THE THOMIST
A SPECULATIVE QUARTERLY REVIEW
OF THEOLOGY AND PHILOSOPHY

EDITORS:

THE DoMINICAN FATHERS oF THE PRoviNCE OF ST. JosEPH

Publishers: Sheed and Ward, Inc., New York City

VoL. VII

APRIL, 1944

No.2

THE VIRTUE OF HUMILITY

T

HE sin of pride which ruined man and his world at the
beginning of time was a gloomy portent of the evil that
would wreck civilization after civilization down the ages.
And God's first curse, that the earth should bring forth thorns
and thistles to sweating man, presaged all too well the effects of
this vice on the course of history. The terrible plight of the
world today is a just punishment for its share in a sin of pride;
we are reaping the thorns and thistles sowed by the " Reformers." of the sixteenth century. The innocent must suffer
with the guilty, till the' nations return to God.
But how can the nations return to God? Only by subjecting
will in Faith and Hope and Love;
themselves once more to
and this is impossible unless they learn the humility taught by
the Son of God in His incarnation and on Calvary, and substitute Christian magnanimity for the pride of Lucifer. These are
the two antidotes for the poison that hardens the mind and the
heart against Christ: magnanimity, by which the extraordinarily gifted man, confident in the God-given talents he pos135

136

SEBASTIAN

CARLSON

sesses, dares to accomplish great things for his fellow-men or
the Mystical Body of Christ;
by which every man,
considering the depth of his nothingness and sin, and God's
excellence as his Creator and Redeemer, is restrained from
attempting anything beyond the measure of his nature and of
the grace given him, yet at the same time from acting beneath
that measure.
Humility is not the outmoded and stiff-corseted virtue of a
happily dead era, but a vital and active force to be promoted by
the Church today as never before. In an age when she must
struggle so against the world's pride, when she needs characters
developed to utter perfection naturally and supernaturally, and
when she still has the schools and seminaries to effect such a
development in her laity, religious, and clergy-in such an age,
humility is absolutely indispensable. It will foster in every
individual either the self-assertion or the self-suppression proportionate to the talents he has received, and thus bring about
fruitful cooperation of the Mystical Body and its visible head
on earth.
If this need is so urgent today, we may ask ourselves, what
has the Church to teach about Christ's legacy of humility? In
particular, what does her greatest theologian say of it? And
from the principles he enunciates, what further can we deduce
about it? These are the questions we will attempt to answer in
these pages.
In his study of humility in the Secunda Secundae of the
Summa Theologiva, St. Thomas follows the method and order
best suited for the speculative treatment of any virtue. Is
humility something virtuous or vicious? Is it a special virtue
with its own formal object? How can it best be defined? What
is its subject, its extent, and its place among the other virtues?
What is its rank and relation to them? What, finally, are its
degrees? The present study will follow the same general plan,
but a section on the interior acts of humility will be inserted
between the consideration of its objects and subject. Following the saint's procedure elsewhere, the final section will be
devoted to the Gift of the Holy Ghost corresponding to it. In

THE VIRTUE OF HUMILITY

137

conclusion, an attempt will be made to determine what development Aquinas made of the doctrine handed down to him
by the Fathers and ecclesiastical writers of the Western Church.
Every exponent of Thomas' doctrine is confronted by a
fundamental problem. He realizes that, if the order of the
Summa be adopted, what must be presented first of all is the
basic part of the matter under discussion, its technical and
hence more difficult aspects. For Thomas insists on first things
first, on starting at the bottom of things, on digging for universal principles. That difficulty could not be obviated in
these pages, and the reader will find the first sections heavy
and labored. They attempt to analyze the essence of humility,
to differentiate it from all other virtues, to define it with all
possible precision. Once the notion of humility is grasped
firmly, however, the rest is easy. The understanding of an
essence is a bow bent taut toward the stars.
As for sources, the principal one, by far, is the Summa
Theologica. There is little on this subject in Aquinas' other
works, though what they do contain is of sterling quality. Free
· use has been made of the Commentators, of special studies on
allied subjects, and of articles in the philosophical and theoto
logical reviews and dictionaries. In the notes, the
Cajetan's commentary on the Summa follow the Leonine edition of the Opera Omnia; but those 'to Thomas' works other
than the Summa follow the pagination and divisions of the
Marietti edition (this being more readily available, in the
majority of cases, than the Leonine). For citing works not
contained in the Marietti or Leonine texts, the Parma Opera
Omnia has been used.

1. THE NATURE OF HUMILITY
A) The Morality of Ilumility

Lowliness, nearness to the ground-this, roughly speaking, is
the meaning of humility as seen in the etymology of the· word
itself. What does reason say of such a characteristic? Is it
the mark of a reasonable man to consider himself lowly and

138

SEBASTIAN

CARLSON

worthless; even to act on this knowledge and refrain from what
is great and lofty, from
from desire for a high position in the world? Upon the answer to this question depends
the morality of humility, its virtuousness or viciousness. It Is
the question proposed by St. Thomas at the outset of his study
in the Summa; 1 and it implies the unending objection of the
world, even of many Christians.
Is not man the lord of all creation, next only to the angels?
His place is among the greatest works of God; he is God's
noblest achievement at the beginning of time.
Thou hast made him a little less than the angels,
Thou hast crowned him with glory and honor,
And hast set him over the works of thy hands.
Thou hast subjected all things under his feet.2
Why then should he humble himself? The objection receives
new strength from the very position of the question on humility
in the Summa. Its author has gone to the limits of speculation
to prove man's dignity as a creature of God and as a son of God,
raised by Him to the level of His own inner life and given the
to spend eternity gazing upon the face of his Maker.
A creature raised far above himself by grace, given a new Law
of Love, and adorned with virtues that are supernatural not
only in mode but even in their substance-what has such a one
to do with humility, with lowliness?
From the viewpoint.of his elevation, nothing. Such a viewpoint considers man not in himself, but in what he has received
from God. And what is that? Everything that has the notion
of being. The Summa, that has praised man so fully, has
likewise shown the source of all his excellence and glory, has
analyzed his nature minutely and revealed all the gifts that
have come down to him from above. Stripped of his divine
plumage, what has he left? Absolutely nothing that has the
notion of being! He is not even the dust and ashes by which
Abraham sought to signify his worthlessness. 8 He is nothing1

n-n, q. 161, a. 1, arg. !!.

• Ps. viii, 6-8.

• Gen. xviii, 27.

THE VmTUE OF HUMILITY

189

ness. Worse, he is nothingness befouled by sin. "In man, two
things can be considered: that which is God's, and that which
is man's. Man's share is whatever pertains to deficiency, but
God's is whatever pertains to salvation and perfection." 4 In
a word, creation, supernaturalization, and redemption are God's
contribution to His rational creature. Man has added sin
alone.
In the face of this truth, what should be the reaction of reason? First of all, surely, to acknowledge it intellectually.
Secondly, to employ it as a practical principle in daily life.
This entails the subjection of man to his Creator, the willingness of the individual to remain in the place allotted to him by
divine Providence, the persevering use of his talents in the
tasks for which they were bestowed upon him by their giver.
Such subjection to divine Providence, born of self-knowledge,
is the essence of humility. It forbids the soul to exceed or fall
below the measure of natural and supernatural gifts meted out
by God; it demands that the rational creature, " considering his
deficiency, hold himself to what is lowly, according to his
measure." 5 " The virtue of humility consists in this, that a
person contain himself within his limits, not extending himself
to what is above him, but subjecting himself to his superior." 6
This is what reason tells us of lowliness of heart. It follows
that it is something virtuous, a characteristic of man acting in
accordance with right reason. Far from being an indignity to
' " • • . in homine duo possunt considerari: scilicet, id quod est Dei, et id quod
est hominis. Hominis autem est quidquid pertinet ad defectum, sed Dei est quidquid pertinet ad salutem et perfectionem" (Summa Theol., II-II, q. 161, a. 8,
corp.). (Hereafter, references to question 161 of the II-II will consist only of the
number of the article and the part of it referred to, thus: Art. 8, corp.)
• " . . . considerans suum defectum tenet se in infimis secundum suum modum
•.. " (Art. 1, ad 1).
8 " ••• virtus humilitatis in hoc consistit ut aliquis infra suos terminos se contineat, ad ea quae supra se sunt non se extendens, sed superiori se subjiciat . . . "
(IV Summa contra Gentiles, c. 55, ad 17) . Throughout ·this study, the words
"superior" and " inferior " have been used merely to transcribe the Latin words,
which mean one who is above or below another. Authority is not necessarily
implied. He is " superior" who is in any way, howsoever insignificant, more
excellent than another.

140

SEBASTIAN

CARLSON

human personality, a hindrance to the development of noble
character, it is an unspeakable glory. "In revering and honoring God, our mind is subjected to him; and it is in this that its
perfection consists. For everything is perfected by being subject to its superior: as the body by being vivified by the soul,
and the air by being enlightened by the sun." 7
B) Humility a Special Virtue

Humility is a virtue, then, because it is according to right
reason. But is it a special virtue? Is it, perhaps, only one
aspect of some other virtue, as frankness is one
of
veracity? Is it merely an element that is present in all virtues,
as moderation is present in all of them? Or has it a formal
object of its own, as prudence has, and fortitude and clemency?
If so, it is a special virtue, one set off definitely from all the rest,
with definite characteristics and its own peculiar functions. 8
Humility regulates the soul's elan toward great things. It
is concerned, accordingly, with the irascible side of the appetite,
that side which faces good not as it is merely desirable, but as
it is arduous and difficult of achievement. In other words,
humility controls and rationalizes hope, the passion which
stimulates man to pursue any future good that he sees will be
hard to attain. It functions in the same general :field as magnanimity and its little sister philotimia, 9 the two virtues that regard the pursuit of honor. Indeed, it seems to coincide with
them in their negative
of withholding the soul from
honors beyond measure. Is humility only a name given them
as they are concerned with this reasonable flight from incom7 " • • • per hoc quod Deum reveremur et honoramus, mens nostra ei subjicitur;
et in hoc ejus perfectio consistit: quaelibet enim res perficitur per hoc quod
subditur suo superiori; sicut corpus per hoc quod vivificatur ab anima, et aer per
hoc quod illuminatur a sole" (Summa Theol., II-II, q. 81, a. 7, corp.).
8 Cf. Art. 1, corp.
• Magnanimity is the moral virtue which makes a person of great talents, natural
or infused, tend to great achievements worthy of great honor. Philotimia, " love of
honor," has no exact English equivalent. It is the moral virtue which inclines a
person of ordinary abilities, natural or infused, to seek the honor and accomplish
the good that is in proportion to those abilities. Cf. Section VII.

THE VIRTUE OF HUMILITY

141

mensurate honors, i. e., with the curbing of hope? Or is there
room for still another good habit in this single plot of human
activity?
·
On first glance, it would seem not. The fact that lowliness
of heart controls hope while magnanimity and philotimia stifle
despair, does not necessitate a distinct virtue for both passions.
One and the same habit is often concerned with opposite
motions of the appetite. 1 ° Chastity, for example, tempers both
the desire for sexual pleasure and aversion to it. The same is
true in the irascible, for example in the case of fear and daring.
The one virtue of fortitude " regards both fear and daring,
being as it were cohibitive of fears and moderative of daring." 11
It is verified also in the case of hope and despair in one who
seeks great honors according to right reason. Magnanimity
strengthens him against the virus of despair, to achieve deeds
worthy of much honor, yet moderates his appetite against
inordinate sallies of hope and the misuse of honors. 12
What becomes of humility, the throttle of hope and of the
immoderate quest of one's own excellence? As has just been
seen, magnanimity both bridles hope, keeping it from unrestrained tendency toward the great, and hardens the soul
against despair, stimulating it to great deeds. Why postulate
another virtue concerned with the quest of excellence? Magnanimity in the pale of great honors, philotimia in that of the
ordinary ones falling to man's lot, would seem to be quite
sufficient. Humility appears to be but a name for the negative, cohibitive side· of these two good habits.
1

° Cf. Summa Theol., I-II, q. 60, a. 4, corp.

Et ideo fortitudo est circa timores et audacias, quasi cohibitiva timorum, et
audaciarum moderativa" (Summa Theol., II-II, q.
a. 8, corp.).
12 Cf. Summa Theol., II-II, q.
"lnde habes, primarium actum magnaJlimitatis, adeoque finem ejus principalem, et objectum formale, esse tendere ad
magna magna honore digna, non quidem propter honorem, sed propter eorum
excellentiam ratione cujus sunt honore digna; actum vera secundarium, esse
moderari appetitum et usum honorum, in ordine ad magna patranda. Ita in fortitudine, actus primarius est sustinere et aggredi; actus secundarius est moderari
timores et audacias" (P. Xaverius Faucher, ·note on Art. 1 in loc., Faucher edition
of the Summa).
11 "

142

CARLSON

Hence, in its act of restraining the soul from desire for undue
honor, magnanimity should receive the name humility. For
the latter term _connotes simply that perfection of character
which keeps man near the earth, humus, from which he originated. If its only end is to bridle hope, it can only be one
aspect of magnanimity-a secondary and negative one at that,
since the principal and positive duty of greatness of soul is to
invigorate man in his quest of extraordinary honors.
A closer investigation of the question, however, leads to different conclusions. Great achievements arduous ill their accomplishment can be considered in two ways, yes-as they enkindle
hope, and as they occasion despair .13 Man can face the great
with two attitudes: he may seek it reasonably and moderately;
he may tum from it reasonably and moderately. . These two
attitudes must be considered more attentively.
On the one hand, in seeking the excellence proportionate to
his talents, he ought not merely to advance firmly; he must at
the same time refrain from advancing unduly. On the other
hand, in fleeing the great, he should not only rein in his
appetite for what above measure, but encourage it to what is
proportionate. Otherwise, he would still either seek in excess
or seek too little.
It is evident, then, that in the appetition of the great: and
difficult there exist: appetition which consists principally in
aggression, but demands moderate abstention; and flight or
aversion, fuga, which consists principally in retreat, but demands moderate aggression. Hence there are not merely two,
but four motions of the irascible appetite in regard to the
arduous, two courting it, two fleeing it. Is it possible for one
virtue to keep this complex activity conformable to reason?
No. The motive for seeking the excellence due to self is wholly
different from the motive for fleeing the great. One tends
toward his own excellence, toward the perfection of his faculties, because the doing so is especially praiseworthy, the unfailing mark of a lofty mind. One flees what is great because
11

Cf. Art. I, corp. mit.

THE VIRTUE OF HUMILITY

148

human nature considered in itself is nothingness, and nothingness is worthy of nothing. It is this ·utter dissimilarity of
motive in the reasonable quest of the great and in the reasonable flight from it that makes two virtues indispensable. Man
must have one good habit concerned first and foremost with
the flight from incommensurate honors-humility; 14 another
concerned chiefly with the seek,ing of the excellence due to
him-magnanimity or philotimia. As St. Thomas says:
In the appetition of the arduous, two virtues are necessary. One
which will temper and restrain the soul, lest it tend immoderately
to what is lofty; this pertains to the virtue of humility. Another
which will confirm the soul against despair and impel it to the
achievement of grand deeds in accord with right reason; this IS
magnanimity .15
Notwithstanding all this, it is still conceivable that some
other virtue, along with its principal function, exercises the
double control just ascribed to humility-legal justice, for instance, whose duty as a special virtue is to make the individual
willingly subject to the common good, and whose proper object
is that common good.16 Though its principal function is to
keep reason in the mutual relations of the .members of a community, yet, because it uses all the moral virtues to obtain its
own end, 17 it necessarily, if secondarily, reaches into the internal
life of the individual and controls his passions and affections. 18
In its human aspect, therefore, humility might be a phase of
legal justice, subjecting one man to another according to law,
directly curbing or spurring ambition, and indirectly restraining or encouraging the inner source of ambition, the appetite
This is humility described by its primary act. Cf. infra, Section III.
circa appetitum boni ardui, necessaria est duplex virtus. Una quidem,
quae temperet et refraenet animqm, ne immoderate tendat in excelsa; et hoc
pertinet ad virtutem humilitatis. Alia vero quae firmet animum contra desperationem et impellat ipsum ad prosecutionem magnorum secundum rationem rectam;
et haec est magnanimitas" (Art. I, corp.). Cf. 1-11, q. 60, a. 4; q. 6I, a. 2;
Cajetan, Oommentarium in Bummam Theologicam B. Thomae, II-II, q. I6I, a. I, I.
1 °Cf. Summa Tkeol., II-II, q. 58; aa. 5, 6.
17 Ibid.
18 Ibid., a. 9; note particularly the answer to the. third objection.
u

15 " • • •

144

SEBASTIAN

CARLSON

for greatness. In its divine aspect, humility would be reducible
to religion, the virtue of the justice group which makes the will
prompt to pay God the subjection it owes Him.
What precisely is it, then, that cuts humility definitely off
from magnanimity and justice, and makes it a special virtue?
As has just been pointed out, it is the motive of humility, that
is, the end which reason has in view in keeping the activity of
the irascible appetite within the bounds assigned to it by
divine Providence. For it is the formal
or object, as it
is called, which distinguishes a virtue from all others. 19 In the
case of lowliness of heart, as will be seen in the next section, it
is the known worthlessness of the ego in comparison with Him
Who created it, raised it to the supernatural order, and redeemed it; in other words, it is the will to be subject to God.
" Humility as it is a special virtue regards most of all the subjection of man to God, because of Whom it also subjects itself
to others, humbling itself." 20
C) The Objects of Humility

Often it is the simple which is bewildering in its apparent
complexity, like the mirror labyrinth at a carnival. Habits are
a case in point; incomposite, spiritual units in themselves, they
bristle with relationships to both mental and extra-mental
reality. The passions and the acts of the superior faculties
which they moderate; the persons and things which attract or
repel the appetites; the persons and things, too, with which
social, political, and religious life are concerned: these are related to virtue as the matter with which it deals. The definite
rational control which it aims to establish in some corner of the
soul is related to virtue as its purpose, its intrinsic end, its
formal object. 21 And the particular good of reason that the
° Cf. the next section, on the fonnal object of humility.
•• " Humilitas autem, secundum quod est specialis virtus, praecipue respicit subjectionem hominis ad Deum, propter quem etiam aliis humiliando se subjicit "
(Art. I, ad 5) •
21 Cf., e. g., Charles Billuart,
Summa Sancti Thomae, Dissertatio prooemialis,
Art. V, init.: " Objectum . . . duplex distinguitur in omni potentia vel habitu,
1

THE VIRTUE OF HUMILITY

145

intellect sees will be obtained by seizing and maintaining that
control-this is related to virtue as its formal motive. 22 These
are what the philosopher and theologian know as the objects of
virtue: the material, the formal quod, and the formal quo
objects respectively. They will be referred to in these pages as
designated above: the matter, the formal object, and the formal
motive. To obtain a. clear and full understanding of humility,
and of its distinction from its sisters and cousins among the
virtues, it will be necessary to study its objects in detail.
1. TheM atter of Humility. The matter of humility is, to put
it baldly, everything. "Humility makes man completely subject to the order [of reason] universally, quantum ad omnia; but
every other virtue, with regard to some special matter." 23 In
other words, there is not a single good,, infinite or infinitesimal,
uncreated or created, personal or impersonal, with the appetition of which humility is unconcerned. One of its degrees listed
by Christian tradition is " to confess and believe oneself use-.
less, and unworthy of anything." 24 This is true despite the
fact that it regulates the irascible appetite, which is called into
play not by every desirable object, but only by the arduous.
The lowly of heart deem even the least good not simply desirable but always difficult, because unobtainable by their own
powers: Considering that part of the ego which is their own,
nimirum materiale et formale. Objectum materiale est id quod a potentia vel habitu
attingitur quidem, non tamen ratione sui sed ratione alterius. Objectum formale
est id quod a potentia vel habitu attingitur ratione sui, et ratione ejus caetera
attinguntur. In objecto formali duplex ratio debet distingui: ratio quae, et est
ipsa res quae attingitur, et dicitur objectum quod, et ratio qua seu sub qua, et est
id quo mediante ratio quae attingitur: et dicitur objectum formale quo seu sub
quo; ita ut ex hac duplici ratione quae et qua integretur objectum formale, quod
est specific;ttivum potentiae vel habitus."
•• Ibid., Tractatus de spe, Dissertatio unica, Art. II, praenota: " ... [objectum]
formale quo est motivum, et ratio propter quam, et sub qua objectum materiale
attingitur ."
••" Ordinationi autem ·facit hominem bene subjectum humilitas in universali,
quantum ad omnia; quaelibet autem alia virtus, quantum ad aliquam materiam
specialem " (Art. 5, corp.) .
•• " ... ad omnia indignum et niutilem se confiteatur et
(St. Benedict,
Regula, Cap. VII (M L 66, 874 A), as quoted by St. Thomas, Art. 6, arg. I).

146

SEBASTIAN

CARLSON

they see their utter incapacity for good; and when reason
prompts them to seek an excellence compatible with their
talents, they advance toward it as to something great in comparison with their own nothingness.
It is common to all appetible things, whether they are excellent
or not, that, according to the rule of humility, they be sought as
things above man's proportion, because the humble address themselves to all things as unworthy of them .... 25 Humility directly
regards all things, whether arduous in themselves or not arduous in
themselves, but all things under the aspect of something arduous.
For what is not arduous in itself takes on the notion of the arduous
for the humble person, because it-takes on the notion of the divine:
since the humble address themselves to all goods as to things that
are God's. 26

Be it as small a thing as cooking a better pot of coffee than
one's next-door neighbor, or as great a thing as taking St.
Peter's place in the Church of Rome; as insignificant a thing
as contributing a dime to the Red Cross; or as munificent a
thing as turning over a fortune of millions to the needs of an
invaded country-all this is matter for humility, as it is ripe
matter for pride. A child, trying desperately to establish her
superiority over a playmate, was heard to boast," Well, anyway, the grass at my grandpa's house is higher than yours!"
Even the possession of unmown grass can be considered a distinction; a distinction is an excellence; an excellence is something harder to obtain and maintain than its opposite, and so
is always the object of the irascible rather than of the concupiscible appetite. In the order of the material or the spiritual,
of the sensible or the intellectual, of the natural or the supernatural, there is nothing outside the ambit of lowliness of heart.
•• " ... commune est omnibus appetibilibus, sive excedant sive non, quod, secundum humilitatis regulam, appetantilr ut supra hominem: quia ad omnia humilis
II).
se habet ut indignus " (Cajetan, Commerntarium, in TI-ll, q. 161, a.
•• " • . • humilitas est directe respectu omnium, scilicet arduorum secundum se
et non arduorum in se, sed tamen omnium est sub ratione ardui. Quia quae non
sunt in se ardua, induunt rationem ardui relate ad humilem, quia induunt rationem
divini: ad omnia siquidem bona se habet humilis ut ad ea quae Dei sunt " (Ibid.,
a. 5: XXII, " Secunda").

THE VmTUE OF HUMILITY

147

All goods are matter for humility, whether they are in themselves great or small. For it is concerned with the same things as
pride; but it is evident that there is pride even in the smallest
excellence, as we see in persons who have to do with mechanics and
the humblest occupations, among whom the very worst pride is
found. For even cooks are proud. 27

H man is so constituted thf,l.t he cail be proud of his ability to
call hogs louder than his neighbor, or to run a machine that
needs but the turning of a crank, it is necessary indeed that the
matter of humility be any arduous good whatsoever.
What has been spoken of so far is the remote matter of the
virtue. The proximate or immediate matter is the soul's natural
inclination to seek its excellence. As has been seen, this is a
motion of the irascible
toward what is at once difficult
and good; in other words, it is the passion of hope. While hope
and desire both look to a future good and so are clearly set off
from joy and pleasure in a good that is present, hope deals with
a great and difficult good, precisely under the aspect of greatness and di:fficulty.28 Hope is the elan of the soul toward an
absent but possible good that will prove hard to attain. It
exists as a passion in the sensitive appetite, as a simple affection of the will in the rational appetite. As a virtue, it is the
theological virtue of hope-but with this, humility has no direct
connection. It is with the passion and the affection that it is
engaged; also with daring, the emotion that springs as it were
naturally from hope; and with confidence, which is " a certain
robustness of hope springing from some consideration that produces a firm expectation of success." 29 Because these emotions
•• " Humilitatis vero materia omnia bona sunt, sive secundum se sint mligna,
sive parva. Quoniam est circa eadem circa quae est superbia: constat autem
superbia esse et in excellentia minimorum, ut patet in mecha.nicis et mediocribus
officiis, in quibus pessima superbia invenitur: sunt enim coqui superbi" (Ibid., q.
161, a. 1: m, jim.).
""Walter Farrell, O.P., A Companion to the Summa, II, 186 (New York: Sheed
and Ward).
•• " . . . quoddam robur spei proveniens ex aliqua consideratione, quae facit
vehementem opinionem de bono assequendo" (Summa Theol., 11-11, q. 129, a. 6,
corp.). Cf. also the following: "Alius autem motus interior in aliquid tendens
est motus spei, et audaciae quae ipsam consequitur. Et hunc motum moderatur

148

SEBASTIAN

CARLSON

and affections are the things which humility moderates, they
constitute its proximate matter.
2. The Formal Object of Humility. The formal object of a
virtue is its precise purpose, that to which it is immediately
ordained. 30 The object of moral virtue in general being to
make man live as a rational animal, that of any given virtue
will be to keep its proper matter within reason. Thus, the
object of temperance is to regulate by reason the use of nourishment and of the sex life; the object of fortitude is to assure
man's conformity to reason in imminent danger of death.
Since the matter of humility is the appetition of personal
excellence, its formal object will be to control this activity by
reason; to see· that man acts rationally in searching for and in
reaching the position intended for him by Providence, neither
going above nor falling beneath it. It " tempers and refrains
the soul, lest it tend immoderately to what is lofty." 31 " It
belongs properly to humility that a man repress himself, lest
he be carried away to things above him." 32 In a word, the
purpose of the virtue is to moderate the appetite tending to
great things. 33
It is to be noted that these expressions of St. Thomas insist
the elan of hope, as if that were the only
on the repression
moderation needed; as if humility never kept hope within the
limits of reason by bringing it up to these limits, instead of
down to them; as if humility did not use hope at all, but merely
sive refraenat humilitas" (Ibid., q. 143, a. 1, corp. post med.). " ... magnanimitas et humilitas, quae quodammode se habent ad spem vel fiduciam alicujus
magni . . . " (De virtutibus in communi, q. unica, a. 12, ad 26). " Ex dictis
habetur, materiarn intrinsecam humilitatis esse internum animi motum et affectum
quae refraenat, ne tendat in sui celsitudinem supra id quod oportet, sed intra
mensuram ex propriis meritis sibi debitam, se contineat" (Cur/IUS Theologiiius
coUegii Salmanticensis, Tract. XII, Arbor praedicamentalis virtutum, n. 188).
•• Cf. Summa Theol., I, q. 1, a. 7, corp.; 1-11, q. 54, a. 2, ad 8.
31 " • .• • temperet et refraenet animum, ne immoderate tendat in excelsa " (Art.
1, corp.).
•• " ..· •. ad humilitatem propHe pertinet ut aliquis reprimat seipsum, ne. feratur
in ea quae sunt supra se" (Art. 2, corp.).
38 " • • • inquantum scilicet humilitaS nihil est aliud quam quaedam moderatio
spiritus " (Art. 4, corp.) .

· THE VIRTUE OF HUMILITY

149

repressed it. They insist on its repression, it is true; but they
do not in the least exclude its encouragement. Because hope
is what it is-a tool of the soul to be employed in overcoming
difficultief:'!and in emergencies of all kinds-a passion that because of the loss of original justice is no longer the slave of
reason but often an unruly subject with partial independence:
because, then, hope is what it is, reason finds that in the
majority of cases it needs a bridle rather than a whip.
It cannot be affirmed that the individual who seeks positions
beneath his ability is rare; however, he is met with only in the
minority of cases. In him, reason moderates hope by stimulating him to act up to his measure, aware, nevertheless, of his
worthlessness save for the divine element in him. But he is
an exception to the rule. Man is born as the 'Iord of creation,
of his own lower self, often of other men. His nature must be
curbed, not spurred, and is inclined to too much ,rather than
too little.
This necessity of restraining immoderate hope is accidental
to humility, inasmuch as reason finds the appetite in the
greater number of men excessively thirsty for greatness. Its
essential purpose is simply to keep the quest of one's own
excellence reasonable. 84 St. Thomas indicates this clearly.
" Properly speaking," he says, " humility is directive and
moderative of the motion of the appetite." 85 Its formal object,
then, is the moderate and reasonable seeking of one's own excellence; 36 it leads man to seek his true place among his fellow
men, knowing all the while that he is of himself unworthy
of it. 37
"'Cf. Summa Theol., I, q. 95, a. 3, ad 1: " ... accidit temperantiae et fortitudini quod superabundantiam passionum repellat: inquantuin invenit passiones
superabundantes in subjecto. Sed per se convenit hujusmodi virtutibus passiones
moderari."
•• " Et ideo dicendum est quod humilitas proprie est ,directiva et moderativa
motus appetitus" (Art.
•• The classically incisive definition of pride, " inordinatus appetitus propriae
excellentiae" (Summa Theol., 11-11, q.
a.
corp.; cf. a. I, ad
clarifies by
contrast this statement of the formal object.
·
•• The double restraint of humility implied here is a feature not often brought

150

SEBASTIAN

CARLSON

This distinction of essential and accidental in its formal
object makes it clear why Christian tradition has always described humility as restraining the soul from all that is beyond
measure. The world and men being what they are, " humility
represses more than it uses hope or self-confidence; hence, excess
is more greatly opposed to it than defect." 38 Pride, the vice
that springs from excessive hope, is farther from humility than
is servility, the vice begotten of hope that is too weak. The
resulting similarity of lowliness of heart and ignoble abjectness
calls to mind the external, superficial resemblance of insensibility (excessive forbearance from bodily pleasures) to temperance. This deceptive likeness is one more reason why
humility is considered by so many as despicable, a thing for
sycophants and shop clerks, a watery serum unbecoming the
veins of a red-blooded American. Uriah Heep, instead of the
Son of God, has become the incarnation of humility.
8. The Formal Motive of Humility. The formal motive of
humility is the special good which reason sees will be obtained
by guiding the appetite firmly in its tendency toward .excellence. If this motive is only the sense of honor which makes
man feel obliged to live up to his abilities, humility and magnanimity coincide. They are not two virtues, but one, since this
sense of honor is likewise the source of magnanimity, and only
those virtues are distinct which have different motivating principles.89 Can· no other reason be assigned for curbing the desire
for greatness and place?
We repeat the vigorous statement of Thomas quoted above,
" Humility . . . regards most of all the subjection of man to
to the attention. The humble man restrains his estimate of himself, knowing he is
unworthy of any good, and at the same time marks out for himself a moderate
goal. Whether he must gear his hope up or down, he advances always ut indignUB,
"as unworthy," and whether his goal be a doctorate or a policeman's job, he would
not have chosen it unless it was in proportion to his abilities.
88 " Humilitas autem plus reprimit spem vel fiduciam de seipso quam ea utatur;
unde magis opponitur sibi superabundantia quam defectus " (Art. 2, ad 8).
88 Cf. Summa Tkeol., I-ll, q. 64, a. 2, corp. & ad 8; a. 8, corp.; q. 60, a. I, corp.;
q. 68, aa. 4, 6, corp.

THE VIRTUE OF HUMILITY

151

God." 40 Even more noteworthy is the following sentence:
" . . . in repressing the presumption of hope, the chief motive
is found in reverence for God, from which it results that
one does not attribute to himself more than becomes him,
according to the grade he has received from God. Hence
humility seems to connote principally the subjection of man to
God." 41 Humility represses hope out of reverence for God,
inasmuch as reverence for Him implies subjection to His Providence. "Humility, as was said, properly regards the reverence
by which man is subjected to God." 42 Man, studying himself
and comparing himself with God, learns his nothingness and
God's all; accepting the vast import of this truth, he subjects himself to God, and subjects himself therefore to His
Providence by assuming the place it has assigned him in the
universe. The formal motive of humility, consequently, is
reverential fear of God. Reason moderates the irascible appetite not only from a sense of honor, but most of all from a sense
of subjection to God. "Humilitas causatur ex reverentia
divina." 48 " Its principle and root is the reverence which one
has for God." 44
. All this will enable the reader to grasp clearly the meaning
of humility. It is the moderation of the elan of the irascible
appetite toward any good whatsoever conceived as an excellence, out of reverential fear subjecting man to God. Its aim
is to withhold man from all that is above him, because to tend
to such things is contrary to the need of subjecting self to God
and to the divine element in one's neighbor.
•• Supra, note 16; cf. Commemt. in Phil., Cap. II, Lect. I (v. 8), p. 91a, post
med. [in Marietti edition]; Commemt. in Job, Cap. XXII, Lect. II (v.
Summa
contra Gemtilea, IV, c. 55, ad 17; IV Semt., d. 88, q. 8, a. 8, arg. 6 & ad 6.
41 " Sed in reprimendo praesumptionem spei, ratio praecipua sumitur ex reverentia
divina, ex qua contingit ut homo non plus sibi attribuat quam sibi competat
secundum gradum quem est a Deo sortitus. Unde humilitas praecipue videtur
importare subjectionem hominis ad Deum " (Art.
ad 8) .
•• "Humilitas autem, sicut dictum est, proprie respicit reverentiam, qua homo
Deo subjicitur " (Art. 8, corp.) .
•• Art. 4, ad 1.
.. " Et utriusque principium et radix est reverentia quam quis habet ad Deum "
(Art. 6, corp.) •

2

152

CARLSON

D) Definition of Humility

With the objects of humility thus determined, it is not difficult to formulate an essential definition. We have seeh that
the matter of humility is every good insofar as the soul sees it
as desirable, yet bE;)yond its own power to attain. Its object is
to moderate the hope impelling it toward this good. Its motive
in keeping the appetite in order is the congruity of being
subject to God.
Two incomplete definitions have already been given, one
from the ,$umma Theologica, the other from the Summa contra
Gentiles. It is the virtue by which a person, "considering his
deficiency, holds himself to what is low, according to his measure." It consists in this, "that a person contain himself
within his limits, not extending himself to what is above him,
but subjecting himself to his superior." 45
.The former is generally quoted as Aquinas' definition; but it
does not mention explicitly the motive of humility; the latter
mentions but does not specify the essential note of subjection.
An exact definition can be framed by completing the former
with the implicit content of the latter. Humility is the moral
virtue by which a person, considering his deficiency, holds himself to what is low according to his measure, out of subjection
to God. If he is truly subject to God, he will subject himself
also to all that there is of the divine in his neighbor; and he
will hold himself not only down to his measure, but if necessary
up to it as well.
St. Thomas seems never to have changed his concept of
humility in any way. In his commentary on the Sentences, one
of the earliest works, he writes that " by humility man subjects himself to God out of reverence, and therefore to others
because of God." 46 It has already been seen that the essentials of his definition appear in a citation from the last book of
the Summa contra Gentiles. 41 On the verse from I Corinthians,
•• Al:t. 1, ad 1; IV Summa contra Gentiles, c. 55, ad 17.
•• " . . . per eam homo se ex reverentia Deo subjicit, et per consequens alii
propter Deum" (IV Sent., d. 88, q. 8, a. 8, ad 6).
' 7 In the second paragraph above.

THE VIRTUE OF HUMILITY

158

" Charity is not puffed up, is not ambitious," 48 he comments in
part as follows: " One seeks his own
inordinately
when he is not content to be held in the grade appointed him
by God. . . . This happens when one is unwilling to be held
under the rule of the divine ordination." 49 Explaining a verse
in II Corinthians, he says, " Pride is inordinate appetite for
one's own excellence. For if one seeks some excellence under
God, provided he seek it with moderation and for a good end, it
can be upheld." 50 A passage in De Malo reads, " The knowledge of truth is antecedent to humility; when one has considered the truth, he does not lift himself up beyond his
measure." 51 " For ' he that hath been humbled ' by wilfully
subjecting himself to God, 'shall be in glory,' which he will
obtain from God; ' and he that shall bow down his eyes ' lest
in his intellect he think any proud thought against God, ' he
shall be saved' "-such is the Angelic Doctor's doctrine in his
commentary on the Book of Job. 5 2 His teaching in the Summa
Theologica has been explained in these pages; and his commentary on the Epistle to the Romans shows no change in
doctrine during the last years of his life.
This I command: " not to be more wise than it behooveth to be
wise." That is, let none be presumptuous, confiding in his sense or
wisdom above his measure. Secondly, he. [Paul] exhorts "to the
mean, saying, "But be wise unto sobriety." That is, I command
•• xiii, 4, 5.
•• " Tunc autem inordinate suam excellentiam quis appetit, quando non sufficit ei
contineri in eo gradu, qui sibi est a Deo praestitus. . . . Quod quidem fit, dum
homo non vult contineri sub regula ·ordinationis divinae" (Comment. in I Cor.,
Cap. Xill, Lect. II (vv. 4, 5), p. 864b).
••" Superbia enim est appetitus inordinatus propriae excellentiae. Si enim aliquis
appetit aliquam excellentiam sub Deo, si moderate quidem appetit, et propter
bonum,- sustineri potest ... " (C01nment. in II Cor., Cap. XII, Lect. ill (v. 7),
p. 509b fin.) .

"' " . . . cognitio veritatis se habet ad humilitatem antecedenter; quia dum
aliquis veritatem considerat, se ultra suam mensuram non effert" (q. 8, a, 8, ad 9).
•• " . . . ' Qui enim humiliatus fuerit,' scilicet Deo se subjiciendo per affectum,
' erit in gloria,' quam scilicet consequetur a Deo: ' et qui inclinaverit oculos,' ne
scilicet per intellectum ·aliquid superbum contra Deum sentiat, ' ipse salvabitur'"
(Cap. XXII, Lect. II (v.
).

154

SEBASTIAN

CARLSON

you. to be wise in measure, according to the grace given you. For
sobriety connotes measure. . . . Thirdly, he teaches how the
measure of the mean is to be decided, saying, " And according as
God hath divided," that is, distributed, " to every one the measure
of faith," th'at is, the measure of his gifts, which is ordained to the
manifestation of faith. 53
Thus, the definition gathered from the Summa Theologica
agrees in all its elements with Thomas' doctrine in his, other
works. It will prove of inestimable value in studying the subject, acts, extent, and rank of humility, and its· relation to the
other virtues.

II. THE SUBJECT AND FoUNDATIONS

OF HUMILITY

A) The Subject
Being a virtue, humility is a habit meant for action; it is a
good disposition of the appetite for one's own excellence. It
gives that appetite a permanent, living channel along which its
activity can flow according to the dictates of reason. It will be
found, consequently, in that part of the soul for whose activity
it creates this channel. In other words, its subject wili be the
irascible appetite. 54
It follows that even though much knowledge of self, and oi
God as man's Creator and supreme Director, are prerequisite to
the virtue, it exists not in the cognoscitive but in the appetitive
side of nature. It cannot be defined as knowledge of self, but
knowledge of self is essential for it.
It is proper to humility to make man curb himself, lest he be
carried away to things above him. To this end, he needs to know
•• " Hoc, inquam, mando, ' non plus sapere quam oportet sapere,' idest, nullus
praesumat, de sensu aut sapientia sua confidens. supra suam mensuram. Secundo
hortatur ad id quod est medium, dicens: ' Sed sapite ad sobrietatem,' scilicet
mando vobis, ut mensurate sapiatis secundum gratiam vobis' datam. Sobrietas
enim mensuram importat. . . . Tertio docet secundum quid accipienda sit mensura
medii, dicens: ' Et hoc,' inquam, ' sicut Deus unicuique divisit,' idest distribuit,
• mensuram fidei,' idest, mensuram donorum suorum, quae ordinatur ad fidei manifestationem" (Cap. XII, Lect. I (v.8), p. 17lb).
••supra, pp. 15-17; cf. Art. 4, arg. 2.& ad. 2.

THE VIRTUE OF HUMILITY

!55

that in which he falls beneath the proportion of what exceeds his
powers. Hence knowledge of one's deficiency belongs to humility
as a rule directing the appetite. But it is in the appetite itself that
humility consists essentially. 55

A habit that controls the activity of some faculty must be in
it; for habit is nothing more than the inclination of the activity
of some faculty to flow in a given moral direction. 56
From the fact that humility is in the irascible, however, it
may not be concluded immediately that it exists only in the
lower part of the soul, as a habit moderating passion. The will
as it tends toward the arduous is also called irascible. 57
quently the question arises, Is humility in both the will and
the lower appetite, or in one of them alone?
It must influence both in some way at least, since excellence
attracts both. A spiritual excellence such as outstanding
virtue, and even a purely material one, when they are apprehended by the intellect as goods in harmony with human nature, become objects of the will. A purely material excellence,
moreover, if apprehended by sense knowledge as an arduous
good perfecting nature, becomes the object of the lower irascible
appetite, which moves toward it with the passion of hope.
Because this hope of excellence is spontaneous and follows
blindly the data presented by the senses, the lower appetite is
attracted to many things incommensurate with the individual's
talents. Rational control, provided by humility, is necessary;
and hence the appetite must be influenced by that virtue; in
other words, the latter must exist in some way in the lower
part of the soul.
That the will's attraction to excellence must be moderated is
•• " ... ad humilitatem proprie pertinet ut aliquis reprimat seipsum, ne feratur

in ea quae sunt supra se. Ad hoc autem necessarium est ut aliquis cognoscat id in
quo deficit a proportione ejus quod suam virtutem excedit. Et ideo cognitio proprii
defectus pertinet ad humilitatem, sicut regula quaedam directiva appetitus. Sed
in ipso appetitu consistit humilitas essentialiter" (Art.
corp.).
56 Cf., e. g., II-II,
q.
a. 3, corp.: " ... subjectum cujuslibet virtutis vel
vitii oportet inquirere ex proprio objecto. Non enim potest esse aliud objectum
habitus vel actus, nisi quod est objectum potentiae, quae utrobique subjicitur."
67 Cf. Summa Theol., I, q.
a. 5, corp., and ad
II-II, q.
a. 3, corp.

i56

SEBASTIAN

CARLSON

self-evident. But does such moderation postulate a habit in
the technical sense of the word? Or is the unaided will capable
of tempering its own exuberance? Virtue exists only where a
faculty must have assistance in order to attain its object.S8
There is no need for a moral virtue in any faculty to direct
it toward a good proportionate to itself, since such a good is its
proper object, that which its very nature fits it to obtain.
Habits, since their raison d' etre is uniquely to perfect the faculties, to diminish their indetermination by reducing them further from potency toward act, are required only when the latter
must act for a good beyond their direct object. 59 The rational
appetite needs a habit only when it must be directed to something beyond its own personal and immediate good-God's
right ·to His creatures' adoration, for instance, which is the
object of
or another's right to lawfully acquired property, which is the object of justice. Hence only those virtues
are in the will which· direct men toward God and their fellowmen, as charity and veracity. 60 There is no need for a fortitude
or temperance of the will, since the object of both is a simple
-good of reason-the control of passion, from the realization
that the nobility of humari nature demands it. " How then
is humility now placed in the will: humility, which has to do
with the passion of hope, and is directed not to the good of
another, but to one's own? " 61 Lowliness of heart is concerned
primarily with the soul's internal life, with the repression of
unlawful desire and wanton hope, only secondarily with man
as he is a social being. It resembles temperance more than it
does justice. Its formal. object is not God's rights nor the
state's rights nor another individual's rights, but the preservation of the good of reason in the propensity of the soul to seek
68 Cf. Summa Tkeol., I-11, q. 56, a. 6, corp. & answers to the objections.
•• Ibid.
•• Ibid.
•• " Quomodo nunc in voluntate ponitur humilitas, quae est circa passionem spei,
et non ad alterius, sed habentis proprium bonum? " Cajetan, Commentarium, in
11-11, q. 162, a. 8: II.) He goes on to say,
est enim objectum superbiae et
humilitatis: sicut universaliter idem est subjectum contrariorum."

THE VIRTUE OF HUMILITY

157

its own .excellence 62-a good which seems perfectly in proportion to the. human will.
But the pre-eminence of this good, its incommensurability
with the human will, is recognized as soon as tht; formal motive,
the specifying principle, of humility is recalled: a sense not
merely of honor, but of the obligation to subject self to God.
Because humility restrains the appetite, keeping it within the
pale of reason indeed, but within that pale as determined by
the reverence man owes to God and to the Providence that has
determined his role on earth 63-because of this, the will is
incapable alone of arriving at the end of humility, and must
have a special habit to aid it. 64 Though it achieves its own
good by humility, yet it tends toward that good as seen in the
light of the divine good, and therefore intimately and vastly
qualified and elevated.
In the will there is no moral. virtue for the good of the person
possessing it, having precisely the natural judgment as its rule.
But the rule of humility is derived from reverence for God. 65

Lowliness of heart has its chief seat, accordingly, in the will.
But, as has been seen, it must also be present in the lower
appetite-not in the same manner or degree, of course, for this
would mean that the one virtue would have two generically
distinct objects, one of the sensible, one of the· spiritual order.
A virtue can exist in two potencies only if it be in each in a
different way-" non ex aequo, sed ordine quodam." 66 It must
be in one principally, as its subject, and in the other as its
Supra, Section I, C, 1.
Supra, Section I, C, 1.
60 The fact that humility
is motivated by subjection to God does not make it
reducible to justice. Cf. infra.
65 " ••• in voluntate nulla est virtus moralis propter bonum habentis, habens pro
regula praecise judicium naturale. Humilitatis autem regula ex divina sumitur
reverentia. Et propterea non obstat supra habita doctrina [Summa Theol., 1-11,
q. 56, a. 6, ad 1]. Ponitur siquidem humilitatis virtus in ordine ad coelestem, non
humanam civilitatem" (Cajetan, Commentarium, in 11-11, q.
a. 3: IV). He
adds an interesting observation: "Unde Philosophus non cminumeravit earn inter
virtutes."
66 Summa Theol., I-II, q. 56, a.
corp.
62
63

158

SEBASTIAN

CARLSON

motivating principle or as a disposition resulting from it,
according as one potency is moved by another, and as one
potency receives something from another." 67 Thus the theological virtue of faith, residing in the intellect primarily and
principally, is also in the will, inasmuch as the will moves the
intellect to assent to revealed truth. It is in the intellect as in
its subject, but in the will as in its imperating principle. 68
The powers of the soul are not disconnected and utterly
sovereign in their own field; on the contrary, they mutually
influence, retard or invigorate one another. 69 Anger inclines
the will to seek revenge; the will can stifle anger or
it to
terrifying extremes. Though the higher faculties move the
lower ones, the dominion they enjoy is not absolute, because all
the powers of the soul move autonomously to their proper
objects; it is a dominion persuasive rather than despotic, moral
rather than physical. 70
The rational faculties, by constantly guiding the lower ones
along certain lines of action, accustom them to operate in one
definite way, and gradually develop in them: a disposition to
obey reason constantly and easily. If the object of this disposition is commensurate with the faculty in which it exists, that is,
if its purpose is merely the subjection of that faculty to reason,
the disposition becomes a true habit. The object of the disposition to courageous action developed in the irascible by
constant obedience to the will, for example, is merely the conformity of the irascible to reason. This disposition becomes the
virtue of fortitude.
If, on the contrary, the object of the disposition is not merely
the conformity of some faculty to reason, but a good to which
the faculty is not immediately and of itself ordained-a good
beyond its own grasp-then the disposition cannot be a complete virtue but remains a mere disposition. It is an instru87 " • • • secundum quod una potentia movetur ab • alia; et secundum quod una
potentia accipit ab alia " (Ibid. The entire article should be read) •
•• Ibid., ll-II, q. 4, a. !!, corp.
•• Ibid., I-II, q. 9, aa. 1-S; q. 10, a. 8; q. !!4, a. 1.
70 Ibid., q. 9, a. !!, ad 8.

THE VIRTUE OF HUMILITY

159

ment which the higher faculty uses to produce acts that move
to and are motivated by a higher good than the lower power
could reach alone.
This is the case with humility. The will, in order to restrain
the soul's inclination to excellences of a material nature, must
control the sensible irascible appetite. By repeatedly forcing
the latter to act according to its commands, it builds up in it a
strong disposition to obedience. The object of this disposition,
however, is not simply the moderation of the elan of the
irascible; it is the subjection of the appetite's activity to God
and His Providence; it is, indeed, the object which the will proposes to itself in keeping within the bounds of reason.
Humility as it exists in the lower part of the soul, therefore, is
not a complete virtue, but a disposition absolutely subject to
the will. Lowliness of heart exists principally and primarily
in the higher part of the soul. 71
This conclusion seems much safer and far more in accord
with general theological principles than the doctrine of some
theologians that there are three or more distinct virtues known
by the common name of humility. 72 It is necessary to postulate only one virtue of humility which is subjected principally
in the will, secondarily in the sense appetite. 73 Whether in the
71 Cf. Cajetan, Oommentarium, in II-II, q. 161, a. 5: XXV, ante med.: " ...
ipsa [humilitas] est subjective principaliter in voluntate, et secundario est circa
passionem spei: quia extendit se ultra sensibilia, ut patet ex ejus contrario, scilicet
superbia, quae maxime est in bonis spiritualibus." Cf. also John of St. Thomas,
Cursua Theologicus, Oommentarium in I-II, qq. 55, 56: Disputatio XV, Art. II,
Qu. II, n. 9.
72 Cf., e. g., Salmanticenses, op. cit., Tract. XII, Arbor praedicamentalis virtutum,
n. 148 fin.: " Et quidem loquendo de habitibus acquisitis, nullum alium cognoscimus
praeter hos duos, cui humilitatis nomen absolute congruat: voluntas enim · in
ordine ad propriam excellentiam absolute consideratam, omninoque sistendo in bono
proprii suppositi, non eget virtute acquisita. . . . Sed loquendo de virtutibus
infusis ... valde probabile censemus ultra duos praedictos dari in voluntate alium
habitum humilitatis in ordine !l'i excellentiam prout consideratur in spiritualibus
sine ordine ad passiones, et etiam sine respectu ad alterum." Cf. also ibid., nn. 80,
144; Disputatio II, Dubium II, n. 54.
•• It is safe to say that this is not merely Thomistic doctrine, but also St.
Thomas', although in the question on humility he writes explicitly only that it is
in the irascible as in its subject (Art. 4, ad
. His answer to this objection im-

160

SEBASTIAN

CARLSON

will or in the lower irascible, it moderates the flight of the appetite from the one motive of subjection to God.
B) The Foundations of Humility in the Reason

Subjected in the will, and existing in the lower irascible as a
strong disposition, humility is in the intellect not in any proper
sense but as an effect is in its cause.
Still, reason has much to do with the virtue, for self-knowledge is a sine qua non of lowliness of heart. " Humility fundamentally and presuppositively connotes the knowledge by
which one, considering his deficiency, deems himself unJorthy
of esteem and honor, and worthy of abjection and contempt." 74
"And therefore the knowledge of one's own deficiency pertains
to humility as a directive norm of the appetite." 75 Without
self-knowledge, there can be no humility; it is the old principle
in a different vest, nihil volitum nisi cognitum. Unless man
knows what he should seek and avoid in the rn.atter of personal
aggrandizement, he will neither seek nor avoid it rightly. His
hope will be as sane or as unbalanced as his understanding of
his ego.
But one cannot realize the depth of his own imperfection
unless he appreciates to some degree the perfection up to which
plies that his opponent is correct in maintaining that " humilitas . . . videtur esse·
in irascibili, sicut et superbia, quae ei opponitur" (ibid., arg. 2) . Hence it is
logical to apply to humility ' his conclusions on the subject of pride: " Si ergo
arduum quod est objectum superbiae, esset solum aliquid sensibile, in quod potest
tendere appetitus sensitivus: oporteret quod superbia esset in irascibili quae est
pars appetitus sensitivi. Sed quia arduum quod respicit superbia, communiter
invenitur et in sensibilibus et in spiritualibus rebus, necesse est dicere quod subjectum superbiae sit irascibilis non solum proprie sumpta, prout est par appetitus
sensitivi, sed etiam communius accepta, prout invenitur in appetitu intellectivo.
Unde et in daemonibus superbia ponitur" (Summa Theol., II-II, q. 162, a. 8,
corp.).
« " . . . humilitatem fundamentaliter et praesuppositive importare cognitionem
qua quis defectus suos considerans reputat se indignum aestimatione et honore;
dignumque abjectione et despectu " (Salmanticenses, op. cit., Arbor praed. virt.,
n. 188).
•• " Et ideo cognitio proprii defectus pertinet ad humilitatem, sicut regula
quaedam directiva appetitus" (Art. 2, corp.).

THE VIRTUE OF HUMILITY

he fails to measure.
companson;

161

There are two terms needed for any

No man can know himself without the means of comparison with
what he ought to resemble. Humility results from self-examination
in the light of God, in which light is the standard of truth and
justice, whereby we measure what we are in the sight of God. 76

It is the knowledge of God, of His power and mercy, that keeps
humility from collapsing in despair u·nder the weight of human
nothingness and sin. Further, a study of man's miserable
achievements in contrast to his desires, aspirations, and
bilities, can produce only a passing sentiment of discouragement that will give way to renewed hope, and in all probability to renewed pride or ambition, as soon as the keenness of
these humiliating thoughts wears off.
The consideration of our own misery may produce a passing
sense of humility, but the virtue, which is an 4abitual disposition,
does not consist in this; reverence toward God is the one cause that
can beget the virtue, and above all render it stable. 77
Knowledge of God, Thomas tells us, is a guarantee of knowledge of self; and the degree of the second corresponds to the
degree of the first.
'' He must increase, but I must decrease." 78 This should be
verified in the moral life of each and every one of us. "He," that
is, Christ, " must increase " in you; that is, you must advance in
knowledge and love of him. For the more you apprehend him by
knowledge and love, so much the more does Christ increase in
you. . . . Hence it behooves men who thus advance to decrease in
their own esteem; for the more one knows of the sublimity of God,
the lower does he consider the littleness of man/a
lillathorne, The Groundwork of the Christian Virtull8 (London, 1886), p. 100.
Marmion, Christ the Ideal of the Monk, p. fl44.
•• John, iii, 80.
•• "' lllum oportet crescere, me autem minui.' . . . Moraliter autem. hdc debet
esse in unoquoque nostrum. ' Oportet illum,' idest Christum, in te 'crescere,' ut
scilicet in cognitione et amore ejus proficias: quia inquantum magis eum pates
cognoscendo et amando percipere, tanto magis'Christus crescit in te ..... Et ex hoc
oportet homines sic proficientes minui in sua reputatione:
quia quanto plus
76
77

162

SEBASTIAN CARLSON

What does self-knowledge teach us that generates the virtue
of humility? What do we learn about self and God in studying
self?
Looking at the latter, we see that we are caused, moved by
forces outside ourselves, limited in our scanty perfection. If
we are reasonable, we are forced to conclude the existence of a
first transcendent Being that made us, moves us, and gives us
a share in its unlimited perfection; we must admit that it is
intelligent and moral, as we are, though in a far higher sense.
In a word, reason tells us that we are creatures of a personal
Creator. Faith proposes the same facts to our belief, and
discloses the sublime truth that we were once raised to share
the very life of God; that of his own free will our first parent
cast the whole human race down from the peak of the supernatural; and that not we, but God, in the form and habit of
man, restored :us to that height. Faith, then, tells us that man
is guilty of casting off from himself the dignity divinely conferred upon him, and that he has been revamped by his Maker.
He is a repair job of the Almighty. Self-knowledge reveals that
he is nothing, that God is all. 80
The Dominican Blessed, Louis-Marie Grignon de Montfort,
describes vividly what man discovers if he studies himself
deeply and is not afraid to admit the disgusting truth.
The sin of our first father has spoilt us all, soured us, puffed us
up, and corrupted us, as the leaven sours, puffs, and corrupts the
paste. . . . The actual sins which we have committed, whether
mortal or venial, pardoned though they may be, have nevertheless
increased our concupiscence, our weakness, our inconstancy, and
our corruption, and have left evil consequences in our souls. Our
bodies are so corrupted that they are called by the Holy Ghost
bodies of sin, conceived in sin, nourished in sin, and capable of all
sin-bodies subject to thousands of maladies, which go on corrupting from day to day, and which engender nothing but disease,
vermin, and corruption.
"All flesh having corrupted its way," we have nothing for our
cognoscit quis de altitudine divina, tanto minorem reputat parvitatem humanam
... " (Comment. in Joann., Cap. III, Lect. V, n. 6, p. lila, ante med.).
so Cf. Garrigou-Lagrange, Lea trois ages de la vie interieure, II, 154 ff.

THE VIRTUE OF HUMILITY

168

portion but pride and blindness in the spirit, hardness in the heart,
weakness and inconstancy in the soul, concupiscence, revolted passions, and sicknesses in the body. We are naturally prouder than
peacocks, more grovelling on the earth than toads, more vile than
unclean animals, more envious than serpents, more gluttonous than
hogs, more furious than tigers, lazier than tortoises, weaker than
reeds, and more capricious than weathercocks. We have down in
our own selves nothing but nothingness and sin, and we deserve
nothing but the anger of God and everlasting hell.81

Bitter medicine, these thoughts; but every man conceived in
sin or guilty of actual sin must swallow it if he would live.
True, Christ in His humanity, and Mary, His Mother, have no
sin to humble them, nor ever had; and the angels and saints of
heaven need fear sin no more. But they are without matter
for' humility no more than we are; they are still creatures, and
their grace and glory is from God. They are perfect, but only
in a certain degree, and not absolutely.
A thing can be called perfect in a certain sense; for example,
according to its natur.e, or according to its state, or time. And in
this way the man of virtue is perfect. But his perfection is found
defective in comparison with God: according to that of Isaias," All
nations are before him as if they had no being at all." 82 And so,
humility becomes every man. 83
'

The Catholic doctrine on free will, grace, and predestination,
particularly as interpreted by the Thomistic School, reduces the
creature still more, to the nadir that is his, and lifts God to the
zenith proper to Him.
Man"s misery extends to the utmost lengths in the order of both
nature and grace. In the order of nature, since we have received
from God our body and soul, the forces of the body and the facul81 True Devotion to the Blessed Virgin, trans. by F. W. Faber (New York, 1909),
pp. 64-66.
•• Isa. XL, 17.
88 " • • • potest dici aliquid perfectum
secundum quid: puta, secundum suam
naturam, vel secundum statum, aut tempus. Et hoc modo virtuosus est perfectus.
Cujus tamen perfectio, in comparatione ad Deum, deficiens invenitur, secundum
illud lsa.: ' Omnes gentes quasi non sint, sic sunt coram eo.' Et sic, cuilibet homini
potest convenire humilitas " (Art. 1, ad 4).

164

SEBASTIAN CARLSON

ties of the soul, also the very motion by which these faculties pass
from potency to act. But especially in the order of grace, in which
our regeneration is gratuitous, the virtues are infused gratis, and
the passing of potency to meritorious act is due to actual grace.
There is nothing in us from ourselves except defect. Finally, the
very perfection that we hold from God is infinitely distaht from
God's perfection; nor, usually, does it correspond to the measure
of our faculties, virtues, and divine inspirations. We must, therefore, fixing our eyes on God's perfection and largess, cast ourselves
down to our own littleness, our own defects, our own nothingness. 84
The theology of St. Thomas is found in words of fire and love
in the inspired writings of Catherine of Siena, whose spiritual
doctrine so amazingly corresponds to that of the Patron of
Schools. It is fitting to close this section with a passage from
her Dialogues, describing the union of knowledge of self and of
God necessary for true humility.
If thou wilt arrive at a perfect knowledge and enjoyment of me,
the Eternal Truth .... thou shouldst never get outside the knowledge of thyself, and, by humbling thyself in the valley of humility,
thou wilt know me and thyself, from which knowledge thou wilt
draw all that is necessary. . . . In self-knowledge, then, thou wilt
humble thyself, seeing that, in thyself, thou dost not even exist; for
thy very being, as thou wilt learn, is derived from me, since I have
loved both thee and others before you were in existence; and that,
through the ineffable love which I had for you, wishing to re-create
you to grace, I have washed you, and re-created you in the blood of
my only-begotten Son, spilt with so great a fire of love. This
blood teaches the truth to him who, by self-knowledge, dissipates
the cloud of self-love, and in no other way can he learn. 85
•• " Haec autem miseria in ordine cum naturae tum gratiae latissime se extendit.
In ordine quidem naturae, utpote qui a Deo accepimus corpus, et accepimus
animam, et accepimus vires corporis et animae potentias, ipsam quoque motionem
qua hujusmodi facultates transeunt in actum. In ordine praecipue gratiae, in quo
et regeneratio est gratuita et v-irtutes infunduntur gratis et transitus potentiae in
actum meritorium actuali gratiae debetur. Nihil in nobis a nobis praeter defectum.
Ipsa denique perfectio quam a Deo habemus distat in infinitum a perfectione Dei;
nee respondet communiter mensurae facultatum, virtutum, inspirationum divinarum.
Oportet igitur nos, oculum fixum habentes in Dei perfectione et largitate, desilire in
parvitatem propriam, in proprios defectus, in nihilum proprium." Petrus Lumbreras, De Fortitudine et Temperantia (Rome, 1939), p. 181.
86 The Dialogue!S of the Seraphic Virgin, Catherine of Siena, trans.
by Algar
Thorold (London: Burnes Oates,
p. 5. See also pp. 14, 19-!21, !29.

THE VIRTUE OF HUMILITY

III.

165

AcTs oF HuMILITY

Since the matter of humility is a:p.ything desirable that is
recognized as an excellence, an act of the virtue is obligatory
each and every time the higher or lower appetite is attracted
toward such a good. From this it is clear that innumerable
exterior acts of humility are possible. But it is not these which
are in question here, nor even such interior acts as the curbing
of intellectual pride. It is the elicited act that is to be discussed, and it alone: the operation which comes directly and
immediately from the virtue, which the virtue is by its very
nature ordained to produce.
1. Acts of the virtues must not be conceived of as entities
really distinct from the operation of the faculties which they
perfect. 86 Virtue merely regulates a faculty's activity, in some
such way as a conduit determines the direction of water flowing
through it. Acts of virtue are rationalized acts of the faculties;
acts of the appetitive virtues are rationalized acts of the appetite. In the same way, an act of humility is the rationally
directed motion of the irascible appetite, whether superior or
inferior, toward excellent good. This is to say that an act of
humility is nothing else than the affection or passion of hope
darting from the soul under the vigilance of reason,;;_the
reasonable quest of the appetite for excellence.
That this is the essential, elicited act of the virtue, is clear
from a consideration of humility
as it exists in any particular intellectual creature, but as it is essentially a good habit
modifying the elan of hope. What was said before of its formal
object should be recalled here: that object is the moderate,
reasonable seeking of one's own excellence; lowliness of heart
leads a person to seek and accept his correct place in the universe, aware that he is abysmally unworthy of it. 87 Naturally,
the words designating the formal object designate also the act,
object and act differing as end and motion toward end. Hence
•• Cf. IV Sent., d. 49, q. 1, a.
87 Supra, Section I, C, 1.

quaest.

ad

166

SEBASTIAN

CARLSON

the essential act of humility is that by which a person, realizing
his unworthiness, hopes for whatever excellence is proportionate
to his God-given talents, because subjection to God demands
it. 88 This is an act proper to humility alone, elicited by no
other virtue. In a word, it is hope reduced to order, out of
reverence for God. 89
2. This conclusion, however, seems to contradict the conviction, universal among Christians, that the first and most
noteworthy effect of humility is to subject the heart to God,
and to others because of Him. No less an authority than
Cajetan maintains that lowliness of heart consists in such
subjection principally.
The principal act of humility is the subjection of self to that
which belongs to God. For as its very name indicates, humility
signifies not an excellence by which one is raised above certain
things as a superior, despising them; but rather, a sort of dejection.
Likewise, neither is the quest of things that are truly great the
principal act of humility; but rather, a certain subjection of the
appetite, as the word itself demonstrates. 90

And Garrigou-Lagrange

points out that not even the extinc-

88 Humility,
as has been seen, involves knowledge of self and God. Frequent
meditation upon these two things produces a disposition in the reason which inclines
it to grasp such thoughts easily and repeat them conaturally.
Because of the
interplay of intellect and will, this disposition is partially the cause and partially
the effect of acquired humility. Hence every act of the virtue is prepared for by
an act of thought, and that is why the act of humility is not defined here as
coming from the appetite only. Its intellectual preparation is indicated in the
words " realizing his unworthiness," its motive in the last phrase, " because subjection to God demands it." The act of the appetite is simply hope, moderated by
reason, tending toward a proportionate excellence; but it is essentially qualified by
the knowledge and motive that have parented it.
89 Hope is likewise ordered or moderated
by other virtues, such as magnanimity
and philotimia, under the influence of their formal motives.
90 " • • • actus humilitatis
principalis . . . est subjectio sui ad id quod Dei est.
Ut enim ipsum nomen ostendit, humilitas non significat excellentiam qua homo
super aliqua feratur ut superior despiciens ea, sed importat dejectionem quandam.
Similiter nee appetitus eorum quae vere magna sunt, est principalis humilitatis
actus: sed magis subjectio quaedam appetitus, ut ipsum nomen monstrat" (Cajetan,
Commentarium, in II-II, q. 161, a. l: V, "ad allatas "). Cf. also ibid., in a"
II, "nee tertium."

THE VIRTUE OF HUMILITY

167

tion of motions of pride is the principal act of humility. There
was never the least trace of that vice in our Lord or in our
Lady, yet they practiced the most eminent lowliness. The
principal operation of the latter consists in something quite
different from the stifling of the inclination to pride.
The proper act of humility consists in inclining self toward the
ground, which is called humus in Latin, whence the name of this
virtue. To speak without metaphor, its proper act consists in
abasing oneself before God and before what there is of God in every
creature. 91

If the essential act of humility is the moderate quest of excellence, how can its " principal " act be the subjection of the
heart to God? The two seem to move in different directions.
In reality, however, they are specifically the same act. The
former is the motion of the appetite toward the object of
humility, the latter is its motion toward the formal motive of
the virtue. Just as the perception of light (the formal quo
object of sight) is an act of the same species as the perception
of something colored (the formal quod object of sight), so an
act that terminates in the formal motive of a virtue is specifically the same as an act terminating in its formal object. 92 The
first perception of a person waking after heavy sleep may be
only light; but that perception is specifically the same act as
when he opens his eyes next and is aware of the ceiling above
him. Both are acts of sight. Numerically, they are distinct;
but they are the same specifically. In the same way, subjection to God, and hope kept in moderation from a sense of the
91 " L'acte propre de l'humilite consiste a s'incliner vers Ia terre, qui se dit humus
en latin, d'oit le nom de cette vertu. Pour parler sans metaphore, son acte propre
consiste a s'abaisser devant Dieu et devant ce qui est de Dieu en toute creature"
(Garrigou-Lagrange, op. cit., IT, 154).
•• Cf. Summa Theol., IT-IT, q. 25, a. 1, corp.: " ... cum ... species actus ex
objecto sumatur, secundum formalem rationem ipsius, necesse est, quod idem
specie sit actus, qui fertur in rationem objecti, et qui fertur in objectum sub tali
ratione: sicut eadem est specie visio, qua videtur lumen, et qua videtur color
secundum luminis rationem." · Cf. also I, Summa contra Gentiles, c. 76, ad 1:
" Omnis . . . virtus una operatione vel uno actu fertur in objectum et in rationem
formalem objecti, sicut eadem visione videmus lumen, et colorem qui fit visibilis
actu per lumen."

3

168

CARLSON

obligation to be subject to God, are both essential and elicited
acts of humility. One may be produced now, the other at
another time; but they are of the same species.
This-subjection which, following Cajetan, we shall refer to in
these pages as the principal act of humility, proceeds first and
foremost indeed from lowliness of heart, but is not proper to it
alone. 93 Both justice and magnanimity at times demand acts
of subjection to God and others, though in their less principal
capacities. The principal function of justice is the establishment of the order of reason in the mutual relations of intellectual beings so that everyone receives his due; and this
involves the subjection of some to others. Essentially considered, however, justice does not contain the notion of subjection; otherwise it could not be properly attributed to God, Who
can be inferior to no one. It necessitates subjection only as it
exists in man. 94 Magnanimity consists chiefly in encouraging
the soul to attempt great things, and in strengthening it against
the poison of despair. A less important function is the subjection of self to others. 95 The principal act of humility, on the
contrary, is the subjecting of the soul to God and the divine,
•• It was said previously that the essential act is " proper to humility alone,
elicited by no other virtue." Here we declare that the principal act, the subjection of self to God, is specifically the same as the essential act, yet " not
proper to it [humility] alone." The apparent contradiction is explained by the
fact that subjection to God is effected by other virtues (and therefore is not proper
to humility), but that subjection to God out of remerrnce for Him is effected by
humility alone (and in this way proper to it) .
•• Cf. Cajetan, Commrntarium, in II-II, q. 161, a. 5: XII: " ... justitiae principalis actus est facere seu ponere rationis ordinem in omnibus, quia omnia ad
commune bonum sunt ordinabilia; humilitatis autem praecipuus est actus per
modum subditi ad omne rationabile se praebere. Cum quibus stat quod esse subjectum sit a justitia secundario. Justitia enim, ut justitia, non facit justum
subditum, alioquin Deus, cui repugnat ratio subditi, non esset proprie justus: sed
ex justitia in aliquo provenit quod sit subditus. Et sic patet quod non est actus
principalis justitiae, sed effectus quidam ejus in al_iquo. Unde in definitione justitiae
non ponitur subjectio, sed debitum, cum dicitur jus suum unicuique tribuere.
Humilitas autem etiam ex ipsa voce dejectionem sonat."
95 For magnanimity secondarily represses the elan of hope lest it tend to a great
thing worthy of honor, precisely because this great thing is beyond one's talents
and abilities; this often involves the subjection or subordination of self to others.

THE VIRTUE OF HUMILITY

169

wherever it is found. In the words of St. Thomas, " As a
virtue, humility involves by its very nature a certain laudable
dejection to the lowly." 96
3. Because " it pertains to the same virtue to seek one opposite and flee the other," 97 it is necessary, besides distinguishing
the principal act of humility, to consider the two aspects of the
essential act. Just as charity both loves God and hates sin, 98
which separates the soul from God, so humility flees from an
immoderate quest .of one's own excellence, and yet seeks that
excellence according to the measure of reason. Only thus can
both pride and its servile contrary be avoided; both acts are
essential to humility. But since, in the great majority of men,
pride is far more apt to ensnare the soul than servility, the
holding down of hope to what is proportionate is rightly called
the primary act of humility. "The principal [that is, primary]
act of humility is to leash hope, lest it run without moderation
toward what is high." 99
At times, however, humility must hold the soul up to what
is proportionate to its· abilities and talents, must encourage it
to forge ahead, knowing its defects, indeed, and its unworthiness even of the place assigned it by divine Providence. This
function, requisite only in the minority of cases, is the 'secondary act of humility. It must be elicited when the soul tends,
actually or habitually, toward the nameless vice, sometimes
called excessive self-abjection or servility, opposed to humility
by excess.100
•• " . . . humilitas, secundum quod est virtus, in sui ratione importat quandam
laudabilem dejectionem in ima " (Art. 1, ad fl) .
97 " • • • ad eandem virtutem
pertinet prosequi unum oppositorum, et refugere
aliud" (Suwma Theol., q. lUI, a. 5, ad I).
•• Ibid.
•• " . . . principalis actus humilitatis est fraenare spem ne immoderate feratur in
excelsa ... " (Cajetan, Commentarium, in ll-II, q. 161, a. 1: V, paragr. 1).
10 ° Cf. Benedict Merkelbach,
Summa Theologiae Moralis (flnd ed.; Paris, 1935),
II, 973 (n. 1047): "Haec inclinat ad imprudentem sui abjectionem quando
redundat in injuriam status vel officii quod aliquis gerit, vel talenti quo praeditus
est, vel in incommodum eorum quibus prodesse debet. Humilitas propter rationabilem causam propriae excellentiae curam prosequitur."

170

SEBASTIAN CARLSON

The primary act of lowliness of heart is hope held down to
the mean dictated by reason; the secondary, hope held up to
that mean. To illustrate the latter: the ardent pursuit of a
political career, taken up after careful and truthful analysis of
one's talents and resources, not for honor or power, but from a
motive of reverence for God and submission to His will, is a
real act of humility. But it is to be noted with regard to this
secondary act that, "embracing subjection [to God and to all
men because of Him], the humble man does not tend even to
what is commensurate except as being subject, neither does he
refuse what is abject except insofar as this is in opposition to
the proper subjection." 101
4. In urging the soul to scorn all that is great in this world
and to love to be little and unknown, the Imitation of Christ
echoes the teaching of every master of the spiritual life since
the dawn of Christianity.
I am He Who teacheth to despise earthly things, to loathe things
present, to seek the things eternal . . . to fly honors . . . to desire
nothing outside of Me ... and above all things ardently to love
Me.1o2

St. Thomas uses the same language. "To despise earthly
sublimity," he says," is proper to it [humility]." 108
In what sense is such disdain of the world proper to humility?
Aristotle refers it to magnanimity/ 04 and the Angelic Doctor,
in his tract on that virtue, follows the philosopher faithfully,
apparently contradicting his own conclusion just quoted. 105
But it is hard to see how contempt for place and dignity can
proceed directly from any habit that has as its matter not the
101 " • • • humilis . . . amplexus subjectionem, non tendit
in condigna nisi ut
subditus, nee ipsa viliora fugit nisi quatenus decenti subjectioni repugnant " (Lumbreras, op. cit., p. 182 (n. 817) ) .
102 The Imitation of Christ, III, 48, n. 8.
103 " ••• ejus est proprium contemnere sublimitatem terrenam " (Art. 5, ad 8) .
104 Ethica Nicomachea, IV, 8. 1124a 18-20; 1124b 5, 6.
105 Summa Theol., II-II, q. 129, a. 8, ad 2:
" ..• magnanimus exteriora bona
contemnit. . • . "

THE VIRTUE OF HUMILITY

171

passions of hatred and aversion, to which scorn must be reduced, but hope, audacity, and confidence.
To solve the difficulty, it is necessary to understand precisely
what is meant by the contempt which the Christian should
have for earthly grandeur. For many writers on mysticism,
and more than one of the Fathers, it has exactly the same sense
that it has in modern English: the estimation of a thing as
mean, vile, worthless, or the strong emotion resulting from such
an estimation-scorn, disdain. Has Aquinas the same concept,
or is the psychological attitude of which he speaks something
analogous to the hatred of father and mother that Christ demanded of His followers-an ordinate love, an ordinate love's
aversion for all that is inordinate? 106 The correct answer to
the question is important, for upon it depends the right Christian attitude to goods of this world, especially honors, dignities,
and high offices. The doctrine of St. Thomas is clear, and to
one familiar with the Imitation and the works of St. Bernard,
not a little startling.
Temporal goods should be despised insofar as they hinder us
from loving and fearing God. . . . But temporal goods should not
be despised when they help us instrumentally to the things that
are of divine love and fear .... 107 Those who despise honors in
such a way as to do nothing unbecoming to obtain them, and who
do not prize them too highly, are praiseworthy. But if one were to
despise honors in such a way as not to care for things truly worthy
of honor, this would be blameworthy .... 108 The magnanimous
man despises exterior goods, inasmuch as he does not esteem them
great goods for which he should do anything unfitting. Yet he
does not despise them to the degree of esteeming them useless for
achieving works of virtue. 109
108

Luke, XIV, !i!6.

bona temporalia debent contemni inquantum nos impediunt ab amore
et timore Dei. . . . Non autem debent contemni bona temporalia, inquantum
instrumentaliter nos adjuvant ad ea quae sunt divini amoris et timoris " (Summa
Theol., II-II, q. l!i!6, a. I, ad 8).
108 " ••• illi qui contemnunt
honores hoc modo quod pro eis adipiscendis nihil
inconveniens faciunt, nee eos nimis appretiantur, laudabiles sunt. Si quis autem
hoc modo contemneret honores quod non curaret facere ea quae sunt digna honore,
hoc vituperabile esset" (Ibid., q. 129, a. 1, ad 8).
100 " ••• magnanimus exteriora bona contemnit, inquantum non reputat ea bona
107 " •••

SEBASTIAN

CARLSON

Contempt for honor and all that is lofty meant for Thomas
only a reasonable avoidance of what, though good under one
aspect, is bad or dangerous under many others. Indeed, it implies love. Earthly sublimity is to be contemned to the degree
that it is an occasion of pride. But when it is genuinely sought
as a means to achieve one's own spiritual good; when it demands only talents one certainly possesses; when it is sought
not as a source of honor and glory or power over others, but as
a means of doing good that could not be accomplished without some personal eminence-then the seeking of an earthly
rank is not only licit but commendable. 110
It is clear that scorn for worldly greatness is nothing more
fanatical than the aversion of an ordinate love for personal
excellence, to all that is inordinate and beyond one's measure.
It is proper to humility in the sense not that it springs from
the virtue as its first elicited act, but that it is implied and
virtually contained in every primary act of the habit. 111
Because, however, hatred and aversion pertain to the concupiscible . appetite, an actual, explicit act of contempt for
incommensurate excellence cannot be elicited by humility but
must be imperated by it. Yet the response of the concupiscible
appetite is so closely and vitally connected with the primary
act of humility, and so directly influenced by the virtue's formal
magna, pro quibus debeat aliquid indecens facere. Non tamen quantum ad hoc
contemnit ea quin reputet ea utilia ad opus .virtutis exequendum " (Ibid., a. 8,
ad !it).
11 °Cf. the following texts:
Summa Theol., II-II, q. 185, a. 1. Quodlibeta, II,
q. 6, a. 11; III, q. 4, a. 9; V, q. 11, a. 22; XII, q. 11, a. 17. Commentarium in
Matt., Cap. XX, n. 2 (vv.26-27), p. 274a post init.; ibid., Cap. XXIII, n. 1,
p. 801b prop. fin. Comment. in II Cor., Cap. XII, Lect. III (v. 7), p. 509b fitn.
Comment. in I Tim., Cap. III (v. 1), p. 199; ibid., Cap. VI, Lect. IV (v. 17),
p. 228a init. Comment. in Heb., Cap. V, Lect. I (vv. 4, 5), p. 844a post med.
111 Cf. Cajetan,
Commentarium, in II-II, q. 161, a. 5: XXIII: " ... quia
humilitatis principalis actus est reprimere appetitum a sublimibus et a sublimiter
se habere (hie est enim modus, hoc est frenum quod humilitas spei ponit ex
reverentia divina); et hoc est virtualiter · contemnere sublimitatem: ideo, 'contemnere sublimitatem terrenam ' humilitatis dictur esse proprium, utpote spectans
ad proprium ejus actum; et non ad secundarium, sicut contingit in magnaninio, qui
principali actu tendit in magna, non contemnit magna. Quamvis etiam alia et alia
ratione uterque contemnat terrena: ut patet ex rationibus magnanimi et humilis."

THE VffiTUE OF HUMILITY

178

motive, that it can truly be called proper to humility. The
same laudable disdain of greatness can be imperated by magnanimity and philotimia, but only through their secondary acts,
since the magnanimous man " tends by the principal act of the
virtue toward: great things, and does not contemn them." 112
To sum up, the essential act of humility is the hopeful quest
of one's own excellence, proceeding according to reason, and·
taken up out of reverence for God and submission to His Providence. As principal, this act becomes a direct act of subjection
to God or to the element of the divine present· in His intellectual creatures. Normally, the essential act consists in hope
that is held down by reason to what is moderate and proportionate (the primary act), a1,1d often results in a sentiment
of contempt and scorn for earthly greatness (the proper act).
Extraordinarily, for example in the case of one suffering from
an inferiority complex, the essential act consists in the encouragement and stimulation of lawful ambition, in the raising of
hope to the mean of reason (the secondary act).

IV. THE ExTENT OF HuMILITY
Humility does hot confine its subjection to God alone. Because it leads· the will to pay reverence not only to Him but to
all that is His, it subjects itself to the divine, wherever it is
found. Making man see that his own part of the ego is less
than nothingness in comparison to God's part, it shows him
also that what he is of himself falls far below what belongs to
God in his fellow creatures. 113 To what conclusions does this
truth lead?
First of all, humility makes man subject to every intellectual
being. One must prefer the divine good in others to what is
his own in himself. He must not prefer, for example, his own
foolhardy audacity in danger to the unspectacular bravery of
the truly courageous man. " Everyone should study what is in
himself-vice, sin, and defect, for example-and compare them
with the good others have from God; and, according to this,
112

Cf. the preceding note.

118

Art. 3, corp. init.

174

CARLSON

believe himself inferior to them." 114 In the concise words of
Thomas, " every man, according to that which is his own,
should subject himself to his every neighbor with regard to
what there is of God in the latter." 115 Precisely what is this
quid divinum in others? " [It is] a real, living reflection of the
Infinite: it is authority, genius, wisdom, goodness, grace, virtue,
sanctity. Whatever its name, whatever its nuance may be, we
must honor it out of respect for God whence it comes, as we
must love our neighbor out of love for God." 116
This degree of humility alone is strictly necessary for
salvation.
Humility does not require that a man subject what there is of
God in himself, to what seems to be from God in another. For
those who participate the gifts of God know that they have them,
according to that of I Corinthians: "that we may know the things
that have been given us by God." 111 And therefore, without
prejudicing humility, men can prefer the gifts they have received
to the gifts of God which seem to have been given to others.U 8

Whereas it is a sin against God Himself to prefer the deficiency
and sin of others to the gifts of God in oneself, another's habit
of rollicking drunkenness to one's own cautious sobriety, yet
humility does not demand that one believe his own gifts are
1 " " • • • quilibet homo debet considerare ea quae in ipso sunt sua, ut vitia,
peccata, et defectus; eaque comparare cum bonis quae alii habent a Deo; et
secundum haec sese illis inferiorem censere" (Fr. Sylvius, Commentarium in II-II
divi Thomae (Douay, 169l8), in q. 161, a. 8: "Primo").
115 " • • • quilibet homo, secundum id quod suum est, debet se cuilibet proximo
subjicere quantum ad id quod est Dei in ipso" (Art. 8, corp.).
116 " ••• un reflet reel, vivant de l'lnfini: c'est l'autocite, le genie, Ia sagesse, Ia
bonte, Ia grace, Ia vertu, Ia saintete. Quels que soient son nom et sa nuance nous
devons !'honorer par respect pour Dieu d'ou il provient comme nous devons aimer
notre prochain par amour de Dieu " (M.-A. Janvier, Exposition de la morale
catkolique: Morale speciale, XII, La vertu de temperance, ll (Careme, 199l2):
L'humilite (Paris, 1928), p. 61)..
117 I. Cor., ll, 12.
118 " Non autem hoc requirit humilitas, ut aliquis id quod est Dei in seipso,
subjiciat ei quod apparet esse Dei in altero. Nam illi qui dona Dei participant,
cognoscunt ea se habere, secundum illud I ad Cor., ' Ut sciamus quae a Deo donata
sunt nobis.' Et ideo, absque praejudicio humilitatis, possunt dona quae ipsi
acceperunt praeferre donis Dei quae ali,is apparent collata" ·(Art. 8, corp.) .

THE VffiTUE OF HUMILITY

175

less than another's, far less that one consider himself the least
perfect creature that ever left God's hands. Nor need one drop
his own reasoned convictions on political affairs, for example,
and submit to the views of another, until he is convinced of his
own error. It is not necessarily pride that makes an artist
prefer his own works to those of Michelangelo. Posterity may
confirm his judgment.
Neither is it a sin against lowliness of heart to feel that one
is not the greatest sinner in the world. The continent daily
communicant need not torture his soul into the belief that he is
worse than the murderers and adulterers of whom he reads in
the daily papers.
Otherwise it would be necessary that everyone deem himself a
greater sinner than anyone else; whereas the Apostle says without
prejudice to humility, "We are by nature Jews; and not of the
Gentiles, sinners." 119 • 120

It would seem that Billuart goes too far when he writes that
" a man can without error, and ought to consider and pronounce himself viler than all, unworthy of God's gifts, and of
no use whatsoever." 121 The word ought, debet, is ill chosen.
Man may, that is exact enough; " for he can deem that there
is some good in his neighbor which he himself lacks, or some
evil in himself which is not in another; whence he can subject
himself to that other out of humility." 122 It is for sanctity's
sake that he ought to do so, but salvation is attainable
without it.
It is to be noted carefully that humility need never resort
Gal., II, 15.
Alioquin oporteret ut quilibet reputaret se magis peccatorem quolibet alio:
cum tamen Apostolus, absque praejudicio humilitatis, dicat: 'Nos natura Judaei, et
non ex gentibus peccatores ' " (Art. 8, corp.) ..
121 " • • • homo potest
et debet absque falsitate se reputare et pronuntiare
omnibus viliorem, donis Dei indignum et ad omnia ineptum " (Billiiart, op. cit.,
Tractatus de temperantia et virtutibus illi annexis, Dissert. VII, Art. IV, 6, I,
" De Htimilitate ") .
122 " Potest tamen aliquis reputare aliquid boni esse in proximo quod ipse non
habet, vel aliquid mali in se esse quod in alio non est, ex quo se potest ei subjicere
per humilitatem " (Art. 8, corp.) •
119

120 "

176

SEBASTIAN

CARLSON

to psychological sophistry. " Humility is to be placed on the
side of truth, not on the side of falsehood." 1·28 Without fear of
error, mau can prefer the divine in others to what is his own in
himself; and he will be as far from falsehood as good is from
evil, as God is from nothingness. 124 Without fear of violence
to his judgment, he can even believe himself the worst of all
sinners. Comparing his share of good with his neighbor's, he
may justly suspect that there is much good in his neighbor,
even if he does not see it, which he himself lacks; and that his
neighbor shows much more gratitude to God for his talents
than he does for his own, and uses them to better advantage. 125
And he may conclude that if even the greatest sinner received
the graces he has received, that sinner would now be swinging
along God's highway with giant strides, not still toddling and
tumbling as he is doing.
One can without error " believe and declare oneself viler than
all men," 126 according to the hidden defects he discovers in himself and the gifts of God which lie concealed in others. Hence
Augustine says, " Think that those than whom you are seemingly
better, are secretly superior." 127 Likewise, one can confess and
believe without falseh.ood that he is good for nothing and unworthy
.so far as his own powers are concerned, in order to attribute his ·
sufficiency to God, according to that of II Corinthians: "Not that
we are sufficient to think anything of ourselves, as of ourselves; but
our sufficiency is from God.'' 128 • 129
123 " Humilitas collocanda est in parte veritatis, non in 'parte falsitatis " (Augustine, De Natura et Gratia, Cap. XXXIV (M L 44,
as quoted by St. Thomas,
Art. 3, arg.
.
124 Cf. Art. 3, ad
" . . . si nos praeferamus id quod est Dei in proximo, .\'!i
quod est proprium in nobis, non possumus incurrere falsitatem."
125 Cf. Sylvius, loc. cit.:
" . . . si bona sua comparet homo cum bonis alterius,
cogitare debet aliqua et fortasse multa bona esse in altero, quamvis sibi incognita,
quae ipse non habet; ac propterea, alterum majori gratitudine prosequi beneficia
divinitus sibi collata, quam ,ipse prosequatur ea quae a Deo accepit. . . . Etsi
defectus, eosque graves in aliis videat, cogitare potest, ac interdum deberet, aliqua
mala etiam notabilia sive nota sive ignota sibi inesse, quae non sunt in aliis."
126 Benedict, Regula, Cap. VII. M L 66, 374 A.
127 De Sancta Virginitate, Cap. LII. M L 40,
128 II Cor., iii, 5.
120 " • • • aliquis absque falsitate
potest ' se credere et pronuntiare omnibus

THE VIRTUE OF HUMILITY

177

Commenting on Paul's words, "For I am the least of the
Apostles, and am not worthy to be called an Apostle, because
I persecuted the Church of God. But by the grace of God
I am what I am," 180 the Angelic Doctor notes that on the
face of it this false, since Paul wa'S not the least but among
the greatest. It is wrong to. tell an untruth out of humility;
why then did Paul call himself the least?
When he says, " because I persecuted the Church of God," he
shows how he is least, and how not least. The least, considering
his past deeds·. . . . " I persecuted the Church of God," which the
other Apostles did not do. . . . And though of myself I am the
least, yet through God I am not the least .. · . . He [Paul] says,
therefore: Of myself I am nothing, but what I am, I am by the
grace of God-that is, through God, and not through myself. 131

There is, consequently, nothing to hinder one who is actually
superior to others from sincerely deeming himself inferior to
all, and ranking himself beneath all in the secrecy of his heart. 182
In doing so, he reaches humility truly sublime: he ·not only
subjects himself to his own betters, and refrains from preferring
himself to his equals-the degree of humility necessary for
not only considers himself beneath his equals-advanced humility; but he even subjects himself to his inferiorsthe acme of Christian humility. 138
viliorem,' secundum defectus occultos quos in se recognoscit et dona Dei quae in
aliis latent. Uncle Augustin us dicit: 'Existimate aliquos in occulto superiores,
quibus estis in manifesto meliores.' Similiter etiam absque falsitate potest aliquis
confiteri et credere ad omnia se inutilem et indignum per proprias vires, ut sufficientiam suam totam in Deum referat:· secundum illud II ad Cor.: 'Non quod sufficientes simus aliquid cogitare a nobis, quasi ex nobis; sed sufficientia nostra ex Deo
est'" (Art. 6, ad 1).
130 I Cor., XV, 9, 10.
131 " ••• cum dicit:
' Quoniam persecutus,' etc., ostendit quomodo sit minimus,
et quomodo non minimus: minimum autem dicit se, considerando praeterita facta
sua ... 'persecutus sum Ecclesiam Dei,' quod alii Apostoli non fecerunt. . . . Et
licet ex me sum minimus; tamen ex Deo non sum minimus. . . . Dicit ergo ... .
Ex me nihil sum, sed id quod sum, gratia Dei sum, idest ex Deo, non ex me ... "
(Comment. in I Cor., Cap. XV, Lect. I (vv. 9, 10), p. 889a).
182 Cf. IV Summa contra Gentiles, c. 55, ad 17; Comment. in Phil., Cap. II, Lect.
I (v. 3), p. 91a post med.
183 Cf. Comment. in Matt., Cap. III, n. 2 (v. 15), p. 52a ante fin.: "'Sic enim

178

SEBASTIAN

CARLSON

The conviction that one is the worst of sinners is a mark of
virtue so lofty and rare that modern students of St. Thomas'
thought see in it a special gift of God, given only to the
predestined few.
The chief source of this heroic humility seems to be an entirely
special light infused in them by God, by which they perceive their
faults and negligences, even though the smallest, to·be unworthy' of
a Christian soul adorned by grace, and offensive to God; and perceive them with such vividness that from this experimental-sense
of their own unworthiness, they can no longer take note of the
greater sins of others. Hence it is clearly evident that this most
perfect humility is a singular gift of God, making the saints immune
to all temptations of vainglory, notwithstanding the gifts they have
received and the people's veneration. 134
SEBASTIAN

CARLSON'

0. p.

Dominican House of Studies,
River Forest, Illinois.

(To be continued.)

decet nos implere omnem justitiam ' (Matt. 8: 15) , idest, decet me habere perfectam humilitatem. Primus gradus est non praeferre se pari, et subjicere se majori,
quod quidem est necessitatis. Secundus cum subjicit se aequali. Perfecta autem,
quando praelatus se subjicit inferiori: et hoc est, ' Sic enim decet,' etc., idest
perfectam humilitatem implere."
, .. " Praecipuus fons hujus heroicae humilitatis videtur fuisse lumen omnino
speciale ipsis a Deo infusum quo proprias culpas et negligentias, etsi valde !eves,
tanta claritate intelligerunt anima christiana gratia ornata indignas, Deoque ofiensivas, ut ex hoc suae indignitatis experimentali sensu, jam ad aliorum majora
peccata attendere non possent. Unde clare apparet hanc perfectissimam humilitatem donum Dei esse singulare, quo sancti illi contra quasvis vanae gloriae tentationes immunes fierent non obstantibus donis acceptis et populorum veneratione "
(J. Guibert, Theologia apiritualis ascetica et mystica (Rome, 1987), n. 858, !t) .
Cf, also: Guibert, Etudes de Theologie mystique (Toulouse, 1980), pp.
Marmion, op. cit., p.

THE PLATONIC THEORY OF THE
CONTINUUM

T

HE proper correlation of the continuous and the discrete remains one of the fundamental problems of philosophy. Various solutions have been proposed, from
the early discussions of the Pythagoreans and the Eleatics to
the contemporary controversies about the theory of aggregates,
the foundations of topology, or the methods of integration.
Some of them are strictly mathematical; while others cover the
wider field of metaphysics. But none seems to be satisfactory
enough to all thinkers.
The fullest theories which have come down to us from
ancient times are those of Plato and Aristotle. Many writers
have extolled the remarkable intuitions of the former at the
expense of the doctrines of the latter, as the Platonic views
seemed to be more in line with the classical conceptions of the
calculus. Such an interpretation, however, does not take into
account the recent views about the foundations of mathematics, which involve more Aristotelian than other elements.
On the other hand, the Platonic views are not only mathematical, but mainly philosophical: hence they should be criticized in themselves, whatever be their partial connection with
successful mathematical methods.
Owing to obvious analogies between the classical Greek
conceptions and the modern views on the continuous and the
discrete, we propose to offer here a short discussion, of the
Platonic Theory of the Continuum, as a background to a critical and historical approach to this important question.
I.

IRRATIONALS

AND INDIVISIBLES

Having found in mathematics the means of rationalizing the
world of knowledge and existence, Plato had to consider the
rationalization of mathematics itself as a preliminary requirement. This operation became particularly urgent when it was
179

180

THOMAS

GREENWOOD

shown that geometry involved many notions which could not
be accounted for by the arithmetic of integers. It was necessary to explain how the discontinuous series of the integers can
generate the geometrical continuum, and how the integers
themselves are obtained.
The difficulties of the early Pythagoreans in their treatment
of similar problems were due .to their inability to establish a
generalized arithmetic ·and to avoid inconsistencies like Zeno's
arguments. This faihJ.re became evident when the irrationals
were discovered. The parallelism between geometry and arithmetic was broken: the Pythagorean concept of number was
no longer adequate. to account for all geometrical forms and,
consequently, for the empirical things corresponding to their
geometrical patterns. In order to save the rational value of
knowledge as illustrated by the truth of mathematics, it was
necessary to revise the conception of number itself, to widen
it so that it might become possible to define " irrational "
numbers as well, and to formulate laws for their addition and
multiplication in terms of the arithmetic of integers.
In fact, Plato could not consider the irrational quantities as
being beyond reason. He even used them in his doctrine of
Reminiscence. In a well-known passage of the Meno, Plato
tried to explain that teaching is only re-awakening in the mind
of the learner the memory of something. A slave is introduced
into a room containing objects the mere sight of which will
make him aware, when subjected to the dialectical treatment,
of universal truths concerning them. Meno is to watch whether
the boy is taught by Socrates in any of his answers; whether
he answers anything at any point otherwise than by way of
reminiscence and really out of his mind, as the reasonable questions of Socrates fall like water on the reed-ground. By putting
to the slave a carefully prepared series of questions, Socrates
leads him to recognize that double the square of any straight
line is not the square on double the line, but the square on the
diag()nal of the original square. 1
1

Memo, 8ft B-85 B:

THE PLATONIC

THEORY OF THE CONTINUUM

181

Surely, the so-called irrationals must be rational somehow, if
the mind has contemplated their patterns in the world of ideas,
and if it " remembers " them when confronted with their actual
geometrical illustrations. " See him now; how he remembers in
the logica,l order, as he ought to remember." And again," Just
now, as in a dream, these opinions have been stirred up within
him." The slave will perform, Socrates assures us, similar acts
of reminiscence on demand, with other geometrical problems,
with any and every problem whatever.
The same idea is also expressed in the Phaedo, when we are
told that the theory of an innate knowledge independent of our
experience here holds " not a bit more about two equal lines
than about the absolute Beauty, and about what is absolutely
just and good, and about all things whatever n; for, if it is
admitted that we are born already possessed of certain mathematical principles apprehended before birth, it is just as true
to say that " we have knowledge, both before and immediately
upon our begetting here, not merely about the equal, and the
greater, and the less, but also about all other things of the
kind." 2 This doctrine that all knowledge is recoverable, by
the way, may be considered Pythagorean, if we generalize the
teaching of the brotherhood about the memory of past lives. 8
There is another reason also for the recognition· of the necessity of the irrationals, and consequently of their capacity for
rationality. In outlining the qualifications and duties of the
members of the " nocturnal council " which looks after the
public safety, Plato points out that public piety must be their
primary concern. But this piety requires the replacement of
the Olympian gods in the public cult by the heavenly bodies
which exemplify the wisdom of the Creator by their conformity
expense of the doctrines of the latter, as the Platonic views
to mathematical law. This regularity can be ascertained by
observing the rhythmic periods of each planet's motion and by
expressing them in terms of the period of any other. For this
• Phaedo, 75.
Cf. A. Cameron, The Pythagorean Background of the Theory of Recollection.
(Wisconsin, 1938.)
3

THOMAS GREENWOOD

purpose, however, something more than the arithmetic of
integers is needed, because the periods of the heavenly bodies,
when compared, are not always commensurable. Hence the
necessity of studying integers and surds. But these numbers
must be considered as pure and not as embodied, and an
account of their derivation must be given before discussing
tl1eir application.
Plato may have approached this problem by a numerical
interpretation of the discoveries of Theaetetus and Eudoxus,
involving the reversion of the relative priority of geometry
over arithmetic. This is, at any rate, the position reached· in
the Epinomis, which goes beyond the mathematical considerations of the Republic. "The first and most important [study]
is of numbers in themselves, not of corporeal numbers, but of
the whole genesis of the odd and even, and the greatness of
their influence on the nature of things." 4 There come next in
order,geometry and stereometry, which prove to be "an evident likening of numbers unlike one another by nature." The
following fragment of Archytas shows that this view was predominant at the time: " I think that in respect of wisdom,
arithmetic surpasses all the other arts,. and especially geometry,
seeing it can treat the objects it wishes to study in a clearer
way. Where geometry fails, arithmetic completes its demonstration in the same way, even with regard to figures, if there
is such a thing as the study of figures." 5
An illustration of the prevalence of arithmetic over geometry
may be found in the Platonic notion of indivisible lines. It may
be remembered how the Pythagoreans would fill the geometrical continuum with points defined as monads having position.
But this view, which implies that a point has a minimum
volume, had been obliterated by Zeno's argument of the unlimited bisection of the straight line, and of the impossibility
of making a line longer, or a volume bigger, by adding one
point to it. Plato did not give direct answers to the difficulties
of the Eleatic. But he objected to the Pythagorean conception
' Epinomi8, 990 (J.

6

Diels, Vora. p. 887.

THE PLATONIC THEORY OF THE

188

of the point, as he did to the Democritean notion of the atom,
which appealed too strongly to materialistic sense experience.
He would not even think of a point in its own right; for he
considered the genus of points a " geometricalfiction."
But he
would speak of a point as the beginning or the principle of a
line, and he would use the term " indivisible lines " in the same
sense.6
Points and indivisible lines could scarcely have been considered by Plato as being identicaL In fact, the last Aristotelian text just referred to implies a radical opposition between them, if the Greek expression ToVrtp p.f:v . . . Toih-o 8e is
properly interpreted. As regards the point, there is no difficulty
in accepting it as a principle (
rather than an element
(cnotxewv) of the line. But it was unnecessary for Plato to
consider the indivisible lines
in the more
recent sense of the Democritean atoms, as the minimum of the
seeable magnitudes. The word
already existed in the
Greek vocabulary in the sense of something which is not actually divided, which is not composed of actually separate parts;
but it did not imply that a magnitude which was not divided
was necessarily indivisible. It is in this original sense that the
word
must have been used by Plato, as it appears from
the only passage of the Dialogues 7 in which it is referred to
explicitly. Consequently, Plato would consider his
not as indivisible lines but as undivided lines, as
magnitudes which are not reduced to a sum of smaller parts, a
conception which agrees fully with his idea of the point indicated by Aristotle himself.
In this sense, as principle of a line, the point cannot be a
static notion. In fact, according to Aristotle the Platonists
taught that " a moving line generates a surface, and a moving
point a line." 8 Thus a line is not made of points added together but is generated by the fluxion of a point; at the same
time, however short a line may be, it cannot be divided into
• Aristotle, Met.
7 Sophist,
D.

4

a
8

De Anima, 409 a 5.

184

THOMAS GREENWOOD

elements which are not themselves lines: it is a continuum.
More generally, the continuum would be produced by the flowing of some undetermined element like the infinite, rather than
by the actual juxtaposition of a large aggregate of actual indivisibles. This would be true of numbers and of geometrical
magnitudes as well, on the ground of the identification of the
xc!Jpa with the infinite, and of the parallelism established by
Plato between numbers· and figures.
It follows that the generation of the continuum, both numerical and geometrical, has to begin with some element. The principle of number and the principle of a line have to be something; they cannot be nothing. Hence, if the notion of the
infinitesimal is involved in any sense in these considerations,
it need not be as an actual indivisible, or as the actual and final
result of a continued subdivision.. It should rather be considered like the undivided genetic element of a magnitude which
can be made as small as we please; or again, like the "intensive" infinitesimal suggested by the idealist thinkers of the
nineteenth century. It is therefore difficult to accept Taylor's
opinion that the Platonic conception of the point as principle
of a line implies the idea of beginning the series of' numbers
with 0 instead of with 1. Besides, the Greeks had no conception
of 0 as a number.
It should not be asserted 9 either, that the Platonic doctrines
involve the first clear conception of the infinitesimal; though
it may be said that Plato "was thinking out the solution of
problems that lead directly to the discovery of the calculus." 10
Nothing in his writings suggests that Plato could supply either
a clear sensory interpretation or a precise logical definition of
the intuitive conception of the infinitesimal which was used by
the discoverers of the calculus. As to the modern logical idea
of the infinitesimal, which depends on the notions of the derivative and of the limit, neither Plato nor his successors could
possibly have thought of it. At that time there was no general
• Hoppe, Zur Geschichte der Infinitesimal Rechnung, p. 152.
Marvin, The Histo,ry of European Philosophy, p. 142.

10

THE PLATONIC THEORY OF THE

185

concept of number in Greek mathematics, and consequently no
notion of a continuous algebraic variable-upon which could be
based the mathematical concept of limit.
It is significant, however, that the intuitions of the infinitesimal and the continuum, vaguely indicated by Plato, were developed by his early successors in the direction of the indivisibles or fixed infinitesimals, which are unacceptable to
modern analysis. In particular, Xenocrates maintained the
existence of indivisibles, and established for them a definite
doctrine which prompted the critical refutation of the Peripatetic tract On Indivisible Lines. But Aristotle himself had
already pointed out 11 that indivisible lines must have extremities and cannot be points; while the definition of a point as the
extremity of a line is unscientific. Modern mathematics upholds
Aristotle in his vigorous opposition to infinitesimal line segments, because it has been unable to offer a logical elaboration
and a satisfactory definition of such indivisibles. Moreover,
even though this ·notion was destined to play an important part
in the early development of the calculus, it was definitely abandoned when modern analysis achieved a rigorous formulation
of its foundations.
II. FUNCTION OF THE ONE AND THE DYAD

It was from Pythagorean premises that Plato attempted the
generation of the arithmetical continuum. Traces of his views
on this matter are found in certain later Dialogues, and mostly
in the Philebus, which is considered as forming the transition
to the final views of Plato concerning forms and numbers. In
this dialogue, which recounts the Pythagorean opposites, the
limit and the infinite, the one and the many, the ideas are
termed ev&.8es or p.ov&.8es; and the elements of things are given
as the limit and the infinite, 12 in true Pythagorean fashion.
This conception without doubt underlies Plato's fundamental
doctrine. For we have it on the authority of Aristotle and
11
12

Topics, 141 b 21.
Pkilebus, 24 A.

186

THOMAS

GREENWOOD

Hermodorus 18 that Plato posited the 'TTEpar; and the ti'1Tetpov as
the two elements (o:-Totxeta) which are present in the ideas and
in all existing things. The 'TTEpar;, which is the limit or the one,
represents unity (ev) and is the form-giving or active element.
The ti'1Tetpov, which is the infinite or the many, represents a
formless matter (ifll:q) and is the form-receiving element. So
that ideas, numbers and sensible things alike, are generated by
the combination of the '1Tepar; and the ti'1Tetpov; that is, from the
infinite and through the limit. In this sense the elements of
numbers are the· elements of things. These views may be related to the doctrine of the same (Ta6rov) and the other
( OaTepov) , which is mentioned in the Sophist, and also in the
Timaeus (35 A), where beillg is stated to be a blend of the
sarne and the other.
The operation of the limit shaping the infinite requires further elucidation, especially as Aristotle claims that it produces
the lines, surfaces, and solids 14 and that it accounts for the
numbers. It ·stands to reason that the limit by itself is sterile.
For it is impossible to explain how number one can be made
to repeat itself and produce other numbers, just as it cannot be
explained how one point by itself may be moved into the
necessary reiteration for the generation of a line. In other
words, with the limit alone we cannot show how mathematical
operations are possible, how mathematics can be extended to
the sensible world, and how the general problem of the one and
the many can be solved.
To be sure, even the participation of the mathematical numbers in the ideal-numbers or number-fo!ffis cannot account
actually for the various arithmetical operations. Indeed, the
forms of numbers are mathematically impotent. The union of
the idea of 2 with -the number one or the limit cannot take
place, as it would bear no fruit: for it would leave us simply
with the idea of 2. or twoness, and the number one uncombined
and unintegrated.
For these reasons, another principle of generation is needed
18

Simplicius, Commentary on Aristotle's Physics, fol. 54 b and 56 b.

"Met. xn, 9.

THE PLATONIC

THEORY OF THE CONTINUUM

187

to account for the real and the apparent. This other element is
the dyad, which is a principle of plurality, movement, change,
and becoming. In the physical world, the function of the dyad
is to produce the plurality. and spatiality of phenomena. By
identifying extension with the stuff of sensible things, the
cosmogony of the Timaeus reduces to the dyad the solid. and
corporeal nature of the universe. In the world of ideas it may
be said that the dyad gives rise to their multiplicity and colors
their relation with a continuity which is not unlike that .of
numbers. It is by virtue of the dyad that the mind glides
without breaks from one idea to another.
In the logical realm, the function of the dyad and its limitation by the one, as indicated in the Sophist, tend to give a
mathematical color to the process of definition. " By the
segregation of more specific within more general ideas, we close
in upon the specific form by bracketing it, as it were, more and
more narrowly, till we have excluded from it everything that is
not its proper essence; just as we approximate to our irrational
numbers by a progressive reduction of the values that are
greater and smaller than the one in question." 15 Thus the
essence of a thing is reached and expressed by a process similar
to the kind of mathematical division which approximates to
the value of a surd, as will be shown presently.
More specifically, the dyad is the principle of numerical
multiplicity and geometrical extension. Thus we are told that
its combination with the limit produces all the even numbers
by multiplication and all the odd numbers by the operation of
the limit which stops, equalizes, and stabilizes the propensity
of the dyad to multiply. 16 But it may be said also that the
cooperation of the one with the great-and-small yields not only
the rational numbers but also the irrationals. Let us see in
detail in what way the combination of the dyad with the limit
or the one generates the numbers in a natural manner.
This construction 17 of the arithmetical continuum requires
Fuller, History of Greek Philosophy, vol. II, p. 891.
Cf. Aristotle, Met. 999 a 9, 1002 a 15, and 1080 b 11.
17 Met. 987 b 14.
10
16

188

THOMAS

GREENWOOD

primarily a clear understanding of Plato's conception of the
infinite: he considers it as an undetermined dyad (a6ptO"Tos
8vas) and- gives it the strange name of p,f:ya Kat p,tKp6v, the
great-and-small. This dyad involves a double function of multiplication and division, but without an upper or a lower limit, in
keeping with its indefinite nature. Further, it has many species,
such as long and short, broad and narrow, high and low, more
and less.
The dyad is undetermined because it is no_t any being in
particular. That is probably why Aristotle identified it with
not-being/ 8 The following fragment of Hermodorus throws
some light on this identification: " Those things which are
spoken of as having the relation· of great to small, all have the
' more and less,' so· that they can go on to infinity in the direction of the ' still greater ' and the ' still less.' In the same way,
the broader and narrower, the heavier and lighter, and everything which is spoken of in that way can go on to infinity. But
what is spoken of as equal and at rest and attuned, has not the
' more and .Jess ' as their opposites have. There is always something more unequal than what is unequal, something more in
motion than that which moves, something more out of tune
than that which is out of tune. Hence that whic}l is of this
nature, is inconstant and formless and infinite, and may be
called ' not being ' by negation of ' being.' " 19 In this sense,
the indefinite continuum of the more-and-less is not " nothing "
but rather it is" not anything" in particular.
It remains to explain why the infinite is a
an undetermined ratio which connotes a formless multiplicity, and why
this duality is a great-and-small. The available references to
Plato's views on this matter give neither the whole of his
thought nor the reasons for his dissatisfaction with the Pythagorean conception of number. In the absence of specific texts
one has to turn to speculation. Some modern writers like
Burnet, Milhaud and Stenzel have rightly suggested that the
18

19

Physics, 192 a 6.
Simplicius, Commentarie-s on Aristotle's Physics, Vors. 247 (Diels).

THE PLATONIC

THEORY OF THE CONTINUUM

189

great-and-small is somehow connected with the irrationals,
especially as it may help to obtain their values by successive
approximations to a limit. But these views are considered by
Taylor, Rey and Toeplitz as too general and conservative to be
fully satisfactory. In fact, certain series converge to a limit
and certain others
smaller than the unit (like 1, t, -1 •..
converge to a limit greater than the unit (like 1, 1 + i, 1 + i
. . . 1 + ) • In both cases the series converge in a simple
sense which does not justify the Platonic notion of the greatand-small. Hence the assumption that Plato must have
thought of a specific way of constructing infinite converging
series.
Working on this view, Taylor 20 suggested an interpretation
of Plato's probable method by using the famous passage in the
Epinomis about the generation of numbers, 21 and
other
considerations of the Platonic dialogues and of later commentators. He took into account, in particular, the properties of
the side and diagonal numbers, and the rule given by Theon of
Smyrna 22 for calculating rational appproximations to
with
.
.
Increasing accuracy.
From these considerations, Taylor concludes that the substitution of a dyad to the single infinite is due to the necessity of
providing a means of checking the interval within which falls
the error of an approximation. Moreover, this dyad is a greatand-small, because it is the limit to which one series of values,
all too large, tends to decrease, and also the limit to which
another series, all too small, tends to increase. As it is impossible to find an identical value for two successive convergents
in the case of an irrational, there is always inequality or tension
between the great and the small; or again, an unrationalized
•• Mind, t. 85, pp. 419-440 (1926) and t. 86, pp. l!'l-88 (1927). These articles
are reproduced in his Philosophical Studies, to which our quotations refer. Against
the general opinion, Taylor regards the EpinomiS as a genuine Platonic writing.
The authenticity of this work, however, does not affect the interest of this interpretation, inasmuch as the EpinomiS is undoubtedly of strict Platonic inspiration.
21 EpinomiS, 990 C-991 B.
92 Expositio (ed. Hiller), p. 48 sq.

190

THOMAS

GREENWOOD

matter in the irrational number. It is the function of the
formal element of number, the one, to equalize (lua,etv) the
great and the small; but it is not as successful for the irrationals
as it is for the' rational numbers where the tension between the
great and the small vanishes.
The specific function of the one to equalize the great and the
small is expressly ascribed to Plato by Aristotle himself. 28 It
is indeed a Platonic conception which appears also in many
other Dialogues. In a passage of the Statesman referring to
the science of measure or metretic (p,eTp'TJnK-IJ), we are told·
that the great and the small must be appraised not only by
their reciprocal relation but also by reference to the just
measure (11por; To p,eTpwv) • What is great is not so with reference to the small only, but also with reference to the just
measure, and the same is true for the
Hence there are two kinds of metretic: one considers the
great and the small with reference to the just measure; the
other considers them simply with reference to one another.
The former may well be assimilated to dialectic, while the
latter is identified with mathematics. In spite of this distinction, metretic does introduce the idea of a common limit between the great and the small, which can be applied to the
problem of the generation of numbers. This application is the
more permissible when we consider that this problem is not
exclusively mathematical, and that dialectic has some bearing
on the foundations of mathematics.
III.

VALUE OF THE. PLATONIC METHOD

Assuming that Plato did think of such a method of rationalizing the irrationals by means of the one and the dyad, then he
should be credited with the first discovery, though in an incomplete form, of the real numbers conceived as the common limit
of two infinite convergent series. In this connection, Taylor
remarks that the Platonic theory must have been inspired by
the same desire for pure rationality which has led to the arith28

Met. 1081 a 24.

"'Statesman., !!88 C-284 E.

THE PLATONIC

THEORY OF THE CONTINUUM

191

metization of mathematics in modern times. " The object
aimed at, in both cases, is to get rid of the dualism between
so-called ' continuous ' and ' discrete ' magnitude. The apparent mystery which hangs about the ' irrationals ' is to be
dispelled by showing how they can be derived, by a logical
process which is transparently rational at every step, from the
integers and the ' rational fractions,' or Myt of integers to
integers. It is precisely the same process, carried further, which
we see in modern times in the arithmetical theory of the continuum, or in Cantor's further elaboration of an arithmetic of
the ' transfinite.' In all these cases, the motive for the construction is to get rid of an apparent mystery by the discovery
in the
unintelligible of the principle of order of which
the integer-series is the perfect and ideal embodiment." 25
The analogy, however, should not be pushed too far; especially as the knowledge of the Greeks about the surds of a
higher order must be accepted only with strong qualifications.
It is true that the study of the solids initiated by the Pythagoreans, and developed diversely by Democritus. and by Plato
himseif, became an important science with Theaetetus and
Eudoxus, who dealt with problems involving cubic roots. Hence
the demand for a method of approximating cubic roots from
the sides of the great and of the small alternately, as in the
case of the quadratic surds, must have been suggested by the
rise of stereometry in the Academy. 26 The simplest illustration
of the general problem involved was offered by the Delian
Problem: in fact, the duplication of the cube is reducible to
the construction of a series of approximations to the real value
from its two sides alternately.
of
But the actual construction of these convergents requires·
certain algebraical methods which were not possessed by the
Greeks, while the absence of an efficient numerical symbolism.
and of an operational system of position increased the difficul•• Philosophical Studies, p. 120.
•• The prominence given to the question of irrational JLiJI<'YJ in the Theaetetus may
be taken as an indication of the influence these views had on Plato's conceptions.

192

THOMAS GREENWOOD

ties of their arithmetical manipulations. Thus Greek mathematics has not even examples of the extraction of a cube root
fully worked out by means of the expansion of (a+ b) 8 , corresponding to the method for square roots elaborated by Theon
of Alexandria. 27 Hence it may be doubted that there was an
arithmetical construction for
to the Academy, even
though Plato may have conceived its possibility on the ground
of the analogy offered by the numerical treatment of quadratic
surds.
The earliest attempt which has been preserved is the evaluation given by Archimedes. 28 All the other solutions loJ.own to
us are geometrical' or empirical in character, and even the
author of the Epinomis .admits that the numbers with irrational cube roots "which have been made unlike, are likened
by another art, namely what its adepts called stereometry."
Moreover, there is no indication that Plato considered irrational roots (or even rational for that matter) of orders higher
than the third. He was too much dependent on his spatial
intuition to imagine any theories of numbers entirely independent of geometry. Hence, he could not have visualized a
general and independent method for the generation of the arithmetical continuum: at best the Epinomis hints at a program
of research more comprehensive than hitherto, for the immediate future.
The generation of the irrationals, however, does not cover
all the aspects of the problem of number. So far, the integers
and their order have figured as given data in the construction
of the continuum. There remains to be considered the manner
in which the determination of the great-and-small by the one
affects the generation of the integers themselves. Plato must
have considered his problem in this perspective, for in his
criticism Aristotle deals with it always in this form.
On the other hand, there is a characteristic passage in the
27 Commentary on Ptolemy's Syntaxis, 469.16-473.8 (ed. Rome).
The extraction
of the cube root of 100 given by Heron in his Metrics (III.
is a description of
an empirical method with no reference to a generalized formula.
Measurement of the Circle, III.

THE PLATONIC

THEORY OF THE CONTINUUM

198

Epinomis (990 E), concerning the production of the integers,
which throws much light on the Platonic method. It shows
that successive multiplication of 1 by 2 gives the geometric
progression 1, 2, 4, 8, representing respectively a point, a line, a
square and a cube. Then comes a reference to the arithmetic
mean, which is equidistant from two given terms, and to the
harmonic mean, which exceeds one term, and is exceeded by
the other, by the same fraction of each term. By reducing
fractions this gives the numbers 9 and 8 respectively. Here it
may be observed that 8 was already given as the cube of 2, and
that there is no indication as to the generation of the other
integers. A more important remark, which will be elaborated
further in this discussion, is that Plato favors distinctly the
process of duplication in the generation of numbers.
This is also the case with the construction of the world-soul.
Here Plato used two basic geometric series (1, 2, 4, 8), and
(1, 8, 9, 27); and he filled up the intervals between. these
numbers with arithmetic and harmonic means, so as to get a
series of thirty-four terms. 29 It is usually thought that this
construction is intended to represent the notes of a musical
scale having a compass of four octaves and a major sixth. It
is more probable, however, that it has less to do with music
than with Plato's religious background and with his ideas about
numbers.
It may be safely suggested that Plato thought of constructing the arithmetical continuum by means of one single process.
In that case he must have rejected the process of addition,
though it yielded the integers in a simple and direct way, because it did not account for the irrationals, which are far more
numerous than the rational numbers. The unity of the generation of all numbers could be saved, however, if the integers
could be obtained by combining the one with the dyad, a
method which already accounted for the irrationals. The idea
of constructing the integers by means of the one and the dyad
•• Timaeus, 35 B-36 B. Cf. also Bury's notes in his translation of the Dialogue
(ed. Loeb, pp. 66-71); Taylor, Commentary on Plato's Timaeus (pp. 136-137);
Cornford, Plato's Cosmology (p. 67 sq.).

194

THOMAS GREENWOOD

may have originated in the simple remark that the values to
which special pai:t:s of infinite series converge need not be
irrationals. The process of unending bisection emphasized by
Zeno makes it apparent: the sum of the segments obtained by
the indefinite bisection of a given length, is that finite line; and
once the real numbers are conceived as limits of series of irrational numbers, it is natural that this conception should not be
confined to irrationals only.
The elaboration of this process is necessarily more complex
than the additive method proposed by the Pythagoreans and
adopted later by the Peripatetics. It involves not only the
combination of the one and the dyad but also the operation of
a particular aspect of the dyad, namely, the reciprocal functions of doubling and halving which yield the simplest numerical ratios. Beginning from the unit, successive duplications
produce the first even numbers in geometric progression. Then,
the first odd numbers are obtained by halving the sum of two
successive even numbers respectively greater and smaller than
the odd numbers obtained. This method, of course, does not
give the first integers in their natural order: hence Aristotle's·
criticism is justified in so far as it concerns this feature of the
doctrine.
This procedure, according to Taylor, involves a double confusion: that of the integers with the rational real numbers and
that of the integers 1 and 2 with the one and the dyad. Consequently, the function of duplication is assigned to the undetermined dyad, although it belongs really to the integer 2 or
auto-dyad. It is difficult to agree fully with these views. In
the first place, if such au elegant interpretation of the Platonic
construction of the integers by means of the one and the dyad
can be given, there is no reason why it should not be extended
to fractions as well. These could be obtained by using the
process of halving; and also by taking lhe arithmetic mean of
successive rational numbers, one greater and one smaller than
the resulting fraction. These numbers could be two integers,
an integer and a fraction, and two fractions. The indefinite
repetition of these operations would yield all the rational real
numbers.

THE PLATONIC

THEORY OF THE CONTINUUM

195

As regards the function of duplication, it can be rightly
assigned to the dyad, for it need not belong to the auto-dyad.
Plato himself could not confuse the in itself with the greatand-small. To identify the expansile and contractile nature of
the latter with the changeless and absolute character of the
former would obliterate what seems to be one of the most remarkable Platonic intuitions, and would introduce confusion
into a theory which otherwise seems relatively clear. 30 In
order to make the distinction between the auto-dyad and the
dyad more significant, the first may be identified with twoness
and the second with tiviceness.81 Now, twoness is the actual
essence of the mathematical number
while twiceness is the
potential ability of any mathematical number to proceed from
itself to another number and to be integrated into measures
and formulas. Hence, twiceness is neither a limit, nor a measure, nor a magnitude, nor a quantitative determinant of any
kind. By its agency, however, by the various aspects of its
functions (greater, less, doubling, halving), and by its combination with the one, twiceness produces all the real numbers.
This interpretation, which is accepted by several modem critics,
brings the dyad of the Philebus into the mathematical fold.
These remarks may have their counterpart in the generation
of the geometrical magnitudes: the undetermined character of
the formless. space (xdJpa) favors the production of any given
ideal magnitude, whether rational or irrational, by means of a
double. series of greater and smaller magnitudes which oscillate
about it, until the limit, or the one, ultimately equalizes them
and produces thereby the given magnitude. Hence a possible
reason for the Platonic confusion between aptOP-ot and /Leye07J
which Aristotle distinguishes persistently. It remains to say
that the results obtained by the combination of the one and
the dyad are not identical; otherwise the numbers (and magnitudes) would be alike. While the operations involved are identical, the results are analogical but different. Hence the one
•• This confusion of the dyad with
may account for some of Aristotle's criticisms of the Platonic conceptions.
81 Cf. Cook Wilson, Classical Review, vol. 10 (1904).

196

THOMAS

GREENWOOD

and the dyad alone suffice to account for every one and all
numbers (and magnitudes), and the auto-dyad need not
appear in the generation of the arithmetical continuum.
The Platonic method of deriving the integers, however, suggests two practical remarks. One is that addition is not avoided
in the process described; for the arithmetic mean, which yields
the odd numbers, requires the addition of two successive even
numbers before halving their sum. Hence this indirect way of
obtaining the odd numbers does not justify technically the
rejection of the additive process. The other remark concerns
the order of the operations involved in the generation of the
integers, which seems quite arbitrary in the Platonic construction. Here, the sequence of the first ten integers involves three
duplications to begin with, then one mean, then one duplication, then two means, then one duplication and one mean
finally. But there is no reason why 3 should not be formed
before 8, and 7 after 10, and there are no indications about the
integers after the decad. In fact, the Platonic sequence of the
first ten integers makes it impossible to formulate a general
rule for the order of the operation yielding the integers, and
consequently a law concerning their succession. Yet, such a
law could be expressed by taking alternately the double and
the arithmetic mean, beginning from the first even number.
This is not, however, the method implied in the Epinomis,
which complicates the whole procedure by assigning a function
to the other mathematical means in the generation of the
integers.
Whatever be the actual technical details of Plato's method,
its inspiration is clear: it is an endeavor to reconcile the incalculable with the calculable, to integrate all types of numbers
and magnitudes into one single genus, and thereby .to make
possible to all the application of the same operational methods.
This attempted unification of the various species of quantity
involves an artificial generation of the integers, a possible construction of the irrationals by means of series, and a closer
assimilation of numbers and geometrical magnitudes. The
interpretation of Platonism which has just been discussed

THE PLATONIC

THEORY OF THE CONTINUUM

197

makes it possible to ascribe to the founder of the Academy a
primitive vision of those remarkable anticipations of later developments. But it is true that neither Plato's extensive writings nor those of his successors contain any direct and final
references about these matters. Even books V, VI and X of
Euclid's Elements cannot be considered as a strict exemplification of the relation between arithmetic and geometry which
Plato may have visualized. On the other hand, the Greeks
had no means of establishing a theory of series with its
attendant notions of limits and infinitesimals.
As regards the construction of the integers, it has little or
no practical value. But it involves two important principles:
one is the necessity of a strict derivation of the integers from
more fundamental notions; and the other is the logical indePlato may have
pendence of multiplication from
perceived both of them, but he had no means of elaborating
them further and of discussing them in their mathematical
setting. Hence he could not attempt to analyze number and
its properties by means of its purely logical elements, as modern
mathematical logic tries to do. Instead, Plato proposed to
justify number with the help of ontological arguments involving references to an ideal world of forms. This endeavor, which
led to the identification of the forms with numbers, was forcefully criticized by Aristotle. Let us now cons.ider the alternative doctrine he proposed.
IV.

THE ARISTOTELIAN

SOLUTION

The views of Aristotle on the generation and nature of
mathematical objects are only an aspect of his fundamental
controversy with Plato's doctrines. Both place mathematical
objects in an intermediate position. But while Plato considers
them a distinct class of objects between ideas and particulars,
Aristotle does not assign to them a separate existence. For
him they are intermediate in so far as the mind places them
between the sensible things out of which' they are imagined
by abstracting the totality of their sensible qualities, and the

198

THOMAS

GREENWOOD

generic essence of the things, which is reached by a further
abstraction eliminating even the extension of their intelligible
matter. In other words, Aristotle denies that mathematical
objects, as universals, are real substances. But he considers
them as non-sensible substances, and thus justifies their empirical foundation and their incorporation as subjects into the
various propositions forming the science of mathematics.
These remarks are amplified with reference to figures and
numbers separately. The mind apprehends geometrical objects
by applying its power of abstraction to actual bodies, until the
only accidents left are the quantitative and the continuous with
their attributes as such. Even particular extension must be
abstracted before the form is reached: as individual differences vanish, all that remain are universals, which are the
proper objects of science.32 But Aristotle would not agree
with the Platonists who identify lines, planes, and solids with
the numbers 2, 3, and 4 respectively; 33 for these geometrical
objects would then lose continuity, which is their essential
characteristic.
For Aristotle, then, the opposition between continuity and
discontinuity accounts for the distinction between figures and
numbers. It also explains why the notion of number is simpler for him than for Plato. While the latter conceives it as a
combination of the limit and the infinite, Aristotle adopts the
more conservative view of number as a collection of units; a
discontinuous plurality. The notion of a unit is obtained by
abstraction, and has its foundation in the ontological character
of the unity of being. Numbers are obtained by adding one
unit to another, and then by adding one unit to the preceding
number; 34 so that numbers are nothing beyond the units of
which they are essentially formed. 36
For the synthetic, dynamic, and formal conception of number, Aristotle substitutes the notion of a whole formed of partitive elements, juxtaposited in succession. Hence he thinks of
•• Met. 1086 a 11 and 1077 b 17.
•• De Anima, 404 b 18.

•• Met. 1080 a 30.
•• Met. 1082 a 15.

THE PLATONIC

THEORY OF THE CONTINbUM

199

number as an integral and discontinuous quantity. He does
not follow the Platonic view of conceiving it as continuous and
almost geometrical. Stressing the cardinal as against the
ordinal aspect of number, he therefore criticizes the Platonists
for counting one, two, three, and so on, without adding successively one unit to the preceding number. 36
Another difference between Plato's and Aristotle's conceptions of number is that the latter dissociates number from the
idea of ratio. Referring to the Platonic doctrine that numbers
are the principles of sensible qualities, Aristotle criticizes the
view that numbers should
called upon to define the essence
of flesh and bones by asserting that these substances are composed, for example, of three parts of fire and two parts of
earth. He justifies his criticism with the remark that such
definitions do not involve numbers, but their ratios. For him,
numbers are always collections of parts of fire, or of parts of
earth, or of units. Hence, they cannot determine the essence of
substances, which results rather from the ratio of the numbers
considered. 37 For Aristotle, then, number is not a particular
case of the more general notions of ratio, relation, or function.
in fact, number and relation belong to two different categories
of being.
With such essential distinctions between figures and numbers, Aristotle destroys the ontological unity of mathematics,
which Plato tried to establish by means of his generalized conception of number. But he builds up the methodological unity
of mathematics on the formal foundations of his theory of
demonstration, which, in turn, finds its justification in the
ontological principles underlying the whole of his doctrine. For
Aristotle, the opposition between the continuous and the discrete in mathematics is only an aspect of the problem of the
rationalization of the irrational, which remains a basic concern
for him as it was for Plato. If the mathematical solution of
the latter is to be rejected, something else must be offered in
its place. Beyond mathematics, Aristotle reaches for an
80

Met.

b

5

87

Met.

b 15.

GREENlVOOD

answer to this riddle with his theory of the infinite, which
reconciles the discrete and the continuous in the depths of
ontology proper.
This doctrine, which is developed in the Physics, is naturally
broached on the analysis of motion, an idea which involves
matter, space, time and numbe.r. It is the perpetuity of matter
and motion, the divisibility of magnitudes, the possibility of
forming larger numbers by addition, and the analysis of time
in respect to increasing and decreasing elements, which point to
the infinite as a common constituent of these notions. And
just as Aristotle's theory of motion is based on the distinction
between act and potency, so his views on the infinite take into
account the same distinction.
Experience reveals that change is an essential character of
the universe: certain things have definite attributes, while
others are in the process of gradually displaying them. From
this angle, the difference between being and becoming calls for
the distinction between act and potency. The process of becoming is called motion, which Aristotle defines as "the fulfillment of what exists potentially, in so far as it exists potentially." 38 Motion is considered here in its most general aspect,
which covers both change of place and growth. Now, the whole
purpose of Aristotle's discussion of the mathematic11l infinite is
to show that infinity is a potency, that it is something which is
always becoming without ever reaching a final form.
By considering infinite extension as a potency, it follows that
the actual division of extension never yields a magnitude which
may be considered as the smallest possible. For this reason,
Aristotle rejects the notion of indivisible lines 39 which had
become, as we have seen, a characteristic doctrine of the
Academy. The Peripatetic tract On Indivisible Lines represents fairly well Aristotle's views on this matter, though it may
not have been written by him. It argues against the theory
of atomic magnitudes by showing their incompatibility with
the principles assumed or proved in mathematics.
as Pkysics, 201 a.

•• Physics, 206 a 17.

THE PLATONIC THEORY OF THE

We are also reminded in the Physics that mathematicians
never use the infinite as such, but simply require that the finite
be as long as we please, and that they reduce all magnitudes by
proportion to quantities they
handle more easily. In both
cases, however, these geometrical fictions scarcely display the
real connection between the mathematical infinite and the
maximum magnitude of the universe. That is why it is suggested that this abstract and formal infinite, which satisfies the
imagination, does not go beyond the v6'11ut<;, and should not
even be confused with the potential infinite.
The Aristotelian theory of the infinite leads naturally to a
specific doctrine of the continuous. This notion, which is an
essential characteristic of motion, is analyzed in the sixth book
of the PhySics after the discussion of place, time, and change
offered in the two preceding books. Aristotle based his definition of the continuous on the intuitive notion of a continuous
magnitude, which requires that the boundaries of two consecutive or contiguous parts are kept together by coalescing into
one and the same limit. 40 Hence the continuum is " that which
is divisible into divisibles that are infinitely divisible." 41
With these premises, Aristotle argues convincingly that every
continuum must be divisible infinitely, and that the i,nfinite
divisibility of extension, of motion, and of time imply each
other, with the infinite divisibility of motion as middle term
between the other two. " The firmness with which he rejects
any suggestion that a line can be divided without remainder
into points, a period of time into moments, or a movement into
infinitesimal jerks-and this at a time when thinkers of repute
believed in all these things-seems to me to indicate that he
had a more mathematical turn of mind than he is usually
credited with. So far as we know, he was the first thinker who
clearly stated the infinite divisibility of all continua." 42
Notwithstanding some obvious difficulties in the details of
the Aristotelian doctrine of the infinite, important consequences
•• Physics,
"- Physics,

a 24.
b.

•• Ross, Aristotle's Physics, p. 70.

THOMAS GREENWOOD

follow from its general pattern. OWing to the irreducible
duality of the infinite, the continuum cannot be made of indivisible parts, and number3 cannot generate a continuum, inasmuch as there is no contact between them. 43 Hence the
discreteness of number rules out the possibility of arithmetizing
the continuum. Considering the restricted arithmetical technique available at the time, no adequate and effective arguments could be found in favor of the Platonic mathematical
intuitions. The primacy of arithmetic maintained by the
younger Pythagoreans, such as Archytas, and expanded by
Plato into a metamathematical doctrine, expressed an a,ttitude
of niind and a pious hope, rather than a technical interpretation
of current mathematical knowledge.
This situation was illustrated particularly well by the difficulties involved in the three famous problems of the quadrature
of the circle, the trisection of the angle, and the duplication of
the cube. Although Aristotle used principally elementary
mathematics for his specific examples, he gave considerable
thought to the question of quadratures, which correspond more
readily to his problem of the infinite. In the four passages
where he mentions the squaring of the lunes and the attempts
to square the circle, he considers indeed the proposed solutions
of these problems as instances of improper arguments, giving
each time his reasons for his assessment. It may be said that
Aristotle's criticism of these early methods of quadrature involves a rather rigid conception of the mutual relations of
arithmetic and geometry. But it is in line with the strict requirements set down by himself for a good demonstration, even
though he knew the Eudoxian method of exhaustion and its
practical value.
It is not improbable that Aristotle's criticisms and his constructive views on the infinite, coupled with the refinement of
the method .of exhaustion, helped in the remarkable improvements of the Alexandrian period. In fact, Euclid and Archimedes used the constructions of Antiphon and of Bryson re•• Met. 1075 b and 1085 a.

THE PLATONIC THEORY OF THE

203

spectively by improving the proofs criticized by Aristotle. But
neither the development of the theory of the higher curves
known in his time, nor the approximate solutions worked out
by Archimedes, nor even the rise of the calculus for that matter,
affected adversely the promptings of Aristotle's logical acumen
with respect to the problem of the continuum.
In these circumstances, Aristotle cannot be blamed for refusing to accept the Platonic conception of number and for
considering the relations between arithmetic and geometry in
the light of the actual technique of the mathematicians and of
his own epistemology. His scientific perspicacity in these matters is proved by the perennial success of his views on the
infinite and the continuous. And these held the ground until
last century, when the continuum was defined more precisely
in terms of the new concepts of number and of separation of
classes. Even in this connection it can be maintained that the
Aristotelian Organon can be correlated more readily than the
Platonic dialectic with the logical refinements of the modern
theories concerning the foundations of mathematics.
THOMAS GREENWOOD
University of Ottawa,
Ottawa, Canada.

THE NATURE AND EXTENT OF PHILOSOPHY
OF NATURE

B

y philosophy of nature we here understand human

knowledge of sensory or changeable or natural things
which is more perfect than the knowledge of them that
is attained by ordinary experience and thought. Concerning
the nature and extent of this more perfect knowledge of nature,
there are eight questions to be decided: (1) Whether there is
need for it? (2) Whether it is a science? (3) Whether it is a
speculative science? (4) Whether it is of any value? (5)
Whether it is in the order of wisdom? (6) Whether changeable
being is its subject? (7) Whether it is one science or many?
(8) Whether method is required to attain it?

I.

WHETHER THERE IS NEED FOR PHILOSOPHY

OF NATURE?

Difficulties
It seems that there is no need for philosophy of nature, for
the following reasons.
1. There is no need for philosophic knowledge concerning
the things which are immediately evident to us, and with which
we are most familiar. Sensible things are immediately evident
to us, and we are most familiar with them. Hence there is no
need for philosophic knowledge of sensible things.
2. There is no need for philosophic knowledge concerning
trivial things. Sensible things are the least of all things, because they come into being and cease to be. Therefore there
is no need for philosophic knowledge of sensible things.
Solution
We have need for a thing when we lack something which we
require for a special purpose, or which we desire for its own
sake and the happiness that it gives. We need clothing and
204

THE NATURE AND EXTENT OF PHILOSOPHY

OF NATURE

205

shelter when we are cold, food when we are hungry, friends
when we are lonely. If we possess only ordinary knowledge of
sensible things, we lack a more perfect knowledge of them
which is possible for us to attain, which we desire for its own
sake and the
that it gives, and which we require for
special purposes.
When we touch or taste or smell or hear or see an object, we
are aware of it as an object that is acting sensibly on us, or
that is simply given or presented to the inind. It
evident
to us that these sensory objects exist, and we are conscious of
the self and know that the self exists and is something sensible.
By reflection and by means of the principle of non-contradiction, by which we know the truth that being is not not-being,
we can distinguish between our knowledge and its object, and
we know that sensible things have or can have existence of
their own which is distinct from the being which they have in
our knowledge of them. Moreover, we are sensibly aware of
many of our own activities, such a8 seeing, eating, walking.
We can remember some things as they formerly appeared and
we know that they are not in· all respects the same now as they
were, but have changed and are changing. And so we are
not only that sensible things exist and can be known by
us, but also that they are not static but dynamic, that is,
moving or· changing sensibly.
When we think that we understand a thing, we do not
wonder about it. We do not wonder that we get wet when we
are out in the rain. Yet we often wonder about natural things,
and this manifests that our ordinary knowledge of them is imperfect. We know only a few of them well, and of these we
know only the more obvious aspects. We do not know exactly
what they are or are made of, nor how or why they are produced and act as they do. Our knowledge of them for the
most part is confused and disorderly, and is largely practical
knowledge of the uses that we can make of them and of the
things that we can construct from them.
But as our experience of natural things increases, we come
to know more of them and to know them more distinctly. All

206

W. H. KANE

of them that we know are changeable and extended, and many
of them are alike in other respects; for example, living things
can somehow move themselves. Hence it seems that we can
know all of them more or less in general. Moreover, the works
of human art and skill, for instance, the automobile and the
airship, manifest that we can know truths about sensible things
that are hidden from ordinary knowledge. We can know the
reasons for these works of human art, what they are, how they
are made and why, and so it seems that we can know also
some of the reasons or causes of natural things. These things
generally appear to be and to act in an orderly way, for
instance, according to motion and time, as the apparent movements of the sun and the moon, or according to location, as
the arrangement of earth, water and air, or according to structure and function, as many plants and animals have similar
structure and activities. Hence it is possible for us to put order
in our knowledge of natural things.
Moreover, we desire to attain a more perfect knowledge of
natural things. All of us admire these things, and are sometimes amazed at them and at the effects that are produced by
them. We wonder at the processions of day and night and the
seasons of the year. We marvel at plants and animals, at land
and water, wind and cloud, sun and moon and stars. We are
particularly astonished at ourselves. The fact that we are
cnrious about these things manifests that we desire to know
them better, and the delight that we derive from seeing and
hearing them manifests that it is delightful for us to know them.
Furthermore, the things which we can make or do depend
upon our knowledge of nature. The useful things which we
can make, for instance, clothing or furniture, are made out of
natural things such as cotton or woolor wood. We could not
make these things if we did not know and have at hand something suitable out of which to make them. The beautiful
things which we can construct, such as pictures or sculptures
or music, are patterned more or less according to the colqrs and
shapes and rhythms of nature. The things which we can do,
(or example, preserve our life and perfect ourselves in health

THE NATURE AND EXTENT OF PHILOSOPHY

OF NATURE

207

and happiness, depend upon our knowledge of ourselves and of
other natural things. Our ordinary knowledge is not sufficient
for making the more difficult things, such as a radio, and the
better we understand ourselves the easier it is for us to control
our desires and fears. Hence a more perfect knowledge of
natural things is required for special purposes.
Thus it appears that when we possess only ordinary knowledge of natural things we lack a more perfect knowledge of
them which is possible for us to attain, which we desire for its
own sake and the delight that it gives, and which is required
for special purposes. Hence there is need for knowledge of
sensible things which is more perfect than the ordinary, that is,
for philasophy of nature.

Reply to Difficulties
1. Even the things with which we are most familiar have

aspects which are hidden from ordinary knowledge and which
we desire to know more perfectly, for instance, what we
ourselves are.
fl. We are naturally inquisitive and desire to know more
about everything that we can know more perfectly. We ourselves are changeable things, and we are especially curious
about ourselves. We wonder how we came to be and how we
operate, and whether we can cease entirely to act and to be.
Hence there is need for philosophic knowledge of changeable
things, particularly for knowledge of ourselves.

II.

WHETHER PHILOSOPHY

oF NATURE Is A SciENcE?

Difficulties
It seems that philosophy of nature is not a science or scientific knowledge, for the following reasons.
1. Science is knowledge of the reasons or causes of things,
which are not perceptible by the senses. But philosophy of
nature is knowledge of sensible things. Therefore philosophy
of nature is not a science.

208

W. H •. KANE

i. Science is knowledge of something that is ,certain. But
sensible things cannot be known with certitude, because they
are contingent. Therefore philosophy .of nature is not a
science.

8. Science is knowledge of something that is necessary or
that cannot be otherwise. But sensible things are not necessary, because they are changing. Hence philosophy of nature is
not a science.
4. Science is knowledge of universal truths.. But sensible
things are particulars, not universals. Therefore philosophy of
nature is not a science.

Bolutipn
The student of nature desires to perfect his knowledge of
sensible things by attaining knowledge of them which is certain
because the reasons for their being what they are and acting as
they do are evident to his mind. This more perfect knowledge
of changeable things is called philosophy of nature. But
knowledge of this kind is science, that is, knowledge of something that is certain because a reason of its being, without
which it cannot be, is known. Therefore philosophy of nature is
a science.
Reply to Difficulties
1. We use the word thing to signify any object of thought,
or any being which can be an object of our thought. Being,
and distinct beings, and distinct modes of being and their kinds
and reasons or causes, are not known by means of our senses
alone, but by some other cognitive power, which is called intellect or reason and which seems to be nourished by the data
of sensory experience. Philosophy of nature is knowledge of
sensible things that are considered not merely as sensible but
as intelligible. We say that we understand a thing when we
know its reasons or causes, as we do when we have received a
gift and know what it is and who gave it, why and how it was
given or sent.

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

Sensible things are contingent in many respects. Yet
they also appear to be and to act in ways that are regular, as
heavy bodies tend to fall, and we have eyes with which we can
see. Even contingent things such as our own walking and
talking can be known with certitude when they are evident
to us.
When we judge of anything that is evident to our mind,
or that sensible things
for example, that being is not
exist, we know it with a necessity that is apparent in the very
act of judging. Necessity in our knowledge is more manifest
when we discover by reflection that we cannot doubt that a
thing is what we evidently know it to be. Even changing
things have some necessary aspects, and we have
necessary knowledge of them. While we are walking, it is necessarily true that we do not remain in the same spot. It is a
necessary truth that changing things are capable of change, as
it is necessarily true that what happens is not impossible, and
that being is not not-being. It is not immediately evident to
us what changing things are or are· made of, why they are
capable of change, what are the changes that occur in them,
how and why they change as they do. These are points of
inquiry in the course of philosophy of nature. Philosophy of
nature is knowledge of the necessary aspects of sensible things
which can be known by reason, presupposing sensory observation and experiment. By observation we know that sensible
things are changing, and by reason we know that they are not
constantly changing under every aspect. A door could not
easily be opened and closed if it were not firmly hinged; and
sensible substance, such as the self, has some stability.
4. It appears that only particular things, such as a man or
a motion or an -act of the mind, exist in nature. By means of
our various senses and sensory perception, we can know different sensory aspects of the same object, for example, the
color and figure and motions of the self. By sensory experience we can know the sensible aspects which are common to

210

W. H. KANE

many objects, for instance, the green of grass or leaves and the
heat of fire. With the intellect we can know all of these objects
under the aspect of being or that which is. We can know distinct beings and distinct states and modes of being, such as
being in nature and being in knowledge, substantial being and
accidental beings of various kinds. Here is something that is
truly wonderful. When we pass from sensory knowledge to
intellectual knowledge,. we can know particular and changing
sensible things in a way that is universal andnecessary.
"'We
can distinguish a twofold· necessity in these things, namely, the
necessity of being or existence and the necessity of essence. In
regard to existence, we know that although sensible things are
changing they cannot both be and not be at once and under the
same aspect. In regard to essence, we do not know what the
individual as such is. But by abstracting from the individual
differences of particular things, we can know more or less clearly
what they are. We can know the essences or natures that are
in things. Sensible things have some essential aspects that are
similar in all; for example, all of them are changeable. There
other essential aspects that are similar in many of them;
for instance, living things can move themselves. These essences
exist in sensible things in a way that is particular and changeable and yet fundamentally universal inasmuch as they are
intelligible. In our intellect, which can know these essences by
abstracting them from their individual differences in sensible
things, they exist in a way that is fundamentally universal inasmuch as we apprehend that which is or exists in many individuals in nature and is multiplied in them. It appears that
the same essences can both be in nature and be in knowledge,
according to distinct states of being, and be one in knowledge
or one essence known, and be many in nature or exist in many
individuals. These essences, considered simply, necessarily are
what they are. Philosophy of nature is knowledge of universal
and necessary truths concerning sensible things which are
known not merely by observation and experiment but by
intellect or reason.

THE NATURE AND EXTENT OF PHILOSOPHY

III.

WHETHER PHILOSOPHY

OF NATURE

OF NATURE

IS A SPECULATIVE

SciENCE?

Difficulties
It seems that philosophy of nature
science, for the following reasons.

IS

not a speculative

1. Philosophy of nature is scientific knowledge of sensible

things. Scientific knowledge of sensible things includes all of
the arts of making both beautiful and useful things, and the
moral disciplines, and these are practical sciences. Therefore
philosophy of nature is a practical science.
2. Speculative science is knowledge of the truth about things
which is loved and sought for its own sake and the delight
that it gives, not for the sake of doing or of making anything
that is distinct from our knowledge of it. But philosophy of
nature is sought in order to do or to make things that are distinct from ·our knowledge of them, for instance, in order the
better to control our power of choice, and in order to make
machines which we cannot make without special knowledge
of .natural things. Therefore philosophy of nature is not a
speculative science.
Solution

We can know sensible things both speculatively and practically, as one can know music by appreciating and enjoying
it or by knowing how to make musical compositions or to play
musical instruments. Knowledge of the truth about the reasons of things, which is loved and sought for its own
and
the delight that it gives, is speculative science. Philosophy of
nature is knowledge of the truth about the reasons or causes
of natural things which is loved and sought for its own sake,
because the student of nature chiefly desires to know the truth
about nature, and because natural things such as stars, minerals, plants, and animals are things that we cannot make,
but can only know more or less perfectly. Hence philosophy
of nature is a speculative science.

W. H. KANE

Reply to Difficulties
1. Philosophy of nature does not include all of our scientific
knowledge of sensible things, but only our speculative science
of nature. Ethics and the various arts both liberal and mechanical are practical sciences, and are concerned with the
things which we can do or make, not for the sake of knowing
the truth about them, but in order to do or to make good or
beautiful or useful things well.
2. Speculative science is not of itself useful or practical, because it consists in knowledge of the general·· truths about
things, not in. knowledge of how to make or to do particular
things that are distinct from our knowledge of them. One
who knows a speculative science is not for this reason a good
man morally, nor a good artist or artisan, whereas one who
has acquired a practical science can easily do or make things
well in. practice. Yet our speculative knowledge. can be extended or applied in practice to the things which we can do or
make, as we can use our knowledge of the stars. in order to
determine the direction that we wish to take when travelling
at night. We use all of our knowledge in order to supply
our various needs and to attain more perfect knowledge and
happiness.

IV.

WHETHER PHILOSOPHY

OF NATURE IS OF ANY VALUE?

Difficulties

It seems that philosophy of nature is of little or no value,
for the following reasons.
1. Knowledge which has no practical purpose seems to be
of no value. Philosophy of nature has no practical purpose,
because it is a speculative science. Therefore philosophy of
nature has no vab,1e.
2. Knowledge of the lesser things is of little value. .Philosophy of nature is knowledge of changeable things, which are
mere trifles. Therefore philosophy of nature is of little value.

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

213

Solution
By the value of a science we understand its dignity and
utility. Philosophy of nature has great dignity and utility, and
so has great value.
The dignity of philosophy of nature is apparent because, in
the first place, it is a science. AU science is of great dignity
because it perfects our power of thought, which is the power by
which we apprehend our end and direct all of our human activities. Science enables us to extend and perfect our knowledge
beyond all that we can learn by ordinary experience and
thought. It helps to satisfy our natural craving for knowledge,
gives better order and greater certitude to our knowledge, and
enables us to direct and to teach others and to solve difficulties
inasmuch as it extends to the necessary reasons of things.
In the second place, philosophy of nature has great dignity
because it is a speculative science. Speculative knowledge is
sought and loved for its own sake, and thus is an end in itself.
It is commonly admitted that ends have dignity, and this
appears in the fact that we honor ends, whereas we praise
means that are well suited for attaining ends. We praise a good
instrument such as a good brush or chisel, but we honor a good
artist and his work, and we especially honor a good man. The
dignity of a speculative science is derived from the certainty
and the nobility of its subject matter. Not all the subject
matters of philosophy of nature are equally certain, that is)
can be known with equal certitude by the power of our natura]
reason; but some essential aspects of natural things and some
of their properties are absolutely certain. Nat ural things are
not all of equal nobility, but Jiving organisms and particularly
human beings have considerable dignity because they an act
for their own perfection as their own intrinsic end, and man
acts with knowledge of his end and choice of the means by
which to attain it. Inasmuch as philosophy of nature extends
to living organisms, and particularly to man, it has very great
dignity, because we can know with perfect certitude some
truths about the self, such as the truth that we have a soul or

214

W. H. KANE

principle of life within us, and because we are natural beings
who can perfect ourselves by controlling some of our activities.
The utility of philosophy of nature is manifested, first of all,
by the fact that it enables us to attain higher speculative
knowledge. It appears that sensible things are the kinds of
beings which we know first, and some of their reasons are most
evident to us. We know that human knowledge and needs
and liberality are reasons for the works of human art, and
that we seek food and shelter in order to preserve our life in
comfort, and use our legs in order to stand and walk and our
hands in order to grasp ,and move things. Through our
edge of natural things we can attain some knowledge of more
universal aspects of being, such as substance and causality,
beauty and goodness and truth, and we can attain a better
knowledge of being as such or that which is. Through our
knowledge of motion and of changing things we can attain some
knowledge of the ultimate cause of motion:, that is, of God. In
our knowledge of living organisms and of their nutritive and
cognitive activities we have some knowledge of beings which
are more or less independent of matter, and through this we
can attain some knowledge of immaterial or spiritual beings.
In the second place, philosophy of nature is useful inasmuch
as it is presupposed as known in acquiring the practical sciences
and by these is extended to practice. For instance, a good
understanding of man is required for the successful practice of
medicine.

Reply to Difficulties
1. Knowledge which has no practical purpose may have
value as an end. Philosophy of nature is an end rather than a
means. Yet it is useful both for attaining higher speculative
knowledge and for attaining greater perfection in practice.
2. Knowledge even of the lesser things is sometimes delightful to us and may have value either as an end or as a means
to ot.ber knowledge and to other activities. From the manner
in wkich natural things operate it appears that there are de:
grees of perfection am(mg them, and that some are of greater

THE NATURE AND E4TENT OF PHILOSOPHY

OF NATURE

215

nobility than others. Animals act as if they have sensory
knowledge, and in this respect seem to surp8.$Sthe plants, while
man seems to surpass all other natural things in knowledge
and in his power to choose what he will do.

v. WHETHER PHILOSOPHY OF NATURE IS IN THE ORDER
OF WISDOM?

Difficulties
It seems that philosophy of nature is not in the order of
wisdom, for the following reasons.
1. Wisdom is knowledge that is both
and practical. But philosophy of nature is not practical knowledge.
Therefore philosophy of nature is not in th{( order of wisdom.
2. Wisdom is knowledge of the highest or noblest things.
But philosophy of nature is knowledge of the lowliest things.
Therefore philosophy of nature is not in the order of wisdom.
3. Wisdom is scientific knowledge which proceeds from first
principles of things that are evident and certain. But the first
principles of natural. things are. not evident to us. Therefore
philosophy of nature is not in the order of wisdom.

Solution
A man is called wise who can put in order the more difficult
things, and who can judge of things justly, acknowledging to
each what is its due. The word wisdom signifies speculative
and practical knowledge .in a high degree of perfection. In this
sense of the term, philosophy as a whole is human wisdom, and
its special parts. are not wisdom, because the parts of philosophy are either speculative or practical sciences. But we also
use the term wisdom in a restricted sense to signify the more
perfect sciences, whether speculative or practical. A science is
said to be perfect if it extends to the ultimate reasons or causes
of its subject matter, because we can best judge of things and
order them in view of their ultimate reasons of being. An
architect who knows the reasons for all the parts of a building
can judge it better than the artisan who does not know all the
6

fll6

W. H. KANE

reasons. The science which extends to the ultimate reasons of
all beings, and which is ,called metaphysics or first philosophy,
is speculative wisdom in the primary sense of the term. There
are other speculative sciences which possess in a lower degree
the perfections which metaphysics has in a higher degree, inasmuch as they extend to the ultimate reasons of particular kinds
of things. These sciences are called wisdom in a restricted and
secondary sense. Philosophy of nature extends to all the proper
reasons or causes of natural things, because these are what
the student of nature chiefly desires to know, and his wonder
does not cease and his curiosity is not satisfied until he knows
what natural things are and are made of, how and why they
are produced and act as they do. Hence philosophy of nature
is in the order of wisdom. It is a speculative wisdom, not the
highest or most perfect.

Reply to Difficulties
1. Wisdom in the unrestricted sense of the term signifies
perfection in knowledge, and is both speculative and practical,
becaui!e perfect knowledge consists not only in knowing the
truth about things but also in rightly ordering things to their
ends. A perfect speculative science is wisdom in a restricted
sense. Philosophy of nature is wisdom in a restricted and
secondary sense, because it is a speculative science which extends to the ultimate reasons, not of all things, but of natural
things.
fl. Philosophy as a whole, and particularly metaphysics, is
knowledge of the highest or noblest things which can be known
by the natural light of human reason. Wisdom in a restricted
and secondary sense is not knowledge of the highest or noblest
things absolutely, but is knowledge of things which are more
or less noble, that is, of real beings or ones which can have
existence of their own and are not merely objects of our
thought, or at least it is knowledge which is perfect in regard to
its scientific form even though its object is not real, as is the
case with logic. Philosophy of nature is wisdom only in a restricted and secondary sense. Inasmuch as it extends to sensible·

THE NATURE AND EXTENT OF PHTILOSOPHY OF NATURE

217

substance and to living organisms, and particularly to man, it
extends to the noblest of sensible things. These things are
nobler than the quantities which are the proximate subject.
matter of mathematics, because mathematical quantities are
those which can be understood apart from all activities and
principles of actibn and even apart from the order which real
quantities have to real existence. Hence philosophy of nature
surpasses mathematics in dignity inasmuch as it extends to
nobler things. But the certainty of the subject matter of
mathematics is greater than the certainty of many matters of
philosophy of .nature, because natural things are contingent
and variable in many respects, and in some respects have little
in them that is intelligible, and so they are especially difficult
to understand. The truths of philosophy of nature are discovered only after much experience and by the labors of many
philosophers through many centuries.
3. Some first principles are evident and certain to us, such
as being and its opposition to not-being, the sufficient reason
or reasons of being
which a thing cannot be, and the
principles of quantities, including points, lines, surfaces, and
discrete quantitative units. Metaphysics and mathematics proceed from these principles when they are understood in a way
that is appropriate to each science. It is not immediately evident to us what the principles of natural things are. But
natural things both are and are extended or corporeal. Hence
metaphysical and mathematical principles, understood in a restricted or special way, are true of natural things. In the
course of philosophy of nature, near the beginning, the first
principles oi natural things are manifested mediately, by means
of the principle of sufficient reason.

VI. WHETHER CHANGEABLE

BEING IS THE SUBJECT OF

PHILOSOPHY OF NATURE?

Difjic11-lties
It seems that changeable being is not the subject of philosophy of nature, for the following reasons.

218

Wo H. KANE

1" The subject of a science is that with which the science is
principally concerned. Philosophy of nature is principally concerned with something that is unchangeable, because it is
knowledge of unchangeable truth about natural things. Therefore the subject of philosophy of nature is not changeable being.
2. In every scientific discipline we presuppose that the
definition of the subject is already known. But we do not
know what changeable being is. Therefore changeable being is
not the subject of philosophy of nature"
3" Every science has one proper subjecL But changeable
being is not one, because it is a kind of substance that is corporeal and changeable both substantially and accidentally"
Therefore changeable being is not the subject of philosophy of
nature.
Solution
The subject of a science is that by reason of which everything is referred to that science, as things are referred to vision
and not to hearing because they are· colo:red and can be seen.
Somewhat as sensory vision is determined with reference to
that which is visible or colored, so also a science is determined
with reference to a proper subject which is intelligible or knowable scientifically. The student of nature desires to know the
truth about natural things, that is, to know what they are and
are made of, what their principles are, how and why they are
produced and act as they do. It seems that we cann,ot attain
speculative science of individual natural things, because there
are so many individuals that we cannot know them all individually, because the differences of individuals seem to be contingent and variable without limit, and because we :recognize
particular individuals by peculiarities which they happen to
possess but do not know what this or that individual as such is.
But if we abstract from the individual differences of natural
things and consider only the aspects in which all o:r many individuals are similar, we can attain intellectual knowledge of
natural things that is more or less universal, and this knowledge is true of all or of many individuals, although it is not the

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

219

whole truth about any individual. We know, for instance,
that natural things are things which can move or change
sensibly, and that living things can somehow move themselves.
We can attain speculative science of natural things by abstracting from their individual differences and considering their essential aspects. We have some evident knowledge of natural
things inasmuch as they appear sensibly to us, and we observe
that they are changing sensibly. It is the changing aspect of
natural things that excites wonder and curiosity in the student
of nature, and he desires to know the principles and causes of
change and of changeable things. The fundamental principles
of change are in natural things themselves, as we know from
our consciousness of the self and of our own activities. We
can attain speculative science of natural things if we proceed
to investigate them inasmuch as they are changeable being, or
that which has in itself fundamental principles of sensible
change or motion; and this knowledge is called philosophy of
nature. As things are referred to sensory vision because they
are colored and can be seen, so things are referred to philosophy of nature because they are or pertain intelligibly to
changeable being, not because they are individual sensible
things of any particular kind. Hence changeable being as such,
that is, as that which is fundamentally changeable, having in
itself principles of sensible change or motion by which it is
fundamentally intelligible or knowable speculatively, is the
proper subject of philosophy of nature. Philosophy of nature
is the science of changeable being, or our rational understanding of changeable being. All the definitions, divisions and conclusions of philosophy of nature are fundamentally in terms of
changeable being. Changeable being is described and divided
in terms of what sensibly appears or changes, and is defined in
terms of the principles of change. Change or motion is defined
in relation to the changeable, and the first principle of change
is proved to be the Unchangeable. Every changeable being is
proved to be a body or extended substance. Living bodies are
defined in terms of the principles of self-movement, which is
manifested sensibly by growth, and the cognitive and appeti-

W. H. KANE

tive functions are investigated and defined as operations of
their sufficient principles in some living bodies.

Reply to Difficulties
1. We .can distinguish between the subject matter of a
science, which includes everything to which the science extends, and its proper subject, which is that by reason of which
everything is referred to the science. The proper subject of
philosophy of nature is changeable being as such, or as that
which is fundamentally changeable and speculatively intelligible through its principles of change. The subject matter
of philosophy of nature is any and every natural body and all
the principles of change. A science is said to be principally
concerned with its proper subject, not its subject matter, because its proper subject is that which is fundamentally intelligible in a scientific way. The first principles of a science are
first principles of its proper subject, or the fundamental intelligible aspects of its proper subject, and everything that is in
intelligible connection with its proper subject is determinable
in a science .. When changeable being is considered as it is intelligible, we can know some unchangeable truths about it, as we
can know some unchangeable truths about artificial things. If
we abstract from the individual differences of particular houses
and consider what a house is as house, not as in this or that
particular instance, we can know the essence of a house, and
can say that a house is a structure suitable for abode or shelter.
This is an unchangeable truth inasmuch as the essence ·of a
house necessarily is what it is, and it is true of all particular
houses, but it is not the whole truth about any particular
house. In like manner philosophy of nature extends to the
unchangeable aspects of changeable being. For the most part
these aspects cannot pe discovered merely by abstract reasoning, as mathematical truths can be discovered, but they are
attained by reasoning upon the data of much experience of
natural things, because the various essential aspects of changeable being are manifested to us through sensible appearances
and sensible change. Moreover, many of the general truths

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

221

concerning various degrees of changeable being are true only
of most but not of all individuals of the kind, because of
the contingencies found in nature. Philosophy of nature also
extends to those correlations of natural things which are
necessary, inasmuch as a certain order exists among them.
2. In every scientific discipline we presuppose that the
definition of the name of the subject is already known, and
also that the subject as such is or is intelligible. Our scientific knowledge does not proceed from universal doubt or ignorance, but from certain truths which we have already attained.
By the term changeable being we understand that which is
fundamentally changeable and speculatively intelligible, having
in itself principles of sensible change or motion. Inasmuch as
we ourselves are changeable beings and are conscious of the
self and _of some of our activities and of some of their principles and reasons, it is most evident to us that this kind of
thing exists and is intelligible. When we know that a thing
exists but do not know exactly what it is, we define it imperfectly in terms of some effect which proceeds from it and which
is more evident to us. For example, we speak of the sun as
that which causes the light of day and the heat of summer. In
like manner we define changeable being imperfectly in terms of
principles of sensible change or motion or sensible appearance,
because these effects ·of changeable being are evident to us.
More illuminating definitions of changeable being and its various essential aspects are disclosed in the course of philosophy
of nature.
3. The term changeable being is complex, but the concept
signified by the term is simple. It is simply the concept of
that which is fundamentally changeable, or of radical changeability. Whether or not there are many changeable beings of
various kinds, and whether they are changeable substantially
as well as accidentally, what the principles of change are, and
what change itself is, these questions and many more are decided in the course of philosophy of nature. The basic concept
of changeable being expresses a supreme generic formality of
that which in nature is any and every natural body, which is

W. H. KANE

abstracted from individual differences and presupposed to be a
kind of substance, and which is precisely the fundamentally
changeable, or that which has within itself fundamental principles of sensible change or motion. This concept is a formal
abstraction which expresses the whole essence of all natural
bodies, but not wholly, and not as body or extended substance,
but as changeable. It expresses changeable being not as closed
or completely determined and completely understood, but as
open to determination and more perfect intellection. It expresses the radically changeable that actually has within itself
fundamental principles of change; that is capable of
change or motion; subject to change whether substantial or
accidental; ordered to all the principles of sensible change;
determinable and distinguishable according to a multitude of
essential aspects of various orders and genera and species,
which are the roots of properties, and of some proper accidents
that are perceptible by our senses, all of which are intelligible
and definable by reason of what it expresses: the fundamentally
changeable. In this concept of changeable being all the conclusions of philosophy of nature are contained radically, and
they can all be developed from it by means of sensory experience and correct reasoning.

VII.

WHETHER PHILOSOPHY

OF NATURE IS ONE SciENcE?

Difficulties
It seems that philosophy of nature is not one science, for
the following reasons.
1. Philosophy of nature is knowledge of the reasons of
changeable being. There are many changeable beings which
are distinct and different from each other and have different
reasons of being, for instance, living and non-living. things.
Therefore philosophy of nature is not one science, but includes
many sciences.
ft. The
of changeable being extends both to changeable substances and to changeable accidents. But substances
and accidents are not known in the same manner, because

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

they are not in the same manner. Therefore the science of
changeable being or philosophy of nature is not one science.
3. Everything to which one science extends is known in one
and the same way. But changeable being is known in different
ways, for example, by ordinary experience and correct reasoning, and by special experiments and with the aid of special
instruments such as the microscope. Hence there are many
sciences of changeable being.
4. Truths which are known in different ways pertain to different sciences. Truths concerning the reasons of changeable
being are known in different ways. Some are known by reasoning from particular instances to a general rule or cause that
is either
or ultimate, and others are known by reasoning from a general truth to a more particular or distinct
conclusion. Hence there are many sciences of changeable
being.
Solution
A speculative science is said to be one in a special sense, or
ultimately specified, if it has a proper subject that is ultimately
specified as intelligible, or knowable with regard to a special
degree of intelligibility, not with regard to the manner of
being which is proper to its subject matter. Things are said
to be
in a special way because we do or can know
them in a special way, as all colored things are said to be
visible. Philosophy of nature has a proper subject which is
ultimately specified as intelligible, namely, changeable being
that is fundamentally intelligible through its principles of sensible change, inasmuch as it can be abstracted· from the individual differences of natural things. When natural things are
considered from a point of view in which we abstract from
less than their individual differences, they are not intelligible
to us speculatively, except as instances of a general truth.
When they are considered from a point of view in which we
abstract from more than their individual differences, they have
a different degree of intelligibility; for instance, that which is
proper to geometry. Within the first degree of abstraction, in
which we abstract only from the individual differences of

W. H. KANE

natural things, the only principles of speculative science that
can be abstracted from them are principles of sensible change.
Hence the proper subject of philosophy of nature is ultimately
specified as fundamentally intelligible in a special degree of
intelligibility, and philosophy of nature is one science in a
specific sense.
Philosophy of nature differs from mathematical physics when
the subject matter of this science is considered from a mathematical point of view, or from a practical rather ·than a
point of view.

Reply to Difficulties
1. In the course of philosophy of nature it is demonstrated
that there are many changeable beings of various kinds. All
of these things are referred to philosophy of nature, even
though their principles are different, because they are all intelligible to us in a special degree of intelligibility, which is that
of changeable being which can be abstracted from individual
differences.
2. Changeable substances and changeable accidents are
known in the same degree of intelligibility when we abstract
them only from their individual differences, somewhat as red
objects and blue objects are known in the same way when we
see them. The diversities between changeable substance and
changeable accidents are diversities in the subject matter of
philosophy of nature.
3. Everything that is known in one speculative science is
known in the same way inasmuch as it is all known from one
ultimately specified point of view, somewhat as all colored
things are known from the point of view of vision. This example is defective because sensory vision cannot apprehend an
object as simply and precisely as the intellect can, and because
the senses cannot apprehend a scientific object which can be
developed logically. In attaining philosophy of nature we presuppose the data of sensory experience of natural things, both
the data of ordinary experience and the data obtained by
special experiments and with the aid of special instruments,

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

225

such as the microscope and the telescope. All the data concerning changeable beings are referred to philosophy of nature
because of its proper subject. The experimental sciences of
nature are sometimes distinguished from philosophy of nature
by reason of their limited subject matter or special methods. A
speculative science, however, is specified by the degree of intelligibility of its proper subject, and its subject matter and
methods are determined by its proper subject.
4. Just as we employ various real instruments, such as the
scalpel and test-tube, in order to obtain more extensive and
exact data concerning natural things, so also we employ various
logical instruments, that is, various definitions, divisions, and
demonstrations, in order to attain a better understanding of
changeable being. All of our speculative science of natural
things is attainable from one ultimately specified point of view,
which is simply the view of changeable being that is obtained
by abstracting changeable being from the individual differences
of natural things and. making it a scientific object by objective
precision and formal abstraction. Philosophy of nature extends
to many conclusions about changeable being, which is intelligible through its principles of change. These conclusions are
not all of equal perfection or dignity when they are considered
with respect to logic or with regard to their subject matter, but
they all have the same degree of intelligibility inasmuch as they
are all equally abstracted from sensible things.
There are many sciences of sensible things which are not
purely speculative, but are more or less directly ordained to
practice. These sciences are distinct from philosophy of nature,
which is a speculative science specified by a general aspect of
natural things which man cannot make but can only understand through its principles of change. Philosophy of nature
extends to everything that is scientifically knowable about
natural things considered as changeable, or having within
themselves principles of sensible change. Furthermore, we may
freely borrow truths which pertain to mathematics or metaphysics in order to perfect our understanding of nature.
Philosophy of nature may be compared to the trunk of a tall

W. H. KANE

and spreading tree. This trunk springs from roots which are the
basic concepts and principles of human thought. It is nourished
by the sap of experience of natural things, and grows strong by
the exercise of reason upon the data of experience. From the
trunk proceed branches which divide and subdivide. These are
the conclusions of the science. An attractive foliage covers the
branches. This is natural history, or descriptive definition of
natural things.
The following outline is presented for the sake of clarity.

<

considered subjectively, or as a being, is a speculative
science which is a habit of the mind or its act;

Philosophy of nature

.considered objectively or intentionally is an order or
principle of conclusions concerning changeable being
that is intelligible through its principles of change. ·
Changeable being that exists or can exist in nature is called the subject of the
science. .Changeable being that is known .is called the object of the science.

<

proper subject

<

as subject
in nature)

subject matter:

imply: the fundamentally changeable;
·
degree of intelligibility: fundament-.
ally intelligible, can be abstracted
from individual differences;
natural bodies and their principles
of change;

<

simply: the fundamentally change·
able apprehended with objective
vrecision and formal abstraction;

Changeable
being
proper object
.
as object (
(in knowledge)
·material

de. gree of intelligibility: actually intelligible, abstracted from individual.differences;
any conclusion about changeable
being.

Point 'of view: the power or act of the mind to abstract from individual. differences and understand changeable
being through its principles of change.

THE NATURE AND EXTENT OF PHILOSOPHY

VIII.

WHETHER METHOD IS REQUIRED

OF NATURE

227

TO ATTAIN

PHILOSOPHY OF NATURE?

Difficulties

It seems that method is not required in order to attain
philosophy of nature, for the following reasons.
1. Method is not required in order to understand that which
is immediately evident to us. Changeable being is immediately
evident to us. Therefore method is not required in order to
understand it.
2. Method is required only when there is need for proceeding in one way rather than another. There does not appear to
be any reason for proceeding in one way in order to attain
philosophy of nature, because many natural things are evident
to us, and we can begin to study any of them we choose. Hence
method is not required in order to attain philosophy of nature.

Solution

By the method of philosophy of nature we understand the
correct and orderly way of proceeding to attain the speculative
science ·of changeable being. Method is required in order to
perform any complex task, such as making shoes or building a
house. It is a complex task to attain philosophy of nature, as
appears from the fact that we cannot perfectly understand
changeable being by one act of the mind. Hence method is
required in order to attain philosophy of nature.
The method which is required in order to accomplish an
enterprise is that order and manner of proceeding by which it
can conveniently be brought to completion. For example, we
can build a house if we know what it is that we desire to build,
not only in general but also in particular, if we have the materials and the tools that we need, and if we begin by laying
the foundation, and then proceed to erect the framework that
will support the walls and roof. Philosophy of nature can be
attained in a way that is proportionally similar to this.
The student of nature
to understand the principles

228

W. H. KANE

and reasons of changeable being as well as he can. Changeable
being is evident to us through its sensory appearance, and is
intelligible through its principles of change, which can be disclosed with the aid of the first principles of reasoning. Hence
in endeavoring to understand changeable being we presuppose
the data of sensory experience, both that of ordinary experience and that obtained by special experiments and with the
aid of special instruments, such as the spectroscope or the
barometer, insofar as such data are needed and available to
perfect our understanding. We also presuppose that the first
principles of reasoning are true with regard to changeable being;
that the whole is greater
for instance, that it is not
than its part; that things have sufficient reason for being what
and as they are; that effects have causes which are sufficient
to produce them; that as a thing appears and aets sensibly, so
it is: something which is fundamentally capable of appearing
and acting in that way; and that as a thing is, so it is apt to
act. In manifesting the truths of philosophy of nature, we
employ various logical instruments, that is, various definitions, divisions, and demonstrations, in; order to show what
the principles and reasons of changeable being are.
We first investigate that which is fundamental in changeable
being, that is, its radical or substantial principles, because the
fundamentally changeable is what primarily is or exists in nature, is intelligible through its principles of change, and is the
subject in which sensory properties are found. The proper
accidents of changeable being, such as motion and quantity, are
modifications of that which is fundamentally changeable, and
are intelligible only in relation
and to its principles. We
first consider changeable being in general, because the basic
concept of changeable being does not express the various numerical, generic and specific degrees, and because we cannot
understand what any particular kind of changeable being is
until after we know what changeable being is in general. Our
next step is to investigate the general properties of changeable being, in order to complete our general knowledge of

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

it; and then we proceed to consider changeable being more
comprehensively.
We investigate changeable being 1llore in particular according to the different kinds of sensible change that it undergoes, because changeable being is manifested to us by sensible
change. It appears that there are three kinds of sensible
change, namely, local motion or change of place, alteration or
change of the sensory qualities such as color or odor, and
growth or change of quantity, which is found in living bodies.
Local motion is more evident to us and more universal in
nature than alteration, and alteration is more evident and
more universal than growth. Hence we proceed to investigate
changeable being first as subject to local motion, then as subject to alteration, and then as subject to growth. In each
juncture we consider first that which is fundamental to an
understanding of what is changeable in these special ways. We
proceed from the more general aspects to the less general or
specific aspects, and we investigate the fundamental or substantial essence, and its properties and proper accidents, and
the correlations found in nature. When there are many special
or specific degrees of changeable being to be investigated, as
there are when we inquire into changeable being as it is found
in the elementary bodies and in their compounds and in organisms whether plant or animal, we consider the simpler
species first, because the simpler ones are easier for us to understand, and the more complex are better understood through our
knowledge of the simpler.

Reply to Difficulties
1. A special method is not required in order to know in an
ordinary way that which is immediately evident to us. But
ordinary experience and thought are not sufficient for determining in a scientific way the truths of philosophy of nature,
particularly in reg_:1rd to the things which are difficult to discover, such as the elementary bodies, or difficult to understand,
such as the nature of the soul. It is an arduous task to obtain
more extensive and more accurate experimental data, and to

280

W. H. KANE

reason correctly from the data. Hence the method of philosophy of nature includes not only the general logical method,
but also a special logical method, together with special techniques which are required in order to obtain special data; just
as the method of building a particular type of house includes
special methods both of building and of preparing the materials
out of which the house is to be built.
2. Many sensory aspects of changeable being are immediately evident to us. Our ordinary knowledge contains some
important truths concerning natural things, and it is not difficult to increase our knowledge in an ordinary way. But this
kind of knowledge is not perfect or perfectly scientific. It is
notably deficient in regard to our understanding of the fundamental principles of natural things, and in regard to an orderly
comprehension of their kinds and properties and their correlations. Moreover, there are many doubts and difficulties concerning these things which cannot be decided until after we
understand the fundamental principles of changeable being and
its general properties. Questions such as those which concern
the nature of organic life, its origin and development, the relation of the soul to the body, the nature and origin and duration
of the human soul, and the nature of our knowledge, cannot be
settled in a sure and orderly way without reasoning from a
fundamental understanding of changeable being. It is not
immediately evident to us in a scientific way that changeable
being has a multitude of numerical, generic, and specific degrees. Hence in order to perfect our knowledge of changeable
being, we must consider it first in general.
It seems natural for us to understand things first in general
and then more in particular. When we see a distant object we
know that it is a body before we know that it is a man, and we
know that it is a man before we recognize the individual.
Moreover, it is convenient in manifesting the truths of a science to investigate its subject first in general and then more
in particular, because if we already understand its general
aspects these need not be considered again when we are inquiring concerning a special aspect or degree. For example, if we

THE NATURE AND EXTENT OF PHILOSOPHY OF NATURE

Outline of some of the chief parts of philosophy of nature

<."I< \ I.
degrees:

gene_ric;
specific;

essence:

of subject;

prmc1p es·

corre abon;

of objecl

in
general

to
action; time;
quantity; place; space;
conditions for

properties
The science
of
changeable
being
.extends:

<

essence:

local motion:

the
properties;
changeable
essences;
.
by l?cal . · elementary bodies<· ·
motion:
proper;bes;
eneral causes and . effects of
local motion in the changeable universe;
essence:
in general<
_.
the
substantial:<
properties
in

chaligeabl\
by
alteration:

in particular: the
compound bodies;

to
accidental:

<

in general;

in particular:
light, sound,
density, etc.;

<

the
changeable
by
growth:

7

in

organic life;
of life;
origin & development;

in

./...the plants;
animals;
man.

W. H. KANE

already know what changeable being is in general, and as
elementary and compound and organic and animal, there is no
need to consider these aspects again when we are investigating
it as. intellective or rational. In this way we can begin our
study of nature with a concept that expresses changeable being
as actually intelligible, apprehended in a degree that is evident
to us, and that is least comprehensive and most universal; and
we can pass orderly through a multitude of concepts which
express changeable being according to different formalities and
degrees that are more comprehensive and less universal, together with concepts of their properties, and of their proper
accidents, and of the correlations in nature. With the help of a
competent teacher, philosophy of nature as a special habit of
mind can be acquired within a moderate period of time. To
master the details and discover new truths about nature is the
vocation of specialists.
w. H. KANE, 0. P.
Dominican House of Studies,
River Forest,

ANOTHER APPROACH TO THE PROBLEM OF
MEANING

T

HERE are at least two ways to approach the problem of
meaning. One approach lies through an analysis of the
modern writers on the problem; it is the one we chose to
follow in a previous article.* It is not the better approach, but
is imposed upon anyone who wishes to communicate with the
moderns. The essential condition of modern communication
is first to relapse exclusively into dialectic (not necessarily
polemical) by way of attempting as far as possible to come to
terms with anybody who has anything to offer on the matter.
This need not be purely negative; it may also be the occasion
for understanding better the general subject concerned. In
this case of the current problem of meaning, the attempt at
initial communication has had to be largely negative; this,
however, is not the primary aim, for through it much can be
learned, not so much of the particular problem discussed as of
the current status of philosophy, particularly in its relation to
experimental science. The issues which may subsequently rise
from this must go beyond the dimension of what has been
called the " problem of meaning," and hence cannot be resolved
even in the present scope. But much can be suggested by way
of anticipating the' eventual issue-the modern problem of
knowledge, and in particular the distinction of philosophy and
experimental science. It is only in that dimension that the real
difficulties here will be fully faced. ·
The second way of approaching again what has been covered
is necessary for several reasons. First, it is the way the problem might better have been approached had not the problem
of communication required consideration (and because of the
current statement of the problem, this other way is stated in
*"The Problem of Meaning," THE TaoMIST, Vol. VI, No.
ISO fl'.

(July, 1948), pp.

234

JOHN A. OESTERLE

terms of it). Second the benefit of an exact terminology, which
can dispense with such an ambiguous word as " meaning," permits seeing more clearly the general confusion which has been
exhibited. What is involved in the previous article, then, can
be translated into this more careful terminology. Third, it
emphasizes the benefit of taking account of what has been
already worked out in the past and can be employed to help
here. Consequently, this second approach shows, secondarily,
that the tradition of thought, available to everyone, can be of
assistance in facing what may be considered problems now as
well as what really are problems at present. This exacts
docility on the part of the philosophically interested (as it
should have exacted of everyone since the Greeks), but a
docility which would make possible real " daring " and advance. It is regrettable that much of current writing is proud
in its ignorance.
What follows, therefore, in this present article, is nothing
more than a brief exposition of a couple of points in John of
St. Thomas' Cursus Philosophicus. I employ him here simply
because I owe to him (as well as what he learned from others)
the perception of several distinctions which happen to be crucial
in connection with the current problem of meaning. He states
in a few words what endless pages of indiscriminate writing at
the present time have failed to cover. This is not an attempt
to enlarge any credit due John of St. Thomas, which is, as
should be evident, completely unimportant; it is only gratification at finding something so helpful and to the point. Hence,
the work of John of St. Thomas is employed as an aid and as a
teacher for what it is worth, which was his intention in writing
his Cursus Philosophicus. 1
1 Perhaps this explanation of why John of St. Thomas is employed is unnecessary.
But so often the use of an " authority " is misunderstood, as there is a popular
notion that any use of authority is uncritical and unoriginal. It is, fortunately,
unoriginal if by " original " is meant one who has learned only from himself. It
is not uncritical, since if there is any authority in a particular philosopher, this can
be discerned to the extent that he has contributed something worth while. I should
be simply dishonest if I did not acknowledge my debt to John of St. Thomas in
this matter. I use him directly as a matter of economy.

ANOTHER APPROACH

TO THE PROBLEM

OF MEANING

235

Now, the one common point of agreement in all the current
writers on the problem of meaning is the assumption that linguistic expression can be meaningless. The problem then
centers on when linguistic expression becomes meaningful or
how to put meaning into any linguistic expression which may
be considered. The solution to this problem was supposed to
be given in the principle of verification, namely that in some
way the verification of a linguistic expression would give it its
meaning. The further issue then was what way this some way
would be. The various answers given to this soon suggested
that something was wrong, that something was confused. This
in turn would lead to the question: Why suppose that verification gives meaning? Is there not some distinction which has
been missed in thus associating verification and meaning?
It is in terms of such questions that the following distinction
made by John of St. Thomas assumes importance; perhaps it
was made so carefully by him because he was facing a similar
confusion in his time. The distinction occurs in connection
with explaining "suppositio." 2
The distinction of John of St. Thomas is as follows:
Suppositio is defined as the " taking of a term for something concerning which it is verified." Many recent authors do not admit
this definition, thinking that suppositio is only the taking of a name
for the thing which it signifies, nor do they distinguish suppositio
from signification or the exercising of signification whereby a word
is substituted in signifying in place of a thing. Whence that old
and accepted principle, that some propositions have a subject which
does not " suppose " and hence if such propositions are affirmative
they are false, is rejected by them, because any name, whether
inside or outside a proposition, "supposes" by the very fact that it
is substituted for something according to the intellect. 3
2 It is perhaps not so curious that this " hoary doctrine " of suppositio is one of
the traditional contributions to logic especially dropped by modern logicians. Urban
(Language and Reality) refers to it and notes its importance, but he fails to make
any use of it. Even H. W. B. Joseph's An Introduction to Logic (Oxford, 1906),
generally assumed to be an exposition of traditional logic, reduces suppositio to a
footnote which begins: " The doctrine of suppositio, as of divers other ' properties
of terms,' has happily fallen into oblivion ... " (p. 14).
•" Suppositio definitur, quod est 'acceptio termini pro aliquo, de quo verificatur.'

JOHN A. OESTERLE

Thus John of St. Thomas, in defining suppositio/ is insisting
that terms or words have suppositio only when they are in a
proposition and hence that suppositio is a property only of propositional terms or words, not of terms or words simply.
This understanding of suppositio, however, was strongly contested in his time, and some writers insisted that suppositio was
merely the employment of any name to signify the understanding of a thing. The consequence is, as John of St. Thomas
points out, a failure to distinguish suppositio from signification
and the further consequence of assuming that any name must
have suppositio whether in a proposition or not. Note here,
for the moment, the ultimate consequence which could be
drawn from such a position: that if any name must have suppositio, and especially if suppositio is confused with signjfication, then it is an easy step to assume that a name has meaning only as it is in the context of a proposition, since it is only
in the context of a proposition that there can be suppositio
(i.e., standing as the logical subject or the logical predicate);
and finally, how easy the step would be .to assume also that
every name must be verified, since suppositio requires verification. It would be interesting to know whether the writers John
of St. Thomas had in mind took these consequences; if so, the
problem of meaning (or more likely, the problem of signification or suppositio) was being argued then.
John of St. Thomas also distinguishes two senses of" substitution " which are useful here:
Multi ex recentioribus hanc definitionem non admittunt existimantes, quod suppositio solum est acceptio nominis pro re, quam
nee distinguunt suppositionem a significatione seu exercitio significationis, qua vox substituitur in
significando loco rei. Unde illud antiquum et acceptatum principium, quod aliquae
propositiones sunt subiecto non supponente, et ideo, si sint affirmativae, falsae sunt,
ab ipsis reicitur, quia omne nomen, sive intra sive extra propositionem, supponit.
hoc ipso quod substituitur pro aliquo apud intellectum." Cursus Philosophicus,
Vol. I, p. 29"10. (All pagination is from the Reiser edition.)
• There is no exact English equivalent for suppositio. " Supposition " fails to
carry the precision, and " supposes " is hopelessly inadequate. As John of St.
Thomas' definition indicates, it is a certain kind of " standing for " within the
proposition.

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

237

In one sense there is representative substitution whereby words
convey to us the things signified; and this is not suppositio, but
signification. In another sense there is a sort of applicative substitution whereby after the intellect takes the representation and signification of a word, it applies this name in various ways in propositions, so thatit stands for that to which someone wishes to apply
it. ' .. 5
text continues on to say, a word may be substituted
As
in two ways, either to represent simply our understanding of
things, or a further substitution of this representation, namely
when it is applied in a certain way in propositions. Thus in
" man is white," not only does " man " represent human nature to me but I also substitute it again to stand for the subject
of that particular proposition.· This further substitution
quires verification, i. e., whether its meaning permits it to be
used in such an enunciation. I£, for example, the signification
of this word " man " could not be verified in this further substitution or use, then it would not be meaningless (or without
signification) but would be without suppositio because of its
signification.
In the light of this distinction (which is simply that between
signification and suppositio, or between the two ways in
we may substitute words) the confusion which is in the current
writings may be seen more clearly and stated in more precise
terminology.
It is clear that the modern writers have confused representative substitution and applicative substitution of words or
5 " ••• Uno modo substitutio
repraesentativa, qua ipsae voces nobis ingerunt res
significatas; et haec non est suppositio, sed significatio. Alio modo est substitutio
quasi applicativa, qua postquam intellectus accepit repraesentationem et significationem vocis,. applicat diversimode in propositionibus ipsum nomen, ut stet pro eo,
cui vult aliquid applicare; sicut cum dico: 'Homo est albus,' ly homo non solum
mihi repraesentat naturam humanam, sed etiam substituo illud pro eo, cui applicanda est albedo per illam copulam ' est.' Unde considerat intellectus, an respectu
talis copulae detur vere et proprie subiectum, quod sit homo, et si datur, vere
substituit tale subiectum in propositione; si autem non invenitur, substitutio est
nulla, sicut si dicerem: 'Antichristus fuit bonus,' 'Adam est albus,' non substituo,
nee supponunt ilia subiecta, quia respectu illius copulae ' fuit' non datur nee
applicatur ' Antichristus,' et respectu illius copulae ' est ' non datur ' Adam,' et sic
vocantur propositiones de subiecto non supponente."
(Ibid., p. 29bl6 sq.)

iSS

JOHN A. OESTERLE

names. Representative substitution is the substitution whereby
we impose names to stand for our conceptions of things. Applicative substitution is a further substitution of these names: the
names (already meaningful) are applied to form a sentence or
a proposition. It is here that verification comes in since the
names have to be verified in relation to each other, or verified
to stand for the parts of the whole which they are to make up.
These writers do not recognize representative substitution,
which is where the meaning of names originates; they only
recognize, in a way, applicative substitution-names as parts
of a larger whole-and it is here that some of them, at least,
seem to think meaning is first obtained.
There is, however, another and greater confusion involved.
It is the failure to distinguish the verification of the proposition
itself from the verification of a word in the proposition; and to
distinguish both of these from signification. The verification
of a proposition, if it can be obtained, gives the proposition its
truth. For these writers, the verification of a proposition gives
it its meaning.· John of St. Thomas insists upon the distinction
of the verification of a word in the proposition, and the verification of the proposition itself. In commenting upon the definition of suppositio-" the taking of a term for something concerning which it is verified "-he says of the " for something
concerning which it is verified " that it must be understood
" for which this taking or substitution of the term is verified,
not of which the proposition is verified. For' the· truth or verification of the proposition is not needed for suppositio, inasmuch as there is suppositio also in the false proposition .... " 6
The failure to distinguish these two verifications results in the
confusion that is apparent in maintaining that only the proposition has sense, that only in the context of a proposition has a
name a meaning. The statement really should be: Only the
proposition has truth; only in the context of a proposition has
a name a suppositio.
• " • . . pro quo verificatur ilia acceptio termini seu substitutio, non de quo verificatur propositio. Non enim requiritur ad suppositionem veritas seu verificatio
propositionis, siquidem etiam in propositione falsa datur suppositio. . . . " (Ibid.,
p. 8()&10 sq.)

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

This also indicates why these writers find it so easy to suppose that there can be a meaningless sentence or a meaningless
proposition. For by supposing that meaning is attained by veri-.
fication, they would further suppose that where there is no
verification there is no meaning. But in the case where there is
no verification of the proposition, the proposition is false; and
there is no verification because the meaning of the proposition
will not permit a verification. Hence we cannot verify precisely
because the proposition has meaning. This may also explain the
attempt to identify "ultimately" truth and meaning. This
position would follow insofar as verification of the proposition is
retained in some way as the principle of meaning. Similarly in
the case of the verification of a name within the proposition. If
the name cannot be verified in the proposition, the name will
have no suppositio (just as, grammatically, a word might not be
a " part of speech " although remaining fully a word as a meaningful element, which could happen in badly constructed sentences-hence not really sentences-where words are present
but are not ordered as " parts of speech ") . And, again, the
name will not be verified in 'its suppositio because of the meaning or signification of the name itself. As John of St. Thomas
points out:
And thus suppositio is acknowledged to be distinguished from
signification, since the signification of a term is permanent and one
while the suppositio can be varied with the signification remaining
the same, because the former depends upon imposition, which does
not change, the latter upon the application and use of the intellect,
by which it applies and uses a term. 7

It is also important to note that it is in connection with
suppositio that we speak of a verification" according to sense"
or " according to intellect." Thus in " ' Man ' is a word " I
verify " man " (by material suppositio) by pointing to the
word " man " and thus show that this sensible thing is to stand
• " Et constat distingui suppositionem a significatione, cum significatio termini sit
autem variari possit eadem significatione manente,
permanens et una,
quia ilia ab impositione, quae non mutatur,•.dependet, haec ab applicatione et usu
intellectus, quo applicat et utitur aliquo termino." (Ibid., p. 1663 47.)

240

JOHN A. OESTERLE

for a word. It is only here that pointing might be of assistance,
although not absolutely necessary; but the pointing would not
be for the -purpose of obtaining meaning, but for illustrating
meaning (i.e., showing its use or application). This verification ad sensum, however, is not the only nor even the primary
way of exhibiting verification in suppositio. It does not have
to be made ad sensum, especially when a verification ad intellectum suffices.8
The point of interest here is that this den_10nstration ad
sensum is an approximation of what is called empirical verification, while the demonstration ad intellectum is an approximation of the attempts of others to verify in ways other than
merely empirical, for example, verification by " authentication."
The writers here, of course, speak in connection with the verification of the proposition itself, rather than with the verification of a name within the proposition, but the point holds as
far as meaning is concerned. In the verification of the proposition, the question is whether truth, rather than suppositio, is
given ad sensum or ad intellectum. Here some have wished to
narrow verification to ad sensum exclusively.
There is, perhaps, a final point which will serve to put the
full force of the distinction of signification and suppositio in a
clearer and fuller dimension. This concerns a more basic distinction, upon which the distinction of signification and suppositio depends. This is the distinction
the first and
second operations of the mind or between simple apprehension
and judgment. Very likely, none of these writers would admit
simple apprehension as distinct from judgment, and yet perhaps
it is just because of this that we have had the principle of
verification proposed so consistently as the principle of meaning. It is in the light of that distinction that we can see
fully the corresponding distinctions of signification, suppositio,
and verification, and what they entail in the present consideration. For this simply takes account of the way in which we
know, so that this distinction of simple apprehension a:qd judg8 " Haec autem demonstratio, quando dico: ' Hoc est ' etc., non requiritur quod
fiat ad sensum, sed sufficit quod ad intellectum demonstretur, quia praeterita et
futura non demonstrantur ad sensum. . •. " (Ibid., p. 80"44.)

ANOTHER

APPROACH

TO THE PROBLEM

OF MEANING

241

ment itself is understood in terms of the most fundamental distinction of all, the distinction of act and potency " which
divides all being." In this way we can understand that it is
our potential mode of knowing which requires three operations
to arrive completely in act:
... this arises from our imperfection of intellect, because we proceed from the imperfect to the perfect and from potency to
act .... 9
The foregoing treatment of signification, suppositio, and verification, while making clear the confusion that has been involved, does not ipso facto point the solution to the problem of
meaning. It is mainly negative in that it shows what is not
the problem of meaning. It also should show the futility of
losing the problem in the ambiguous English word " meaning." In fact, the problem, in more accurate terminology, concerns signification, as is evident from the way in which John
of St. Thomas proceeds. It is, then, perhaps not so curious that
John of St. Thomas treats the matter of signification in such
detail in the first volume of the Cursus Philosophicus. Here
again, a brief consideration of his work-this time on signification itself-will prove helpful in understanding the dimension
in which the " problem of meaning " should be cast.
John of St. Thomas defines the sign as follows: "that which
represents to
knowing power something other than itself." 10
In order to understand this definition fully, John of St. Thomas
points out, we should have to consider knowing, and the four
causes of knowing. 11 And here we can see at once what will
9 " • • • ex imperfectione
nostri intellectus id provenire, quia procedimus de
imperfecto ad perfectum et de potentia ad :oJ,ctum.... " (Ibid., Vol. HI, p.
367•17 sq.) Cf. the commentary of St. Thomas on this in Post. Anal., Bk. I, lect.
l, n. 4.
10 " Id, quod potentiae
cognoscitivae aliquid aliud a se repraesentat."
(Ibid.,
Vol. I, p. gaul.)
11 " Quae definitio ut melius innotescat,
oportet considerare, quod est quadruplex
causa cognitionis, scilicet efficiens, obiectiva, formalis et instrumenta!is. Efficiens
est ipsa potentia, quae elicit cognitionem, sicut oculus, auditus, intellectus. Obiectum
est res, quae movet vel ad quam tendit cognitio, ut cum video lapidem vel hominem.
Formalis est ipsa notitia, qua redditur potentia cognoscens, ut visio ipsa lapidis vel

JOHN A. OESTERLE

have to be ultimately the real problem. It will be the problem
of knowledge itself, for only in terms of knowing can representing and signifying, which are contained within knowing, be
fully understood. This is the significance of the fundamental
statement of John of St. Thomas: " Igitur facere cognoscere
latius patet quam repraesentare, et repraesentare quam significare." 12 Knowing is more extensive than representing, and
representing is more extensive than signifying.
It is in this dimension that the analysis of signification has to
be understood. For facere cognoscere embraces everything pertaining to knowing-the effici'ent, objective, formal, and instrumental causes. Repraesentare-which concerns everything by
which something is made present to the knowing power 18embraces three of the causes, the objective, formal, and instrumental. Significare concerns only the formal and instrumental
causes.
The sign is defined as a kind of representing. By means of
representation, the medium of joining the object and the knowing power is explained. The medium is both the representation
whereby the physical object is represented in the impressed
species, as in the principle of knowing, and also the representation whereby the intentional object is represented in the expressed species,as in the term of knowing. 14
Thus all signifying is representing, but not the converse.
What distinguishes signification from representation is that signification is that kind of representation which " represents
other than itself," whereas we can speak of an object, or that
which is known, as simply representing itself in being known.
The distinguishing characteristic of a sign is that there is a real
difference between it and what it signifies. The sign must
hominis. Instrumentalis est medium, per quod obiectum repraesentatur potentiae,
sicut imago exterior Caesaris repraesentat Caesarem." (Ibid., p. 9"22 sq.)
'"Ibid., p. 9b7,
18 " Repraesentare dicitur de omni eo, quo aliquid fit praesens potentiae .• ; . "
(Ibid., p. 9b80.)
14 The treatment
of the problem of rcpraesentare is considered by John of St.
Thomas in Vol. III, Q. 8, A. 8, p. 101 sq. In Question 6 of the same volume,
articles 2 and 8 treat' in great detail the necessity of the intentional species. The
role of intentional species in knowledge deserves re-statement and re-emphasis in
modern psychology.

ANOTHER

APPROACH

TO THE PROBLEM

OF MEANING

always be ordered to the signified; the sign is always dependent
upon. the signified. The importance of this can be seen in connection with words, which are kinds of signs. Words cannot
be understood except in terms of their signification. This indicates the futility of a principle of verification since it seeks to
obtain a signification (" meaning ") which must already be
present in order to have a verification.
The point here is not only the former one, that representation is more extensive than signifying, but that signification
adds to representation the relation of dependence to what is
signified. By thus distinguishing representation and signification, we shall not confuse the two and their respective problems, nor shall we lock ourselves forever in a void of signs supposedly signifying only themselves. It is the nature of a sign to
point to something else (even though this may still be another
sign), to refer to something other than itself, and hence a sign
can never be isolated apart from its relation of dependence to
what it signifies. To ask questions concerning what it is that
is known, or how an object is made present to the knowing
power, is to go beyond the dimension of signification. This does
not eliminate difficulties, but distinguishes where difficulties
belong. Signification will not settle the problem of knowledge,
although because signifying is contained within knowing much
can be determined about knowing through signifying. For example, the mode of signifying will indicate the mode of knowing; the language of the poet differs from the language of the
scientist.
In the dimension of signification, then, the elements are the
sign, the signified, and the knowing power, each distinct from
the other; the problem is their relation to each other, and, in
terms of this, the division of signs. Thus the question is
whether a sign is related only to the signified, or only to the
knowing power, or to both. 15
15 Cf. Oursus Philosopkicus, 7 ol. I, Q. 21, A. 8, p. 668 sq.
I must make clear
my intention in proceeding in this way in the analysis of signification. This intention is to expose briefly the work on this matter of John of St. Thomas who is, in
this respect, a model "semanticist." Economy of space dictates condensed writing

244

JOHN A. OESTERLE

The definition of the sign involves both the knowing power
and the signified (the" aliquid aliud a se repraesentat "). This
implies that the sign must be related to both. To ignore the
part the knowing power plays in signification would be to identify words, for example, with the things they signify-reifying
language-which some contemporary semanticists have also
protested against. On the other hand, to ignore the signified
would be to fail to distinguish the dependence the sign must
have on what it signifies.
Thus the sign must be related to both the knowing power and
the signified. With customary diligence, John of St. Thomas
asks whether there is only one relation, involving the knowing
power and the signified as unequal terms within this same relation, or whether the sign is related distinctly and separately to
each. The question, abstract as it might seem, assumes great
importance in the analysis of signs.
There certainly seems to be a sense in which two relations
could be distinguished in the sign, for there appears to be a
difference whether the sign is related to the signified or to the
knowing power. The relation of the sign to the signified has
already been mentioned in distinguishing signification from
representation, which was obtained by the aliud a se, the relation of dependence of the sign to something other than itself.
Hence the sign would be related to the signified as subordinate
to it. The sign depends upon the signified as the measured depends upon a measure, a critical point for semantics. The
relation of the sign to the knowing power, however, seems to be
different. Here the relation seems to be one of dominance,
rather than dependence: the sign 16 represents to the knowing
and a reliance upon philosophical terminology, which is, of course, only common
language made precise. What would be more desirable here is a dialectical examination of John of St. Thomas' work in relation to contemporary semantics, but
that would exceed the present limits. However, at the conclusion of this. short
exposition of John of St. Thomas' semantics, a brief comparison will be made with
a central point in Ogden and Richards, who are probably the most influential
contem:Porary semanticists.
16 As will be evident later in the divisions of signs, we are referring here to
formal signs as distinct from instrumental signs.

ANOTHER APPROACH TO THE PROBLE]d OF ]dEANING

power. The knowing power must depend upon the sign for the
representation of the object. However, in specifying this, John
of St. Thomas insists that more is involved than the notion of
sign. In insisting upon this relation of dominance, it is the
object that must be ultimately considered, and it is only insofar
as the sign takes the place of the object in representing it
that it can be said to exercise a relation of dominance over the
knowing power. 17 So to the extent that the sign substitutes
for the object (the signified) it does dominate the knowing
power, for it is the means by which the knowing power is specified. This may seem like a fine distinction, but it is John of
St. Thomas' way of safeguarding the objectivity of knowing
and signifying: the object is always the "dictator"; so is the
sign insofar as it substitutes in representing it to the knowing
power. But insofar as it signifies the object, the sign, too, is
" dictated to." This is sheer objectivity, i.e., the definition of
knowing. In this way, then, there might be two relations in
the sign: its subordinating relation to the signified, and its
dominating relation to the knowing power to the extent of
presenting the object to it. 18
But there is also a sense, and a more proper one, in which
there is only one relation involved in signification, This is by
considering the sign, not as relating to two equal terms-for
this would give two distinct relations-but as relating to one
directly and the other indirectly. Here the sign itself is considered more precisely, and if representation and signification
are carefully distinguished (and it was to conserve this that
1 7 " ••• quod potentia et signatum ut termini directe attacti postulent duplicem
relationem, ex eo constat, quia potentia non respicitur directe nisi a suo obiecto
vel movente vel terminante; potentia enim
respicit ohiectum ut ohiectum,
signum autem non dicit directe rationem obiecti, sed substituentis pro obiecto et
medii inter signatum et potentiam, ergo directe respicit signatum, pro quo substituit, in quantum signum est. Ut ergo directe respicit potentiam, indiget sumi
in ratione obiecti et non in ratione signi.... " (Ibid., p. 664b49-665•14.)
18 " Si potentia
et signatum considerentur ut termini directe attacti per relationem, necessaria exigunt duplicem relationem in signo, sed hoc modo signum
respicit potentiam directe ut obiectum, non formaliter ut signum."
(Ibid., p.

664"41.)

246

JOHN A. OESTERLE

John of St. Thomas first considered a double relation in the
sign) , then signification properly involves a single relation
which embraces both the knowing power and the.;signified, but
not equally nor in the same way.19 And it is in this way that it
can be said that the function of the sign is to represent the
signified to the knowing power, understanding by this that the
sign attains the signified directly and the knowing power indirectly. The signified is that which the sign represents; the
knowing power is that to which the sign represents the signified. This emphasizes the essential role of the sign, the role of
substitution for the signified, and this touches the very heart
of the problem of signification. For the difficulty underlying
semantics is that we cannot get to things themselves immediately, and it is in virtue of this that we need signs. The thing
or object has to be represented to the knowing power, and
signification is the means by which this representation occurs.
And it is in terms of this relation of the sign to the knowing
power and to the signified that the distinction of kinds of signs
can be made and understood. 20
10 " Si vero consideretur potentia ut terminus in obliquo attac.us, sic unica relatione signi attingitur signatum et potentia, et haec est propria et fonnalis ratio
signi." (Ibid., p. 664"47.)
•• " Hinc nascitur duplex divisio signi. Nam qua parte signum ordinatur ad
potentiam, dividitur in signum formale et instrumentale; quatenus vero ordinatur
ad signatum, dividitur penes causam ordinantem illud in naturale et ad placitum
et ex consuetudine " (p. 9b4S-10"4).
The foregoing treatment of how the sign is related to the knowing power and to
the signified is most important, even though given here somewhat summarily. It
considers the sign secundum ae, and John of St. Thomas' treatment of this is the
most elaborate in the whole tradition. He· recognizes the need of distinguishing
carefuHy the role the sign plays in knowing, in particular the formal sign, which
is ignored in contemporary semantics. He emphasizes the importance of the sign
for logic, since all the instruments of logic are defined in terms of the sign: " Quia
erge tam terminus q'l!am oratio et propositio et reliqua instrument& logicalia per
significationem definiuntur, eo quod intellectus cognoscit per conceptus significativos
et loquitur per voces significativas, et in universum omnia instrument&, quibus ad
cognoscendum et loquendum utimur, signa sunt, ideo ut logicus exacte cognoscat
instrument& sua, scilicet terminos et erationes, oportet, quod etiam cognoscat, quid
sit signum " (p. 9"6-18) .
From his very detaile4 examination of Ule sign (cf. the q11estions treated from
pages M8 to
I have chosen to present in CCULdeased form his question os. the

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

9l47

In the relation of the sign to the signified, the more familiar
division of signs occurs. That is, this division of signs is the
one commonly recogQ.ized,probably because the relation of the
sign to the signified is more obvious. This is the division of
signs into natural and artificial. The natural sign exhibits
some natural connection between the sign and the signified, as
in the common examples of smoke signifying fire or clouds signifying rain. Such a sign is called natural also because it
signifies the same to everybody.
The artificial sign is a sign that is in some way devised or
imposed voluntarily by man. These are the most recognizable
signs of all since they are deliberately devised and made to
be signs. They embrace all spoken and written language, symbolism, ritual, codes, gestures, etc. It is here, however, that
John of St. Thomas insists upon a further distinction within
artificial signs. There is a further dilference in the way these
signs are arbitrarily imposed by man. Some artificial signs
have a certain measure of binding authority in their use; others
do not. The first kind John of St. Thomas calls ad placitum;
the second, ex consuetudine.
This further distinction of artificial signs has a certain
amount· of practical importance. The ad placit'l,tm signs are
those which have a definite political or social aspect, and to
that extent require the sanction of public authority behind
them. This is the case with words, since language is a social
affair. Language cannot be treated wholly arbitrarily; ad
placitum is not ad libitum. This distinction is recognized, for
example, in suits of slander or libel where words are granted to
have a social and not merely private significance, and hence
involve responsibility. 21 Likewise, the condition of communicarelation of the sign to the knowing power and the signified, and his discussion of
the divisions of signs because of their pertinence in exhibiting the extent really
involved in the "problem of meaning." The appreciation of this can best be seen
in the comparison with Ogden and Richards, which follows below. The work of
John of St. Thomas on signification deserves a much fuller exposition than is
possible here.
21 Another instance to show how words are regarded as primarily ad placitum ·is
found in the way in which trademarks are acquired. Since langnage is social and

8

248

JOHN A. OESTERLE

tion with language is the acceptance of public authority in the
use of words. This justifies the existence of academies and dictionaries, which determine what socially accepted significations
words are to have.
On the other hand, words still remain arbitrary signs-they
are ad placitum, and not natural. This avoids supposing that
there is a natural correctness about words, or that words signify
naturally (hence, the same for all) just as smoke signifies fire.
There is a sense, perhaps, in which it could be said that
word " x " should signify such and such (but the " should "
here expresses only the social authority that is recognized in
language) . It could not be said that the word " x " must
signify such and such in the sense that a natural sign must
because of its natural connection with the signified. Words
as words are essentially artificial or arbitrary in the sense of
ad placitum, since they are products deliberately made to
signify, and since what they signify they need not necessarily
signify. 22
The distinction of words as artificial rather than natural, and
as ad placitum rather than ex consuetudine 28 has an important
bearing on the problem of meaning. Contemporary writers
usually admit the distinction between natural and artificial
signs, but none make any further distinction within artificial
signs. This may contribute, in part, to the problem of whether
words are natural or conventional since if this means either
has public (not private) authority and use behind it, a trademark is adopted by
indicating in some way that the words in question are being altered from their
accepted social usage. It is a manner of altering language from public to private
use. Ordinary common names thus become proper names. Frequently, odd spelling
is employed to indicate the transition.
•• The issue of whether words are natural or not is an old one. Plato in Cratylua
seems to take the position that names have a natural correctness in their representation of things. Among the current writers, Mr. Urban also seems to hold that
names are not mere nomi;,a, not merely conventional (cf. THE TuoMisT, Vol. VI,
No.2, p. 197, n. 87). On the distinction of what is natural and what is artificial in
language, vd. St. Thomas, De lnterpretatione, lect. 6, nn. 7-8.
•• Ex consuetudine signs are signs with no public authority behind them, but
merely· custom and use. John of St. Thomas gives the example of napkins signifytree would be another example.
ing a meal. The

ANOTHER APPROACH TO THE

OF

natural or ex consuetudine, there are difficulties with either;
But if it is realized what it means to say that words are ad
placitum, then it will also be realized how words of themselves
cannot be expected to give their meaning, since there is that
arbitrariness about words. Nor do words depend exclusively
on the way any person happens to use them, since they are not
as arbitrary as that; nor, finally, are they to be verified for
their significance, since it is only in virtue of their significance
that they come to be words.
The relation of the sign to the knowing power gives the
division of formal and instrumental signs. This is a more difficult division of signs to see because of the intimate connection
of signifying and knowing. For the same reason, it is a more
important division relative to the " problem of meaning." Two
initial points must be made here.
First, we must remember that by careful distinction John of
St. Thomas has insisted there is only one complete relation
involved in the sign, the signified, and the knowing power.
Nevertheless, the knowing power and the signified are two
terms in this relation, although not equally so. The signified is
always the ultimate term of this single relation; the knowing
power is the term " in obliquo." Although the relation thus
remains unbroken, the sign can be related subordinately, within
this comprehensive relation, to its two unequal terms (the
sense of the double relation) . In now considering the relation
of the sign to the knowing power, we do not ignore the signified,
but consider the sign as substituting in place of the signified or
object. Hence, the sign is considered more " ut obiectum, non
formaliter ut signum." 24 As will also be evident, this concerns
the formal sign rather than the instrumental sign; not that the
formal sign is not fully a sign, but rather that its essence as a
formal sign consists in its being that intentional form which is a
sign.25
Second, the division of signs into formal and instrumental is
•• Vd. n. 18, supra.
•• Vd. Our. Phil., I, Q. XXII, Article 1, p. 698 sq. on the difficulties regarding the
formal sign as properly a sign, upon which the following chiefly relies.

250

JOHN A. OESTERLE

neither more nor less extensive than the division of signs into
natural and artificial. Since the relation of the sign, knowing
power, and signified remains one, both divisions of signs include
all signs, only under different aspects. For example, all formal
signs are natural signs although not vice versa, and hence
instrumental signs jnclude both natural and artificial signs. The
difference in the two divisions is a difference of emphasis. The
division into formal and instrumental signs is the emphasis
upon signs as interior and exterior to the knowing power. The
division into natural and artificial is the emphasis upon the
manner in which signs are connected with the signified. This
diversity of emphasis serves to make clearer the role of signifying in knowing.
The distinction of the instrumental sign involves no difficulty. Because it is always exterior to the knowing power, it
is something of a knowable object in itself, and hence is more
obviously a sign. Examples given of signs are almost always
instrumental signs; words, in this division, are instrumental
signs, and the importance of recognizing
as instrumental
signs will soon be apparent. The distinguishing characteristic
of the instrumental sign, as is evident from its being exterior
to the knowing power, is that it must itself be known as an
object in order to know what it signifies. A word has to be
known as a word to know what it signifies.
" Sed tota diflicultas est circa signa
The formal
sign, being interior .to the knowing power, is less familiar and
less obvious. This very fact makes the grasping of the formal
sign difficult. It is not easy to understand the distinction of a
sign within the knowing power which at the same time is not
the knowing power itself, nor the act of knowing. This very
minute precision can be made more .clear by starting with an
instrumental sign, such as the word. Words are extrinsic means
of signifying things understood. Words of themselves do not
signify directly and immediately things, but only in virtue of
knowing. Hence we depart from the ambiguity and void of
instrumental signs to get at the knowing which is expressed
through them. But the process of knowing is complex. John

ANOTHER APPROACH

TO . THE PROBLEM OF MEANING

251

of St. Thomas, following St .. Thomas, distinguishes four elements in the process of knowing. 26 These elements are: 1) the
thing which is understood (the object), 2) the intelligible
species by which the intellect is aroused into aCt (the impressed
species), 3) the act of understanding, and 4) the conception of
the intellect (the concept, the expressed species), only analytically distinct from the act of understanding. All this is involved in order for the knowing process to occur in the mind,
by which it is possible to signify extrinsically or instrumentally
by words, for example.
In this way signification can be understood within the knowing power or intellect; the knowing power needs signification to
inform it. In this distinction of the elements involved in the
knowing process, the signification will be the concept, that term
of the knowing process whereby the knowing power, fully in
act, expresses the intentional likeness of the object. It is in this
manner that the concept is the formal sign.27 The concept
cannot be an instrumental sign since the concept is not an object known in any way (except reflexively). It is a formal
sign because it signifies by representing directly and immediately the object. In terms of the other division of signs, the
concept is a natural sign because of its natural connection with
the signified, being its intentional form and likeness.
The formal sign (of which the concept is the intellectual
instance) 28 is thus a pure medium in signifying. This is its
•• Vd. p.
sq. Cf. St. Thomas, De Potentia, Q. 8, Art. 1.
•• In conformity with the above distinction of the four elements· involved in the

knowing process, John of St. Thomas proceeds to discuss which of them is the
formal sign, and why only the concept is. In Q. XXII, then, Article is " Utrum
conceptus sit signum formale." Article 8: " Utrum species impressa sit signum
formale." Article 4: " Utrum actus cognoscendi sit signum formale."
There is, perhaps, no reason to elaborate on the need of distinguishing these four
elements in the knowing process, because of its importance in the whole traditional
analysis of knowing. Again, however, it would be desirable to eXplore this distinction in a more dialectical manner for the purpose of communication since, as
will be evident, it is a necessary and ignored part of current semantics.
•• The other instance is the conesponding expressed species in sensitive knowing; vd. p.
" EtiWt idolum seu species expressa sensibilis in potentiis
interioribus est signum formale respectu talium potentiarum."

JOHN A. OESTERLE

sharp distinction from the instrumental sign which, to some
extent, is a quod and not a quo. Here again, John of St.
Thomas follows St. Thomas in carefully distinguishing the various senses of a medium in knowing. 29 The formal sign is a
medium in quo, as distinct from a medium sub quo or even
medium quo. And it is a medium in quo not, of course, in the
sense that a mirror is a medium in which one sees his image,
which is still extrinsic to the knowing power and only a material likeness,
a medium in which the knowing power is
intrinsically informed with the likeness of the object. There
is, then, no mediate knowing of the formal sign, but an immediate forming of the knowing power itself. This is the sense
of. the medium in quo of the fopnal sign. " Habet enim rationem medii in quo, quia numquam se, sed aliud a se
repraesentat .... " 80
This, too, agrees with the original definition of a sign: "that
which represents to the knowing power something other than
itself." This definition applies equally to formal and instrumental signs, since both represent something other than themselves. The important point, however, is the difference, which
is in mode of signifiying, and which must be emphasized once
more. The instrumental sign represents something else mediately; it must be itself known as an object in order to signify.
The formal sign represents something else immediately; it is
known, not as an object, but formally as that in which the
object is represented to the knowing power. Since, then, the
formal sign is interior to the knowing power while the instrumental sign is extrinsic, the instrumental sign must thus be a
consequence of and dependent upon the formal sign, except in
the case of a purely natural instrumental sign, which the word
is not.
In brief review, then, the work of John of St. Thomas on
signification, as summarized here, has shown the following. The
definition of the sign gives the elements of signification: the
sign, the knowing power, and the signified. One comprehen•• Cf. p. 69Sb35 aq.

80

p. 696 8 46.

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

sive relation is involved: the sign relates directly to the signified
and represents it to the knowing power. In terms of this relation, divisions of signs are made. Natural and artificial signs
arise from the connection of the sign with the signified. The
further distinction of artificial signs into ad placitum and ex
consuetudine is necessary, especially in understanding words as
signs. Formal and instrumental signs arise from the connection of the sign with the knowing power. The formal sign
(e. g., the concept) is interior to the knowing power; the instrumental sign (e. g., the word) is exterior. There is no difficulty
in distinguishing the instrumental sign; the formal sign, because
of its role within knowing, is difficult to grasp. Unlike the
instrumental sign, the formal sign is a pure medium since it
wholly signifies something other than itself, and is in no way a
knowable object in itself. The crucial point, then, is the distinction of the formal sign from the instrumental sign. In
other terms, this is the difference between a concept and a
word, which shows the dependence words have upon concepts.
It is at this point that the analysis of John of St. Thomas
can be compared with a current work on semantics. The purpose of this comparison is to show what there is in common in
the two treatments as well as what is different and, as a result,
to see where the original " problem of meaning " leads. For this
comparison
important part of Ogden and Richards' The
Meaning of Meaning has been chosen because of its recent
influence and because here the problem is posed in terms of
signification. Also, contrary to the foregoing writers with their
principles of verification, Ogden and Richards at least recognize
the relative unimportance of words as words, that they must
already have significance, and hence that the problem then
becomes the manner in which words signify.
Ogden and Richards approach the point in question as
follows:
By leaving out essential elements in the language situation we
easily raise problems and difficulties which vanish when the whole
transaction is considered in greater detail. Words, as every one
now knows, " mean " nothing by themselves. . . . It is only when

fl54

JOHN A. OESTERLE

a thinker makes use of them that they stand for anything, or, in
one sense, have "meaning." They are instruments. . . . But for
the analysis of the senses of "meaning" with which we are here
chiefly concerned, it is desirable to begin with the relations of
thoughts, words and things as they are found in cases of reflective
speech uncomplicated by emotional, diplomatic, or other disturbances; and with regard to these, the indirectness of the relations
between words and things is the feature which first deserves
attention.
This may be simply illustrated by a diagram, in which the three
factors involved whenever any statement is made, or understood,
are placed at the corners of the triangle, the relations which hold
between them being represented by the sides. The point just made
can be restated by saying that in this respect the bas.e of the
triangle is quite different in composition from either of the other
sides.

T H 0 uGH T Of\

.STANDS FOR
( Cl'l'l imputed

'(elation)

TRUE.
FIG. I.

Between a thought and a symbol causal' relations hold. When
we speak, the symbolism is caused partly by the reference we are
making and partly by social and psychological factors-the purpose for which we are making the reference, the proposed effect of
our symbols on other persons, and our own attitude. When we
hear what is said, the symbols both cause us to perform an act of
reference and to assume an attitude which will, according to circumstances, be more or less similar to the act and the attitude of
the speaker.
Between the Thought and the Referent there is also a relation;

.ANOTHER APPROACH

TO THE PROBLEM OF MEANING

255

more or less direct (as when we think about or attend to a coloured
surface we see)' or indirect (as when we "think of" or "refer to"
Napoleon), in which case there may be a very long chain of signsituations intervening between the act and its referent: word-historian-contemporary record-eye-witness-referent
(Napoleon).
Between the symbol and the referent there is no relevant relation other than the indirect one, which consists in its being used by
someone to stand for a referent. Symbol and Referent, that is to
say, are not connected directly (and when, for grammatical reasons, we imply such a relation, it will merely be an imputed, as
opposed to a real, relation) but only indirectly round the two sides
of the triangle. 81

The point that appears to be insisted upon most in this triangular presentation of Ogden and Richards is that there is no
direct relation between the " Symbol " and the " Referent."
Loosely translated into the terminology of John of St. Thomas,
this means that the instrumental sign has no direct or necessary connection with the object even though, for example,
smoke itself is so related to fire, a point John of St. Thomas
would likewise insist upon, although he takes it pretty much
for granted. John of St. Thomas finds no difficulty with the
instrumental sign; it likely seemed evident to him that since
the instrumental sign is extrinsic to the knowing power no one
would identify it with the object or referent. Ogden and
Richards, however, make a great point of this indirect relation
of symbol and referent, and seem to think that until recently
it was universally misunderstood. It is not clear what or whom
they intend·by this. But the most likely instances now of such
a misunderstanding would be the holders of the principle of
verification who wish precisely, by verification, to establish a
direct relation between words and objects. The point of agreement, then, between Ogden and· Richards and John of St.
Thomas is the role of the instrumental sign; the difference is
that John of St. Thomas takes this as evident while Ogden and
Richards make this the main point.
In connection with this same point, it is not clear in Ogden
81 Ogden and Richards, The Meaning of Meaning. 5th edition. Harcourt, Brace
and Company, New York, 1988. pp. 9-12.

256

JOHN A. OESTERLE

and Richards the sense in which the imputed relation between
the symbol and referent becomes " true." This may mean: 1)
the sense in which a proposition expressed by certain symbols
is verified as true; 2) the sense in which symbols stand for
certain parts of an expressed proposition, as in suppositio; or 3)
the sense in which symbols, such as words, are imputed to
stand for (even though only indirectly) referents and are,
consequently, "true" as merely signifying. The third sense
would involve the same confusion exhibited in the principle of
verification, i. e., signification and verification. The second
sense would confuse signification and suppositio. The first
sense is the only one in which " true " could justifiably appear,
but it is rather dubious that this is what they intend to impart.
Another point of agreement is the relation of " Symbol " to
" Thought or Reference." Translated into the terminology of
John of St. Thomas this would. mean that the instrumental sign
depends wholly upon the concept, which is the force of the ad
placitum. The agreement here is in the arbitrariness of instrumental signs as means of signification, and that to get at the
meaning of words, for example, is to go to the thought behind
the words, or to get at the thought which is being expressed
more or less arbitrarily in extrinsic signs.
Here, however, whatever agreement there is appears to cease.
There may be more, but this cannot be determinded on the
basis of what is expressed in The Meaning of Meaning. It is
difficult, if not impossible, to determine the meaning of Ogden
and Richards' explanation of the relation of " Thought or
Reference " to " Referent " since it is given in very general and
ambiguous expression, e. g., " It is Thought (or, as we shall
usually say, reference) which is directed and organized, and
it is also Thought which is recorded and communicated." 32
Later on, attempts to explain the mental process by reaction
to stimuli or even by a " purified " behaviorism depend upon
the extent to which one is content with identifying " I am
thinking of A " with " My thought is being caused by A," or
•• Ibid., p. 9 . . . passim.

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

identifying the mental process with reaction to match-strikings,
bell-ringings, and other stimuli. 33
It would seem that it is just here that the semantics of John
of St. Thomas would be of service. The semantics of Ogden
88 Cf. Chapter lll. "Sign-Situations,"
which, in part, runs as follows:
" The effects upon the organism due to any sign, which may be any stimulus
from without, or any process taking place within, depend upon the past history of
the organism, both generally and in a more precise fashion. In a sense, no doubt,
the whole past history is relevant: but there will be some among the past events
in that history which more directly determine the nature of the present agitation
than others. Thus when we strike a match, the movements we make and the
sound of the scrape are present stimuli. But the excitation which results is different from what it would be had we never struck matches before. Past strikings
have left, in our organization, engrams, residual traces, which help to determine
what the mental process will be. For instance, this mental process is among other
things an awareness that we are striking a match. Apart from the effects of similar
previous situations we should have no such awareness. Suppose further that the
awareness is accompanied by an expectation of a flame. This expectation again
will be due to the effects of situations in which the striking of a match has been
followed by a flame. The expectation is the excitation of part of an engram
complex, which is called up. by a stimulus (the scrape) similar to a part only of
the original stimulus-situation.
" . . . An engram is the residual trace of an adaptation made by the organism
to a stimulus. The mental process due to the calling up of an engram is a similar
adaptation: so far as it is cognitive, what it is adapted to is its referent, and is
what the sign which excites it stands for or signifies.
" The term 'adapted,' though convenient, requires expansion if this account is
to be made clear-and to this expansion the remainder of the present chapter is
devoted. Returning to our instance, we will suppose that the match ignites and
that we have been expecting a flame. In this case the flame is what we are
adapted to. More fully, the mental process which is the expectation is similar to
processes which have been caused by flames in the past, and further it is ' directed
to ' the future. If we can discover what this ' directed to ' stands for we shall have
filled in the chief part of our account of interpretation.
" Besides being ·' directed to ' the future our expectation is also ' directed to '
flame. But here ' directed to ' stands for nothing more than 'similar to what has
been caused by.' A thought is directed to flame when it is similar in certain respects to thoughts which have been caused by flame. As has been pointed out
above, we must not allow the defects of causal language either to mislead us here
or alternatively to make us abandon the method of approach so indicated. We
shall find, if we improve this language, both that this kind of substitute for
' directed to ' loses its strangeness, and also that the same kind of substitution will
meet the case of ' direction to the future ' and will in fact explain the ' direction '
or reference of thinking processes in general.
"The unpurified notion of cause is especially misleading in this connection since

258

JOHN A. OESTERLE

and Richards appears to remain wholly within instrumental
signification. All signs, for Ogden and Richards, are instrumental signs; all signs are subject to " interpretation." 84 Hence
their difficulty in attempting to elucidate the connection between Thought and Referent. Because they recognize only
instrumental signs, they cannot treat the relation of Thought
and Referent semantically; hence the departure from semantics
at this point and the quite arbitrary positing of the behavioristic presumption. Behaviorism, purified or unpurified, cannot
use signs intelligibly.
The semantics of John of St. Thomas, on the other hand, is
concerned only incidentally with instrumental signification.
The whole point and force of his analysis is to distinguish and
recognize the role of formal signification. The formal sign, of
course, is only the semantic way of understanding the concept,
just as the instrumental sign is the semantic way of understanding words or any extrinsic symbols. In moving to the
level of formal signs, then, we depart from the more obvious
part of semantics and enter the part intimately connected with
the knowing process. It is perhaps for this reason that current
semantic analysis is inadequate, since it has no means of recognizing the formal sign. As a result, today's semanticists adopt
the expected course of denying or ignoring the role of the formal
it has led even the hardiest thinkers to shrink from the identification of 'thinking
of' with' being caused by.' The suggestion that to say' I am thinking of A' is the
same thing as to say ' My thought is being caused by A,' will shock every rightminded person; and yet when for ' caused ' we substitute an expanded account,
this strange suggestion will be found to be the solution . . . " (pp. oil-55) •
It is, perhaps, hard to conceive of a more burdened explanation.
•• " If we stand in the neighborhood of a cross road and observe a pedestrian
confronted by a notice To Grantchesterrdisplayed on a post, we commonly distinguish three important factors in the situation. There is, we are sure, (1) a Sign
which (it) refers to a Place and (8) is being interpreted by a person. All· situations in which Signs are considered are similar to this." (Ibid., p. fll.)
Contemporary writings agree in general on the need of such " interpretation " in
all signs. Cf. C. I. Lewis, Mind and the World Order (New York, 19it9), especially Chapter III. For a misunderstanding of the " interpretation " of Aristotle's
De Interpretatione, cf. Charles W. Morris, Foundations of the Theory of Signs
(University of Chicago Press, 1988), p. SO. Vd. on this point St. Thomas, De
Interpretatione, Book I, lect. 1, n. S.

ANOTHER

APPROACH

TO THE PROBLEM

OF MEANING

259

sign. By reason of their so doing, the problem of knowledge
for them becomes insoluble or non-existent. For all instrumental signification, by the nature of the case, must remain
inadequate, since it is a consequence of knowing. It shows only
the expression of knowing, not knowing itself. Formal signification, on the contrary, is the signifying in the knowing process
itself: it is the relation of " Reference " to " Referent," the
nexus of the mind and object. But we must then recognize
that here we enter the dimension of the problem of knowledge
and go beyond the problem of signification. The formal sign,
the concept, can be understood ultimately only in terms of how
there is any knowledge at all.
However, the insufficiency of the instrumental sign, which,
negatively, shows the need of the formal sign, can be indicated.
Any instrumental sign, by the nature of the case, involves
ambiguity. This is what is meant by "interpretation " for,
being that kind of sign-being only instrumental-it must be
interpreted since it ·can signify more than one thing. The
instrumental sign depends for its signification, not upon itself,
but upon the signification it is expressing. Hence it is the signification it is expressing which must be obtained in communication. But to obtain the signification the instrumental sign is
expressing is to go beyond the instrumental sign itself. Since,
then, the instrumental sign is only the extrinsic expression of
signification, there is nothing to prevent one and the same
instrumental sign from expressing different significations. If,
there were only instrumental signs there would be
inescapable ambiguity, and hence no communication would be
possible; there would be only an endless regress of ambiguous
signs. Communication, then, depends upon formal signs, which
is only another way of saying that instrumental signs, even to
be signs at all, must depend upon formal signs.
This may be put more clearly by taking words as instances
of instrumental signs and concepts (notions, ideas) as formal
signs. Words are essentially ambiguous (which, of course, is
not the same as meaningless) . Any word, as a word, need not
express the signification it does-this is the sense of the ad

260

JOHN A. OESTERLE

placitum. Nor need any word, as a word, express only the
one signification it may in a particular case express. One and
the same word, or one and the same group of words, may
signify various things; it all depends upon the precise signification the user of the words intends to convey through the words.
Nor does the user of the words depend wholly upon the words
for what he wishes to express through them; if he did, he himself would also be lost in ambiguity. But he knows what he is
signifying through words which may be ambiguous to others.
This involves the concepts or notions which he has and which
he is expressing with some arbitrariness in words. Thus it is
this signification, the concept, which he intends to signify
instrumentally to someone else. Hence, communication is possible only in formal signs expressed instrumentally, and not
only in instrumental signs alone.
The role of the formal sign can be shown more positively
by the use of a diagram. The triangle of Ogden and Richards
appears to be an over-simplification, as it would be in ignoring
the problem of knowing and the role of the formal sign. In
taking account of this, the diagram might be something like
the following. (See Fig. II.)
Starting with instrumental signs (the most obvious), the
diagram makes· clear the arbitrary (ad placitum) connection
of instrumental signs and formal signs. Several instrumental
signs are arrowed to the formal sign to indicate there is not a
one-to-one correspondence. The same formal sign (concept)
may be expressed by different instrumental signs. The reverse
would also hold: one instrumental sign may express different
formal signs. This emphasizes the arbitrariness involved in
this relation. The truncated arrow leading from the instrumental signs to the object shows that only an indirect relation
is there.
The formal sign (the concept) signifies naturally and directly
its signified, the object. This relation is direct and natural
because of the complete dependence of the formal sign upon the
object, i. e., the formal sign takes its whole being in representing the object, and hence the sense in which formal signification

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

POVv'ER

objechun)

FORMAL-

SIGN

_{!lgf..:rgct

(CONCEPT)

OBJECT

-

CV4trious ins tnc.mevdnl siS"&
$4(C:/j Q.S -.JOYds)

(The froc
w

zth QYYOW' SOLI'\3 fYo I'Y\

Object
pv-essed
Fo.,. Comm u. ni ce>.!iol'l.

poweY".)

FIG. TI.

l ns

to .species
on

tm-

JOHN A. OESTEIU.ll}

is the same for all. The dotted line running from the forma]
sign to the knowing power indicates that this representation of
the object is to the knowing power. There is no "interpretation " involved in this signification, hence the necessity of
having one continuous line running from the object through the
formal sign to the knowing power. The line is dotted from the
formal sign to the knowing power to show the attaining of the
knowing power " in obliquo " by the formal sign. The line and
dotted line from object to knowing power (really one line) illustrates the comprehensive relation involved in the sign, knowing power, and signified which John of St. Thomas elaborates so
extensively. The arrow extending from the formal sign to the
knowing power indicates the sense in which the formal sign
can be related to the knowing power distinct from its relation
to the object (the sense of the double relation); here, however,
" signum respicit potentiam directe ut obiectum, non formaliter
ut signum." The point of all this is always the objectivity of
knowing.
Finally, lines are drawn from the knowing power to indicate
the other elements involved in the whole knowing process, the
impressed species and the act of knowing, both of which are
prior to the formal sign which is the term and manifestation of
the knowing power. The arrow extending from the object to
the impressed species is the last point in terms of signification,
but the first point in terms of knowing. For the object inaugurates the whole process by the impression of its species
upon the knowing power which, aroused into act, manifests its
likeness of the object in the formal sign, the term of the
knowing process; then, we signify instrumentally.
It is at this point and in terms of this sketchy diagram that
we can see somewhat the extent of the original "problem of
meaning." The holders of the principle of verification as the
principle of meaning do not even get to the recognition of
instrumental signs; they are entirely in reverse since they must
suppose, to be intelligible, that words as such are not signs since
their significance must yet be obtained by verifying in some
way. Ogden and Richards recognize instrumental signs and

ANOTHER APPROACH

TO THE PROBLEM OF MEANING

see how they must already have significance, since it is when
"a thinker makes use of them that they stand for anything."
But, in seeing this, they do not likewise see the need of more
signification or, perhaps better, the need of signification different from instrumental signification. For this hiatus, they
rely upon a purified behaviorism which, as a matter of fact, is
outrageous semantically.
But it is here that we also see how we have to pass beyond
the level of semantics itself and into the problem of knowing.
The formal sign, while excellent semantics, is understandable
only in terms of knowing since it is a part of it. The " problem
of meaning," then, becomes intelligible as the problem of signification while the problem of signification becomes intelligible
fully in the .problem of knowledge.
" Igitur facere cognoscere latius patet quam repraesentare, et
repraesentare quam significare." This is the semantics of John
of St. Thomas.
JoHN A. OESTERLE

9

BOOK REVIEW
Principles for Peace: Selections from Papal Documents-Leo XIII to Pius
XII. Edited by REv. HARRY C. KoENIG. Milwaukee: Bruce, 1948.
Pp. :xxv + 894, with ip.dex. $7.50.
We must be deeply grateful to the Most Reverend Members of the
American Hierarchy who serve on the Bishop's Committee on the Pope's
Peace Points for undertaking to present to us this generous volume of
Papal documents, which can serve as a sure guide for Catholic thinking
on peace and the making of peace. The words of the Holy Fathers from
Leo XIII to Pius XII are directed for the most part to the Catholics of
the world; on Catholics rests the burden of bringing peace to the world.
As Pius XII boldly stated in his message last Christmas: " The progress
of mankind in the present confusion of ideas has been a progress without
God and even against God; without Christ and even against Christ. In
saying this we do not wish or intend to offend the erring ones; they are and
remain our brethren. It is fitting, however, that Christians reflect on that
share of responsibility which belongs to them for the P.,esent afflictions.
Have not many Christians made concessions to those false ideas and ways
of life which have been so many times disapproved of by the teaching
authority of the Church? "
Catholics, then, above all others should ponder over and study carefully
these words of Christ's Vicars on earth. First of all, they should with
grateful hearts humbly thank Almighty God for having so disposed the
ways of His Providence that in the crises of the past decades we have had
such leaders as Leo XIII, Pius X, Benedict XV, Pius XI, and Pius XII.
The rest of us have had a difficult time trying to follow where they led; in
fact, we have for the most part fallen far behind them, either ignoring
their appeals or timidly apologizing for their audacity. Perhaps this
grouping of their inspired utterances within the covers of one volume may
arouse us from our lethargy.
Secondly, Catholics should draw great comfort from this succession of
Papal documents.. Since the outbreak of the war numerous writers have
appeared in books, magazines and newspapers with critical analyses of the
evils that precipitated the conflict. Place alongside these diagnoses some
of the warnings of Leo XIII: they read like prophecies, until one remembers that a Catholic thinker does not have to recur to the trial and error
method nor is he bound down by the experience he can gain in his own
short lifetime; rather he has behind him the wisdom of centuries, above
him the wisdom of God, with which he can without difficulty predict rather
accurately the outcome of men's weary journeying away from God and

264

BOOK REVIEW

265

Christ. This prophetic tone is especially discernible in the writings of Leo
XIIT; perhaps because we can so easily verify their fulfilment. In view
· of this we should not accuse the present Pontiff of pessimism when he
threatens future war and destruction if the voice of Christ and His Church
remains unheeded. God could not be so unmerciful as to give us peace
while we still reject Him and His Son. The world is on the wrong road;
as· yet there is little evidence that it intends to return to the right road:
why then be optimistic?
The reader will find in this volume a minute analysis of the causes of
war and of division among men; causes that are individual, social and
international. There are, among others, egoism, envy, greed, hatred, false
liberalism, unequal distribution of economic goods, diversity of language.
With the exception of the last, they can all be remedied, for they all spring
from perverse human wills. In these pages you will find no hopeless falling
back on determinism, economic, geographic, political, historical or what
you will. The Popes place the blame squarely on the shoulders of human
beings; they do not hesitate (and here they are practically alone) to remind the rulers of the world of their obligation in conscience and before
God to put an end to the causes of .war. Many times we are tempted to
doubt the sincerity of our rulers; we have heard so many reasons assigned
for the past war besides the one that was proclaimed publicly. It is helpful, then, to have the reassurance of the supreme moral teacher of Christendom that while we may be fooled, God is never fooled; His judgments
fall upon governors and governed alike and our chief obligation is to make
certain that we do our part in bringing about ultimate peace.
There are many other important reminders for Catholics in these pages.
In a letter to Cardinal Lorenzo Nina, the new Secretary of State, Leo XIII
recalls a previous message he had delivered to the world: " ... We said
that the chief reason of this great moral ruin was the openly proclaimed
separation and the attempted apostasy of the society of our day from
Church, which alone has the power to repair all the evils
Christ and
of society. . . . From this it was easy to conclude that if in past ages the
Church was able to bestow upon the world such signal benefits, she can
also do it most certainly at present; that the Church, as every Catholic
believes, being ever animated by the Spirit of Christ-Who promised her
His unfailing assistance-was by Him established teacher of truth and
guardian of a holy and faultless law; and that, being such, she possesses
at this day all the force necessary to resist the intellectual and moral decay
which sickens society, and to restore the latter to health."
We must have our post-war plans; we should not be too sanguine of
their success. There is only one plan that has any certitude about it, the
plan that is embedded in the apostolic mission of the Catholic Church.
When the determining majority of the world are united to Christ and to

His

BOOK REVIEW

His Church there will be some hope of permanent peace. Only the great
of this world can sit down at the peace table and draw up the plans for
peace; only the little ones can make peace come into the world. The
great could find much wisdom in the pages of this volume; the little ones
can discover the secret of peace making, which ultimately rests in their
hands. At the beginning we quoted from the present Holy Father's 1948
Christmas message (which is not included in this book); we may conclude
with the continuation of that citation: " Reflection on yourselves and
your deeds, and the humble recognition of this moral responsibility will
make you realize and feel in the depths of your souls how necessary it is
for you to pray and work in order to placate God and invoke His mercy
and to participate in the salvation of your brethren." That is not a very
complicated peace plan.
JAMES

M. EGAN, O.P.

BRIEF NOTICES

Tomas de Aquino y la Psicopatologia. By DR. E. EnuARDo :KRAPF. No.2
in the series of monographs of the" Index de Neurologia y Psiquiatria"
published by R. Orlando. Buenos Aires: " Editorial Index." 1948.
Pp. 48, with bibliography. 2 pesos.
Much has been written concerning St. Thomas' normal psychology. His
thought in the field of psychopathology, or abnormal psychology, .remains
to date relatively untouched. This is due in large measure, as the author
notes, to the fact that many capable historians of psychiatry acknowledge
in passing St. Thomas' merits as a philosopher, but fail to concede him
even the smallest niche among psychopathologists. Zilboorg is a recent
prominent member of this class. Others, among whom might be mentioned Kopp, while recognizing St. Thomas' importance to the science,
have written only abbreviated treatises based on works falsely attributed
to the medieval Doctor.
Dr. Krapf strives to show the extent to which modern psychopathologists
are indebted to St. Thomas. This he does by indicating with pertinent
quotations the similarity between many basic tenets proposed seven hundred years ago and those held today. Observations on pathogenic processes,
the author relates, that are now associated with Freud and HughlingsJackson are to be found at least in principle in the writings of St. Thomas,
e. g., " Quando intellectus non dominatur, agunt animalia secundum phantasiam " (De Anima, 3, 6) . Likewise, a similarity exists between Freud's
fundamental concept of two forces or instincts, the sexual and the aggressive, and St. Thomas' considerations regarding the concupiscible and the
the light of equivalents for the latter used by modern French Scholastics:
" appetit de conquete " and " appetit de combat." However, it is to be
understood that St. Thomas didn't ascribe to those two appetites the
omnipotence that Freud postulated for the sexual and aggressive tendencies.
Boring, the eminent historian of experimental psychology, names the
French physiologists of the eighteenth century as " the logical and perhaps
actual progenitors of the James-Lange theory of emotion." Lange's theory,
however, with its stressing of vasomotor changes, has just as logical a forebear in that proposed by St. Thomas. Substitute the Scholastic term
passion for emotion, the word heart for circulatory movements of the blood,
and we find the two opinions practically identical.
Part of the criticism levelled against Kopp can be applied to Dr. Krapf's
monograph. It is far too brief, though it will serve as an excellent outline
for further study for those interested in psychiatrical problems. In reply
to his justly sharp observation about the lack of writings devoted to the

268

BRIEF NOTICES

study of St. Thomas' opinions in psychopathology, we will here presume to
refer the reader to A Theory of Abnormal Cognitive Processes written by
the Rev. Dr. Robert E. Brennan, 0. P. This work based on principles of
It has, aside
St. Thomas was published in Washington, D. C. in
from its many other merits, a more extensive bibliography than is to be
found in Dr. Krapf's treatise.

Mediaeval Studies: Vol. V, 1943. Toronto, Canada: Pontifical Institute
of Mediaeval Studies. Subscription: $5.00.
The fifth volume of Mediaeval Studies contains the following series of
articles: "The Handbook of Master Peter Chancellor of Chartres," by V. J.
Kennedy, C. S. B.; "Sur le Doctrine de l'Aseite divine," by J. Maritain;
" A List of Photographic Reproductions of Mediaeval Manuscripts in the
Library of the' Pontifical Institute of Mediaevel Studies, Part II-Authors," by R. J. Scollard, C. S. B.; "The Logos as a Basis for a Doctrine of
Providence," by M. M. Marcia, I. B. V. M.; "Greek Works translated into
Latin before 1350" (continuation), by J. T. Muckle, C. s:B.; "Tlie Conception of Substance in the Philosophy of the ' Ikwan as-Sefa ' (Brethren
of Purity)," by Emil L. Fackenheim; "A Thomistic Glossary on the Principle of the Pre-eminence of a Common Good," by I. T. Eschmann, 0. P.;
" Maistre Nicole Oresme, Le Livre du Ciel et du Monde," Text and Comentary (continued) Livres III et IV, with a Critical Introduction by A. D.
Menut and A. J. Denomy; 0. S. B.

Traditio: Studies in Ancient and Mediaeval History, Thought and Religion,
Vol. I, 1943. New York: Cosmopolitan Science & Art Service Co.,
Inc. Subscription Price: $6.50. Single copies: $7.50.
Among the outstanding articles in this latest periodical dedicated to historical research are the following: " Orientations theologique chez Saint
!renee," by Th.-Andre Audet, 0. P.; "Oriental Influence in the Gallican
Liturgy," by Joannes Quasten; "Missa Grecorum, Missa Sancti Johannis
Chrisostomi," by Dom Anselm Strittmatter, 0. S. B.; "Studien zur Theologie des zwolften Jahrhunderts,': by Artur Landgraf; "The Notitia Intuitiva of Non-Existents according to William of Ockham," by Philotheus
Bohner, 0. F. M. In the Preface the Editors explain the purpose of this
new periodical: "Studies in ancient and mediaeval history, thought and
religion: in this first volume, they are taken from the fields of Classical as
well as Christian Antiquity, of Liturgy and Patrology, of Historiography,
Scholasticism, Canonical Jurisprudence, and Political Theory. This selection of departments of scholarship which are but too often anxiously segregated will convey to the reader the general program which was in our mind
when we chose for the new enterprise the name Traditio: it represents an

BRIEF NOTIClllS

effort toward comprehensive knowledge of all the living forces, forms, institutions, and ideas which have made, both .in the Church and in secular
society, the texture of history something more than a mere deposit of
dates and facts." Despite this explanation, we have some regret that the
name Traditio was chosen; it is for the Catholic thinker the name of the
vital principle inherent in the Catholic Church, which makes her the
supreme Teacher of Mankind under the direction of the Holy Spirit. Sacred
Scripture, the writings of the Fathers and Doctors of the Church, other
ancient writings and monuments ·are merely witnesses to this vital Tradicentury can only be studies of the
tion. Articles in a periodical of the
witnesses to Tradition; the Church herself is the only. means accessible for
the accurate determination of Tradition. In any other field of research, the
use of the word Traditio would not have been so misleading.

The Man from Rocca Sicca. By REGINALD M. CoFFEY, O.P. Milwaukee:
Bruce Publishing Co., 1944. Pp. xi+ 140. $1.75.
The author .of this new life of St. Thomas Aquinas set out to present
the man, who was also a scholar and a saint. Much has been written on
Thomas the Scholar and his thought. Something has been done on Thomas
the Saint. However, we often look and look in vain for a straightforward
account of the life of St. Thomas. We have it in this work. It will be an
aid also to those who are interested in the thought of St. Thomas, for the
author has carefully made note of the literary activities of St. Thomas
during the course of his life. There is no false separation in this book;
Fr. Coffey is very careful to show that Thomas was the man he was, but
he was a scholar and a saint.

BOOKS RECEIVED
S.M. C. Once in Cornwall: Legends of Saints and Dragons. New York:
Longmans, Green & Co., 1944. Pp. 179, with index. $2.00.
Hughes, E. J. The Church and the Liberal Society. Princeton, New
Jersey: Princeton University Press, 1944. Pp. xv + 307, with index.
$3.00.
Hughes, Philip. The Popes' New Order. New York: The Macmillan Co.,
1944. Pp. viii + 331, with index. $2.50.
Manning, W. F. (Editor). The Life of St. Dominic in Old French Verse
(Harvard Studies in Romance Languages, Vol. XX). Cambridge:
Harvard University Press, 1944. Pp. xiii + 358, with index. $4.00.
Mauriac, F. The Eucharist. (Translated by M. Dufrenoy.) New York:
Longmans, Green & Co., 1944. Pp. 75. $1.50.
Moore, P. S. & Dulong, M. Sententiae Petri Pictaviensis 1. (Publications
in Mediaeval Studies, VII.) Notre Dame, Ind.: University of Notre
Dame Press, 1943. Pp. lxii + 326, with indices.
Nash, A. S. The University and the Modern World. New York: The
Macmillan Co., 1944. Pp. xxiv + 312. $2.50.
Reardon, J .. J; Selfishness and the Social Order. (Catholic University of
Washington, D. C.:
America Philosophical Series, Vol. LXXVII.)
Catholic University Press, 1943. Pp. xiv + 220.
Rosalia, Sister M. Teaching Confraternity Cla8ses. Chicago: Loyola University Press, 1944. Pp. xi+ 257, with index. $1.00.
Thomas, G. F. (Editor). The Vitality of the Christian Tradition. New
York: Harper & Bros., 1944. Pp. xi+ 358. $3.00.

!t70