same subject in the commentary on
the Sentences. 51 First of all, whereas only five difficulties occur
in the corresponding article in the Sentences, in this article
there are fifteen. In the earlier work, moreover, the whole
article was written chiefly from the viewpoint of the appetite.
Here the bulk of the article is given over to a general discussion of the principles whereby powers are distinguished from
each other. Finally, whereas in the Sentences St. Thomas had
distinguished the ratio superior from the ratio inferior primarily
on the grounds that the objects of the former are eternal and
necessary while the objects of the latter are temporal and
contingent, in the De V eritate his treatment is far more profound. He first points out that potencies which are the acts
of determinate organs are specified by the nature of their objects; however, any "part" or potency of the soul which does
not use a corporeal organ in its act is not thus determined and
hence, in a certain sense, its object may be said to be infinite.
The intellectual powers of the soul fall under this later category and, consequently, they cannot be distinguished or specified simply by the formal diversity of their objects. Another
principle of specification must be used, and the only one possible seems to be the different formality (ratio) under which
each intellectual faculty knows or attains its object. By virtue
of this same principle, morever, it can be easily seen that there
is no real distinction between the ratio superior and ratio infe-rior, for the objects of both are known only insofar as they are
immaterial. It is possible, nevertheless, to distinguish mentally
the ratio superior f:rom the ratio inferior, for the objects of the
former are immaterial in themselves, whereas the objects of the
latter are made immaterial through the action of the agent
intellect. 52 Another basis for distinction can be found in the
De Veritate, q. 15, a. !i!.
Ibid., corpus: Utraque autem, scilicet superior et inferior, secundum communem
rationem intelligibilis ab anima humana apprehenditur; superior quidem prout est
immaterialis in seipsa, inferior autem prout a materia per actum intellectus agentis
51

52

" RATIO

INFERIOR " AND " RATIO

SUPERIOR "

relations that arise out of the metaphysics of knowledge; for
the intentional being possessed by our concepts of those things
which are above the soul is inferior in perfection to the being
possessed by those things in themselves, and the intentional
being constituted by our concepts of things below the soul is
superior to the being which these things have in themselves.
Hence, on the basis of the esse of its concepts, the soul is related
in two different ways: it has rights over that which is inferior
to it, duties to that which is superior. 53 Thus, with these two
principles, SL Thomas easily overcame the difficulties latent in
his presentation of the doctrine in his commentary on the Sentences; a solid basis for the rational distinction between the two
ratio's was established; and the new principle of union (the
common immateriality of their objects) pennitted him to drop
entirely the principle used earlier, namely, the fact that both
ratio's terminate in a practical conclusion. The present principle allows for a union on both the speculative and practical
levels.
St. Thomas makes another important extension of the theory
of ratio superior and ratio inferior when he comes to treat sin.
The ratio superior, he points out, does not have as its exclusive
object only what is eternal and unchangeable. Any principle
which a man might choose as the ultimate basis for his valuejudgments can be its object: "There is no one who does not
judge that something is the end of human life; and, when he
uses that as a basis for his deliberation, he is using higher
reason." 54 This notion is simply a development of St. Thomas'
denudatur. This, of course, is a decided change in St. Augustine's original theory
of the lower part of the soul, whose objects were strictly material and were not
made abstract by the intellect.
53 Ibid.:
Sunt enim quaedam naturae anima rationali superiores, quaedam vero
inferiores. Cum vero omne quod intelligitur, intelligitur per modum intelligentis:
rerum quae sunt supra animam, intellectus est in anima rationali inferior ipsis
rebus intellectis; earum vero quae sunt infra animam, inest animae intellectus
superior ipsis rebus, cum in ea res ipsae nobilius esse habeant quam in seipsis.
Et sic ad utrasque res diversam habitudinem habet, et ex hoc diversa sortitur
officia.
•• Ibid., q. 15, a. 4, ad finem: Nullus enim est qui non aestimet in aliquo esse

356

R. W. MULLIGAN

interpreting St. Augustine's phrase, " eternal reasons," in such
a way as to have it signify abstract first principles in general; 55
but it is, however, a decided modification of the original theory
as found in the writings of St. Augustine and as it was presented
in the works of many of St. Thomas's contemporaries and immediate predecessors. When St. Thomas discusses the problem
of delectatio morosa in the present work, he does not mention
either the higher reason or the lower reason in the corpus of the
article, 56 despite the fact that this problem had ordinarily been
treated
this way from the time of Peter Lombard. 57 It is
impossible to determine, of course, whether this occurred by
accident or design; but what is clear is this: that apparently St.
Thomas did not think that it was necessary to have recourse to
the theory in order to set forth his own ideas on a subject
that had been traditionally associated with it.
Similarly, when St. Thomas treats synderesis in the De Veritate, he does not mention the ratio superior or ratio inferior in
the principal part of the artide. 58 In answer to one of the arguments trying to show that synderesis is the same as ratio superior, however, he points out why there must be a difference
between the two. With characteristic moderation, he begins by
admitting that there is some resemblance between them, for
the habitual knowledge of the universal principles of law, i.e.,
synderesis, includes knowledge of some of the things which
pertain to the " eternal reasons "-for example, the principle
that God must be obeyed. Hence, there is a certain affinity
between synderesis and the ratio superior. In fact, St. Thomas
continues, synderesis has for its object certain principles that

in

finem humanae vitae; et cum ex illo deliberationem accipit, ad :rationem superiorern
pertinet.
55 Ibid., q. 8, a. 7, ad 3 (third series of replies):
Anima convertitur rationibus
aeternis inquanturn irnpressio quaedam rationum aeternarum est in mente nostra,
sicut sunt principia naturaliter cognita, per quae de omnibus iudicat ....
66

Ibid., q. 15, a. 4.

See, for example, St. Albert, In II Sent., d. !;14, F, a. 18, ad !il (Borgnet edition:
XXVII, 408); St. Bonaventure, In 11 Sent., d. 24, p. 2, a. 2, q. !;! (Quaracchi
edition: II, 581).
58 De Verit., q. 16, a. l.
57

" RATIO

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357

are also the object of the ratio inferior-for example, the principle that one must live according to reason. 59 Consequently,
there is also a certain resemblance between synderesis and the
ratio inferior. However, the ratio superior is quite different
from synderesis, because the former has for its object things
that are unchangeable by nature, whereas the latter has for its
object merely truths that are unchangeable, and an
able truth can be derived from things that are, in themselves,
contingent and changing. 60 In a sense, then, synderesis resembles both the ratio superior, whose objects are immaterial in
themselves, and the ratio inferior, whose objects are made immaterial by the action of the agent intellect.
It should be noted that in this article St. Thomas defines
synderesis as " a natural habit of the first principles of the
practical order, which are the principles of natural law." 61 By
implication, therefore, he makes the principles of the natural
law also a partial object of the ratio superior. Hence, it is not
quite accurate to present St. Thomas's theory as though the
ratio superim uses as norms for its judgments only divinely
revealed law, whereas the ratio inferior uses as its norms the
principles of natural
The ratio superior proceeds from
the principles of the law of nature as well as from those of the
law of grace; and the ratio inferior proceeds from the determinations or applications of the law of nature that are to be found
in civil legislation or from a consideration of an act's intrinsic
•• Ibid., ad 9: Synderesis neque nominat rationem superiorem neque inferiorem,
sed quid communiter habens se ad
In ipso enim habitu universalium
principiorum iuris continentur quaedam quae pertinent ad rationes aeternas, ut hoc
quod est Deo esse obediendum; quaedam vero quae pertinent ad rationes inferiores,
utpote secundum rationem esse vivendum.
60 Ibid.:
Dicitur enim a.liquid incommutabile propter incommutabilitatem naturae;
et sic divina incommutahilia sunt. Et hoc modo ratio superior incommutabilibus
intendit. Dicitur etiam aliquid incommutabile propter necessitatem veritatis, quamvis sit circa res secundum naturam commutabiles. . . . Et hoc modo synderesis
incommutabilibus intendere dicitur.
61 Ibid., corpus:
Est quidam habitus naturalis primorum principiorum operabilium,
quae sunt natura.lia principia iuris naturalis; qui quidem habitus ad synderesim
pertinet.
•• Cf. Vernon J. Bourke, Ethics (New York, 191H), p.

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R. W. MULLIGAN

decency, its utility, or general conformity with man's dignity as
an intelligent being. This point, however, will be touched on
again when we discuss St. Thomas's teaching in the Summa
Theologae.
Only two other articles in the De V eritate contain matter
relevant to the question of ratio superior and ratio inferior. In
the first, an article on conscience, St. Thomas writes that in a
practical syllogism, terminating in the judgment of conscience,
synderesis proposes as major premise some general principle
such as "Nothing is to be done that is forbidden by the law of
God." The minor premise will be drawn from the knowledge
had by the higher reason, e. g. "Sexual relations with that
woman are forbidden by the law of God." The judgment of
conscience will be formed in the conclusion, " I must abstain
from that act." 63 Similarly, synderesis may propose as major
premise some other principle such as "What is unjust is to be
avoided," and if the ratio inferior provides as minor premise the
information that a particular act is unjust, the conclusion of
conscience will be that this act is to be avoided. 64 What is noteworthy here, of course, is that it is now the function of the ratio
superior and ratio inferior to pass judgment, not on a type or
class of acts (as it was their function in the parallel passage in
the Sentences 65 ) , but on particular acts. In other words, their
function now seems to resemble very closely the function of an
Aristotelian ratio particularis. 66
The remaining significant passage in the De V eritate occurs
when St. Thomas takes up the kind of knowledge Adam had in
the state of innocence. " In its natural condition," St. Thomas
writes, " the object of the higher reason is not the divine essence
63 De Verit., q. 17, a.
corp.: Ut si ex iudicio synderesis proferatur, nihil
prohibitum lege Dei esse faciendum; et ex superiori rationis notitia assumatur,
concubitum cum ista muliere esse prohibitum lege Dei; fiet applicatio conscientiae
condudendo, ab hoc concubitu esse abstinendum.
•• Ibid.
65 II Sent., d. 24, q.
a. 4, sol. We have summarized this section earlier in this
article.
•• In the article on conscience in the Summa Tkeol. (I, q. 79, a. lS), St. Thomas
omits any mention of the ratio superior and ratio inferior.

"RATIO

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AND "RATIO

SUPERIOR"

359

itself, but certain intelligible characters flowing from God into
the mind, as well as other intelligible characters :received from
creatures. Both of these bring us to the perfection of seeing
eternal things." 67 Aside from the relevance of this passage to
a study of the use which St. Thomas made in his works of the
theory of the higher and lower reason, it shows also that for him
the object of the higher reason was not necessarily what is
received from God through revelation but it can be also those
things which we know about Him through reason alone. 68
Between 1259, which seems to be the terminal date for the
composition of the De V eritate, and 1266 when the Prima Pars
of the Summa Theologiae was begun, 69 there occur no passages
of any length or importance to this matter. The fact is worth
noting, for the period 1259-1266 covers the years during which
the Summa contra Gentiles was written. In the Prima Pars of
the Summa Theologiae, however, St. Thomas makes use of the
theory once again. The general teaching in this section of the
Summa is the same as that found in the commentary on the
Sentences and in the De V eritate; but St. Thomas' approach is
quite different and, in a sense, more comprehensive, for he now
links up the two ratio's with the two movements characteristic
of the human intelligence, namely, the "order of discovery"
and the " order of judgment."
Beginning his discussion with a citation of St. Augustine's
classical description of the higher reason as that " which contemplates and takes counsel from what is eternal," and of the
67 De Ve1·it., q. 18, a. l, ad 9: Superioris rationis obiectum, secundum conditionem
naturae, non est ipsa divina essentia, sed rationes quaedam a Deo in mentem influentes, et a creaturis acceptae, quibus ad aeterna conspicienda perficimur. See also
Ibid., q. 18, a. 2, corp.: Ita igitur in homine duplex cognitio erat: una qua cognoscebat Deum conformiter angelis per inspirationem internam: alia qua cognoscebat Deum conformiter nobis per sensibiles creaturas.
68 The source of St. Thomas' theory of Adam's infused knowledge was probably
what Peter Lombard wrote in II Sent., d. 28, c. 8 (Quaracchi edition: I, 418):
Cognitionem quoque Creatoris primus homo habuisse creditur. Cognovit enim ...
quadam interiori aspiratione, qua Dei praesentiam contemplabatur.
Cf. Hugh of
St. Victor, De sacramentis, I, vi, 14 (PL 176: 271).
•• See M. Grabmann, Die Werke des hl. Thomas von Aquin. Beitriige zur Geschichte der Philosophie ... , Band XXII, Heft 1/'J, (1949), p. 29'},.

360

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lower reason as that " which is intent on temporal things," St.
Thomas points out that there is a certain order in our knowledge of these two kinds of things, for, although it is true that
our knowledge of temporal things is the medium whereby we
know " things eternal," 70 it is also true that, in a certain sense,
our knowledge of things eternal is a medium whereby we know
temporal things. He explains this reciprocal relationship as
follows. In the order of discovery, the mind reasons from temporal things to a knowledge of the existence and attributes of
God. Once having obtained this kind of knowledge, the mind
reflects again upon nature and sees it, no longer in isolation,
but dynamically directed towards God, its final end. The judgments it makes upon nature as a consequence of this new,
richer knowledge, belong to the " order of judgment "-the via
iudicii. 71
The " order of discovery " is proper to the ratio inferior and
is subordinate to the " order of judgment," proper to the ratio
superior, since it is a means towards it. Moreover, although it
is possible to distinguish the two orders, the motion of reason is
but one-" the order of judgment" constituting but the term
or perfection of the movement of the mind, begun with the
"order of discovery." Consequently, there is no real distinction
between the ratio superior and ratio .inferior. They are simply
two functions of one power or potency. 72
Sum1na Theol., I, q. 79, a. 9, corp.
Ibid.: Nam secundum viam inventionis, per res temporales in cognitionem devenimus aeternorum . . . ; in via vero iudicii, per aeterna iam cognita de temporalibus iudicamus, et secundum rationes aeternorum temporalia disponimus. This
whole section seems to be a development of what St. Thomas wrote earlier, in
connection with conscience, in De Verit., q. 17, a. 1, corp.: Et haec duplex via in
operativis distinguitur secundum duplicem viam quae est in speculativis; scilicet
viam quae est inveniendi et iudicandi. This notion is applied for the first time to
the ratio superior and ratio inferi01; in the Summa Theol., loc. cit.
72 Summa Theol., I, q. 79, a. 9, corp.:
Sed eadem potentia rationis est, ad quam
pertinet et medium et ultimum. Est enim actus rationis quasi quidam motus de
uno in alind perveniens; idem autem est mobile quod pertransiens medium pertingit
ad terminum. Unde una et eadem potentia rationis est ratio superior et inferior.
Sed distinguuntur, secundum Augustinum, per officia actuum, et secundum diversos
habitus; nam superiori rationi attribuitur sapientia, inferiori vero scientia.
70

71

"RATIO

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SUPERIOR "

361

Two things are to be noted in this striking section of the
SUJnma. First of all, since the knowledge of God which the

ratio superior ultimately attains is had through creatures, there
is no question but that this is natural knowledge of Him, not
supernaturally revealed knowledge. Secondly, our knowledge
in a certain sense makes a complete circle. "\Ve are led to a
knowledge of things eternal through our knowledge of created
things; but, once we acquire knowledge of the former, we make
new judgments about created reality. In other words, once the
intellect in that part of its movement called " the order of
discovery" attains a knowledge of the ultimate cause o£ things,
as it would from the evidence of generation and corruption,
"the order of discovery" is replaced by "the order o£ judgment." The object of reason is no longer created obje.cts and
secondary causes but the first cause; and it is now the ratio
superior that is operative. The wisdom o£ metaphysics replaces
the science of natural philosophy; and, in its sapiential contemplation of God, the mind finds in Him the source of all
truths, of all being, of all principles. God is to be the supreme
guide in life, for all other truths are judged by their conformity
with this subsistent Truth: " The principles which the lower
reason uses are drawn from and directed by the principles of
the higher reason." 73 It is in this passage that St. Thomas
succeeds most fully, we believe, in assimilating St. Augustine's
theory of the two parts of the soul into his own system of
philosophy. Without altering the original significance and inspiration of St. Augustine's thought, St. Thomas successfully
disengaged the theory from its neo-Platonic implications as well
as from the clumsy additions of the early mediaevals, to make it
a coherent description of the dialectical activity of the human
mind moving from creatures to God and returning once again
to creatures. 74
•• Ibid., ad !i!: Principia quibus utitur inferior ratio, deducuntur et diriguntur a
principiis superioris rationis. Cf. lbd., I-II, q. Hi, a. 4, corp.: Manifestum est autem
quod superior ratio est quae habet de omnibus iudicare, quia de sensibilibus per
rationem iudicamus; de his vero quae ad rationes humanas pertinent, iudicamus
secundum rationes divinas, quae pertinent ad rationem superiorem.
•• Commenting on this passage in the Summa, the late J. Peghaire, C. S. Sp ..

R. W. MULLIGAN

Yet it cannot be said that St. Thomas considered the ratio
superior and ratio inferior as such to be an essential or integral
part of his system. For instance, when he discusses synderesis
in the Summa, he makes no use of them, despite the fact that
explicit reference is made to SL Augustine's theory in one of the
objections. 75 Again, in the principal article in the Summa on
conscience, no mention at all is made of either the ratio superior
or the ratio inferior. 76
St. Thomas seems to have composed the Quaestiones Dispntatae de Malo after finishing the first part of the Summa and
before beginning the first part of the second section of this
latter work. 77 In the De Malo, he makes very limited use of
the ratio superior and ratio inferior, and, in the only passage
in which he speaks of them at any length, he simply repeats
what he had written in earlier works, namely, that moral judgments based on " human " standards of utility or decency are
predicated of the ratio inferior. 78 He also :refers to the two
movements of the ratio superior, one " natural " and spontaneous, the other under the control of faith-a notion which,
as we have seen, appeared in his commentary on the Sentences. 7 "
There are only two passages of any significance to this matter
in the Prima Secundae, which was probably written shortly
after the De M alo.80 In the first, St. Thomas simply applies the
wrote in his lntellectus et ratio selon S. Thmnas d'Aquin (Paris, 1939), p. 149:
Nons ne connaissons Yraiment Ia nature des choses creees qu'en les pla<;ant a Ia
lumiere des choses divines, puisque dans 1.m monde comme le concevaient saint
Thomas et saint Augustin, Ia valeur veritable et par consequent Ia vraie nature
d'un etre depend de Ia place qu'il occupe dans l'ordre voulu par Ia :Providence
de Dieu.
76 Summa Theol., I, q. 79, a. 12, obj. 3.
76 Ibid., a. 13. See, however, Quodlib. III, a. 26, corp.
77 See F. Van Steenberghen,
Siger de Brabant d'apres se-S oeuvres inedites (Louvain, 1931), vol. I, p. 749.
78 De Malo, q. 7, a. 5, corp.:
Si quidem deliberatio rationis sumitur in aliquibus
rationibus temporalibus, puta quod aliquid sit utile vel inutile, decens vel indecens
secundum opinioncm hominum, dicetur esse peccatum in inferiori ratione; si vero
deliberatio fiat per rationes aeternas, puta quia est concordans vel discordans praecepto divino, dicetur esse peccatum in ratione superiore.
79 II Sent., d. 24, q. 3, a. 5.
80 See F. Van Steenberghen,
loc. cit.

"RATIO

INFERIOR"

AND "RATIO

SFPERIOR "

:363

principles he had laid down concerning the nature of the two
ratio's in the Prima Pars. Every practical judgment that immediately precedes action, he points out, is ultimately derived
from a hierarchy of values: we judge sensible things by our
reason, and, in turn, we judge human principles by divine reasons or standards. Hence, the judgment o£ final decision or
consent to an act must be predicated of that power whose
object is the divine reasons or principles, and this power is the
higher reason. 81 In the second passage of any interest, St.
Thomas again asserts that the standards which the ratio inferior
uses in its moral reflections are "created" standards, such as
the standard of private or social utility, whereas the norms the
ratio superior uses are the commandments of God, as known by
faith or by reason. The relation of an act to human" created"
standards is studied by the philosopher; its relation to the
eternal law of God is studied by the moral theologian. 82 It may
seem strange to many to find St. Thomas putting ethical considerations concerning the natural law into the realm of moral
theology; but it must be remembered that to St. Thomas and to
most of his contemporaries moral philosophy or ethics usually
meant the Aristotelian notion of ethics, which considered man
only as a part of the city or state. St. Albert the Great expressed this traditional view when he wrote: " The good of man
81 Summa Theol., I-II, q. 15, a. 4, corp.:
Manifestum est autem quod superior
r ..tio est quae habet de omnibus iudicare, quia de sensibilibus per rationem indicaruns; de his vero quae ad rationes humanas pertinent, iudicamus secundum rationes
divinas, quae pertinent ad rationem superiorern. Et ideo quamdiu incerturn est an
secundum rationes divinas resistatur vel non, nullu.m indicium rationis habet
rationem finalis sententiae. Finalis autem sententiae de agendis est consensus in
actum. Et ideo consensus in actum pertinet ad :rationem superiorem, secundum
tamen quod in ratione includitur ....
•• Ibid., q. 74, a. 7, corp.: Manifestum est autem quod actus humani regulari
possunt ex regula rationis humanae, quae sumitur ex rebus creatis, quas naturaliter
homo cognoscit; et ulterius ex regula legis divinae, ut supra dictum est. Uncle cum
regula legis divine sit superior, consequens est ut ultima sententia, per quam
indicium finaliter terminatur, pertineat ad rationem superiorem, quae intendit
rationibus aeternis. The passage to which St. Thomas refers in this text is ibid.,
q. 71, a. 6. Here in reply to the fifth objection he writes: Dicendum quod a theologis consideratur peccatum praecipue secundum quod est offensa contra Deum;
a philosopho autem morali, secundum quod contrariatur rationi.

364

R.

vv·. MULLIGAN

discussed by philosophers is simply his good as a citizen " ; 83
and St. Thomas himself declared: " The Philosopher's intention is to treat the virtues as they are ordered to civil life.
Although the " Philosopher " mentioned here is, of
• • ." 84
course, Aristotle, St. Thomas considered Aristotle's ethics as
being typical of a purely philosophical ethics. 85 Hence, as soon
as man's relation to God is considered, we go beyond the
"Ethics of the City" and enter into the realm of theology, for
man's final end transcends his function as citizen and his
natural capacities. 86 Yet this does not mean that the norms on
which the ratio superior makes its moral judgments are exclusively theological; for the primary object of the ratio superior
is the eternal law, of which the law of nature is a part.S 7 Hence,
the norms used by the higher reason are the norms of the law
of nature, as well as of the law of grace. 88
The Secunda Secundae, composed during the years 1271-72,
is St. Thomas' longest and most detailed treatise on the virtues,
but it contains very few :references to either the ratio superior
or to the ratio inferior. There are occasional allusions to St.
Augustine's teaching on wisdom as belonging to the higher
reason and science to the lower, 89 and, at one point contemplation is said to be prior to action because the contemplative
"pa:rt" of our :reason, the ratio superior, directs the active
•• ln Ill Sent., d. 27, A, a. l, ad l (Borgnet edition: XXVIII, 509).
•• Summa Theol., II-II, q. HH, a. 1, ad 5.
•• IV Sent., d. H, q. l, a 1, tertia quaestio-ad 4: Philosophi autem non consideravemnt virtutes dirigentes in actibus hnmll.llis prout ordinantur ad Dei providentiam, sed prout ordinantur ad bonum humanum. See M. D. Chenu, 0. P.,
" Les ' Philosophes ' dans Ia philosophie chretienne medievale,'' Revue du sciences
phil. et t!Wol., XXVI (1937), 27-40.
•• Ill Contra Gentiles, c. 147: ffitimus finis hominis in quadam veritatis cognitione constitutus est quae naturalem facultatem ipsius excedit. For a splendid
analysis of St. Thomas's teaching on man's ultimate end, see the unpublished
thesis of Jules J. Toner, S. J., The Notion of Spiritual Nature according to St.
ThomWJ Aquina11 (University of Toronto doctoral dissertation, 1952).
•• Summa Theol., I-II, q. 91, a. 2, c.: Et talis participatio legis aeternae in
rationali creatura lex natural is dicitm:·.
•• Ibid., q. 71, a. 6, ad 5: Per legem aetemam regulemu:r in multis [italics ours]
quae excedunt rationem humanam, sicut in his quae sunt fidei.
•• E. g., ibid., II-II, q. 45, a. 8, c.

" RATIO INFERIOR " AND " RATIO SUPERIOR "

365

"part," the ratio inferior.90 However, in this long treatise on
the moral life, no question, no article is devoted to a detailed
exposition of the theory.
The third part of the Summa, which belongs to the years
1272-73, similarly contains very few references to the two
ratio's. It is only when St. Thomas comes to treat the sufferings
of Christ that he makes any extensive use of the theory. He
writes, for example, that although the entire soul of Christ
suffered when its lower "·parts" suffered, nevertheless His ratio
superior considered in itself did not suffer, for it was firmly
fixed upon God. 91 In the succeeding article, St. Thomas elaborates somewhat on this point, asserting that although the
higher part of the soul of Christ did not suffer, since it enjoyed
the beatific vision at all times, nevertheless it can be said that
His entire soul suffered, for His sorrow was in His soul, the
substantial form of His body. 92 It should be noted, however,
that the use of the ratio superior in connection with the sufferings of Christ was probably quite common during the time
St. Thomas wrote the third part of the Summa. It is found, to
mention only two examples, in the works of both St. Albert and
St. Bonaventure, who treat it as being a fairly well-known
teaching. 93 Hence, St. Thomas's use of this notion may indicate, not that he held it to be important, but simply that he
hesitated to abandon a traditional treatment of a theological
problem such as the knowledge and sufferings of Christ.

00

01

Ibid., q. 182, a. 4, c.
lbid., III, q. 46, a. 7, c.: Superior ratio non patiebatur in Christo ex parte sui

obiecti, scilicet Dei, qui non erat animae Christi causa doloris, sed delectationis et
gaudii. This whole question had to be handled with great delicacy, for St. Albert
writes In Ill Sent., d. 15, A, a. 8, sol. (Borgnet edition: XXVIII, 270) : Fuit enirn
praedicatum quod Christi anima non fuisset passa secundum partem superiorem a
quodam abbate, sed Parisiis ab universitate Magistrorurn pro haeresi condemnatum
est.
•• Summa Theol., Ill, q. 46, a. 8, corp, and ad I.
•• See St. Albert, In Ill Sent., d. 15, A, a. 8 (Borgnet edition: XXVIII, 269);
St. Bonaventure, In Ill Sent., d. 16, a. 2, q. 2 (Quaracchi edition: II, 490-97).

366

R. W. MULLIGAN

v
Reviewing the texts of St. Thomas in which the ratio superior
and ratio inferior play a role, one is led to conclude that the
doctrine is not a critical one for his general noetic. The same
impression is reinforced if one notes the numerous passages in
his works where he might easily have made use of the theory
but failed to do so.94 Moreover, in his commentary on the
Sentences, SL Thomas employs the notion of ratio superior and
ratio inferior almost exclusively in those sections where his contemporaries had employed it when commenting on the text of
Peter Lombard-a fact which seems to indicate that St. Thomas
was merely following an accepted procedure. 95 The bulk of St.
Thomas' treatment of· the two ratio's in his more independent
works, the De Veritate and Summa Theologiae, occu:rs in conjunction with the problem of delectatio morosa, but the conjunction had been made almost a century previously by Peter
Lombard and a tradition had been established by later mediaevals before St. Thomas took up the matter. It should be noted,
too, that his principal exposition of the two ratio's in the De
V eritate is to a large extent simply a general discussion of the
principles whereby faculties are specified; 96 and in the Summa
a good part of one of the key texts is given over to a discussion
of the scientificum and opinativum in Aristotle. 97 In short,
because of St. Thomas's general tendency to treat the two
ratio's in theological questions only when others had done so
and because of his failure to develop or fully exploit the resources of this theory when the occasion was present for doing
so, it seems quite certain that St. Thomas did not consider the
doctrine of ratio superior and ratio inferior to be of capital
importance.
•• To cite only a few
in the Summa Theol., I, q. 12, a. 12; ibid., q. 12,
a. 13; ibid., q. 84, a. 5; ibid., q. 88, a. 1. Any one of these passages concerning the
soul's knowledge of God provided numerous opportunities for a treatment of the
ratio superior, but it is not mentioned even once.
•• On the authority of the magistri, see M. D. Chenu, 0. 1'., Introduction a
l'etude de saint Thomas d'Aquin (Paris, 1950), p. 114.
97 Summa Theol., I, q. 79, a. 9, ad. 4.
•• De Verit., q. 15, a. 2.

" RATIO INFERIOR " AND "RATIO SUPERIOR"

367

What is to be remarked, however, is the complete mastery
of St. Thomas in finally incorporating its valuable elements into
his own writings. What St. Albert partially succeeded in doing
St. ,Thomas did with such success that the theory was entirely
freed from the neo-Platonic implications with which it had been
burdened by the middle of the thirteenth century, and it was
made to conform with the general lines of his own profound
thought. As Jacques Maritain has observed, the doctrine of
ratio superior and ratio inferior as found in the writings of
St. Thomas remains rich in possibilities for the Christian
philosopher. 98

R. w. MULLIGAN, s. J.

Loyola University
Chicago, lllinoiB

01

Jacques Maritain, Sc:ir.1we et aageaae (Paris, 1985), p. fl65.

ORTHODOXY OF THE TRANSFINITE
NUMBERS

1

'RANSFINITE numbers have aroused lively controversies between mathematicians and philosophers. The
twofold problem of their nature and significance is still
open, despite their scientific use and value. In trying to solve
it, one must ignore the conflicting opinions of experts and
rather take into account the actual practice of the theory of
sets and the technical discussions among mathematicians concerning their systematization and applications.
Galileo was the first to draw attention to certain curious
properties of classes of numbers, when he showed that the
unending sequences of natural numbers and of even numbers
are coextensive. Yet ,his contemporaries refused to consider
such sequences as wholes and thus pronounced themselves
against " infinite " numbers. Among the empiricists, Hobbes
argued in his Elements of Philosophy that the human mind
gives a finite character to whatever it determines: if therefore
one speaks of an infinite number, one gives to number an indetermination which is not appropriate to its notion. In his
Essay Concerning Human Understanding, Locke held that the
idea of an infinite number implies the impossible adjustment of
a fixed standard to an increasing magnitude. For him the idea
of an infinite quantity is contradictory; because it is impossible
for the mind to possess simultaneously such a fixed idea and
also the vision of all the successive numbers which make it; in
other words, it can never grasp the completion of such a ceaseless repetition.
Among the rationalists, Descartes stated in his Principles of
Philosophy that an entity which has no limit must be considered as indefinite and not as infinite. In his New Essays
Leibniz denounced " the absurdity of the actual notion of an
368

ORTHODOXY

OF THE TRANSFINITE

NUMBERS

369

infinite number, since the infinite cannot be a true whole," and
he rejected the idea of an actual infinite magnitude. Though he
recognized the similarity of the classes of the natural and of the
even numbers, he affirmed that the idea of a number of all
natural numbers implies a contradiction. Curiously enough, he
pronounced himself in favor of an infinitely small being in his
metaphysics, although he would deny that an infinite line is
composed of parts.
These remarks have now an historical interest, as no theory
of infinite numbers existed at the time. Proper discussions of
the transfinite began with the Cantorian creation of infinite
sets, and developed with the contributions of Weierstrass and
Dedekind to the philosophy of number. From the outset controversies centered on the validity of the axiom that the whole
is necessarily greater than the part, on the contradictions
suiting from the application of the categorical properties of the
finite to the infinite, and on the existence and constructibility of
transfinite numbers. A triple question is involved in the last
difficulty: the value of the axiom of Zermelo, the meaning of
the hypotheses of the continuum and of the succession of alephs,
and the problem of knowing if the set of real numbers is ordered
o:r not. Such discussions became permanent fixtures of mathematical logic, especially since the famous quarrel between Russell and Poincare about the foundations of analysis.
Mathematical tradition was limited previously to the study
of finite numbers, which restricted the full investigation of the
properties of number. With the establishment of a mathematical theory of infinite sets, a specific doctrine was needed
to explain and justify their peculiar characters. The Cantorian
creation of the theory of sets does not require an actual infinite,
or the sensory representation of infinite numbers, or even the
necessity of counting all the units of such aggregates. A set is
not an empirical but a conceptual totality generated according
to precise laws. Thus, the number w is a symbol representing
in a way the rule that there is no last element within the
succession of natural numbers. Likewise, every transfinite num-

370

THOMAS

GREENWOOD

her stands for a law of generation of a class of numbers taken
as a whole.
But these considerations do not eliminate the infinite from
the construction of transfinite numbers. That is why Kronecker
was one of the first to question their validity, by taking an
attitude worthy of a Pythagorean of strict observance. In order
to give precision to the exposition of mathematics, he wished to
banish from it the indetermination involved in the infinite and
in intuition. He thought that mathematics should be established on finite constructions utilizing natural numbers exclusively. In particular, the mathematical objects should be
constructed in a finite number of steps, and not by using purely
logical operations or transcendental (a priori) proofs of their
existence. The finitist school, now represented by Brouwer and
his disciples, stretched this attitude to its final logical conclusion, by questioning the validity of the Principle of the
Excluded-Middle and consequently of an important portion
of mathematical analysis.
By applying this rule of constructibility to mathematical
notions containing the word all in their expression, one :reaches
the paradoxes which characterize them as illegitimate totalities.
Going beyond the arguments stated by Zeno of Elea more than
two thousand years ago,
indicated in 1897 that
the ordered collection of all the ordinal numbers defines a
new ordinal number which is not part of that initial totality.
In
Bertrand Russell inquired if the class of aU classes
which are not members of themselves is a member of that
class. Whether affirmative or negative the answer involves an
antinomy.
This is the famous paradox Russell stated in a letter to Frege,
who had written his monumental Grundgesetze der Arithmetik
(1893-1903) to provide a logical foundation for the idea of
number. By rightly defining a cardinal number of a given class
as the set of all the classes similar to it, Russell undermined the
bases of Frege's construction. Yet, the works of Frege and their
tJubsequent utilization by Russell himself, who thought of

ORTHODOXY

OF THE TRANSFINITE

NUMBERS

371

avoiding their main difficulty by his theory of logical types,
opened up a fertile field for the logical interpretation of mathmatics.
If this attempt could not be decisive, it made it possible for
transfinite numbers to find a respectable place in the body of
science. The technical prolegomena relative to these numbers
show clearly that the mathematical reality of transfinite numbers is fully acceptable. Their theory, which seems to be
exempt from technical contradictions, is connected with the
common basis of established scientific knowledge and has important application in several branches of mathematics.

*

*

*

*

The philosophical question remains whether the transfinites
are true numbers. 'We may answer by showing their agreement
with the basic Aristotelian theses on number and quantity
which may be summarized as follows: (1) Quantity is an
accidental property and not a constitutive element of substance.
(2) Quantity and substance cannot be separated in the concrete world, since quantity makes substance divisible and gives
extension to it by ordering its parts. Thus quantity makes
possible the division of a given whole into discrete parts having
the same nature as the whole. (S) Quantity manifests itself
under two irreducible aspects: the continuous and the discrete.
(4) The discrete generates the idea of number. (5) Number
is a specific plurality measurable by the unit (multitudo mensurata per unum) ; it is a collection of units which is finite or
undetermined.
(6) There is no actual infinite in relation to
number or magnitude. The characteristic of number rests in
its ability to be increased or decreased at will, with a different
result for each operation. Hence, it is impossible to think
actually of the totality of all numbers.
Taken too literally, the classical theses on number may seem
incompatible with the notion of the transfinite. However, by
using a wider conception of number resulting from a biunivocal
correspondence between distinct classes as well as some remarkable analogies of the transfinites with certain classical species

372

'.rHOMAS

GREENWOOD

of numbers, the transfinite can well be integrated into the
traditional notion of number properly interpreted. Such extensions are permitted in the perspective of the successive
generalizations of the notion of number, from the Pythagorean
integers to the modern theories of algebraic and transcendental
numbers. It is unnecessary to stress here the incompatibility
of attributes: it is more important to rationalize the novelties
which science has succeeded in integrating into its vast field,
so as to justify their subsisting side by side with the older
contributions.
The notion of the transfinite is not based on an actual infinite, even though we consider as totalities classes whose members have never been enumerated completely. In the second
order of abstraction, such conceptual constructions are permissible and practicable. Thus a circumference of a given
radius can be considered as a determinate and infinite totality:
It is the non-enumerable set (transfinite power of the continuum) of points equidistant from the center of the circumference" This definition identifies an ever-increasing number of
points with a complete whole" For operational considerations,
modern science gives to the number of this set as a whole a
particular quality which differentiates it from any type of
finite number"
At this stage an important distinction in the notion of the
infinite must be mentioned. The actual infinite involves a nonlimitation required by the fulness of the pure act: only God
can give being to the actual infinite" But in the potential infinite, the non-limitation is due to the indetermination of potency itself. Hence, it is possible to imagine a non-limitation
as due to a definite intelligent act, which somehow exceeds or
continues an undetermined and always incomplete succession
of similar acts. The resulting concept is not a potential infinite
involving an addition without end, but a pre-precise and finite
notion which
in the mind the indetermination of the
potential infinite. A transfinite number is therefore properly
determined as such; but the number of its actual elements is
undetermined, since their enumeration or the :repetition of a

ORTHODOXY

OF THE TRANSFINITE

NUMBERS

373

biunivocal correspondence never stops, owing to the endlessness
of the integers series.
To be sure, a transfinite number is actual in one sense and
potential in another. Its nature does not depend on its quantitative continuum or on the number of its elements; but on the
qualitative mode of the indefinite generation of its elements as
a set. And as it is possible to conceive different qualitative
modes of producing sets, it is legitimate to introduce distinctions within the transfinite and to conceive a variety of transfinite numbers. Moreover, since potency as such is capable of
several determinations, it allows differences between them. Although expressed as numbers, these differences are qualitative,
since they are accounted for by the mode of determining and
grouping the possible elements of the given potency. For example, there is a quantitative difference between prime numbers
and odd numbers, although both species use the same integers
in explaining their distinctive characters. It is then possible to
extend the notion of number to these species or sets, because
they entail a numerical continuum ultimately reducible to integers and because they can be subjects of operations.
The symbols or marks of the various transfinite numbers
express their unity as complete wholes or totalities, as well as
the intelligent act which distinguishes one from the other in the
first place. The foundation of their diversity is not the number
or the individual quality of their elements: it is the quality of
the sets of indefinite multitudes, as signified by distinct symbols, which constitutes the form of the various transfinite
numbers. As such they are really in esse and not in fieri as one
may be tempted to conceive them. Thus the differences between the various alephs are due to the specific generation of
each one of them. Again transfinite ordinals are distinct
between them, because of the specific rule of order each
represents. Although each of these various numbers entails an
infinity of elements, their numerical indetermination does not
affect the stability and the specificity of the rational essence
of the transfinites. On the contrary, this very indetermination
6

374

THOMAS

GREENWOOD

allows the construction of specifically different transfinite
numbers.
Ingenious devices have been invented to work out biunivocal
correspondences between various categories of numerical elements, and to establish the first fundamental distinction between enumerable and non-enumerable sets. The power of a
set is equal to or greater than the power of the continuum,
when its elements cannot be enumerated actually. The difference between enumerable and non-enumerable sets is conditioned by the use of a biunivocal correspondence, and not by
numerical relations. In both types of sets, the number of their
elements cannot be computed. They differ by the manner in
which their elements are grouped. This qualitative distinction
entai.Is different laws of construction, different mode of generation and hence different marks (numbers) to symbolize their
sets.
In the light of these remarks, we may understand better the
expressions " many " or " all and part " when applied to the
transfinite. A numerically determined whole and a numerically
determined part of it are actually unequaL But if a whole and
its part have both an indefinite number of elements, then their
presumed inequality cannot be verified actually. In fact, by
establishing a biunivocal correspondence between their homologous elements, it is soon realized that this process can be
continued indefinitely, thus making it impossible to determine
actually the intuitively presumed inequality of the two sets:
hence the decision to consider them as equal. Particular considerations concerning the equality of two intuitively unequal
wholes need not be analyzed at this stage, because the distinctions just made are adequate and precise. Whatever be the
order of the elements of two sets or their transfinite ordinal
numbers, these sets may be considered equal, when their elements can be arranged in such a manner as to allow a biunivocal correspondence between them. In this sense only can it
be loosely said that the whole is equal to the part. Such views
constitute the ground of the many theorems concerning the
properties of sets and of the transfinite cardinals, as well as of

ORTHODOXY

OF THE 'rRANSFINITE

NUMBERS

37 5

the operations relative to cardinal and ordinal transfinite
numbers.
These developments show that the arithmetic of the infinite
entails a calculus of qualitative groups of elements rather than
of quantitative groups of units. As the arithmetic of the infinite
thus differs from ordinary arithmetic and from classical algebra,
it is appropriate to insist on some fundamental implications.
The discrete essence of number is expressed by its relation
to the unit. As a collection of units, finite or infinite, a number
becomes one by reason of the order or the measure of its elements. But this oneness or unity in itself is transcendental,
though the number as such may be predicamental, since it adds
to being a reason of extension, measure or order. Against this
Thomistic attitude, Scotus and Suarez denied that a number
may be one by its own nature and asserted that its unity is
constructed by the mind. That is why some think that the unit
or number 1 is not formally a number, but only the principle
of number. This Pythagorean and Platonic confusion of number 1 with the transcendental or existential one is dispelled by
the Thomistic distinction between the transcendental and the
predicamental aspects of number.
Transfinite numbers are not determined by comparing a multitude with a unit, but by comparing a multitude as a set with
another multitude with respect to a biunivocal correspondence.
It is true that the idea o£ unity is somehow implied in the
notion of biunivocal correspondence, and even in the concept of
transfinite number considered as a single class. Yet the unit is
not used here as a term of comparison, but as a means of comparison. In a biunivocal correspondence, the actual number of
pairing operations is not counted; it suffices to show that they
can be carried out without leaving any unpaired elements. By
insisting on the mode of pairing the elements of two sets rather
than on the quantity of such operations, it is possible to avoid
casual paradoxes in the concept of infinite sets, to establish
significant differences between transfinite numbers, and to
specify the meaning and use of the notions of ' all ' and ' part '
when applied to such constructions. Again, the transcendental

376

THOMAS

GREENWOOD

unity of a transfinite number is not considered as a: numerical
entity, but as a qualitative totality of elements. The mark of a
number is given to such a set after its qualitative comparison
with another infinite totality of elements.
These developments show that transfinite numbers do not
increase or decrease by simple numerical units, as in the case of
ordinary numbers, but by qualitative blocks or sets; and the
results of such operations depend on the specific construction
of such blocs or sets. It is even possible to verify fine distinctions in the manipulation of transfinite ordinals, where operations are determined by the notion of order and its varieties.
Hence, operations with the transfinite are bound to yield results
different from those with ordinary numbers. To be sure, such
a difference was already noted with the use of the classical concept of infinity when the fundamental operations of arithmetic
applied to the symbol ( oc) give results different from those
involving ordinary
The need of making operations with the mathematical infinite has been known for a long time: it was manifest in the
quadratures of the ancients, as wen as in the modern inventions
which place a mathematical harness on limits, series, differentiation and integration, which use infinity in their own manner.
Likewise, the infinite is manipulated by the analytic, the projective and the differential methods in geometry. But all these
operations never pointed to any specifications in the single concept of the mathematical infinite, of which the sign ( oc.) still
remains the classical representation. While it is now possible
to think of distinct levels within the infinite, and to characterize
each of them by the special symbols of the transfinite numbers.
The mathematical existence of transfinite numbers is more
clearly affirmed by the absence of any internal or external contradiction in their notion. In fact, it is possible to conceive the
existence of infinite and different multitudes, without limiting
the power of divine creation. For the absolute power of God
can create indefinitely new multitudes of angels and other
beings, leaving to our reason the care of ordering them. Now,
transfinite cardinals reflect in their manner this very possibility

ORTHODOXY

OF THE TRANSFINITI<J

NUMBERS

377

of divine creation; while the indefinite ways of grouping these
multitudes would have their mathematical coun'terpart in the
transfinite ordinals. Nevertheless, there is no multitude of coexistent well-ordered substances, for there are no actual infinite
or transfinite numbers, although these concepts entail the
mathematical infinite. Finally, as the generation of transfinite
numbers is obtained by recurrence indefinitely repeated, the
existence of the totality of transfinite numbers is not mathematically affirmed. Hence, the theory of the transfinite has
nothing to do with t}le actual infinite.

*

*

Controversies about the transfinite have resulted from the
discovery of some famous paradoxes in the theory of sets and
from the impossiblity of constructing certain sets.
Here is an example of one of the paradoxes of Bertrand
Russell. Let us suppose that we are to make a catalogue of just
those books which did not mention themselves in their contents.
Should the catalogue include itself or not in the works listed?
In the negative, it fulfills the rule of belonging in the catalogue
and should be included. In the affirmative, it fails to fulfill the
requirements for being included. This antinomy seems to make
an answer to our question impossible. In general, some sets of
classes include themselves and some do not. But it seems formally impossible to affirm whether a set includes itself or not,
when it is defined as a set to which belong all those and only
those classes which do not include themselves as members.
Many paradoxes of Russell, Richard, Burali-Forti and others
burden the logical clarity of the theory of sets and seem to
imperil the proper use of the laws of thought. Mathematicians
such as Brouwer even go as far as to question the Principle of
Excluded-Middle. In fact, in the paradox just mentioned, it
seems impossible to decide whether or not to include the catalogue in the booklist as defined. This apparent difficulty of
applying universally the Principle of Excluded-Middle affects
the constructibility of certain sets: the only way then to justify
their existence is by using the method of indirect proof, which

THOMAS

GREEN"\VOOD

gives no direct means of constructing questionable sets and
which prompted Brouwer to reject a sizable portion of higher
mathematics.
While we do not propose to discuss here these opinions, we
submit that the paradoxes of the theory of sets are not absolute: they arise partly from the confusion between the qualitative and the quantitative aspects of classes, and partly from
using the formal notion of a set or class without specifying
sufficiently its applications. By ordering properly the
matical and the logical attributes of a set, it should be possible
either to ignore certain questions as nonsense or to resolve the
paradoxes involved in them.
The logico-mathematical difficulties of the theory of sets have
divided mathematicians into three distinct schools of thought.
The intuitioniets or finitists represented by Brouwer admit as
legitimate only the sets which it is possible to construct.
though many sets are justifiable indirectly by showing the
absurdity of their impossibility, the convenient postulate of
Zermelo, which supports these indirect proofs, only adds fuel to
the controversy. Consequently, intuitionism rejects as invalid
that fairly large portion of mathematics which involves all nonconstructible classes currently used in modern analysis. Yet.
this attitude may seem rather odd, when one realizes that the
parts of mathematics considered as legitimate by the finitists
involve a large measure of intuition in their structure. The
formalists with Hilbert as their principal representative are
more liberal in accepting those sets which do not involve contradictions. Yet formalism meets also its difficulties; for it is
impossible to formalize mathematics completely. In particular,
Godel has shown the impossibility of proving the non-contradiction of the foundations of arithmetic. Finally, the conceptualists legitimate the widest field of mathematics by requiring
simply the ideal existence of the notions in use. The conflicting
attitudes of these three schools obviously affect their views on
the nature of the transfinite and of mathematics generally.
For our part, we may offer the following conclusion: transfinite numbers can be incorporated legitimately as numbers in

ORTHODOXY

OF THE TRANSFIKI'l'I<J

NC:\IBERS

:nO

mathematics, by interpreting the general notion of number as
a set of classes and by attributing to it some qualitative determinations of the mathematical infinite. Moreover, although
transfinites do not derive immediately from experience by a
direct abstraction, nevertheless their conception begins with
experience, since the mind considers finite classes first before
rising to the conceptual vision of infinite classes. Hence, transfinite numbers are constructions of the mind based on empirical
data and reaching beyond according to permissible formal analogies. Finally, the difficulties involved in the analysis of
transfinite numbers are inherent in their notion and do not
necessarily conflict \Vith the fundamental doctrines of traditional philosophy. An adequate interpretation of these difficulties allows integration of the transfinites into its wide system
as legitimate developments of science.
THOMAS GREENWOOD

University of Montreal
Canada

NOTES ON OUR CONTRIBUTORS
KEVIN A. WALL, 0. P., S. T. Lr., S. T. L., is professor of philosophy at St.
Albert's College, the Dominican House of Studies, Oakland, California, and a contributor to THE THoMIST.
R. W. MuLLIGAN, S. J., received his doctor's degree at L'Institut Superieur
de Philosophic in Louvain and spent two years in post-graduate
work at the Sorbonne (Paris). At the present time he is chairman of
the department of philosophy at Loyola University in Chicago.
THOMAS GREENWOOD, Ph. D., professor in the Faculty of Letters at the
University of Montreal, has taught philosophy at the University of
London (1930-1940), at the University of Ottawa {194'll-1949), and
other institutions.
GEORGE F. J. LAMouNTAIN, M.A., before joining the staff of Aquinas
College, Grand Rapids, Mich., taught at St. Joseph's College, Collegeville, Indiana. He has done graduate work at The Catholic University of America and at Georgetown University.
WILLIAM J. HILL, 0. P., S. T. I..r., S. T. D., teaches dogmatic theology at
the Dominican House of Studies, Washington, D. C. He is the
author of Proper Relations to the Indwelling Divine Persons.
WILLIAM A. WALLACE, 0. P., S. T. Lr., S. T. L., M.S., professor of natural
philosophy at the Dominican House of Philosophy, Springfield, Ky.,
is a member of the Albertus Magnus Lyceum for Natural Science,
River Forest, Ill.
THOMAS C. O'BRIEN, 0. P., S. T. Lr., Ph. D., teaches natural theology at
the Dominican House of Philosophy, Dover, Mass.

880

BOOK REVIEWS
De Noetica Geometriae, Origine Theoriae Cognitionis. AucTORE P. HoENEN,
S. J., Romae: Apud Aedes Universitatis Gregorianae, 1954. Pp.
cum indice analytico.
The latest work by Fr. Hoenen sums up his studies on the foundations
of geometry and the relevance of such studies to the formation of a general
theory of scientific knowledge. Parts of the text have appeared in various
articles in the Gregorianum from 1938 to 1943, but more than half of the
work is original and the remainder has been emended and edited to give
support to the author's main thesis. Fr. Hoencn's principal purpose is to
examine the axiomatic foundations of Euclidean geometry with regard to
major points that have come under modern criticism, and on the basis of
this to propose an incomplete system of primitive (indemonstrable) propositions from which geometry can be deduced. His study is a noetic one in
the sense that it is the function of noesis to make explicit the principles that
are intuitively grasped by the mind in actu exercito, and then to clarify
these by reflection (so that they can be understood) in actu signata. The
author is at pains to show as a major conclusion of his work that this contribution is not only a possible beginning of noetic science, or a theory
of knowledge, but is in fact the necessary beginning of all scientific
methodology.
This main thesis of Fr. Hoenen is not without its controversial aspect.
Yet the fundamental work that underlies it is quite sound and of considerable interest to those attempting to evaluate contemporary mathematics and logic from an Aristotelian viewpoint. In order then to recapitulate this contribution of Fr. Hoenen for the benefit of American readers, the
first part of this review will be a synopsis of the main points in the development of his thesis. This will then form the basis for a brief analysis of
the aspects most open to criticism in the light of traditional Aristotelian
doctrine on scientific methodology.

*
The first chapter of De Noetica Geometriae is devoted to a statement of
the problem that is central to all scientific thought, but which is normally
encountered first in the mathematical sciences. Actually it is a twofold
problem, and it may be stated in this way: Whence arises the necessity of
mathematical judgments respecting first principles and indemonstrable
propositions, and whence arises the exactitude which is found in mathe-

381

BOOK HEVIEWS

matical concepts and has no counterpart in our sensible experience? These
are the fundamental difficulties, but related to them are other problems that
are much discussed by contemporary thinkers, such as the arithmetization
of the continuum, the status of Euclid's fifth postulate, and the limitations
of axiomatics. The author is of the opinion that a good start was made by
Aristotle in delineating the general approach to all these problems, but
he bemoans the fact that no one in the scholastic tradition has done anything to develop Aristotle's doctrine and apply it to current difficulties.
Thus he is aware that he is moving into a virgin field in which he cannot
hope to give all the answers, but he is interested more in making a good
beginning than in expounding a complete systematic development.
The problem of necessity is approached in the second chapter and the
solution is given, as might be expected, in terms of the Aristotelian theory
of formal abstraction. Fr. Hoenen begins dialectically, furnishing many
examples of judgments that are regarded as necessary by ancient and
modern mathematicians. Then he seeks the common feature associated with
this necessity, and expounds it in terms of the notions of implicit judgment
and virtual judgment which he has explained at length in his Reality and
Judgment According to St. Thomas (Chicago: Regnery, 195Q). His conclusion is that necessary judgments are arrived at by formal abstraction
through which it is seen (intued) that there is a formal connection which
necessitates whatever is predicated of the subject. Experience is needed
only insofar as these truths are abstracted from sense data, and compared
to the other sciences, mathematics requires little experiential knowledge.
In casibus mathematicis ... habemus abstractionern forrnalem, et ideo
intuernur nexurn formalem, ideo necessarium erit id, quod de sttbiecto
praedicabitur. Sed, ut sciamus quid praedicandum sit, debemus respicere
data sensitiva, sive in irnaginatione sive ope sensuurn externorum, quod
est, 1tt verbis Caietani iterum 1ttam?LT, ' proprium motivurn et determinativurn' praedicati. (p. 61)
The notions developed in the secoml chapter are applied immediately
to the problem of exactitude, the treatment of which is quite extensive and
extends through the third and fourth chapters. The key difficulty is that
sense data do not possess the exactitude with which they are clothed in
mathematical treatment. If geometry takes its beginnings from sense
knowledge, how can it achieve perfect exactness? This is not only a
question of the nexus betwe"n exact notions, but of the very existence of
such notions themselves.
The third chapter therefore takes up the general discussion of the existence of mathematical points, lines, and surfaces. Fr. Hoenen here emphasizes the order of knowing, and points out that the concept of an extended
body or solid is given immediately in our knowledge. A necessary judgment
then puts us in contact with the first property of extended being, its

BOOK UEVIEY\S

383

divisibility. Thus the solid can be divided into two parts and these will be
limited by the division. The limit exists between the parts, and by its very
nature is an indivisible, for otherwise there would be more than two parts.
This indivisible which is extended in two directions is called a "surface"; it
is not necessarily a" plane," unless the solid is divided in a very special way.
The surface can in turn be divided into two parts, and again there will be
an indivisible limiting the parts, hut itself extended in one direction, which
is called a " line "; this too need not be a " straight line " unless the surface
is divided in a special way. Finally the line can be divided into two parts,
and the ultimate indivisible effecting this division is the " point." It is
completely indivisible regardless of the way in which the line is divided, and
therefore brings the divisive process to an end.
Dimensions correspond to these various ways in which a body can be
divided. They exist mathematically in extended being and consequently can
exist in nature. But can the notion of dimension be defined strictly? Quid
sit dimensio, definitione technica, quae constat ex genere et differentia
specifica, definiri nequit. Tamen haec notio est perfecte clara; quid sit,
perfecte intelligitur ex processtt supra delineaio. Ens extensum q·uod habet
tres dimensiones, est extensum quod triplicem illam divisionem sustinet; et
in hoc ente extenso dari possunt limites, qui duas dimensiones habent, resp.,
unam vel nullam. Habemus legitimam 'definitionem operativam.'
(pp.
77-78)
At this point the author takes up the question of infinite divisibility to
show that a line is not merely a collection of points. He explains the
notion of " locus of points " used in analytic geometry and proves that the
line generated is truly continuous. He also discusses briefly the process
involved in geometrical construction to make clear that this is not purely
arbitrary, but that the :mind of the mathematician is bound by the exigencies of the matter in which he makes his constructions.
Having disposed of the difficulty about the existence of indivis;bles, Fr.
Hoenen proceeds in the fourth chapter to treat of the exactitude of figures
and relations. Geometers consider their lines and figures absolutely exact,
but such entities have no counterpart in sense experience. 'Whence does
this exactness arise? Also how can relations of exact equality
congruent triangles, etc., be deduced?
The solution to both these problem is found to be rooted in knowledge of
extended being as it is the principle of individuation in the mathematical
order. Extended being attained by intellectual abstraction is homogeneous
continuous quantity, intelligible matter that is absolutely uniform. This
makes possible not only the multiplication of figures in exactly the same
species (formally and quantitatively), but also furnishes the basis for
numerically distinguishing between figures simply by their position or situs.
Fr. Hoenen explains that the moving of figures in this continuum is not

384

BOOK REVIE1"/S

the same as a physical motion. Velocity and other factors are irrelevant, the
only things significant being the new place and the notion of direction
implicit in the motion. Applying these notions to the congruence of figures,
he indicates how exact conclusions are possible, and this not purely from
arbitrary suppositions but from the very nature of the continuum.
Concludere possumus: sicut in abstrahendis notionibus exactis superficiei,
lineae, puncti (tanquam indivisibilium omnino vel sub certo respectu) ex
datis inexactis sensitivis, mens nostra, ex intellecta natura extensionis, non
solum notiones exactas concipit, sed ea obiecta 1nathematice existere intelligit, ita etiam in casu congruentiae ex intellecto extenso, ut est principium
individuationis, figuras exacte aequales, solo situ differentes, non solum
concipit sed eas existere intelligit et ex iis logice alias veritates deducere
potest. Et ea quae antea videbamus, pro hoc casu repeti possunt: manifestum est, nos non (libere) creare haec obiecta; non volumus figuras
congruentes existere, sed detegimus eas ut possibiles in extensione, quae
est materia intelligibilis ex qua fipi possunt. (pp. 1H-H2)
The further question of exact geometrical figures is approached through
an examination of primitive notions following the method of axiomatics.
The author proposes a problem respecting the meaning of the two statements, " a point is situated in a line " and " a line passes through a point,"
in order to focus attention on the notion of direction which he states as
primitive. The concept of angle, for instance, derives from that of direction.
So does the definition of straight line: Linea erit recta, si directio secundum
quam per unum punctum transit, ulterius in ea, specifice eadem, conservatur, si per quodcumque punctum subsequens vel praecedens eadem
directione, sine deviatione, transire pergit. Si in uno puncto habetur
abrupte mutatio directionis, erit ' linea fracta' ; si directio modo continuo
variatur, erit linea curva. (pp. 120-HH) The plane can also be defined
from sense experience using the notions of straight line and direction:
Superficies sensibiliter plana, quae in experientia nostra datur, talis est, ut
per quodvis punctum transeat integrum continuum (fascis) sensibiliter
rectarum, quae totae in superficie sitae sunt; omnis recta quae duo puncta
arbitraria superficiei iungit, integra in ea sita est; haec superficies ex neutra
parte concava est. (p. 122) With these notions established as the quid sit,
a simple examination of the continuum suffices to answer the question
an sit. Such exact figures can exist in extension that is intelligibly homogeneous, notwithstanding the fact that they are not immediately verified
in sense experience.
Fr. Hoenen briefly reviews Euclid's definitions and shows that the great
geometer was quite consistent in framing these in the most fundamental
manner possible. Then he approaches the problem of the famous parallel
postulate to see whether this, though not immediately evident, can be
justified through the use of the primitive notion of direction. He is ac-

BOOK REVIEWS

385

quainted with the attempts of many modern mathematicians to do just
this thing, and rejects their formulations:
Loco harum notionum usi sumus notione directionis; sed et haec iam
saepius ad decidendum nostrum problema introd1wta est; inter philosophos
v.g. a Renouvier. Et ibi quidem id est immediate evidens: per punctum
extra rectam situm, unicam tantum eiusdem exacte directionis duci posse.
Sed si haec notio non genetice explicatur et eius existentia, simul cum
existentia rectae et plani, et eorum connexionum, non intelligitur et ope
principii individuationis examinatur, subiacet difficultatibus, quas antea a
mathematicis prolatas audivimus. lnde hanc notionem et has existentias
omni cura examinabamus. Et in nostro modo evolvendi notionem directionis
exactae, illae difficultates, ut vidimus, non subsistunt; et totus processus
problema solvere videtur. (p. 139).
Yet the author allows that a non- Euclidian geometry, at least for two
dimensions, can be real and cites the pseudosphere of Beltrami as a figure
in which such a geometry is verified. This admission, however, is accompanied by a reservation on the terminology used in such geometries; they
may use the same terms and axioms as classical geometry, but the exact
sense of the terms and axioms undergoes change in the non-Euclidean
application. (p. 140) Nevertheless this possibility raises a serious problem
about the certitude of a Euclidean view of the universe and the general
validity of classical geometry. Fr. Hoenen resolves this by stating that
sensible objects in which the conclusions of non-Euclidean geometries are
verified are nothing more than a part of the objects of classical geometrythey are objects that really lack curvature in a higher space. Rather than
state that such objects are excluded in classical geometry, he would prefer
simply to note
they were not examined in that geometry, and thus
make the defect one of ignorance rather than error. But he does observe
how remarkable it is that aU the properties of a non-Euclidean continuum
can be deduced from postulates stated in exactly the same terms as Euclid's
with the sole exception of the fifth postulate. (p. H!il)
Thus far in his work Fr. Hoenen has attempted to justify the foundations
of classical geometry in the most primitive formulation possible. Now in
the fifth chapter he raises the question of the ideal of science implicit in
axiomatics, in an attempt to see how rigorous one can be in formally stating
and justifying first principles. He contrasts the strict axiomatics of the
early logical positivists with Aristotelian methodology . as expounded in
the Posterior Analytics, and shows how there has been some rapprochment
between the two views; at least many moderns have corrected the earlier
notions on formalism to admit that primitive notions for any system are
basically undecidable within that system. Then he proceeds to justify the
incompleteness of his own examination of first geometrical principles on the
grounds that any more justification is practically and theoretically impossible.

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BOOK REVIEWS

In any conceptual manipulation that goes on in the mind, the tenns that
are used must ultimately make sense--otherwise the process is meaningless.
This is obviously necessary in any subject-predicate relationhip; it is uo less
necessary in the process whereby first principles are justified. The mind
moreover uses a certain natural logic, and continually has res<.rt to
phantasms in the judicative process. This logica utens shows up as an implicit syllogism of the mode Barbara that accompanies every mental operation. For example, when it is deduced from the equation ax 2
bx + c
that ax 2 -bx -c
0, there is implicit the syllogism: Every equation
which is properly transposed from a valid equation is itself valid; but ax 2
-bx -c
0 is properly transposed from a valid equation; therefore it
itself is valid.
lnde habemua quod primo observamus: in omni tali proceaau in mente fit
ayllogiamua (typi Barbara); non exprimitur verbis, sed mentaliter dirigit
actum affirmandi conclusionem; id non facit, ut aupra dictum eat, ut norma
extrinseca, sed ut activitaa intellectua ipaius mentis, ut ' natura.' Est igitur
in 'actu exercito '; investigatio nostra noetica non introducit
ayllogismum, sed eiua praesentiam detegit; facit eum transire ex actu exercito in ' actum signatum.' (p. 178) .
Thus Fr. Hoenen defends the Aristotelian theory of demonstration and
the spontaneous character of logical thought by insisting that even the
rules used in modern logistics presupposes the validity of the logical processes their users are attempting to justify rigorously. In the light of his
analysis, the notion of rigor in use among thorough-going formalists is seen
to be naive in the extreme. The author makes a telling point of the
attempt to derive the notion of number in the Principia Mathematica:
Notamus insuper: in logistica, secundum Whitehead et Russell, et in
aliis quoque systematibus, ipsi numeri arithmetici non ut cogniti auppo·
nuntur; eorum notiones et propositiones, quae de eis valent, modo logistico
post immenaum laborem praevium, inveniendae sunt. Tamen in centeni,
formulis quae praecedunt, adsunt v. g. in systemate interpunctionis, et haec
systemata punctorum intelligenda aunt, et in senau naturali adhibenda aunt.,
et ibi intrat sive agnitio figurae geometriciae, sive ordo numerorum naturalium, sive potiua utrumque. Intuitive adhibentur ea, quae poat multum
laborem tandem aliquando cognosci dicuntur. (pp. 182-188)
Yet he does acknowledge the value of axiomatic formulation, particul..rly
to lay bare the logical structure of the sciences. (p. 194)
Having cleared away difficulties respecting the problems of necessity and
exactitude, and also having delineated the contribution of axiomatics to the
clarification of primitive notions and mental operations, Fr. Hoenen turns
to the fundamental subject of geometry in chapter six. He states that this
subject is not constituted by the possible figures whose properties are
deduced from first principles, but by the structure of extension itself from

=

=

=

BOOK REVIEWS

387

which those principles flow. And the structure of which he speaks is the
non-deformed Euclidean structure of extension that is fundamental to all
other structures. (p. 198} He excludes "empty" space as the subject, and
makes several precisions on the meaning of the concept of space, showing
that ultimately all such notions must be reduced to the extension of bodies.
(p. 207) He delineates the role of sense knowledge and imagination in
attaining this proper subject, and indicates that these play a necessary
but ancillary role to the intellect, which makes its judgment solely from
the intelligibility of the matter itself. (p. 211)
The clarification of extension as it is intelligible matter is relegated to
the final chapter of the book. Having noted that continuous quantity i11
the fundamental subject of geometry, Fr. Hoenen now shows that geometrical figures are themselves proper passions of the subject. They are
contained potentially in the subject, and are actualized through construction, which itself constitutes a demonstration of existence. (p. 224) The
construction is performed in Euclidean geometry through the use of ruler
and compass. Yet despite the fact that sensible representations are inexact,
the possibility of exact construction is perfectly understood and used in the
mental operation. (p. 227)
Under the formal abstraction of mathematical science, matter is seen to
have a twofold intelligibility, one passive and the other active, the latter
arising from the former. Passively, it is first known as figurable, then as
able to individuate figures of the same species, then as able to merge
figures on contact. And this intelligibility in turn gives necessity to the
operations of the mind actively considering such a subject. Constructions
are made, and properties are deduced, but these are not arbitrary in any
way. They are determined by the very nature of extension itself; the
matter is necessary, and this of itself necessitates the mental activities.
Mistakes can be made in any mental activity, of course, but these are per
accidens to the science and are brought about by fatigue or inattention,
not by the matter being considered. (p. 233)
This finally brings Fr. Hoenen to the main conclusion which he feels is
intimated by his study of the foundations of geometry, viz., that this type
of mathematical knowledge is the beginning of a general noetic theory.
Nam noetica est scientia, quae naturam ipsius intellectionis, noeseos, perscrutari intendit. Et consideratio principiorum mathematicorum non tantum de facto est prima pars noeticae, sed id necessaria est, si cognitio nostra
intellectiva ex sensibus derivari debet. (p. 237) He summarizes the reasoning that leads him to such a conclusion in the following words:
Breviter resumamus. lntelligere est intelligere 'aliquid '; hoc 'aliquid'
designat obiectum determinatum, specificatum. In origine hoc obiecturn
nondum potest esse ' ipsum intelligere ' in genere; debet esse obiectum externum a sensu accepturn. Et in hi.v primae intelli[Jibilitates, quae in mente

388

BOOK REVIEWS

nostra inveniuntur, sunt principia primitiva mathematica, non tantum axiomata, sed etiam aliae propositiones primae, i. e., immediatae, quae in
deductione mathematica applicantur. Sed non sunt principia ' physico..'
N oetica, quae examinat intellectionem nostram, scire debet ' quid sit intelligere' et id originaliter experitur in 'casibus mathematics.' (p. 240).
The author indicates that the general lines of development of this noetic
science will first be in the realm of mathematical science, then that it should
be extended to metaphysics, and finally that the return should be made
to physics insofar as this is possible in view of the difficulty of the latter's
subject matter.

*

*

*

For purpose of analysis, it will be convenient first to consider the geometrical portion of Fr. Hoenen's contribution, and then to evaluate this
in its bearing on a general noetic science.
The problems of necessity and exactitude delineated by the author are
indeed the central ones that must be met in defending the Aristotelian
concept of mathematical science. The solutions to these problems which
are given are, in the mind of this reviewer, the correct ones. Ultimately
the difficulty must be resolved in light of the teaching on formal abstraction, because this is essential to understanding how the necessary, exact
propositions of any science can be asserted about a reality that is sensibly
contingent and imperfect.
It seems that Fr. Hoenen somewhat discredits the scholastic tradition,
however, by overlooking the contributions of Cajetan and John of St.
Thomas, to say nothing of St. Thomas, in developing Aristotelian doctrine.
Obviously, immediate application to the difficulties of modem mathematics
will not be found in these great commentators, but solutions to the basic
problems have already been given by them and only await application by
one who comes in contact with a modem difficulty. Benefit is to be derived,
no doubt, from thinking these things through for ourselves, and certainly
in expressing the doctrine in language intelligible to our contemporaries,
but great originality is rarely required and sometimes even results in error
that can easily be averted by patient study of the tradition. Significantly,
Fr. Hoenen's erudition is more apparent in his citation of modern mathematicians and in his refutation of their pronouncements, than in his utilization of scholastic source material.
Originality of thought, on the other hand, does characterize the contribution of the author in his study of the foundations of geometry. His
justification of " direction " as a primitive notion is particularly stimulating
and of obvious utility. Perhaps this discussion could have been improved
by a detailed examination of the limit concept involved when it is said
that a line has a direction as it" passes through a point." Such terminology
can be confusing and indeed might imply a contradiction, if the usual
qualifications made in the calculus are not rendered explicit.

BOOK REVIEWS

389

Another bit of terminology that can cause confusion is the way in which
Fr. Hoenen speaks of verifying the quid sit of geometrical concepts first,
and then proceeding to verify their an sit. This is directly opposed to the
normal process of knowing, and is criticised in the Posterior Analytics as
an impossible order of questioning. It is possible to know the quid sit and
the an sit simultaneously, but never the quid sit before the an sit (II Post.
Anal., Lect. 7) . What the author obviously intends by the quid sit is
really the quid nominis, but these are quite different notions in classical
terminology.
The evaluations of non-Euclidean geometry and axiomatics, though far
from being the last word on these difficult subjects, are nevertheless worthwhile parts of the book. Yet there are two difficulties that this reviewer
would like to raise concerning Fr. Hoenen's conclusion that non-Euclidean
geometry is a real science which considers a part of the objects of classical
geometry unnoticed by the classicists. The first respects axiomatic formulation. If, as Fr. Hoenen admits, the axiomatic structure of non-Euclidean
geometry appears the same as Euclidean geometry (except for the fifth
postulate), but actually the sense of the terms is changed, how can the
scientific character of the former be preserved? For instance, if a line is
actually curved, and is spoken of as straight, is this not a dialectical use
of the word " straight " ? What is really intended by the term is " approximately straight " or " apparently straight," and this cannot be the basis for
strict scientific reasoning.
The second difficulty respects the reality of the objects considered in nonEuclidean geometry. Fr. Hoenen takes the position that such objects really
lack curvature in a higher space: Nam ea obiecta, etiam ea quae sensibiliter stmt similia obiectis geometriae cl/1$sicae ( et de his agitur in problemate exactitudinis) non sunt nisi pars obiectorum geometriae classicae; sunt
What he intends by
revera obiecta incurvata in spatio altiori. (p.
"higher space" is not at all dear. His entire preceding analysis is devoted
to the justification of the three-dimensionality of the real continuum (homoloidal space). Can a space of higher dimensionality then be spoken of as
real? Use of the term " dimension " to embrace time and qualitative heterogeneities introduced by the presence of sensible matter would seem to be
nothing more than equivocation. Thus, on
basis of the arguments
offered, Fr. Hoenen's conclusion appears over-drawn. More warranted
would seem to be the inference that non-Euclidean geometry is either a
dialectical extension of classical geometry, or a mixed science resulting
from the application of mathematical principles to the objects of physical
science.
We turn now to the evaluation of the author's thesis that noetic science
has its necessary beginning in an examination of the foundations of
geometry. Actually to call this a " thesis " is an over-statement; it is ex-

7

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pre&sed in the form of a conclusion, but it has more the appearance of an
after-though worked into the last twenty pages of the text. Not only is
there a considerable intuitive jump from antecedent to consequent, but
there seems to be little relevance of one to the other. Whence the summary
judgment of this reviewer: non sequitur.
In fact, the very idea of a science devoted to noetic problems is highly
questionable. The multiplication of " sciences " during the past century
has so fractionated and compartmented scientific knowledge as to now
render it practically inaccessible as a comprehensible whole. The current
emphasis should be on restoring unity to scientific thinking, not on further
decimating it.
Any science, whether it be a real science or rational science, presupposes a certain act of intellectus in understanding its first principle. Generally a dialectical inquiry at the outset suffices to bring the investigator to a
grasp of these first principles. If he refuses actively to consider them, he
is not an apt subject for acquiring the science. If he refuses them as
erroneous, he cannot be refuted by the scientist as such, but must be
referred to the supreme science which exercises a sapiential role in defending
first principles, viz., metaphysics. :Further, all scientific speculation about
the real world reduces either to physics, mathematics, or metaphysics,
depending on the degree of abstraction involved in attaining the object of
the science. But there ean also be a seientific treatment of the reflex
activity of the mind in ordering its concepts, and this gives rise to a
rational science, viz., logic.
The problem of knowledge as it relates to the foundations of geometry
pertains in a way to all these sciences. It is a physical problem in the
psyehological sense, insofar as knowing is the act of a form in sensible
matter; it is geometrical insofar as it is eoncemed with the properties of
iutelligihle matter; it is metaphysical insofar as it defends the existence
and truth of first prineiples under the aspect of being, completely separated
from matter; and it is logieal insofar as the mind reflects on the necessity of
its own activity in ordering the concepts of the science.
Under the name of " noetics," Fr. Hoenen is considering all these aspects
of knowledge except the psychological one. Granting, for purposes of discussion, the " scientifie " character of such an enterprise, there is no
inherent necessity that a general noetics should take its start from
geometry, as opposed to any other real science. As a metaphysical problem,
the neeessary starting point is not mathematics but physics, insofar as
metaphysics is the post-physieal seience (d. W. H. Kane, 0. P., "The Subject of Metaphysies," THE THOMIST, Vol. XVIII, No. 4 (1955). And as a
logical problem, there is no inherent reason why logic, even material logic,
should take its start from mathematics. Demonstration can be seen independently in any subject matter by natural logic, and refleetion on demon-

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391

stration and its prerequisites enables the rules to be formulated for a
material logic (ars logica); the deduction of these rules as true properties
then produces the science of logic (scientia logica). It is certainly true
that the simplicity and intelligibility of mathematical objects make them
the easiest matters on which to reflect. But the exclusive use of mathematical matters in which demonstration is always through the formal cause,
also restricts the formulation of rules concerning the other causes, and this
limits the development of logical science.
It would seem that the most obvious argument against Fr. Hoenen's
conclusion is his own admission in the preface: Sunt philosophi, forte non
pauci, qui ubi in elucubmtione philosophica effata geometrica, vel mathematica in genera, etiam si de simplicissimis agitur, obviam habent, statim a
lectione et studio deterrentur. (p. 7) If such scholars have mastered philosophy, notwithstanding their abhorrence of mathematical science, there
is no necessary connection
geometry and noetics in general.
Moreover, in view of the author's preeminence as a cosmologist at the
Gregorianum, it is surprising that he should so reject the noetic character
of his own science: physics. It seems inconceivable to this reviewer that
he should compare the two statements: hoc corpus est figurabile and hoc
corpus est electrizabile per frictionem (p. 237) , and conclude to the basic
unintelligibility of physics. At least he might have proposed the physical
proposition: hoc sensibile est mobile. The questions at the level he is
investigating are not in the order of an sit tale, but rather properties immediately connected with the quid sit; otherwise they are not productive
of true scientific knowledge, which must be propter quid. And electrification, by friction or otherwise, is not a primum cognitum in the physical
order.
These, then, are the major points on which Fr. Hoenen's work appears
open to criticism. Insistence on such shortcomings should not be taken
as a condemnation of the work, for there is much of value in it and parts
might even be suitable for translation into English (e. g., Chap. II through
VI). Basically, this reviewer is opposed to the subtitle of the work, Origine
Theoriae Cognitionis, because he does not think it is either justified or
justifiable. Otherwise the main burden of De Noetica Geometriae is a
cogent defence of Aristotle's concept of science; it counteracts the excessive
preoccupation with formalism found among contemporary mathematicians,
and delineates the proper role of
in establishing the foundations of
mathematical science.
WILLIAM

Dominican House of Philosophy
St. Rose Priory
Springfield, Kentucky

A. WALLACE, O.P.

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Approaches to God. By JAcQUES MARITAIN. Translated by PETER O'REILLY.
W01-ld Perspectives, Vol. I. Edited by Ruth Nanda Anshen. New
York: Harper, 1954. Pp.
Man is a complex being and so his spirit finds many approaches to the
God who is the primal thing in his existence. These "reaches" to God
are first of all cognitional; love and service come later. But intelligence
has a dual role: one logical and discursive, functioning in its proper clime
of essences; the other intuitive and non-scientific, simply grasping the
concrete act of existing. The end of either is an awareness of the divine
actuality; an awareness that is the normal effect of intellection, thus universal-even connatural for mankind, and anteceding any and all activity
of supernatural faith. St. Paul wrote of it in terms of being the preamble
to faith, " For the invisible things of God are dearly seen by the visible
things which He has created."
lt is these philosophic and pre-philosophic contacts of the human intelligence with its Maker that constitute M. Maritain's " approaches " to God.
" Approaches " is a happily-chosen word. Only five of them are properly
demonstrations of God's existence; the remainder of them derive from an
experimental encounter with reality in which by quasi-intuition, previous to
any philosophic or theological ratiocination, the being and pre-eminence of
the Divinity is phychically held for certain.
AU that M. Maritain has to say in this little volume he has said before;
it is scattered throughout with references and citations from many of his
earlier efforts among them The Degrees of Knowledge which is being republished. This is less a criticism of this present work than a testimony to
the author's prodigious output. And indeed the book is fully adequate to
its writer's intention of grouping in an articulated whole all those varied
initial movements in the natural order of man's spirit towards God which
Thomism envisions.
These "approaches" can be readily grouped into five categories: (1) a
primordial pre-philosophic knowledge of God achieved in the natural intuition of being,
the five demonstrations of St. Thomas, (3) a " sixth
way" in the intellect's reflexive intuition of its own spirituality, (4) three
ways of the practical intellect' in its experience of beauty, moral goodness,
and the holiness of the saints, (5) the natural desire for the vision of God.
Briefly, we may offer reflections upon them in order.

I. The Natural and Pre-Philosophic Knowledge of God. Here M. Maritain discerns a primordial contact with God in and through the intellect's
intuition of the concept of being " in the intuitive perception of the analogical content of the first concept, the concept of Being." The psychological " moments " of this intellectual apperception, prior to every scien-

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tific elaboration, are as follows: (1) an intuition of the concrete act of
existing of things, (2) an awareness of one's own existence as distinct from,
limited, and threatened by that of others, (3) a grasp (still intuitive) of
unlimited or absolute existence, (4) a prompt, spontaneous reasoning, as
natural as this intuition (and as a matter of fact more or less involved in
it) "whereby, ... I see that Being-with-nothingness, such as my own
being, implies, in order that it should be. Being-without-nothingness-that
absolute existence which I confusedly perceived from the beginning as
involved in my primordial intuition of existence." This offers some
difficulties.
First of all, the concept of being is universal and abstract, and this
precludes its acquisition by way of an intuition. If intuition involves the
immediate grasp of a thing in its very individuality and unique wholeness,
it is incompatible with abstraction. Abstraction is always partial knowledge, leaving something behind and precising a " form " that is common
to many. An intuition of the concrete existent is understandable, but not
an intuition of being as such. True, the abstractive process here (in ens
ut sic) is sui generis, for "the differences of being are formally being."
Nothing is left behind; ens actually and formally contains all that participates being in any way whatsoever. Yet it does so only indistinctly and
confusedly. If it be better said that the concept of being is transcendental
rather than abstract, its acquisition still goes beyond an intuition.
The only sense in which it might be considered as a quasi-intuition is in
its lack of discourse and demonstration. Thus the first principles of reason
are considered as acquired through an abstractive process but in a quasiintuitive manner.
Secondly, can it be maintained that this pre-scientific grasp of being
includes an intuition, in the looser sense, of the analogical nature of being?
Being is analogical; but does not the concept have to be considerably
refined-through much reflection and comparison-before it expressly signifies this? This does not seem to be intued in the sense of presenting itself
to the mind as self-evident. It is per se nota in se but not quoad nos.
And thirdly, if an analogy like that of inequality be grasped by the mind
in a rather simple intellectual act, still the analogy involved here, between
uncaused and caused being, between Subsistent and participated being, is
that of attribution and is not possessed without some ratiocination (vulgar,
and as yet unscientific) on the principle of causality and participation.
Briefly, the author seems here to have weighted towards intuition what
is really only the uncritical knowledge achieved by "common sense"i.e., a natural and spontaneous reasoning process which becomes when
formulated in scientific terminology the philosophical equivalent of St.
Thomas' Quarta Via.
II. The Quinque Viae of St. Thomas. The presentation

here of St.

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Thomas' classic five demonstrations is: a non-controversial one, {any explicit dealing with the conflicting interpretations of contemporary Thomists
is obviously beyond the author's declared scope); brief (though the actual
text of St. Thomas in q.2, a.3 is reproduced in notes at the end of the
volume); and significant (for he does deal with the difficulties which inescapably confront the mind reared in modern scientism and in terms of
that science rather than the archaic language of the ancient physics). The
succinctness seems to be the end-product of some penetrating thinking on
these classic proofs, but this may appear too neat and abbreviated for
readers without some Thomist background. This might explain the review
in the New York Times (Oct. 31, 1954) by W. N. Pittenger quoting
Maritain as maintaining that these do not constitute five specifically
distinct proofs. Maritain is quite correct in insisting on a formal, specific
distinction. (p. 23) The context of the proofs here, of course, is philosophical
unlike that of the Summa.
III. The Intuitive Experience of the Proper Life of the Intellect. Here
M. Maritain offers a sixth "way," an addition to the five of St. Thomas.
The intellect's intuitive reflection upon its own act issues in a perception of
its own spirituality, i.e., its attribute as transcending the conditions of time.
In this, the author understands that it can dimly surmise its own nonpersonal, eternal pre-existence. The subject of this pre-existence is perceived to be Self-Subsistent Thought.
l'reviously regarded as " belonging to the domain of research hypotheses " this reasoning is now proposed as constituting, " a genuine proof, a
rationally valid way leading to a firmly established certitude." Its distinction from the five Thomistic proofs rests in this that it does not derive
from a fact observed in the world of sense, nor does it have recourse to the
principle concerning the impossibility of an infinite regress.
Nevertheless, this proof has very great kinship with the Tertia Via. The
temporal posits the existence of the Eternal· just as contingency requires
the existence of the Necessary Being. In actual fact, the latter is the more
ultimate reasoning since eternity is a passio of necessity. However, the
major difference is the transference from the metaphysical to the psychological order. The timeless aspect of created thought is not reasoned to, but
grasped in a vital experience. And it is not the logically perceived and
reasoned truth, but the su.bjective experience which proves.
There is no difficulty in seeing how the reflex experience of our own
intellection (intellectus superior) as only extrinsically subject to the conditions of temporality gives birth to the idea of intellection without such
limitation. Then, the real existence of Subsistent Thought is readily deduced
through the invocation of efficient and exemplar causality. But it is a
little different to approach this truth in terms of an intuition that my
thought is eternal in the Self Who is God. For this thought which is

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395

eternal is not, in every sense, mine. Without invalidating it as a highly
personal and experiential way to God, the psychological emphasis does
make this proof very subtle, and seems to weaken its objective probative
force.
IV. Ways of the Practical Intellect. (a) Aesthetic Experience. The
mind of man can come to an awareness of beauty, which in virtue of its
transcendentality stands in relation to an Absolute Beauty; is a correspondence with the beauty of God. This is poetic experience as delineated from
mystical experience whether natural or supernatural. It rests upon a knowla non-rational, quasi-intuitive nature. Such
edge by · eonnaturality-of
contact of the intellect with being is familiar to the Thomist, of course
(e. g., that which issues from the Gift of Wisdom in mystical contemplation), but not the designation of it as "non-conceptual."
It seems a
misunderstanding of the role of the universal mental " species " to see it as
an impediment to the spontaneous knowledge that poetry demands. How,
after all, can the beauty of the creature, reflective of God's, be in the
perceiving mind save intentionally-i.e., by an " intention " or " species " P
And why cannot the activity of the interior sense powers such as the
imagination and the vis cogitativa, subordinate to but simultaneous with
the conception of the intellect, upon the unique, singlar existent account
for this non-abstractive aspect of the cognition?
Maritain has pioneered much with the principles of St. Thomas in
aesthetics, and, it may well be that the rich originality of his mind has
achieved its surest expression in this area. But his insistence upon nonconceptual knowledge has never been convincing. The authority of St.
Thomas himself cannot be invoked in favor of it; and it gives rise to
serious difficulties. This is not to slight the contributions of Maritain to a
Thomistic aesthetic; his efforts here are still unsurpassed.
(b) Moral Experience. Morality is something relative, a conformity. It
implies an absolute. When the formal motive of my action is the good for
its own sake I come close (I approach) to Him who is good in virtue of
Himself-to Goodness Itself. This is to know God without being aware
of it. There comes into being a conformity of intellect with its transcendent
object (the Separate Good) effected by the will. (p. 98) This "unconscious knowledge ... tends to pass into consciousness," where it " creates
in the soul dispositions and inclinations which assist reason in its conscious
exercise to discover the truth which corresponds to them." Against the
background of such a moral experience it is still possible to deny consciously the existence of God, but this is only a theoretical atheism. Practical atheism requires a contrary moral experience " whose characteristic
is the rejection of all transcendence."
This is the argument from the intuition of moral obligation. When
formulated philosophically it is usually understood as a variation on the

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Tertia l'ia. The first principle of the practical order is per se known and
gives a knowledge of participated practical truth. From this one can
deduce the existence of the efficient and exemplary cause thereof-Who is
Practical Truth per essentiam. But Maritain has changed the focus. In
the free choice of moral good, when the formal motive is the bonum
honestum, " this very same act tends all at once beyond its immediate
object, towards God as the Separate Good." This is readily understandable. But isn't the tendency only a virtual one? Some conscious knowledge
of God would seem to be required before the ordainment (even in actu
exercito) could be designated as "actual and formal." (p. 96) This argument is constructed here very persuasively; its implications were more fully
explorf.:d in the author's earlier "Range of Reason."
(c) Lastly there is the Testimony of the Friends of God, the example
of the mystics, so forceful to the mind of Bergson. This is only an auxiliary
"way," confirming or re-enforcing convictions gathered elsewhere.
V. The Natural Desire to See God. Having surmised the Author of
nature in His effects, there arises in man (and totally naturally) an aspiration to grasp in an intellectual intuition the very essence of the Deity.
There is no disputing that an avenue to God lies open to the human mind
here--and one that nature herself· offers to the entire species. But the
precise possibilities, and the limitations implicit in this angustia of the
spirit need to be noted well. A subtle analysis of this natural longing is
thus called for-and the procedure is of necessity a theological one. The
beatific vision promised us is, in very fact, supernatural-substantially
and
not merely modally so. Only in the light of such a revelation can it be
understood what is involved in the hypothesis of a " natural vision " of
conclusion pregnant in this revelation is that any such
God. Now the
natural vision is actually. an impossibility. For God is supernatural-of an
entirely different order than that which lies mirrored in creation. He is
more than First Cause and Ultimate End of this universe. He is ThreePersons-of-One-Nature. As such, He cannot be seen save by those whose
spiritual powers have been elevated to a formal, physical yet analogical
participation of God's own intellect and intellection. Nature tends, therefore, to what is de facto an impossibility. But here Maritain is saying that
this natural tendency establishes rationally the possibility (not the fact)
of a vision of God. (p. 118)
The confusion arises from the signification which the term " natural "
bears in this context. The desire is not natural in the sense of innate. If so,
it would be implanted by the Author of nature and thus be a tendency to
what is not only possible but in some sense due. Faith perceives the error
here.
Nonetheless Maritain writes: "There is in the human intellect a natural
desire to see in His essence that very God whom it knows through the

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things which He has created." (p. 109) And he adds, " according as it
emanates from nature, it is a natural and necessary desire." (p. 111) These
words can too readily suggest that the desire is a pondus naturae of the
very faculty of intellect. Surely what St. Thomas means in I, q. H!, a. 1
is that man desires to see God, through his intellect-i. e., that the vision
is to be elicited by the intellect, but that the desire is rather elicited by the
will. The elicited character of this tendency is more certainly indicated if it
be characterized as free rather than necessary-as do the majority of St.
Thomas' commentators after Banez' time. As elicited, the desire is
measured by the knowledge which calls it into being-and it cannot go
beyond such knowledge. Now naturally the intellect cannot know whether
or not it is possible for it to see God. What is does know is that there is
lacking any positive reason for believing that such vision in impossible.
Thus the desire remains conditional and inefficacious. As John of St. Thomas
notes (De Fide: D. II, a. 3, n. 10), it is one thing to judge that something
is not impossible in itself and quite another to judge that it does not appear
impossible to us.
In what sense, then, is this desire natural? In the sense that its specifying
object is God as formaliter natural-God as the First Cause. This is to
intue Him as He transcends the universe He has brought into being, yet
being of the same order as it. Here it is the mode in which He possesses
the perfections of this world (as uncreated, infinite, pure act, etc.) that
distinguishes Him from creatures. (The Beatific Vision, on the contrary,
is properly God's alone--in its very being and not solely in God's mode of
possessing it.) Reason knows that it cannot grasp such an Object naturally,
yet it desires conditionally such vision to be accomplished within itself
supernaturally. But the supernaturality here is completely relative, as being
above the intellects's natural endowments without being outside of what
the Author of nature can bring it to. Thus when Maritain states that
reason, without the illumination of faith, can establish the possibility of an
order superior to nature (p. 113) (he does not mean the supernatural order
as presented by faith), this is super-natural only in a relative way, as in a
lesser fashion the angelic nature is above the human. Pure reason, then,
can reach to the existence of this transcendent order which is proper to
Subsistent Being; it knows that such is within the ambit of its adequate
object (ens ut verum), even if beyond its proper object (quidditas rei
sensibilis) -and so is there born a natural longing for what is beyond its
natural powers. (Maritain designates it as " trans-natural ") . But there is
no knowledge of the very quiddity of the Divine Reality, and from this
side (i.e., that of the object) vision may well be an impossibility. And
indeed this is so, unless man be elevated, not to the order proper to the
First Cause, but to that proper to God in His inner Three-Personal life
as Author of Grace. In short, it seems to be going a bit far to say that the

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rational establishment of an order superior to nature means that, ". . .
through the divine generosity man can therein be rendered capable of
knowing God in His essence." (p. 113) This is not to suggest that M. Maritain understands that the natural desire is innate, nor that a desire cannot
be at once elicited and necessary. Neither is it to deny that this natural
desire is a very effective suasio; an argument of probability having its own
urgency.
All this is not to place merely cerebral strictures on M. Maritain's vital
insights into man's natural pathways to God. It is only to express a
caution that these be not overstated. Most of them are heavily weighted
towards intuitionism and need the perspective which a strictly philosophical
and theological evaluation can impose. It remains true they are " approaches " and not all " proofs "; God initiates them as He will and they
are not to be bent to fit our mental categorizing of them. All of them are
far removed from genuine "religious" experience; and, needless to say, they
are remote from that contact with the living God which is possible only in
the luminosity of Faith and in the activity of Grace.
This book is Volume One of a series entitled "World Perspectives,"
edited by Ruth Nanda Anshen. Its purpose is to recapture the authority
of truth and human totality " on the basis of the sacredness of each human
person and respect for the plurality of cultures." St. Thomas, who took
truth where he found it, would approve.
WILLIAM J. HILL, 0. P.
Dominican House of Studies
Washington, D. C.

The Modern Predicament.
Pp. 405 with index.

By H. J. PATON.

New York: Macmillan, 1955.

The phrase thrust upon the reader by this book is "a point of view."
For the modern predicament is brought into focus by the author's examination of the opposition between the points of view of science and of religion,
an opposition whose acuteness makes modern a much older difficulty. Each,
science and religion, is led to an impasse, surmountable only by an acceptance of its diametrical opposite: science to a practical impasse, the
scientific inadmissibility of religious and moral truths necessary for practical
life; religion, to a theoretical impasse, the speculative indefensibility of
tenets necessary to religion's rationality. The line of reconciliation, in turn,
becomes rather a matter of recognizing that opposite points of view need
not be taken for real contradiction, but simply for a different perspective
upon reality. Professor Paton's main concern, in fact, is to make religion's

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point of view less " speculative " and consequently less of an impasse to
that of science.
But the problem demands of the reader that he determine the perspective
of the author himself. Professedly it is philosophical, directed towards the
philosophy of religion, for the book is the finished product of the Gifford
Lectures of Hl50-l951, a series endowed as a study of "natural theology."
While this latter is not to be understood in any scholastic sense, the
definition of perspective remains philosophical. The intent of this philosophical study is to determine the principles that make religion possible;
the grounds necessary to it that it be religion and not something else; and
in so doing to set out some philosophical defense of religion. But there is no
such thing as an indeterminate " philosophical " viewpoint; there are the
viewpoints of diverse philosophies, each characterized by its premisses, its
roots, and, unfailingly, by its assumptions. With Professor Paton, the
nature of religion, the condition of its survival, its extrication from the
modern predicament, are determined by his own philosophical perspective.
His philosophy is suspected by the reader in the preliminary examinations of possible grounds for religion, especially of any speculative effort
towards super-empirical truth, and particularly of St. Thomas' quinque viae.
The positive exposition of the author's own mind leaves no doubt; this is
the Transcendental-philosophie of Immanuel Kant rephrased, and refurbished with allusions to contemporary trends of thought. With his preceptol', Professor Paton assumes the object of human knowledge to be
immanent; its scope limited to the empirical order; its real content no
more than the sum of sensation; its " objectification " or " categorical characterization," the synthesis of a priori forms and material elements. Seen
in its core, the work is a tedious repetition of Kant; its main problem not
one of religion, but of criteriology. In this regard, it is particularly significant that in discussing the possibility of any sort of " realism," in the sense
of man's ability to attain reality as it is in itself (das ding an sich), the
author refers to such a theory as " Platonism," seeing in Aristotelianism a
merely accidental difference; that the " form " should be looked for in things
themselves, not as separated. Such an attitude points out the absolute
inability of the author to conceive of any essential difference between
Plato and Aristotle; to suspect even the possibility of an intelligence whose
object is being, reality, which in its turn is intelligible. For such a position
implies metaphysics, and as such merits only the contempt of the author;
but it is a contempt nourished by centuries of unchallenged assumptions,
one that only reasserts the seemingly unbridgeable gap between the Thomist
and his contemporaries.
Proceeding from a Kantian point of view, the findings of the author
are not surprising. Religion's point of view is in no wise metaphysical, but
moral; religious truths are not speculatively justifiable, nor intelligible, but

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practi<:aUy acceptable and experientially fruitful. To make religion reasonable, to free it from absurdity and the danger of science's opposition, is
to make it non-reasonable and is to empty it of any pretended alliance
either with a divine revelation made intelligible, even if incomprehensible,
to man or with truths naturally attainable and defensible by speculative
reason. Rather, in the face of the latter, the philosophy of religion will best
serve religion by recognizing the inability of the human mind to reach any
certain· knowledge about God, and by that recognition provide an impetus
for a volitional belief and hope in a suspected but undetectible reality.
Thus the point of view of religion is to be made a calculated, confessed
speculative agnosticism, inviolable by science, along with an acceptance of
truths about God and man, imperatively practical, and practically imperative--even for the scientist.
Within the general framework of his book, Professor Paton has offered
his reflections upon nearly all the main currents of contemporary philosophical thought. Especially noteworthy are his consideration of Logical Positivism, in the person especially of Professor Ayer, and his expose of propositions of " non-sense "; the reflections upon phychoanalysis and religion; the
occasional remarks concerning the Kierkegaardian horror and dread. For
the Thomistic metaphysician, he repeats a question found in Kant, but in
another sense presented by Cajetan; Suarez, the manualists, and one which
underlies many eon temporary discussions of the quinque viae in philosophy.
Taken philosophically do they have a religious end; are they formally to
be advanced as demonstrations precisely of God's existence? Repeating
Kant's criticism, the author sees in them an implicit and invalid illation
from the finite to the infinite, which amounts to an appeal to the ontological
argument. While this difficulty is based upon the Kantian gnoseological
assumptions, placing the realm of being beyond the grasp of the human
mind, perhaps scholastic philosophers have provided grounds for the fact
of the denial, by misrepresenting the function of Metaphysics in that phase
called "Natural Theology," and by a consequent misinterpretation of the
q1tinque viae. Professor Paton's examination of them affords another
occasion for self-examination on this point.
There must finally be mentioned another point of view with reference to
the Modern Predicament. · It is the theological point of view. While the
work purports itself to be philosophical, by reason of the matters upon
which it touches, it becomes in many instances, a kind of super-theology.
Of Sacred Theology St. Thomas has said that it exceeds all sciences in
dignity, in certitude, in subject; that it pertains to Sacred Theology, as
Wisdom, to judge concerning all others, and to reject as false what is
opposed to its principles, for these are a kind of impression of God's own
knowledge. Such a point of view is utterly distasteful to the present
author; his frequent sallies against the doctrinal and theological positions

BOOK REVIEWS

401

of the Church attest to that. But in spite of the author's distaste, the
Catholic theologian does have in a true sense the privileged sanctuary which
this author relegates to himself. From this sanctuary he must judge the
work of Professor Paton as containing errors against the teaching of the
Faith. Assuming as infallible the often ridiculously contrived theories of
German historical criticism, he questions the Divinity of Christ, the inspired
character of Sacred Scripture, the infallibility of the Church, etc. His
considerations of the writings of St. Teresa and St. John of the Cross, as
well as his discourses about grace are purely natmalistic. His discussion
of Divine Providence is based upon an attitude that man is meant solely
for a naturally happy life, free from pain or suffering, so that when these
are present, there is no possible sense in which God can be
as providently good. The details of his judgments are not of much consequence; it is enough to say that he has presumed to judge all things, and
that on a basis of equality, with the backgrounds of both philosophical
and scientific assumptions, and in so doing set himself above both the
natural and the supernatural orders. Obviously such a distinction, with all
that it entails in approaching the particular questions of God, man and
the world, can have no meaning to one who has undertaken to make the
very judgment which such a distinction would preclude. At the same time,
the Catholic theologian has the duty and the right to judge, to point out
error, to dispute over the natural truths whose misunderstanding has led
to such errors; and to regret that where the synthesis of Faith, that is an
elevation of man's intellect and reason, has been lost, there has emerged
a synthesis of science and speculation that denies to man the power to
know truth, and to God, the power to make Himself understood.
THOMAS

Dominican House of Philosophy
Dover, Mass.

C. O'BRIEN, 0. P.

BRIEF NOTICES
hnprudence in St. Thomas Aquinas. By CHARLES J. O'NEIL. The Aquinas
Lecture, 1955. Milwaukee: Marquette University Press, 1955. Pp.
176. $!il.OO.

H it be true that St. Thomas Aquinas' most original contribution-in
the best sense of the oft misused phrase--to Christian thought is his moral
theology, it can also be said that his treatment of prudence (H-H, qq. 4755) is representative of that originality to a high degree. In his treatment
of the virtues in general in the I-II, Aquinas insists on the necessity of prudence for the perfection of moral life. ". . . an intellectual virtue is needed
in the reason, to perfect the reason, and make it suitably affected towards
things ordained to the end; and this virtue is prudence. Consequently,
prudence is a virtue necessmy to lead a good life" (I-II, q. 57, a. 5).
Yet, for some mysterious reason manualists give rather short shrift to
prudence, despite its key location among the virtues. Even the earliest
moralists recognized its vital importance and its role in the moral life of
man. Thus, Epicurus writes: " The greatest good is prudence; a more
precious thing than even philosophy; from it spring all the other virtues "
(Letter to Monoeceus, Diogenes Laertius, Epicurus, Book X, sec. l3!i!).
Perhaps the Roman philosopher is a trifle over enthusiastic, but the shift
of emphasis on the part of the manualists from prudence to the other
virtues remains baffling.
It is, then, heartening to see a contemporary Thomist of Dr. O'Neil's
stature in an incisive monograph analyze the nature of imprudence in St.
Thomas' moral system. The distinguished professor of philosophy at Marquette University sets out to explain a divergence in Aristotle and St.
Thomas. The Stagirite makes no provision for any treatment of the vice
of imprudence while " St. Thomas is perfectly at ease in assigning the vice
of imprudence its proper place, its special sin, and its various parts."
(p. 3) It is the author's contention that this divergence between two
moralists of such repute can tell us something of the nature of man. We
might add that it also deepens our knowledge of prudence itself since, as
Aquinas reminds us, "One opposite is known through the other, as light
through darkness." (I, q. 49, a. 1)
Dr. O'Neil first excludes the possibility that Aristotle had no word for
imprudence or that he lacked a technique which he might employ to define
it. He concludes that Aristotle very definitely ruled out the possibility
of a vice opposed to prudence, one, that is, which might be called imprudence. The Aristotelian definition of prudence itself, insists the author,

402

BRIEF NOTICES

403

rules out the possibility of a vice of imprudence. " The logos which is prudence, therefore, is in its last analysis sheer intelligibility. It is essence.
Now essence is other than many things: cause, for example, and multiplicity, and existence. It is also tolerable of many things: cause, for example, and multiplicity, and existence. But that of which it is utterly
intolerable is contradiction. Therefore, if there were an imprudence conceivable with this prudence there would simply be no prudence. One should
recall that a triangle which is a non-triangle simply is not. And a prudence
which is a true habit and a straight logos admits no imprudence." (p. 18)
Next Dr. O'Neil studies the structure of imprudence in St. Thomas
utilizing Aquinas' Commentary on the Ethics, the Secunda-Secundae, and
the Commentary on the Epistle to the Romans together with isolated passages from other works. It is this section that Dr. O'Neil displays a penetrating acuteness in delineating with clear precision the teaching of St.
Thomas on the nature of imprudence. The author's examination of the
development of the thought of St. Thomas as well as the implications latent
in Aquinas' thought is worthy of high praise. He points out how St.
Thomas transforms the Aristotelian moral man and makes him more beautiful " because in St. Thomas his intelligible beauty is that of the existing
image of God." (p. 110)
Despite his obvious attempt at a lightness of style Dr. O'Neil's lecture
does not always achieve that intelligibility we might desire in a work of
scientific character. But notwithstanding his occasional lapses into somewhat complicated metaphors, his work is a significant contribution to
Thomistic thought on a most neglected subject.

Beginnings: Genesis and Modern Science. By CHARLES HAUJIET. Translated by E. P. Emmans, 0. P. Dubuque: The Priory Press, 1955.
Pp. 319 with index. $3.25.
Guide to the Bible, Vol. II. By A. RoBERT and A. TRICOT. Translated by
Edward P. Arbez, S. S. and Martin R. P. McGuire. New York:
Desclee, 1945. Pp. 649 with index. $6.00.
The two generations from Pius X to Pius XU have witnessed a remarkable development in scriptural studies and interpretation. It is not that
there have been many new interpretations; but rather, exegetes are coming
to enjoy more and more the atmosphere of the freedom of the children of
God. Certainly, Catholics may voice opinions today which they would not
have dared to do fifty years ago, when even some of the great minds in the
Church were unable to distinguish between Lagrange and Loisy. Those
were indeed times which tried men's souls; the tide of rationalism had to

404

BRIEF NO'l'ICES

be checked, and this was done vigorously in the condemnations of the
Pope and the decrees of the Biblical Commission. Slowly the clouds of
controversy lifted, and by 1945 Pope Pius XII in his Divino Afflante
Spiritu felt it was time to remind exegetes that there still remain " serious
problems," with which they must " grapple again and again " in an attempt
to find satisfactory solutions. The Pope also added, significantly: " Let
nil the other sons of the Church bear in mind that the efforts of these
resolute laborers in the vineyard of the Lord should be judged not only
with equity and justice, but also with the greatest charity."
Beginnings might well. be described as a report on how the request of
the Holy Father is being answered. M. Hauret presents first a general
introduction to the whole Bible, and then proceeds " to explain, without
attempt at erudition and from a practical point of view, the doctrinal
content of the first three chapters of Genesis." In particular, he takes up
the six days, the creation of the first man and woman, the Garden of Eden
a11d the temptation, and the Protoevangelium. For the benefit of teachers
he ends with an excellent chapter on " Practical Conclusions."
Although Beginnings is intended for the educated layman, not a few
theologians would profit from even a quick reading. With a succinctness
and clarity that make it highly recommended, this book shows the direction
by contemporary exegesis. From the pedagogical point of
being
view it is eminently practical. At regular intervals the author draws. up a
list of conclusions which arc certain, as well as those which are merely
conjecture. He makes a distinction between the imagery and the historical
reality of Genesis, since now greater emphasis is being laid on " the
scenario and the literary form of the drama."
At first glance much of this modern interpretation seems contrary to
the 1!)09 decree of the Biblical Commission which denied that we may teach
these chapters contain fables derived from mythologies and cosmologies
belonging to older nations, but purified of all polytheistic error and accommodated to monotheistic teaching by the sacred author. Indeed, the Commission reiterated just a few years ago that it saw no need to change its
careful wording. M. Hauret, however, shows how we must take the decree
against the historical background of the Modernism of the times. At the
same time progressive exegesis must venture to take the background of
mythological documents into account without succumbing to the temptation of reducing the Bible to the level of mythology. This is what Catholic
biblical scholars seem to be doing with no little success.
Again, we may not teach that these chapters contain allegories and
symbols destitute of any foundation in objective reality but presented under
the garb of history for the purpose of inculcating religious and philosophical
truth. This is quite different from the present tendency to treat those
chapters under the literary form called "historical parable." This term,

BRIEF NOTICES

405

incidentally, can be traced back to Cajetan. It is a giant step forward, and
the exegetes have prudently limited this literary form to the first chapters
of Genesis, for it cannot be applied to the history of Israel, nor to the
Gospel accounts.
While great progress is being made, all the problems of Genesis are by
no means settled, and M. Hauret is the first to admit it. The principle of
St. Thomas and St. Augustine can still bear repeating, that " since Holy
Scripture can be explained in a multiplicity of senses, one should adhere to
a particular explanation only in such a way as to be ready to abandon
it if it be proved with certainty to be false, lest Holy Scripture be exposed
to the ridicule of unbelievers, and obstacles be placed to their believing "
(I, q. 68, a. I). The faith will never be embarrassed by works of the
quality of Beginnings.
Guide to the Bible has a broader aim, as its title implies. The original
French work was published more than fifteen years ago, but the translators
have brought it up to date with copious footnotes, historical supplements
and additions to the bibliographies. This volume contains a great deal of
biblical theology, but its value for theologians will be uneven. They will
undoubtedly be interested in the brief summaries of the life of Christ,
the development of New Testament doctrine and the development of Old
Testament doctrine on such points as suffering, angels and the resurrection
of the body (implied in the burial of patriarchs; clearly taught in !l Maccabees). One chapter, "The Bible and Theology," is also to be recommended. The rest of the volume, however, while providing excellent historical and geographical background ·for a better understanding of the
sacred text, will be difficult reading for the most part. It presupposes a
fairly good knowledge of archaeology. Therefore, it might be better first
to read Albright's Archaeology of Palestine, so as to proceed from the more
known to the less known. Nothing must be left undone to understand as
well as possible the word of God.

Antiche e Nuove Edizioni degli Opuscoli di San Tommaso d'Aquino e il
Problema della loro Autenticita. By GIOVANNI F. Rossi, C. M. Piacenza: Collegio Alberoni, 1955. Pp. 74 with index.
Father Rossi focuses needed and timely attention on an important
critical problem-the question of the authenticity of the minor works
(opuscula) of St. Thomas Aquinas. It is an important problem owing to
the variety of subjects which the Angelic Doctor handles in these works;
it is timely because two new editions of the opuscula, by Fr. J. Perrier
(Lethielleux, Paris, 1949, which is still in progress) and by Fathers R.
Spiazzi, R. Verardo, and M. Calca.terr11 (Marietti, Turin, 1954), have
recently been published.

8

BRIEF NO'fiCES

Unfortunately the Dominican editors of these editions are still under the
spell of the exploded hypothesis of Pere Mandonnet (formulated in 1!.110)
that Reginald of Pipemo, associate of St. Thomas for many years, compiled an official catalogue of his works. Consequently they reject as spurious, or print as doubtful, works that are not found in this catalogue.
::\Iichelitsch, Grabmann, and other serious scholars have demonstrated on
incontestable and positive documentation that Mandonnet's hypothesis is
pure imagination, that the only scientific method for establishing the
authenticity of the opuscula is by studying the universal manuscript tradition. They· proved that works edited by Mandonnet as doubtful are
incontestably the work of St. Thomas.
Father Rossi subscribes to the Grabmann position and demonstrates the
uecessity of reexamining the whole problem of the authenticity of the
opuscula. Only when the manuscripts have been studied will it be possible
to fix the number, list the titles, and edit critically the entire corpus of
the minor works of St. Thomas. To prepare for this undertaking he
examines the problem of authenticity and studies the formation of seven
of the earliest manuscript collections, six of the early catalogues, and seven
printed editions of the minor works.
In terminating his study the author crystallizes his findings in a useful
. table of ninety-one reputed minor works of Thomas and cites the manuscripts, editions, and catalogues which contain or list them, indicating which
have been placed in doubt. It thus appears that more than half the number
have been challenged by one or other editor since 1490. At a glance we
realize that the editors, thus, far, instead of pursuing a constructive course
have been successively more destructive, wresting more and more of his
scientific production from St. Thomas. Yet this process has never been
carried out on the sole scientific basis admissible-an unbiased, scientific
examination of the entire manuscript tradition. J\Iandonnet and the current
editors have brought the process to the point of the ridiculous by the
wholesale manner in which they have questioned the authenticity of various
works. In case after case, supporting themselves on the theory of an
official catalogue, they have listed and edited as doubtful, opuscula which
have a venerable and strong manuscript tradition. For example, four of
the early manuscript collections, three of the six catalogues, and three
of the printed editions studied by Fr. Rossi list the De natura accidentis
as authentic. Yet these editors consider it doubtful. Before deciding such
an important point they should have studied exhaustively the evidence of
the manuscripts. Rossi, on the other hand, in other studies of the problem,
rehabilitated, on the basis of sound manuscript tradition at least eleven of
the opusc,ula considered by the editors as doubtful.
Fr. Rossi has done a distinct service to Thomistic studies in writing this
monograph. Once more, and again conclusively, he demonstrates that

BRIEF NOTICES

407

J\1andonnet's erroneous, and very harmful, hypothesis of an " official catalogue " of the Thomistic works should be relegated to the oblivion it so
richly deserves, so that no more will it ride rough-shod over authentic
manuscript tradition and over the memory and works of St. Thomas.

The Mystery of the Woman. Edited by EDWARD D. O'CoNNOR, C. S.C.
Notre Dame: The University of Notre Dame Press, 1956. Pp. 106.
$'?.75 ..

Filial piety is always to be admired. When it is accompanied by honest
gratitude it is doubly pleasing. The University of Notre Dame has been
humbly conscious of its blessings and the special protection it has received
from its l\Iother and Patroness, Our Lady. This volume represents an
attempt to express gratitude in a way which is most pleasing to Mary,
through a sane and solid treatment of her glories and her prerogatives. The
result is a confident and pleasing contribution to the literature of Mariology.
The University has chosen as the theme and limiting principle of the
work the words of the Marian liturgy: "Rejoice, 0 Virgin Mary, Thou
alone hast destroyed all heresies! " In developing the theme, the editors
have included three doctrinal and two historical essays. The doctrinal
essays discuss the office, preparation, and glorification of the Virgin Mother.
The historical essays admire her obvious protection of the United States and
her particular concern for her University, Notre Dame. The simplicity of
theme and, in particular, the fortunate choice of essays and authors, have
successfully resulted in a unified, brief, yet completely satisfying, sounding
of the depths of Mary's theology.
The first doctrinal essay is titled " Theotokos- The Mother of God "
and is authored by Walter J. Burghardt, S. J. of the Jesuit Seminary, Woodstock, Maryland. This essay is particularly valuable for its expression and
discussion of the present day emphasis on Mary's relationship to the
Mystical Body of Christ, His Church. There is a scholarly parallel drawn
between Ephesus' declaration of Mary's maternity in regard to the physical
Christ and the same doctrine in its extensions to the Mystical Christ. The
implications of the parallel are especially well indicated through the solidity
of theological reasoning.
The second essay was written by Ferrer Smith, 0. P., Regent of Studies
for St. Joseph's Province of the Dominican Fathers. His subject, "The
Immaculate Conception," develops the implications of " Ineffabilis Deus "
,Yith partieular regard for :Mary's victory over sin through the glories of
her grace. The reader will be impressed with the way these discussions
complement the content of the first essay. With the Immaculate Con-

408

BRIEF NOTICES

ception and its preparation in grace, Mary was well fitted for her physical
and graceful Motherhood.
The third essay discusses the glory of Mary as manifest through her
Assumption. This essay, written by Msgr. George W. Shea of Immaculate
Conception Seminary, Darlington, New Jersey, emphasizes the contributions
to theological thought and Catholic piety made by the recent definition
of the dogma of Mary's Assumption.
The historical essays, written by Daniel Sargent and Eugene P. Burke,
C. S. C., trace the .evidences of Mary's benefactions in regard to the country
as a whole and the University of Notre Dame in particular. Both authors
speak with the authority of scholarship and experience. With the calmness
of conviction, Mary's hand is seen in American History and the Notre
Dame story. The two essays quite pleasingly round out the tremendous
import of the practicality of the theological discussions of the first three
essays.
The University of Notre Dame should be complimented for their wisdom
in publishing these essays (originally delivered in symposium form to the
students and faculty at the University in 1954.) In so doing, the University has given articulate voice to its own gratitude toward Our Lady
and has made another positive contribution to solid theology and Marian
devotion.

The Lord. By RoMANO GuARDINI. Chicago:

Regnery, 1954. Pp. 546.

$6.50.

The chapters which comprise this book are the " spiritual commentaries
of some four years of Sunday services undertaken with the sole purpose of
obeying as well as possible the Lord's command to proclaim him, his message and works." (p. vi) In his introduction, the author forewarns his
readers that they may encounter unaccustomed ideas, turns of thought
meant only to stimulate reflection on the mystery of God " which has
been hidden for ages and generations, but now is clearly shown to his
saints. . . . " (Col. l: 26-27)
As the title suggests, Monsignor Guardini is concerned in this book with
certain aspects of the life and teaching of Our Lord and Savior, Jesus
Christ. He explains that these "meditations" (which must be taken in
a broad sense) make no claim to completeness nor do they attempt to
recount in chronological order or logical sequence the life of Christ. Rather,
they select from Christ's life " this or that teaching, event, trait, miracle
for thought, as it happens to warm to life." (p. vi) In point of fact, however, the matter covered does correspond, at least in broad outline, to the
history of Our I.ord's life, as the following section headings will testify:

BRIEF NOTICES

409

I. The Beginnings; II. Message and Promise; III. The Decision; IV. On the
Road to Jerusalem; V. The Last Days; VI. Resurrection and Transfiguration; VII. Time and Eternity. A brief conclusion (two and one half
pages) completes the 87 chapters of this large book.
No one could reasonably deny that in certain respects, at least, this is a
very profound book. It is undoubtedly the work of a man who is both
learned and thoughtful. He moves in the world of mysticism and metaphysics, exegesis and history with equal grace. For his study of Christ
Guardini has meditated often and long upon the Gospels, but he has also
drawn much material from the Acts, the Epistles, and the Apocalypse.
Finally, there are his personal reflections, which, more often than not, are
" flights of the mind and the imagination to the higher levels of knowledge
where the heart, if properly guided by theology, is perhaps more at home
than is the mind itself, and where it opens doors to the deeper mysteries
of the gospel story."
Despite the sublimity of its theme and the general high quality of its
expression, The Lord left this reviewer somewhat dissatisfied. Briefly,
Guardini, though often profound and always devout, is sometimes annoyingly vague; again, his pen is least facile when there is question of the ,
exposition of scholastic theology. On the question of private property and
the nature of man, Guardini, in speaking of the " baseness " of ownership,
states: "The baseness lies in the root of property its(jlf. Sin has destroyed
the possibility of natural ownership without fetters upon the owner or
injustice to others. In the sight of God even the most innocent ownership
is unjust." (p. 181) Neither the proximate nor remote context is of much
help in clarifying the thought of the author, especially with respect to
the word " natural." Passages whose phrases are equally disturbing occur
in the chapters on "Christian Marriage and Virginity," (p. Q70 ff.) where
the expression " natural " again is confusing, and " Destiny and Decision."
(p. QOS ff.)
The Monsignor promised us " unaccustomed ideas." He is, indeed, a man
of his word.

The Material Logic of John of St. Thomas. Translated by YvEs R. SIMON
and Others. Chicago: University of Chicago Press, 1955. Pp. 67Q with
indexes. $10.00.
The need for source books of Scholastic Logic is evident enough inasmuch
as text-books and manuals simply cannot supply the basic materials from
which their concise statements are drawn. This, the English translation of
certain sections of the classical Logica Materialis of John of St. Thomas,
places at the disposal of the serious student one of the major achievements
of Thomistic Logic.

.no

BRIEF NOTICES

Recognizing that the formalized, scientific language of the Scholastics
does not readily lend itself to precise translation, the present translators
give evidence of having expended every effort to express the thought in
clear, simple, and modern language. In the main they have been completely successful in giving a true and accurate expression of the doctrine
of John of St. Thomas. There are, however, a few instances in which the
usc of different terms or a change of phrase may have better served the
purpose of t)1e student using the text. Unhappily, the notes provided by
Dr. Simon do not seem quite as successful as the translation. In some
cases those used to illustrate and explain the text are too prolix, a difficulty
that could be overcome by questions directing the reader to common
experiences of reality.
Beginners, of whom Jacques Maritain speaks in the Preface, are often
confused by the division of Logic into material and formal even to the
point of missing the essential unity of the science. It would seem to this
reviewer that a clear presentation and explanation of this unity would
have added immeasurably to Dr. Simon's Foreward. Too, his " the relevance of the division into material and formal logic is indirect in the case
of the first two operations" is somewhat unsatisfactory. The fundamentals
of logic realized in the first and developed in the second operation of the
mind determine largely the doctrine. of the third operation. To speak of
them, then, as having indirect relevance is true, but at the same time they
are of enormous importance to the science of logic. John of St. Thomas
himself is very careful in his development of the doctrine of the Predicables,
and it may be disputed that they are of lesser clarity than that which
results from them.
This translation is a definite and valuable contribution to fill the need
for basic texts in philosophy, and the above points of criticism in no way
detract from this value.

Dogmatic Theology, Vol. I.-The True Religion. By G. VAN NooRT, Translated by John J. Castelot, S. S. and William R. Murphy, S. S. Westwith index. $6.00.
minster: Newman, 1955. Pp.
This first volume of a projected ten-volume series introduces itself to
the reader by a double introduction, one to the entire field of theology,
the other to fundamental theology. The bulk of the book, however, concentrates on an abstract analysis of religion itself followed by a consideration of the concrete truth of the Christian-Catholic religion. Two appendices constitute particular apologies: the first treats revealed religion before
Christ, the second Christ's teaching and St. Paul's position regarding the
Parousia. Besides the general index, there are special indices for Scripture
and for authors.

BRIEF NOTICES

411

The translation into readable, not excessively technical, English gives
evidence of the qualifications of the translators who unite this translating
ability with their special scientific competence. It was a happy thought to
combine a professor of scripture with a professor of dogmatic theology. The
publisher likewise has done well to produce a handsome volume with large,
readable print. Yet one wonders about the wisdom of such an expensive,
and sometimes unnecessary, layout. For instance, there are six pages of
introduction and notes for the first article when there are hardly five of
actual text. But the work itself is destined, we are told, for a very wide
reading public: the priests who confess their long years in the ministry
have made their consultation of Latin texts onerous, the seminarians who
find their mastery of the theological language insufficient for genuine
understanding, but especially the Sisters, Brothers and educated laymen
who want to consult a complete and technical study of theology in the
vernacular. Some of these people· are going to find the expense of ten
volumes excessive, and might wish for a more compact arrangement.
The formal content of this volume, however, is well chosen. Too often
fundamental theology becomes a miscellaneous file; in this case, there has
been a prudent use of the principles of selection. One example is the brief
historical outline which is well conceived and executed. Doubtless its very
brevity and selectivity will make any reader, with particular preferences,
disappointed at some omission. The present reviewer, for instance, would
suggest at least one addition. While the omission of St. Anthony, the first
Franciscan teacher and doctor, may be justified by the fact that the frame
of reference is systematic theology, one wonders at the little attention
given to the Scotistic school of the golden age. A quotation from a nonScotistic theologian would be apt: "Scoti Schola nu.meros·ior est omnibus
aliis simul sumptis." (Joannes Caramuel, Theologia Internationalis, lib.
cap. 8, Disp. 10,
p.
Lugduni, 1664.)
The presentation and critique of the method of immanence given as an
epilogue to the article on the recognizability of revelation is splendidly done.
There is a place for a psychological approach as well as the philosophical
and historical. The two need not, indeed should not, be mutually exclusive.
The treatment of the sublimity of the Christian-Catholic religion, to cite
but one example adroitly employs the two approaches to a very successful
conclusion.
The general fault of the volume, if fault must be found, is the paradoxical
one of at once too much and too little. Probably the fault is endemic to
apologetics itself which, though it had its rise in the early Christian
apologies, has developed very slowly so that it is only within the last
century that it has come to be considered as a science demonstrating the
rational credibility of the Catholic faith and a science in its own right.
In this slow development, apologetic has embraced much material which

412

BRIEF NOTICES

belongs in other places, to comparative religion, natural theology, history,
dogma properly speaking and sacred scripture. While the present work, as
has already been said, wisely employs the principle of selectivity in order
to avoid repetition, from a material point of view at least, three volumes
of apologetics, even under the aspect of an introduction to theology, seem
disproportionate in a ten volume work.
Likewise, since the present work is not a simple translation, but a
revision of a revision, there is an unwieldly conglamoration of footnotes and
annotation in the text as well as at the bottom of the page; then there
are copious references, comments and further additions at the end of
each section. Some of these could be pruned; some extended. One example
may be sufficient; number five on page 30 states: " E. Haeckel considered
the Catholic veneration given to relics and images a vestige of fetishism."
There is no further indication as to Haeckel's identity, to where or why
he said this. Still speaking of " too little " and the need for extension, the
translating revisors might have touched on the reestablishment of Israel
in connection with Christ's predictions about the temple and the city of
Jerusalem and His predictions about the Parousia. While it is true that
the Jews do not yet have the old capitol and that the new Israel may not
be the religious Juda, the contemporary fact of the reestablishment has
import for apology if not for apologetics.
Nevertheless, imperfect though it is, this work fills a real need, and is a
worthwhile contribution to American culture as well as to Catholicism.
From the technical point of view, a great service has been rendered in
simply bringing extensive bibliographical references up to date. The bibliography shows something else, that other vernaculars have works of theology which are not only complete and technical, but original. Perhaps
one of the greatest services of this translation-revision is that it paves
the way for such a work in English.

BOOKS HECEIVED
A Carthusian. They Speak by Silenceg. New York: I.ongmans, Green,
1956. Pp. 146. 7s 6.
Ayer, A. J. & Others. The Revolution in Philosophy. New York: St.
Martin's Press, 1956. Pp. 126. $2.50.
Balthasar, Hans von. (tr. by A. V. Littlesdale). Elizabeth of Dijon and
Her Spiritu.al Mission. New York: Pantheon, 1956. Pp.
Carol, O.F.M., Juniper B. Fundamentals of Mariology. New York:
Benziger, 1956. Pp. 223 with index. $3.75.
Clark, Gordon H. What Presbyterians Believe. Nutley, N.J.: Presbyterian
& Reformed, 1956. Pp. 141. $2.00.
Craig, Samuel G. Jesus of Yesterday and Today. Nutley, N.J.: Presbyterian & Reformed, 1956. Pp. 186.
Fricke!, 0. S. B., Michael. Deus totus ubique Simul. Frciburg: Herder,
1946. Pp. 164.
Gardeil, 0. P., H.-D. L'Oeuvre Theologique du Pere Ambroise Gardeil.
Soissy sur Seine: Le Saulchoir, 1956. Pp. 180. Fr. 600.
Gardeil, 0. P., H.-D. (tr. by John A. Otto). Introduction to the Philosophy
of St. Thomas Aquinas, Vol. Ill. Psychology. St. l,ouis: Herder,
1956. Pp. 316 with index. $4.00.
Harding, Arthur L. (e(l.). Religion, Morality and Lau!. Studieg in Jurisprudence, Ill. Dallas: Southern Methodist University Press, 1956.
Pp. 210 with index. $3.00.
Hitschmann, Edward. Great Men. New York: International Universities
Press, 1956. Pp.
$4.00.
Hofmann, Hans. (tr. by Louise P. Smith). The Theology of Reinhold
Niebuhr. New York: Scribner's, 1956. Pp. !il69 with index. $3.95.
Hutchison, John A. Faith, Reason and Existence. New York: Oxford,
1956. Pp. 314 with index. $4 ..50.
Jolivet, Regis. Le Dieu des Philosophes et des Savants. Paris: Librairie
Artheme Fayard. Pp. 128. Fr. 300.
Kroner, Richard. (tr. hy John E. Smith). Kant's Weltanscflauung. Chicago: University of Chicago Press, 1956. Pp. 130.
Kirk, Russell. Beyond the Dreams of Avarice. Chicago: Regnery, 1956.
Pp. 349. $4.50.
Metzger, Henri. St. Paul's Journey in the Greek Orient. New York:
Philosophical Library, 19.1)6, Pp. 75. $2.75.
Miegge, Giovanni. (tr. by Waldo Smith). The Virgin Mary. Philadelphia:
Westminster Press, 1956. Pp. 190 with indexes. $3.50.

413

BOOKS UECEIVED

:Hiller, Oscar \Y. The Kantian Thing-in-itself or The Creative Mind. :Kew
York: .Philosophical Library, 1956. l'p. 160 with index. $3.75.
Lewis. (ed. by Ruth Nanda Anshen). The Tran8jonnation of
Man. World Perspectives, Yol. 7. New York: Harper & Bros., 1956.
Pp. 267. $3.50.
:\ahm, 1\Iilton C. The Ariist as Creator. Baltimore: Johns Hopkins Press,
1956. Pp. 361 with index. $5.50.
O'Connor, C. S. V., Daniel A. Catholic Social Doctrine.
\Vestminster:
Newman, 1956. Pp. ;216 with index. $3.00.
O'Connor, C. S.C., Edward D. (ed.). The ll1ystery of the WommL 1'\otre
Dame: University of
Dame Press, l!J56. l'p. 160. $2.75.
Philips, Gerard. The Bole of the Laity in the Clmrch. Chicago: Fides,
HJ5G. Pp. 175.
Ple, O.l'., A. & Others. illystery and Myst.icisrn. New York: Philosophical
Library, Hl.J6. Pp. 137. $-4.75.
Rondet, S. J., Henri. (tr. and ed. by Donald Attwater). Saint Joseph.
New York: Kenedy, 1956. Pp. Q5Q. $4.00.
Sartre, Jean-Paul. (tr. by H4zel E. Barnes). Being and Nothingness. New
York: Philosophical Library, 1956. Pp. 707 with index. $10.00.
Sdmeider, Herbert \Y. Three Dimensions of Public 11!forality. Bloomington:
Indiana University Press, 1956. Pp. 166. $3.00.
Smith, Charles. Scnsism. Vols. l & 11. New York: Truth Seeker, 195(i.
Pp. 1686 with index. $10.00.
Smith, S. J., Gerard. The Truth That Frees. The Aq-uinas Lecture, 1956.
Milwaukee: Marquette University Press, 1956. Pp. 96. $2.00.
Warfield, Benjamin B. Calvin and Augustine. Nutley: Presbyterian &
Reformed, 1956. Pp. 518. $4.95.
Wuellner, S. J., Bernard. Dictionary of Schola8tic Philosophy. Milwaukee:
Bruee, 1956. Pp. 154. $4.25.