Jacques Maritain Center: Thomistic Institute

Aquinas on Measure

Alice Ramos
St. John's University
Jamaica, New York

The notion of measure in Aquinas seems to be omnipresent; one has only to consult a Thomistic database to realize the pervasiveness of this concept throughout Aquinas's works; despite this fact, however, relatively few studies of it have appeared in Neo-Scholastic metaphysics.(1) A discussion of measure is of central importance in Aquinas' metaphysics of infinite and finite being, in the relationship of creatures to God, and in the ordering of all things to their end. The movement of the procession of creatures from God and their reversion to Him both involve measure;(2) the measure theme is thus closely associated with the Neo-Platonic doctrine of circulatio, according to which every effect turns back by nature to the cause from which it originates, for in its likeness to the source lies the perfection of the effect.(3)

While at the metaphysical level Aquinas is perhaps especially indebted to Pseudo-Dionysius and to the Book of Causes for his development of the measure theme,(4) in questions of epistemology Aquinas relies heavily on Aristotle. Because of the epistemological relevance of this theme to his metaphysics, in particular to the relationship of creation to the divine intellect, I will first draw attention to Aristotle's importance in Aquinas's thought on measure, and then proceed to consider the pivotal role given to the measure theme in Thomas's metaphysics. My interest in what measures beings will also extend to what measures them in activity and thus measures the way of their returning to their source. The return of creatures to their origin, their longing for perfection, is made possible by their continual approach, their approximation, to the measure.

In his commentary of Aristotle's remarks on knowledge as the measure of things and as measured by things, Aquinas admits that knowledge is somewhat like measuring, since measure is defined as a principle of knowing, that which makes known the quantity or intensity of a thing. However, Aquinas maintains that it is truer to say that the mind is dependent on the object of knowledge and is thus measured by it, for a thing is measured by that on which it depends.(5) When we know something, we are being measured by the object, since the latter acts as a measuring instrument applied to us from the outside. Just as we apply a ruler to measure the length of a line, so our knowledge is being measured by the object outside us, rather than our measuring the object. The only case in which human knowledge measures things, according to Aquinas, is in artistic creation, where our knowledge serves as the measure of the object produced.(6) Aquinas seeks to safeguard the objectivity of knowledge by arguing that beings are independent of our knowing them, that our knowing them cannot be their measure in any absolute sense, and that it is the independent beings themselves which determine or measure our knowledge.(7) We do, however, also consider knowledge not only from the side of the object but also from the side of the subject, for things are known according to the mode of the knower, of the recipient. In knowing, the human soul is passive before the object, for it is not constructing or changing the object; the action of knowing remains within the soul; the receptivity of the soul consists in its passing from first act to second act or activity. The passing of the human soul to the act of knowledge is only made possible through its dependence on the object. The latter is therefore measuring the knowing subject and thus remains unchanged as the soul actively receives it. Once again, the object is the measure of our knowing; our knowledge is not the measure of things.(8)

When we turn, however, from Aquinas's psychology or theory of knowledge to his discussion of the relationship of creatures to God, we find the measure theme developed from Neo-Platonic sources. Creatures are related to the divine intellect, to absolute being. Given the simplicity of the divine essence, being and knowing in God are identical, and the beings He creates are known and measured by Him. According to Aquinas, "The divine intellect is, as the first measure, not measured; a natural thing both measures and is measured; but our intellect is measured, and measures only artifacts, not natural things."(9) Created realities are therefore placed between the divine intellect, measure of all that is, and the human mind, measured by created beings and ultimately by the divine mind. Aquinas therefore describes the divine understanding as "the measure and cause of every other being and every other intellect."(10) Once established that God is the universal cause of beings, Aquinas concludes that just as the truth of our intellect is according to its conformity with its principle, that is, to the things from which it receives knowledge, that truth of those same things is in turn according to their conformity with their principle, which is the divine intellect. The relationship of the human intellect to its objects can then be used as an analogy for considering the relationship of creatures to their cause. The one-sided relationship between the human mind and its objects, whereby those objects are the measure of the mind, without being changed in their being when known, serves as an analogy for the one-sided relationship between the divine intellect, the absolute measure of all created being and intelligility, and the things to which God has given being. Although the analogy may not be perfect, it does provide us with some metaphysical understanding of the dependence of created beings on the infinite being.

Aquinas explains the relationship between creation and God as a real relation, since creatures depend on God as the principle of their being, whereas in God the relation to the creature is only a relation of reason. Just as creatures, finite participations in being, cannot modify the infinite being from which they originate, so also the human subject in being actualized by the objects it knows cannot modify or structure the objects themselves. The subject-object relationship does therefore provide some understanding of the relationship which holds between finite and infinite being.(11)

As mentioned before, Aquinas's development of the measure theme in his metaphysics derives from Neo-Platonic sources, there is, however, another idea from Aristotle which has an important place in his metaphysics, namely, that the unit is the true measure in the genus of quantity. This idea will be developed by Aquinas in Neo-Platonic fashion: the One is the measure of all that is, and is present to each being in an analogous way, as unity is present in each number.(12) In Aquinas's account of the hierarchy of being, God is invoked as the measure of the scale: a created being has its place or grade in the scale as it approaches to God and recedes from potentiality and non-being. What is first, simplest, and most perfect in each genus is said to be the measure of everything else in that genus.(13) As the most perfect and simple being, God is the measure of all substances, as He is also the measure of all accidental being. Just as unity is the measure in numbers, so analogously God is the measure of all things in all genera and not simply the principle or perfection of one given genus.(14) Aquinas insists that God is not a member of any genus: He is not a measure proportionate to anything; God and creatures are not in the same genus.(15) God is called the measure of all things, insofar as everything has being and according to its being approaches Him.(16) All beings other than God which are substances have some sort of composition and therefore recede from the divine simplicity.(17) The mode of being of each creature is a contracted participation in the perfection and being of God. The creature as a finite mode of being is the causal effect of the infinite measure, of what is maximally being. Since the being of creatures is contracted or determined by their essence, creatures exist only by participation, and thus although there is a similarity between God and creatures, there is always an infinite distance between them.(18)

What is by participation is caused by what is essentially. Being by essence, Being itself, is the Neo-Platonic One from which proceed in an orderly way a multiplicity of beings, each of which takes its place or grade in the scale of being according to its closeness to the Highest Being, the First Cause, which proximity determines the mode of a thing's being. All things other than the most perfect and simple being are characterized by composition which accounts for their falling away, as it were, from the divine simplicity, the One. The composite beings of matter and form, or essence and act of being, are unlike the cause whose essence is one with its being. Created beings have therefore contracted being, imperfect being; what they are is not identical with their being. As a result of this imperfection, there is then a natural desire towards a fuller actuality, a desire for assimilation to the cause from whence created beings originate.(19)

I wish now to turn from a discussion of the First Being, the One, and a hierarchy of beings which are by participation and are thus referred to a maximum being as to their measure, to a consideration again of the relation of creatures to the Divine Intellect. We spoke earlier of the divine understanding as the measure of every other being and of every other intellect. Things are termed true because of their conformity with the divine intellect. And since as we said before, being and knowing are identical in God, the beings He creates are known by Him and are thus true. The being and the truth of creatures are therefore convertible. Just as there is a hierarchy in being, there is also a hierarchy in truth.(20) The relation of creatures to the divine intellect can be understood according to the model of art. Aquinas says: "The emanation of creatures from God is as the coming forth of artifacts from the artificer. Therefore, just as from the art of the artificer the artificial forms flow into matter, so also do all natural forms and virtues flow from the ideas in the divine mind."(21) These ideas are the exemplars of all things; they are the forms to the likeness of which things are made. The likenesses of things which exist in the divine mind are the measures of the truth of all things, since a thing is said to be true insofar as it imitates that upon which it was modeled.(22) That things should be made in imitation of a model is intended by the agent. The first efficient cause thus acts by intellect, and is therefore the first exemplary cause of all things.(23) Aquinas insists that for the production of anything, an exemplar is necessary so that the effect may receive a determinate form. An artificer produces a determinate form in matter by reason of an exemplar, which he either beholds externally, or which is interiorly conceived in his mind. Since it is clear that things made by nature receive determinate forms, this determination must be, according to Aquinas, reduced to the divine wisdom as its first principle, for the order in the universe consisting of a variety of things was devised by divine wisdom.(24) In the order of being and truth, God as the first efficient and exemplary cause is the maximum, the external measure, according to which creatures participate more or less in being and truth.

The form of each thing, on the other hand, may be regarded as the intrinsic measure by which God determines how much of being a creature is to receive, that is, to what degree the creature is to participate in the likeness of God.(25) The higher the form therefore the more intense will be the act of being it receives. "Each form determines the being of a thing by mediating it in a measured/measuring way with the Being itself of God."(26) The form is therefore a measure of perfection and a participation in divine likeness; it is thus spoken of as "something divine and desirable."(27) So, to speak of the forms of things in relation to the ideas or exemplars in the divine mind enables us to understand nature as related to and dependent on divine art. "All natural things were produced by the divine art, and so in a sense are God's works of art."(28) They are related to the divine intellect as artifacts to art, and so just as the work of an artisan is said to be true insofar as it achieves the conception in the mind of the artist, so also all natural things are said to be true insofar as they each have their own form, according to which they represent divine art.(29)

Now the measure of natural things, which has also been termed here the exemplary cause, is the fullness of divine perfection.(30) The exemplar which is really identical to the divine essence, is imitated by every creature in its own way. But creatures imitate the divine essence in a deficient way, since each is a finite imitation of the infinite exemplar. Thus, each copy will fall short of the original model. Since no one creature could perfectly represent the fullness of God's perfection, it was necessary that it be represented by a diversity of things in different ways. And since things are differentiated according to the possession of diverse forms from which they receive their species, the diversity of things will then "represent, according to diverse forms the one, simple form of God."(31) Different grades of being are due to the possession of diverse forms and species. The order of forms, of grades of perfection, is constituted in relation to an Origin which possessess all perfections in unity. The diverse forms, the different grades of perfection, are in a relationship of more or less proximity to the divine exemplar, just as numbers are in relation to unity.(32) The more a thing is like the divine essence, the exemplar, the more perfect it is. As things originate from the highest being and first principle, a multiplicity of ordered beings represent what is in God in a unified and simple manner. Aquinas describes the diversity of ordered being to the One in the following way: "All perfections of things descend in a certain manner from the vertex of things, God.... And because perfect unity is found in the vertex of things, i.e., God, and the more one, the more virtuous and worthy each thing is, the consequence is that the further one recedes from the first principle, the greater the diversity and variety found in things."(33) The One and Simple effects a vertical order or hierarchy of things, and together with the diverse grades of being which the divine art brings forth for the perfection of the universe, there is also metaphysical continuity and a "wondrous connection of things." Aquinas borrows from Pseudo-Dionysius in saying: "Divine Wisdom has joined together the last things of higher degree to the first things of lower degree."(34) Many examples are given of how this connection is made at all levels of the scale of being. And it is precisely in the unity of man where the continuity and harmony of distinct levels of power and perfection are observed. Humans not only have being, but life and knowledge. Everything proceeds from the unique first principle according to a certain mutual continuity and reciprocal relation: the order of bodies touches that of souls, the latter joins the realm of intellects, and the order of intellects at its most sublime point is united to the divine.(35) The harmonious and proportionate arrangement of different beings, of different parts, thus constitutes a whole, one universe of things, where "higher things contain the lower in an unbreakable order," and where there is an "unfailing succession of things, not in the sense that there are everlasting genera but that without any gap some members follow after others as long as the course of this world lasts."(36)

Divine art is thus responsible for this hierarchical and continuous ordering of beings; like an artist who arranges the different parts of his work in different ways, God disposes and orders His creatures by putting them on different levels.(37) In this way, the diversity of beings, each in its own mode, form, or measure, imitates the divine exemplar and thus participates in the likeness of the divine essence.(38) Everything imitates the exemplar, the divine essence, or the first form, the form of forms.(39) The form of things is thus truly "something divine and desirable."

Now as we said before, natural things are called true because of their conformity with the divine intellect, because they possess a proper form according to which they imitate the divine art. Aquinas tells us that things are more true in the divine Ideas, in the Exemplary Cause or in the Word, than they are in themselves. In saying this, Aquinas is referring to the truth of things, for in the Word the truth of things is greater than it is in the things themselves.(40) For in themselves the caused always fall short in their imitation of the cause. And since the form through which a thing has being is received in matter, it is thereby limited and particularized, just as being when it is received in a specific essence is limited. As a result, the caused, the copy, desires to return to the model, to the original. The Origin and the End are identical. Creatures endowed with a certain likeness to the divine revert to the cause, to be perfectly reassimilated into their absolute exemplary source.(41) Making use of the Neo-Platonic doctrine of circulatio, according to which everything which emanates from the One returns to the One, St. Thomas writes in his Commentary on the Divine Names: "Every effect turns itself back (convertitur) to the cause from which it has come, as the Platonists say."(42) In their desire for perfection, all things turn back to the universal Exemplar, to the One. Elsewhere Aquinas says: "An effect is most perfect when it returns to its source; thus...circular motion (is) the most perfect of all motions, because in their case a return is made to the starting point. It is therefore necessary that creatures return to their principle in order that the universe of creatures may attain its ultimate perfection."(43)

In the return of creatures to their Origin, the measure theme is relevant once again, for what measures things in being will also measure them in activity, in their movement toward actualization and perfection, in the attainment of their end. As we saw above, the universe comprises a scale of perfection, a vertical order or hierarchy of beings and together with these grades of being, there is also metaphyscal continuity. Distinct individual beings in the scale are related to each other and thus constitute a unity, an order. Things are ordered to each other: they are prior or posterior to each other, and are also said to be more or less according as they approach the standard, that is, the measure, or recede from it. The standard for this ordered universe is the external measure, the exemplary cause, fullness of perfection, whereas through form, their intrinsic measure, creatures have a mode of perfection. Now this order of creatures in the universe which is due to Divine Wisdom is only one kind of order, for there is a twofold order which is found in things: the one kind, just mentioned, is that of the parts of a totality among themselves, as the parts of a house, for example, are mutually ordered to each other. The second kind of order is that of things to an end and this order is of greater importance than the first. Since order is related to reason, man's reason discovers or beholds the order of things in nature; his reason does not establish this order. Man's reason, however, not only discovers the order in the universe, it also makes a certain order. Human reason in deliberating establishes order in the operations of the will.(44) And it is this order which will enable man to perfect himself, to unite himself to the Origin, which is his end, and to bring everything else to its end. The perfection of man will thus involve an ordering of the self, such that it will produce a greater unity within man, which will bring about a closer approach to the One.

Now we have referred to the Origin of the order of caused things, according to the distinction of their natures and levels, as Divine Wisdom, the Exemplary Cause, even Divine Art. The order of the operations of things, whereby they draw nearer to their ultimate end, also proceeds from Divine Wisdom. God orders the actions of things toward their end by governing them; He provides governance and regulation for things through the providence of His wisdom.(45) So Divine Wisdom is responsible for the gradation among things which are distinct from each other and for the diversity of forms and operations which will lead creatures to their end; while the ordered scale of beings is due to the type of the Divine Wisdom which Aquinas calls the exemplar or art, the ordination of the operations of things to their ultimate end is due to the type of the Divine Wisdom named law. As Aquinas says: "Just as in every artificer there pre-exists a type of the things that are made by his art, so too in every governor there must pre-exist the type of the order of those things that are to be done by his government. And just as the type of the things to be made by an art is called the art or exemplar of the products of that art, so too the type in him who governs the acts of his subjects bears the character of a law.... Now God, by His wisdom, is the Creator of all things, in relation to which He stands as the artificer to the products of his art.... Moreover He governs all the acts and movements that are to be found in each single creature.... Therefore as the type of the Divine Wisdom, insofar as by It all things are created, has the character of art, exemplar or idea, so the type of Divine Wisdom as moving all things to their due end bears the character of law. Accordingly, the eternal law is nothing else than the type of Divine Wisdom, as directing all actions and movements."(46)

In speaking of law, Aquinas will once again have recourse to measure, since law is referred to as a rule and measure of acts; in the human person law is found in two ways: as in him that rules and measures, for the rule and measure of human acts is reason, that is, the first principle of human acts.(47) Human reason is not, however, of itself, the rule of things, but rather the principles impressed on it by nature are general rules and measures of all things that relate to human conduct, "of which the natural reason is the rule and measure, although it is not the measure of things that are from nature."(48) In the order of activity, man's reason appears therefore to be an intrinsic measure. However, in another way law is in man as in that which is ruled and measured insofar as he participates in the rule or measure. Because all things are subject to divine providence, they are ruled and measured by the eternal law; they participate in the eternal law insofar as from its being imprinted on them they derive their respective inclinations to their proper acts and ends. Now since the rational creature participates in divine providence by being provident for itself and for others, it is subject to Divine providence in a more excellent way than lower creatures, for man has a share of eternal reason by which he has a natural inclination to his due act and end, and man's participation in the eternal law is called the natural law.(49) So in addition to an intrinsic measure for human conduct, there is also an extrinsic measure: Eternal Reason or Eternal Law. In the return of creatures, and more specifically of man, to their Origin which is also their End, there are thus two measures: reason and law, just as there are two measures of creatures in their origination from the cause: form and exemplar.

Aquinas accepts from Neo-Platonism the principle that in the conversion of the effect to the cause from which it proceeds, each thing desires its good, and since the good of the effect derives from its cause, it seeks its cause as its own good; it turns to the cause through desire. What is imperfect desires the perfect.(50) Man, in particular, therefore, is perfectible. While it is true that things are said to be good in virtue of their form by which they have being, Aquinas holds along with Plato that things are said to be good in virtue of the exemplary form of the Good.(51) Everything is good in virtue of its similitude to the Good. In the effect, however, the good is not just something to be but also something to be done. Created beings strive therefore toward complete goodness; the form of a thing, its first act, can be further actualized in the accidental order.(52) From the form follows an inclination to the operation that is suitable to the thing, and this inclination is the natural appetite to the end. As Aquinas says: "...that which is less perfect always exists for the sake of what is more perfect; consequently, as matter exists because of form, so the form which is the first act can be explained by virtue of the operation, which is the second act; and, therefore, the operation is the end of created things."(53)

Now in relating the form by which the creature has being to the form of forms or the exemplary cause, we said that the effect may be considered a copy or image of the model, of the exemplar, and that it represents the exemplar, its measure, to a greater or lesser extent. In the order of created beings, man is more properly image of the exemplar because he is intelligent; nonetheless, man as image will tend to assimilate himself to the cause, to become more like the cause through his operation. Perfection of the image will thus consist in likeness to the cause through activity. Aquinas distinguishes likeness from cause in this manner: "...likeness may be considered...as signifying the expression and perfection of the image. In this sense Damascene says (De Fid. Orth., ii.12) that 'the image implies an intelligent being, endowed with free choice and self-movement, whereas likeness is said to belong to the love of virtue, for there is no virtue without love of virtue."(54) Likeness to the Exemplar necessitates therefore virtue, since virtue orders man to the good, to his end; through virtue man orders his life in accordance with reason and thus acts in agreement with his proper form, with what he is, or what might also be called his rank or order in nature. St. Thomas insists that "what is against the order of reason is properly against the nature of man as man; what is according to reason is according to the nature of man as man."(55) The order of reason contains what man ought to do to be morally good; right reason is therefore the standard or measure for moral acts, since it takes into consideration the order or rank or grade in which man falls in deciding how he should live (what we previously called the intrinsic measure, metaphysically considered), it discovers his relations to God and other creatures (his place, as it were, in the scale of being, higher or lower than other beings) and in view of these relations decides what is a good act. And as was said before, reason not only knows the order of things in nature, it also makes order in the operations of the will and also of the sense appetites. Man's will can of course reject the direction, the measure of reason.

In order that man perform operations consequent upon form, upon his rational nature, virtue is necessary. In perfecting man's powers, virtue allows the powers to fulfull their purpose, to perform operations in accordance with rational nature. Aquinas says: "... the nature of virtue is that it should order man to good. Now moral virtue is properly a perfection of the appetitive part of the soul in regard to some determinate matter. And the measure or rule of the appetitive movement in respect of appetible objects is the reason. But the good of that which is measured or ruled consists in its conformity with its rule; thus the good of things made by art is that they follow the rule of art. Consequently, in things of this sort evil consists in discordance from their rule or measure. Now this may happen either by their exceeding the measure or by their falling short of it, as is clearly the case in all things ruled or measured. Hence it is evident that the good of moral virtue consists in conformity with the rule of reason. Now it is clear that between excess and deficiency the mean is equality or conformity. Therefore it is evident that moral virtue observes the mean."(56) The mean can also be described as the good that is measured by reason. Virtue therefore allows the individual man to do just what is right, that is, the mean, what is proportionate to the individual man. Now to say that reason makes order in the will is to say that reason habituates the will to perform actions that are proper to man's place in the universe.(57) And only in respecting the original order of the universe, the arrangement of the diverse levels of beings, and more specifically his own rank or grade within the totality, can man be united to the Origin, which is also his End. Man reaches perfection, becomes more like the Exemplar "by using his reason to put order in his operations so that he will accustom himself to perform acts which will be fitting to the order he has in nature."(58) Just as the metaphysical status of things is such that they are in order, so too in the ethical realm there is an order which man makes by disposing himself in a proper way.

For man to perform actions that are in conformity with his rank or grade in the universe, man must dispose himself fittingly. Just as divine art orders the different parts to each other thus disposing them in a harmonious arrangement, an ordered whole, so man should dispose himself in order to be in a harmonious state within himself and in relation to others. As Aquinas puts it: "Mode of action follows on the disposition of the agent; for such as a thing is, such is its act. And therefore, since virtue is the principle of some kind of operation, there must preexist in the operator in respect of virtue some corresponding disposition. Now virtue causes an ordered operation. Therefore virtue is an ordered disposition of the soul, insofar as ... the powers of the soul are in some way ordered to one another and to that which is outside."(59) To be virtuous then means that man has properly ordered, related the powers within him, such that reason orders the will and the will can in turn order the lower powers of man; virtue also allows for maximum performance on the part of the activities of man's powers, thus bringing the powers and man to perfection. The proper ordering of man's powers, of his activities, through virtue, will also bring about, as Aquinas adds, man's proper ordering to what is outside, that is, to be virtuous implies good relations with others, just as in the scale of being everything is properly related, fittingly ordered. It is not strange that Aquinas, in addition to naming right reason the rule and measure of human acts should also speak of the virtuous man, of the good man, as the measure in all human affairs.(60) And the more virtue, the more will man approximate the cause; hence the virtuous man becomes a model for others.

Now when man orders his dispositions through virtue, through the rule or measure of reason, he is heeding that appeal in his nature for the order that God places in creatures.(61) There is thus no conflict between the internal measure of reason and the external measure of Eternal Law or Reason. The latter, of which man's nature participates, urges man to live in such a way that his lower potencies are ordered by his higher ones, that his life be ruled and measured, so that he not only perfect his nature but order himself to God as his end. For in the last analysis, it is the Eternal Law, Eternal Reason, which will measure our ultimate perfection, or lack of it; we will either conform to the standard or not. If we are found in conformity to the measure, then we will have perfected our nature, our truth, eminently found in the Divine Intellect and thus have reached beatitude and returned to our Origin.(62)

Finally, the measure theme in Aquinas can, I believe, also be found in another order, that of supernatural virtue, grace, and divine life, but that order provides material for the topic of a future paper.

Alice Ramos

St. John's University

Jamaica, New York


1. i. James M. McEvoy, "The Divine as the Measure of Being in Platonic and Scholastic Thought," in Studies in Medieval Philosophy, ed. John Wippel (Washington, D.C.: The Catholic University of America Press, 1986), pp. 85-116. See also of McEvoy, "Biblical and Platonic Measure in John Scottus Eriugena," in P. Morewedge, ed., Philosophies of Existence Ancient and Medieval (New York, 1982), pp.

2. ii. For a Neo-Platonic discussion of the measure theme, which concentrates on God as the measure of finite beings, as well as the procession of creatures from God and their return to Him, Proclus's Elements of Theology are an excellent source (for example, props. 39 and 117). Proclus's views reappear in both the work of Pseudo-Dionysius and in the Liber de Causis. See Theological Elements in The Philosophical and Mathematical Commentaries of Proclus, tran. Thomas Taylor (London: T. Payne & Son, 1792).

3. iii. See Jan A. Aertsen, "The Circulation-Motive and Man in the Thought of Thomas Aquinas," in L'Homme et son univers au moyen âge (Acts of the 7th International Congress of Medieval Philosophy), vol. I, Louvain-la-neuve, 1986, pp. 432-439. And M.-D. Chenu, Introduction à l'étude de S. Thomas d'Aquin (Paris: Vrin, 1954), pp. 266f.

4. iv. Cf. Aquinas's Commentary on the Book of Causes, trans. Vincent A. Guagliardo, Charles R. Hess, and Richard C. Taylor (Washington, D.C.: The Catholic University of America Press, 1996), p. 107: "[S]ince the first being gives being and infinity to intelligences, it is the measure of first beings, namely, of intelligent things, and consequently of second beings, namely, of sensible things, inasmuch as the first in each genus is the measure of that genus insofar as, by approaching it or receding from it, something is known to be more perfect or less perfect in that genus." Chapters 4 and 5 of Pseudo-Dionysius's Divine Names also deal with the measure theme: God or the Good is for Pseudo-Dionysius the measure of all creatures, but Himself is unmeasured.

5. v. See Comm. in X Met., lect. 2, nn. 1956-57: "[W]e do not know [objects of knowledge] in the same way that we know something by means of a measure. For something is known by a measure as a principle of knowledge; but things are known by sensory perception and by intellectual knowledge as by a cognitive power or cognitive habit. Therefore [the cognitive powers] are called measures figuratively, because in reality they are measured rather than measure.

6. vi. In X Met., lect. 2, n. 1959: "And if there is a science which is the cause of the thing known, it must be this science which measures that thing, just as the science of the master planner is the measure of things made by art, because anything made by art is complete insofar as it attains a likeness to the art. It is in this way that the science of God is related to all things."

7. vii. Ibid. See also in X Met., lect. 8, 2095.

8. viii. McEvoy, "The Divine as the Measure of Being in Platonic and Scholastic Thought," pp. 108-10.

9. ix. De Veritate, q. 1, a. 2, in corp.

10. x. ST I, q. 16, a. 5, resp. and ad 2.

11. xi. McEvoy, "The Divine as the Measure of Being...," pp. 110-11.

12. xii. In I Sent., d. 8, q. 4, a. 2, ad 3; cf. De Potentia, q. 7, a. 3, in corp. and ad 7.

13. xiii. In I Sent., d. 8, q. 4, a. 1, and In I Sent., Prol., q. 2, a. 2, ad 2.

14. xiv. ST I, q. 11, a. 3, ad 2: "One which is the principle of number is not predicated of God, but only of things which have being in matter. For one the principle of number belongs to the genus of mathematical things, which have being in matter, but are abstracted from matter according to reason. But one which is convertible with being is a metaphysical entity, and does not depend on matter in its being. And although in God there is no privation, still, according to the mode of our apprehension, He is known to us by way only of privation and remotion. Thus there is no reason why a certain kind of privation should not be predicated of God; for instance, that He is incorporeal and infinite. And in the same way it is said of God that He is one." And ST I, q. 11, a. 2, resp.: "One is opposed to many, but in various ways. The one which is the principle of number is opposed to multitude which is number as the measure is to the thing measured. For `one has the nature of a primary measure, and number is multitude measured by one,' as is clear from the Metaphysics. But the one which is convertible with being is opposed to multitude by way of privation; as the undivided is to the thing divided."

15. xv. ST I, q. 13, a. 5, ad 3 and q. 3, a. 6, ad 2. In both texts Aquinas emphasizes that God is not a measure proportioned to the things measured.

16. xvi. ST I, q. 3, a. 6, ad 2. See Edward Mahoney, "Metaphysical Foundations of the Hierarchy of Being According to Some Late-Medieval and Renaissance Philosophers," in P. Morewedge, ed., Philosophies of Existence Ancient and Medieval (New York, 1982), p. 169.

17. xvii. In I Sent., d. 8, q. 5, a. 1; see Mahoney, "Metaphysical Foundations...," p. 169.

18. xviii. De Veritate, q. 2, a. 3, ad 16 and a. 11, ad 4; q. 23, a. 7, ad 9. See also Mahoney, "Metaphysical Foundations...," p. 170.

19. xix. Mahoney, "Metaphysical Foundations," pp. 170-01. See also A. Ramos, "Activity and Finality in St. Thomas," in Angelicum, 1991, pp. 231-53.

20. xx. See Jan Aertsen, Nature and Creature (Leiden: Brill, 1988), p. 189.

21. xxi. In II Sent., d. 18, q. 1, a. 2.

22. xxii. See De Veritate, q. 4. See also ST I, q. 15, a. 2, resp.: "Inasmuch as [God] knows His own essence perfectly, He knows it according to every mode in which it can be known. Now it can be known not only as it is in itself, but as it can be participated in by creatures according to some degree of likeness. But every creature has its own proper species, according to which it participates in some degree in likeness to the divine essence. So far, therefore, as God knows His essence as capable of such imitation by any creature, He knows it as the particular type and idea of that creature: and in like manner as regards other creatures. So it is clear that God understands many particular types of many things, and these are many ideas." Cf. note 24.

23. xxiii. See Aertsen, Nature and Creature, pp. 164-65.

24. xxiv. ST I, q. 44, a. 3, resp. Note how these ideas or "master forms contained in the divine intelligence" (sed contra) do not posit multiplicity in God Himself: "[T]hese ideas, though multiplied by their relations to things, in reality are not other than the divine essence, according as the likeness to that essence can be shared in different ways by different things." See Aertsen, Nature and Creature, pp. 172-73.

25. xxv. Aertsen, Nature and Creature, p. 142.

26. xxvi. Rudi Te Velde, Participation and Substantiality in Thomas Aquinas (Leiden: Brill, 1995), p. 232.

27. xxvii. Aristotle, Physic. I, 9, 192a, 16-17; In I Physicorum, lect. 15, n. 135. Cf. Summa Contra Gentiles, III, chap. 97. See also Ramos, "Activity and Finality in St. Thomas," p. 232.

28. xxviii. ST I, q. 91, a. 3, resp.

29. xxix. In I Perih., lect. 3, 30. Just as the knowledge of the artisan is the measure of the artifact produced since the artifact is true to the extent that it conforms to human art, so also divine knowledge is the measure of the truth of natural things. God's knowledge is prior to His effects, just as the knowledge of the artisan is prior to his artifacts, and thus both are the measure of their creations. According to Aquinas, "That which is the measure in any given genus is most perfect in that genus.... But the divine truth is the measure of all truth. For the truth of our intellect is measured by the thing outside the soul, since our intellect is said to be true because it is in agreement with the thing that it knows. On the other hand, the truth of a thing is measured by the divine intellect, which is the cause of things.... In the same way, the truth of artifacts comes from the art of the artificer," in Summa Contra Gentiles I, chap. 62. Natural things are thus situated between God's knowledge and our knowledge; by His knowledge God is the cause of natural things from which we receive knowledge. Natural things, which give themselves, as it were, to be known, are prior to our knowledge and measure our knowledge, whereas the knowledge of God is prior to natural things and is their measure. See ST I, q. 14, a. 8, ad 3.

30. xxx. Fran O'Rourke, Pseudo-Dionysius and the Metaphysics of Aquinas (Leiden: Brill, 1991), p. 215. See ST I, q. 47, a. 1, ad 2.

31. xxxi. De Veritate, q. 2, a. 1.

32. xxxii. Summa Contra Gentiles III, chap. 97: "[D]iversity of forms must be according as one is more perfect than another: for which reason Aristotle (8 Metaph.) likens definitions, whereby the natures and forms of things are indicated, to numbers wherein species are diversified by addition or subtraction of unity, thus giving us to understand that diversity of forms requires divers degrees of perfection."

33. xxxiii. Summa Contra Gentiles IV, chap. 1.

34. xxxiv. Summa Contra Gentiles III, chap. 97.

35. xxxv. O'Rourke, Pseudo-Dionysius..., pp. 265-267.

36. xxxvi. In De Div. Nom., chap. 4, p. 277. I am using Vernon J. Bourke's translation of chap. 4, lect. 5-6, of the Exposition of Dionysius on the Divine Names found in The Pocket Aquinas (New York: Washington Square Press, 1960). See also Alice Ramos, "Beauty and the Perfection of Being," in Proceedings of the American Catholic Philosophical Association, 1997.

37. xxxvii. De Veritate, q. 5, a. 1, ad 9.

38. xxxviii. In referring to Wisdom xi.21, Aquinas understands measure, when referred to creatures, as their mode of perfection. See Summa Contra Gentiles III, chap. 97: "Thus it is said (Prov. iii. 19, 20): The Lord by wisdom hath founded the earth:.... Again (Wis. viii.I) it is said, that divine wisdom reacheth from end to end mightily, and ordereth all things sweetly. And (ibid. xi.21): Thou hast ordered all things in measure, and number, and weight, where by measure we are to understand the quantity, mode, or degree of perfection in each thing: by number, the multitude and diversity of species resulting from the various degrees of perfection; and by weight the various inclinations of things to their respective ends and operations, agents and patients, and such accidents as result from diversity of species."

In ST II-II, q. 27, a. 6, Aquinas also refers to Augustine who says that "the measure which nature appoints to a thing is its mode." See also ST I, q. 5, a. 5, sed contra and resp., the question is "Whether the essence of goodness consists in mode, species, and order."

39. xxxix. See Aquinas's Commentary on the Book of Causes, p. 130: "[S]ince the form, which is the principle of action, is, in [what is complete among us], limited and participated, it cannot act by way of creation or infusion, as does what is totally form, which in itself is totally productive of other things by a participation in itself."

40. xl. ST I, q. 18, a. 4, ad 3 and De Veritate q. 4, a. 6. See also Aertsen, Nature and Creature, pp. 180-82.

41. xli. O'Rourke, Pseudo Dionysius..., p. 235.

42. xlii. In De Div. Nom., chap. 1, lect. 3, 94.

43. xliii. Summa Contra Gentiles II, chap. 46.

44. xliv. In I Ethicorum, lect. 1, 1-2.

45. xlv. Summa Contra Gentiles III, chap. 64.

46. xlvi. ST I-II, q. 93, a. 1, resp.

47. xlvii. ST I-II, q. 90, a. 1, resp.

48. xlviii. ST I-II, q. 91, a. 3, ad 3.

49. xlix. ST I-II, q. 91, a. 2, resp.

50. l. O'Rourke, Pseudo-Dionysius..., p. 235.

51. li. Aertsen, Nature and Creature, p. 340.

52. lii. Ibid., p. 354.

53. liii. ST I, q. 105, a. 5, resp.

54. liv. ST I, q. 93, a. 9, resp.

55. lv. ST I-II, q. 71, a. 2, resp.

56. lvi. ST I-II, q. 64, a. 1, resp.

57. lvii. Frank Yartz, Order and Moral Perfection (Diss. St. Louis, 1968), p. 105.

58. lviii. Ibid., p. 137.

59. lix. ST II-II, q. 55, a. 2, ad 1.

60. lx. In IX Ethicorum, lect. 4, 1803: "Every man in fact does friendly acts for himself insofar as he considers himself virtuous, since virtue and the good man seem to be a standard for everyone. For what is the perfect being in any order of reality must be considered a measure in that order, because all other things are judged more or less perfect according as they approach or recede from what is most perfect. Consequently, since virtue is the proper perfection of man and the virtuous man is perfect in the human species, this should be taken as the measure in all man's affairs." See also ST I, q. 1, a. 6, ad 3 and ST II-II, q. 60.

61. lxi. Yartz, Order and Moral Perfection, p. 128.

62. lxii. Man's ordered powers and activities will enable him to perfect the truth of his being. The greater the perfection or goodness of the truth of man's being, the greater will be his happiness.