On That In Which Beauty Consists(c) 2013 Bart A. Mazzetti N.B. The reader will observe that on many pages where I have text in parallel columns, there is a wide gap of blank space. For whatever reason, this is the result of Scribds conversion process and not in my original. The program also does not support my SGreek font. For these and any other anomalies in the layout of the text I apologize in advance.

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TABLE OF CONTENTS I. A BRIEF CONSIDERATION OF THE PRINCIPLES OF BEAUTY. II. THE BEAUTIFUL ACCORDING TO PLATO. III. THE BEAUTIFUL ACCORDING TO ARISTOTLE. IV. ON DISPOSITION. V. ON SYMMETRY. VI. ON BEAUTY AS CONSISTING IN A DUE PROPORTION OR SYMMETRY OF THE PARTS TO THE WHOLE AND OF THE PARTS TO EACH OTHER. VII. THE BEAUTIFUL ACCORDING TO ST. THOMAS AQUINAS.VIII. ON THE PERFECT.

IX. SUMMARY STATEMENTS PERTAINING TO BEAUTY. X. SUPPLEMENT: II. ON CLARITAS OR LUSTRE IN RELATION TO GLORIA. XI. FORM AND FIGURE IN RELATION TO CLARITAS. XII. THE PRINCIPAL MEANINGS OF TO KALON AND TO AISCHROS.

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I. A BRIEF CONSIDERATION OF THE PRINCIPLES OF BEAUTY. 1. Primary Texts. Cf. Plato, Laws II (668d669e) (tr. Thomas Pangle, rev. B.A.M.):Ath. What then, if someone doesnt know what each of the bodies of the things imitated is? Would he ever know what is correctly executed in them? What I mean is something like this: [would he ever know,] for instance, whether [the statue] has the proportions of the body and the positions and arrangements of each of the parts, how many [parts] there are and how they fit next to one another in the appropriate order, and also the colors and shapes, or whether all the things have been put together in a confused way? Do you think someone can ever know these things if he is completely ignorant of what the living thing is that has been imitated? (emphasis added)

Cf. Aristotle, Metaph., XIII. 3 (1078a 311078b 6) (tr. W. D. Ross, rev. B.A.M.):Now since the good and the beautiful are different (for the former always implies conduct as its subject, while the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do [35] not expressly mention them, but prove attributes which are their results or their definitions, it is not true to say that they tell us nothing about them. The chief forms of beauty are order and symmetry [1078b] and definiteness, which the mathematical sciences demonstrate in a special degree. And since these (e.g. order and definiteness) are obviously causes of many things, evidently these sciences must treat this sort of causative principle also (i.e. the beautiful) as in [5] some sense a cause. But we shall speak more plainly elsewhere about these matters.1414

Apparently an unfulfilled promise. (emphasis added)

Cf. Aristotle, On the Parts of Animals, I. 1 (641b 16-23; 642a 14- 30) (tr. William H Ogle):And that the heaven, if it had an origin, was evolved and is maintained by such a cause, there is therefore even more reason to believe, than that mortal animals so originated. For order and definiteness are much more plainly manifest in the celestial bodies than in our own frame; while change and chance are characteristic of the perishable things of earth. [20] Yet there are some who, while they allow that every animal exists and was generated by nature, nevertheless hold that the heaven was constructed to be what it is by chance and spontaneity; the heaven, in which not the faintest sign of haphazard or of disorder is discernible! It is plain then that there are two modes of causation, and that [15] both of these must, so far as possible, be taken into account in explaining the works of nature, or that at any rate an attempt must be made to include them both; and that those who fail in this tell us in reality nothing about nature. For primary cause constitutes the nature of an animal much more than does its matter. There are indeed passages in which even Empedocles hits upon this, and following the [20] guidance of fact, finds himself constrained to speak of the ratio (logos) as constituting the essence and real nature of things. Such, for instance, is the case when he explains what is a bone. For he does not merely describe its material, and say it is this one element, or those two or three elements, or a compound of all the elements, but states the ratio (logos) of their combination. As with a bone, so manifestly is it with the flesh and all other similar parts.

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[25] The reason why our predecessors failed in hitting upon this method of treatment was, that they were not in possession of the notion of essence, nor of any definition of substance. The first who came near it was Democritus, and he was far from adopting it as a necessary method in natural science, but was merely brought to it, spite of himself, by constraint of facts. In the time of Socrates a nearer approach was made to the method. But at this period men gave up inquiring into the works of nature, and philosophers diverted their attention to political science and to the virtues which benefit mankind. [30] (emphasis added)

Cf. also Aristotle, On the Parts of Animals I. 5 (645a 23-25):(tr. William H. Ogle) Absence of haphazard and conduciveness of everything to an end are to be found in natures works in the highest degree, and the resultant end of her generations is a form of the beautiful. (tr. Hippocrates G. Apostle) Indeed, things which are formed not by chance but for the sake of something exist in the works of nature [25] most of all, and the end for whose sake a thing is formed or came to be has the rank of nobility [or beauty, to kalos].

N.B. As is clear from the mention of disorder in the first passage from Aristotle cited above, the form of the beautiful at issue here is that of taxis or order; for a thing cannot have its species when the parts of an integral whole are put together in just any way; the possession of such orderliness importing an absence of haphazard. For what the Philosopher speaks of as the primary cause, cf. Aristotle, De An., II. 4 (416a 15-20) (tr. Hippocrates G. Apostle):[B]ut a thing which is composed by nature of all [the elements] has a limit and a [certain] ratio [of elements] with respect to both size and growth, and these [i.e. limit and ratio] belong to the soul and not to fire, and to the formula rather that to the matter of the thing.1

Cf. Aristotle, Metaph., XI. 3 (1061a 29-b 3) (tr. W. D. Ross):As the mathematician investigates abstractions (for before beginning his investigation he strips off all the sensible qualities, e.g. [30] weight and lightness, hardness and its contrary, and also heat and cold and the other sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two, sometimes in three dimensions, and the attributes of these qua quantitative and [35] continuous, and does not consider them in any other respect, and examines the relative positions of some and the attributes of these, and the commensurabilities and incommensurabilities of others, [1061b] and the ratios of others; but yet we posit one and the same science of all these thingsgeometry)the same is true with regard to being. (emphasis added)

2. Comparison of texts.1

Cf. St. Thomas Aquinas, In V Meta., lect. 18, n. 5 (tr. B.A.M.): For each thing is perfect when no part of the natural magnitude, which belongs to it according to the species of its proper virtue, is lacking to it. Now just as any natural thing possesses a determinate measure of natural magnitude according to continuous quantity, as is said in the second book of the De Anima [II. 4, 416a 15ff.], so also any thing possesses a determinate quantity of its natural virtue. But, as Aristotle states, the possession of a determinate quantity of magnitude is a function of the ratio of the elements composing the thing. Consequently, inasmuch as a thing composed of elements is marked by a limit and a certain ratio with respect to those elements, it will possess those forms of the beautiful called symmetry and order. From the foregoing, one sees how definiteness arises from symmetry, which in turn involves order. See further below.

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Aristotle, Meta., XIII. 3 (1078a 371078b 1) (tr. W. D. Ross) The chief forms of beauty are order [taxis] and

Aristotle, Meta., XI. 3 (1061a 36-b 1) (tr. W. D. Ross) and [as the mathematician] examines the relative positions [tas pros allla theseis] of some and the attributes of these,

symmetry [or commensurability, summetria] and the commensurabilities and incommen[1078b] and surabilities [tas summetrias kai asummetrias] of others, [1061b] definiteness [or the limited, to horismenon], and the ratios [tn de tous logous] of others. which the mathematical sciences demonstrate in a special degree. [the relation of ratio to limit being indicated by De Anima, II. 4 (416a 15-20) (tr. H. G. Apostle): [B]ut a thing which is composed by nature of all [the elements] has a limit and a [certain] ratio [of elements] with respect to both size and growth, and these [i.e. limit and ratio] belong to the soul and not to fire, and to the formula rather that to the matter of the thing.

For an elaboration of Empedocless understanding of the ratio of the elements, cf. Aristotle, On Generation and Corruption, II. 7 (331 37-333b 22) (tr. H. H. Joachim):A further objection to the theory of Empedocles is that it makes even growth impossible, unless it be increase by addition. For his Fire increases by Fire: And [333b] Earth increases its own frame and Ether increases Ether. These, however, are cases of addition: but it is not by addition that growing things are believed to increase. And it is far more difficult for him to account for the coming-to-be which occurs in nature. For the things which come-to-be by natural process all do so either [5] always or for the most part in a given way; while any exceptionsany results which are in accordance neither with the invariable nor with the general ruleare products of chance and spontaneity [luck]. Then what is the cause determining that man comes-to-be from man, that wheat (instead of an olive) comes-to-be from wheat, either invariably or generally? Are we to say Bone comes-to-be if the elements be put together in such-and such a manner? For, according to his own statements, nothing comes- [10] to-be from their coming together as chance has it, but only from their coming together in a certain proportion. What, then, is the cause of this [proportional coming together]? Presumably not Fire or Earth. But neither is it Love and Strife: for the former is a cause of association only, and the latter only of dissociation. No: the cause in question is the essential nature of each thingnot merely to quote his words) a mingling and a [15] divorce of what has been combined. And chance, not proportion, is the name given to these occurrences; 19 for things can be combined as chance has it. The cause, therefore, of the coming-to-be of the things which owe their existence to nature is that they are in such-and-such a determinate condition: and it is this which constitutes the nature of each thinga nature about which he says nothing. What he says, therefore, tells us nothing About Nature.20 Moreover, it is this which is both the excellence of each thing and its good: whereas he assigns the whole credit to the combining. (And yet [20] the elements at all events are dissociated not by Strife, but by Love: since the elements are by nature prior to the god, and they too are god.) (emphasis added)

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19 20

See Empedocles, frag. 8 Diels-Kranz. About Nature (peri\ fu/seoj) was the title of Empedocles scientific poem,

Cf. St. Thomas Aquinas, Commentary on Aristotles De Anima translated by Kenelm Foster, O.P. & Sylvester Humphries, O.P. (New Haven, 1951), Book II, lect. 8 (in part):TEXT 415b28416a18 BOOK II, CHAPTER IV, CONTINUED THE VEGETATIVE PRINCIPLE CONTINUED TWO ERRORS REFUTED Empedocles is mistaken here, adding that growth occurs in plants by their sending a root downwards, because earth is by nature below, and also upwards because of fire. 324 Nor did he understand aright up and down; for these are not for all things the same as for the Universe; but roots of plants correspond to the head, in animals, if it is permissible to identify organs by their functions. For we reckon those organs to be the same which perform the same operations. 325-7 Besides, what holds fire and earth together if they tend in contrary directions? They must come apart if there is nothing to prevent this. But if there is such a thing, it must be the soul; and be also the cause of growth and nourishment. 328 Now it seems to some that the nature of fire is the sole cause of growth and nutrition; for it certainly seems to be the only one of the bodies and elements that is self-nourishing and selfincreasing. Whence the notion that it is this that is operative in plants and animals. 329-30 It is indeed a concomitant cause, but the cause absolutely is not fire, but rather the soul. For the increase of fire is infinite so long as there is anything combustible. But there are limitations to all things that subsist naturally, and some definite principle governs their dimensions and growth. And this belongs to the soul, not to fire, and to a specific principle rather than to matter. 331-2 ST. THOMASS COMMENTARY LECTIO EIGHT 324. The Philosopher has just shown that the activities we call vegetative have their origin in the soul. He now proceeds to refute two errors on this subject, which he deals with respectively in two sections; the second of which begins at Now it seems to some that the nature of fire. In the first section he begins by stating the error, and then, at Nor did he understand attacks it. Regarding the error itself, we should note that just as Empedocles refused to explain other cases of purposeful arrangement in Nature by any natural finalityfor example he said that animals had the sort of feet they have, not in order to help them to walk, but simply because the matter of that part of their bodies happened to be arranged in that sort of way; so also the growth of living things he ascribed merely to the motion of light and heavy bodies. Observing that living things increase their size in different directions, e.g. up and downas is evident in plants, which thrust their roots down and their branches uphe said that the downward growth of plants was due to the earth in their composition, which is heavy and therefore necessarily tends downwards; whilst their upward growth was due to fire which, being light, must tend upwards.

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329. Next, at Now it seems to some, he states another theory; which, at It is indeed he then disproves. Unlike the theory of Empedocles, which put the causes of growth and nutrition in both earth and fire, this theory ascribes them only to fire. 330. The reason given is that the cause of anythings modifications or motion would appear to be whatever had such modifications or motions essentiallye.g. fire, being essentially hot, is the cause of heat in things that contain other elements as well; and in the same way earth is the cause of heaviness. Now of the elements fire alone seems to feed itself and to grow ; if we take these terms in a superficial sense. Therefore fire alone would seem to cause growth and nutrition in plants and animals. But whether fire really feeds itself and grows will be made clear later. 331. Then he attacks the above opinion. But note its grain of truth. All food has to be cooked, and this is done by fire, so that fire does play a part in nutrition, and consequently in growth also; not indeed as the principal agent (which is the soul) but as a secondary, instrumental agent. To say then that fire is a sort of concurrent or instrumental cause of growth and nutrition is true. But it cannot be the principal cause or agent, as he goes on to show. 332. The principal agent in any action is that which imposes the term or natural limit upon what is done; thus in artificial things like boxes or houses the limit or term is fixed, not by the instruments used in the work, but by the art itself. The instruments, as such, are quite indifferent as to whether they are used to produce a thing of this shape and quantity or of that. A saw, as such, can be used to cut wood for a door or a bench or a house, and in any quantity you please; and if it cuts wood in this or that particular shape and quantity, this is due to the man who uses it. Now in Nature each thing obviously has certain limits to its size and its increase; each thing grows to a certain fixed pattern. For as each species of thing requires its own accidental modifications, so it needs its own measure of quantity, though some margin must be left to material differences and other individual factors. Men are not all equal in size. But there is a limit both to their largeness and their littleness; and whatever determines this limit is the true principal cause of growth. But this cannot be fire, because the growth of fire has no naturally fixed limits; it would spread to infinity if an infinite amount of fuel were supplied to it. Clearly, then, fire is not the chief cause of growth and nutrition, but rather the soul. And this is reasonable enough, for the quantitative limits of material things are fixed by formthe specific principlerather than matter. Now the soul of a living being is to the elements it contains as form is to matter; the soul, then, rather than fire, sets the term and natural limit to size and growth.1

Cf. Aristotle, Poetics ch. 7 (1450b 341451a 15 (tr. B.A.M. based on Theodore Buckley):Further still, since that which is beautiful, whether it be an animal or anything else which is composed of certain things, should not only [35] have these things arranged, but also not just any chance sizefor the beautiful consists in size and orderhence, neither can any very small animal be beautiful; for the contemplation of it is confused, since it is effected in a1

For the related notion that a natural body is not infinitely divisible with respect to quantity, cf. St. Thomas Aquinas, In I Physic., lect. 9, n. 9 (tr. William Wallace, O.P.): Although a body, understood mathematically, is infinitely divisible, a natural body is not divisible to infinity. For in a mathematical body all that is considered is quantity, and in this there is nothing that is repugnant to division, whereas in a natural body there is a natural form that requires a determinate quantity, just as it requires other accidents. Wherefore quantity cannot be found under the species of flesh unless within certain determined limits.

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nearly insensible time; nor yet a very large animal; [1451a] for it is not contemplated at once, but its being one and a whole escapes the view of the onlookers; such as if there should be an animal of ten thousand stadia [in length]. And so, as in bodies and in animals there should be size, but such as can be easily seen; so also in plots, there should be length, but this such as can be [5] easily remembered. But the definition of the length with reference to contests and the senses does not fall under the consideration of art. For if it were necessary to perform a hundred tragedies, the performance would have to be regulated by a waterclock, as they are said to have been at one time. But the definition according to the nature of the thing is this, that the plot is [10] always more beautiful the greater it is, if at the same time it is perspicuous. But in order to define it simply, one may say, in whatever extent, in successive incidents in accordance with likelihood or necessity, a change from bad fortune to good fortune or from good fortune to bad fortune takes place, is a [15] sufficient limit of the size.

Cf. Aristotle, Top., III. 1 (116b 19-23) (ed. & tr. Loeb):And that is better which is inherent in things which are better or prior or more highly honored; for example, health is better than strength or beauty. For health is inherent in moisture and dryness and in heat and in cold, in a word in all the primary constituents of the living creature, whereas the others are inherent in the secondary [constituents]; for strength is generally considered to reside in sinews and bones, and beauty to be in a certain symmetry of the limbs.1

3. According to St. Thomas Aquinas. Cf. St. Thomas Aquinas, Summa Theol., Ia-IIae, q. 27, art. 1, ad 3 (tr. B.A.M.):To the third it must be said that the beautiful is the same as the good, differing only in account. For, since the good is what all things desire, it belongs to the account of the good that the appetite be brought to rest in it; but it pertains to the account of the beautiful that the appetite be brought to rest in the sight or knowledge of it. And for this reason those senses especially look to the beautiful that are the most knowing, namely, sight and hearing, the servants of reason, for we call sights and sounds beautiful. But in the sensibles belonging to the other senses we do not use the name beautiful, for we do not call tastes or smells beautiful. And so it is clear that the beautiful adds to the good a certain order to a knowing power, so that that is called good simply which is pleasing to the appetitebut that is called beautiful the very apprehension of which pleases.

Cf. St. Thomas Aquinas, Summa Theol., Ia, q. 5, art. 4, ad 1 (tr. B.A.M.):To the first it must be said that the beautiful and the good are the same in subject because they are founded on the same thing, namely, the form, and for this reason the good is praised as beautiful. But they differ in account. For the good properly regards the appetite; for the good is what all things desire. And so it has the account of an end, for the appetite is, so to speak, a certain movement toward a thing. But the beautiful regards a knowing power, for things which please by being seen are called beautiful. For this reason beauty consists in a due proportion,2 since the sense is delighted in things that are duly proportioned, as in things similar to itself. For the sense, and indeed every knowing power, is a certain ratio. And1

Cf. Plato, Timaeus 87 d-e (tr. B. Jowett): Just as a body which has a leg too long, or which is unsymmetrical [e] in some other respect, is an unpleasant sight. 2 Note that debita proportio primarily means having the membra or limbs of the body commensurate.

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because knowledge comes about by assimilation, but similitude [likeness] regards the form, beauty properly pertains to the notion of a formal cause.

Cf. St. Thomas Aquinas, Summa Theol., IIa-IIae, q. 180, art. 2, ad 3 (tr. B.A.M.):To the third it must be said that beauty, as has been said above, consists in a certain lustre and due proportion. Now both of these are found in reason as in a root, to which pertains both a manifesting light and the ordering of a due proportion in other things.

Cf. St. Thomas Aquinas, In I Sent., dist. 31, q. 2, art 1, c. (tr. B.A.M.):But according to Dionysius (De Div. Nom., c. 4), two things come together in the account of beauty, namely, consonance and lustre. For he says that God is the cause of all beauty insofar as He is the cause of consonance and lustre, just as we say that men are beautiful who have proportionate members and a resplendent color. To the these two the Philosopher adds a third where he says that beauty does not exist except in a sizable body (Nic. Ethic., IV.6); and so small men can be called commensurate [or well-proportioned] and good-looking, but not beautiful.

4. On bodily beauty. Cf. Cicero, Tusc. Disp., iv, xiii (tr. B.A.M.):Of the body there is a certain fitting arrangement of the members accompanied by a certain agreeableness of color which is called beauty.

Cf. St. Augustine of Hippo, City of God, XXII. 19 (tr. slightly rev. B.A.M.):For all bodily beauty consists in the agreement of the parts, together with a certain agreeableness of color. Where there is no agreement, the eye is offended, either because there is something lacking, or too small, or too large. And thus there shall be no deformity resulting from want of agreement in that state in which all that is wrong is corrected, and all that is defective supplied from resources the Creator knows of, and all that is excessive removed without destroying the integrity of the substance. And as for the pleasant color, how conspicuous shall it be where the just shall shine forth as the sun in the kingdom of their Father! Matthew 13:43 This brightness we must rather believe to have been concealed from the eyes of the disciples when Christ rose, than to have been lacking.

Cf. St. Thomas Aquinas, Summa Theol., IIa-IIae, q. 145, art. 2, c. (tr. B.A.M.):I reply that it must be said that, as may be gathered from the words of Dionysius ( De Div. Nom., c. iv), in the account of the beautiful or becoming both lustre and due proportion come togetherfor he says that God is called beautiful as the cause of the consonance and lustre of the universe. For this reason the beauty of the body consists in this, that a man have the members of his body well-proportioned, together with a certain due lustre of color. And likewise spiritual beauty consists in this, that a mans conversation, or his action, be well proportioned according to the spiritual lustre of reason.

Cf. St. Thomas Aquinas, In Dionysii de Div. Nom., cap. 4, lect. 5 (tr. B.A.M.):

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For thus we call a man beautiful by reason of an appropriate proportion in quantity and in situation and by reason of his having lustre and a bright color. And so proportionally in the rest of things it must be admitted that each thing is called beautiful insofar as it has its own kind of lustre, whether spiritual or bodily, and insofar as it has been established in a due proportion.

Cf. St. Thomas Aquinas, In IV Sent., dist. 44, q. 3, art. 1a, c. (tr. B.A.M.):I reply that it must be said to the first question that in the human body there can be a twofold deformity. In one way from the lack of any limb [or member, membri]: thus we say that mutilated things are ugly; for in them there is a lack of due proportion to the whole. And deformity of this kind, without a doubt, will not be in the bodies of the damned, since all bodies of both wicked and good will rise again whole, as was said above when the integrity of the resurrected body was treated of. In another way deformity arises from an undue disposition of the parts, either an undue quantity, or quality, or situation [or position, situ]which deformity is, moreover, incompatible with a due proportion of the parts to the whole. Concerning these kinds of deformities and like defects such as fevers and similar ailments which sometimes are the cause of deformity, Augustine remained undecided and doubtful (Enchiridion xcii) as the Master in the text says (Sent. iv, D, 44).

Cf. Marcus Tullius Cicero. De Officiis. Translated by Walter Miller. Loeb Edition (Cambridge, 1913), I. 98:For, as physical beauty with harmonious symmetry of the limbs engages the attention and delights the eye, for the very reason that all the parts combine in harmony and grace, so this propriety, which shines out in our conduct, engages the approbation of our fellow-men by the order, consistency, and self-control it imposes upon every word and deed.

5. Bodily beauty in sum. According to Cicero, of the body there is a certain fitting arrangement of the members accompanied by a certain agreeableness of color which is called beauty (Cicero, Tusc. Disp., iv, xiii). In the same vein, St. Augustine says that all bodily beauty consists in the agreement of the parts, together with a certain agreeableness of color (De civitate Dei, CXXII, xix; XI, xxii). Likewise, St. Thomas Aquinas states that the beauty of the body consists in this, that a man have the members of his body well-proportioned, together with a certain due lustre of color. For thus we call a man beautiful by reason of an appropriate proportion in quantity and in situation and by reason of his having lustre and a bright color. But note that, by a fitting arrangement of the members, Cicero presumably means the same as Plato, where the latter states that: At any rate, you will allow that every discourse ought to be a living creature, having a body of its own and a head and feet; there should be a middle, beginning, and end, adapted to one another and to the whole? (Plato, Phaedrus 264c, tr. B. Jowett) This species of beauty is that of order, and corresponds to a due disposition of parts in a whole, or disposition simply. The agreement of parts spoken of by St. Augustine, on the other hand, appears to pertain to their mutual adaptation; whereas St. Thomas speaks of a due disposition in quantity, where a part is neither too big nor too small in reference to the whole,1 and a due disposition in situation, which pertains1

Cf. Timaeus 87 d-e (tr. B. Jowett): Just as a body which has a leg too long, or which is unsymmetrical [e] in some other respect, is an unpleasant sight.

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to the order among the parts, as we have already said. Unmentioned in the foregoing texts is the possession of a due disposition with respect to shape or figure, which, like claritas, pertains to quality. 6. On deformity in the body. Cf. St. Augustine of Hippo, City of God, Book XXII:Chapter 19.That All Bodily Blemishes Which Mar Human Beauty in This Life Shall Be Removed in the Resurrection, the Natural Substance of the Body Remaining, But the Quality and Quantity of It Being Altered So as to Produce Beauty. What am I to say now about the hair and nails? Once it is understood that no part of the body shall so perish as to produce deformity in the body, it is at the same time understood that such things as would have produced a deformity by their excessive proportions shall be added to the total bulk of the body, not to parts in which the beauty of the proportion would thus be marred. Just as if, after making a vessel of clay, one wished to make it over again of the same clay, it would not be necessary that the same portion of the clay which had formed the handle should again form the new handle, or that what had formed the bottom should again do so, but only that the whole clay should go to make up the whole new vessel, and that no part of it should be left unused. Wherefore, if the hair that has been cropped and the nails that have been cut would cause a deformity were they to be restored to their places, they shall not be restored; and yet no one will lose these parts at the resurrection, for they shall be changed into the same flesh, their substance being so altered as to preserve the proportion of the various parts of the body. However, what our Lord said, Not a hair of your head shall perish, might more suitably be interpreted of the number, and not of the length of the hairs, as He elsewhere says, The hairs of your head are all numbered. Luke 12:7 Nor would I say this because I suppose that any part naturally belonging to the body can perish, but that whatever deformity was in it, and served to exhibit the penal condition in which we mortals are, should be restored in such a way that, while the substance is entirely preserved, the deformity shall perish. For if even a human workman, who has, for some reason, made a deformed statue, can recast it and make it very beautiful, and this without suffering any part of the substance, but only the deformity to be lost,if he can, for example, remove some unbecoming or disproportionate part, not by cutting off and separating this part from the whole, but by so breaking down and mixing up the whole as to get rid of the blemish without diminishing the quantity of his material,shall we not think as highly of the almighty Worker? Shall He not be able to remove and abolish all deformities of the human body, whether common ones or rare and monstrous, which, though in keeping with this miserable life, are yet not to be thought of in connection with that future blessedness; and shall He not be able so to remove them that, while the natural but unseemly blemishes are put an end to, the natural substance shall suffer no diminution? And consequently overgrown and emaciated persons need not fear that they shall be in heaven of such a figure as they would not be even in this world if they could help it. For all bodily beauty consists in the proportion of the parts, together with a certain agreeableness of color. Where there is no proportion, the eye is offended, either because there is something awanting, or too small, or too large. And thus there shall be no deformity resulting from want of proportion in that state in which all that is wrong is corrected, and all that is defective supplied from resources the Creator wots of, and all that is excessive removed without destroying the integrity of the substance. And as for the pleasant color, how conspicuous shall it be where the just shall shine forth as the sun in the kingdom of their

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Father! Matthew 13:43 This brightness we must rather believe to have been concealed from the eyes of the disciples when Christ rose, than to have been awanting. For weak human eyesight could not bear it, and it was necessary that they should so look upon Him as to be able to recognize Him. For this purpose also He allowed them to touch the marks of His wounds, and also ate and drank,not because He needed nourishment, but because He could take it if He wished. Now, when an object, though present, is invisible to persons who see other things which are present, as we say that that brightness was present but invisible by those who saw other things, this is called in Greek ; and our Latin translators, for want of a better word, have rendered this ccitas (blindness) in the book of Genesis. This blindness the men of Sodom suffered when they sought the just Lots gate and could not find it. But if it had been blindness, that is to say, if they could see nothing, then they would not have asked for the gate by which they might enter the house, but for guides who might lead them away. But the love we bear to the blessed martyrs causes us, I know not how, to desire to see in the heavenly kingdom the marks of the wounds which they received for the name of Christ, and possibly we shall see them. For this will not be a deformity, but a mark of honor, and will add lustre to their appearance, and a spiritual, if not a bodily beauty. And yet we need not believe that they to whom it has been said, Not a hair of your head shall perish, shall, in the resurrection, want such of their members as they have been deprived of in their martyrdom. But if it will be seemly in that new kingdom to have some marks of these wounds still visible in that immortal flesh, the places where they have been wounded or mutilated shall retain the scars without any of the members being lost. While, therefore, it is quite true that no blemishes which the body has sustained shall appear in the resurrection, yet we are not to reckon or name these marks of virtue blemishes.

Cf. St. Thomas Aquinas, In IV Sent., dist. 44, q. 3, art. 1a, c.: Parallel translations:(tr. English Dominican Fathers) (tr. B.A.M.)

I answer that, Deformity in the human body is I reply that it must be said to the first question of two kinds. that in the human body there can be a twofold deformity. One arises from the lack of a limb: thus we say In one way from the lack of a limb: thus we say that a mutilated person is deformed, because he that mutilated things are ugly; for in them there lacks due proportion of the parts to the whole. is a lack of due proportion to the whole. Deformities of this kind, without any doubt, will not be in the bodies of the damned, since all bodies of both wicked and good will rise again whole. Another deformity arises from the undue disposition of the parts, by reason of undue quantity, quality, or placewhich deformity is, moreover, incompatible with due proportion of parts to whole. Concerning these deformities and like defects such as fevers and similar ailments which sometimes result in deformity, Augustine remained undecided and doubtful (Enchiridion And deformity of this kind, without a doubt, will not be in the bodies of the damned, since all bodies of both wicked and good will rise again whole, as was said above when the integrity of the resurrected body was treated of. In another way deformity arises from an undue disposition of the parts, either an undue quantity, or quality, or situationwhich deformity is, moreover, incompatible with a due proportion of the parts to the whole. Concerning these kinds of deformities and like defects such as fevers and similar ailments which sometimes are the cause of deformity, Augustine remained undecided and doubtful

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xcii) as the Master remarks (Sent. iv, D, 44).

(Enchiridion xcii) as the Master in the text says (Sent. iv, D, 44).

7. The principles of deformity and of its opposite, being well-formed:Deformity in the human body is of two kinds. one arises from the lack of a limb, = lack of wholeness (defectus integritas)

another deformity arises from the undue = lack of due proportion (defectus debita disposition of the parts proportio) deformity arising from the lack of a limb: thus = lack of due proportion of the parts to the we say that mutilated things are deformed, whole because in them there is a lack of due proportion to the whole deformity arising from the undue disposition of the parts: by reason of undue quantity, quality, or situation (or position) which deformity is, moreover, incompatible with due proportion of parts to whole Hence, one may surmise that well-formedness in the human body will be of two kinds: one will arise from the possession of all the = possession of wholeness (integritas) limbs, = possession of due proportion (debita another from the due disposition of the parts proportio) well-formedness arising from the possession of = possession of due proportion of the parts to all the limbs: thus we say that wholes are well- the whole formed, because in them there is a due proportion to the whole well-formedness arising from the disposition of the parts: by reason of due quantity, quality, or situation (or position) which loveliness is, moreover, compatible with due proportion of parts to whole due = possession of due disposition in quantity = possession of due disposition in quality = possession of due disposition in situation or position = lack of due disposition in quantity = lack of due disposition in quality = lack of due disposition in situation or position

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8. On beauty in sum. beauty consists in a due proportion of the parts to the whole (= integrity or perfection) according to situation or position (= order) to each other (= consonance or due proportion) according to quantity (= symmetry, understood as commensurability) according to quality (= luster or brilliance [claritas], having to do with luminosity or intelligibility) in shape or figure (= the limited or definiteness) in color or coloring (which exists in a surface) 9. Divisions of beauty. 1. Into its species or specific parts: (a) order (b) symmetry (c) the limited or definiteness 2. Into its constituents or quasi-integral parts: (a) wholeness or integrity (b) due proportion or consonance (c) lustre or brilliance (etc.) Note here that beauty regards commensuration and what is becoming inasmuch as it consists in a due proportion of the parts to the whole with respect to quantity, which is what symmetry consists in.

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II. THE BEAUTIFUL ACCORDING TO PLATO. 1. The role of symmetry or proportion and color. Plato, Soph., 235d-e.(tr. F. M. Cornford). STRANGER: One art that I see contained in it is the making of likenesses (ei)kastikh/). The perfect example of this consists in creating a copy that conforms to the proportions of the original [kata tas tou paradeigmatos summetrias tis] in all three [e] dimensions1 and giving moreover the proper color to every part [eti chrmata apodidous ta proskonta hekastois].2 (ed. John Burnet; tr. H. N. Fowler). Stranger I see the likeness-making art as one part of imitation. This is met with, as a rule, whenever anyone produces the imitation by following the proportions of the original in length, breadth, and depth, and giving, besides, [235e] the appropriate colors to each part.3

2. Two principles of the beautiful according to Plato, Soph., 235d-e: In order to produce an accurate imitation, one must preserve the proportions of the original [kata tas tou paradeigmatos summetrias tis] in length, breadth, and depth, as well as give the appropriate colors to each part [chrmata apodidous ta proskonta hekastois].

3. The three greatest forms of the beautiful as touched upon by Plato. Cf. Plato, Laws II (668d669e) (tr. Thomas Pangle, rev. B.A.M.).Ath. What then, if someone doesnt know what each of the bodies of the things imitated is? Would he ever know what is correctly executed in them? What I mean is something like this: [would he ever know,] for instance, whether [the statue] has the proportions of the body and the positions and arrangements of each of the parts, how many [parts] there are and how they fit next to one another in the appropriate order, and also the colors and shapes, or whether all the things have been put together in a confused way? Do you think someone can ever know these things if he is completely ignorant of what the living thing is that has been imitated?41

For if the proper proportions are not preservered, then the thing will be ugly: cf. Timaeus 87 d-e (tr. B. Jowett): Just as a body which has a leg too long, or which is unsymmetrical [e] in some other respect, is an unpleasant sight. Cf. also Sophist 228b-c (tr. F. M Cornford): Str. And when things having motion, and aiming at an appointed mark, continually miss their aim and glance aside, shall we say that this is the effect of symmetry among them, or of the want of symmetry? Theaet. Clearly of the want of symmetry. Hence symmetry in the parts of the body consists in having an appropriate size relative to the wholewhich consists in hitting the mark aimed at by nature (in making a thing) or by art (in making a likeness of a thing). 2 On the role of symmetry and color in bodily beauty, see the texts of Cicero, Augustine, and St. Thomas Aquinas given below. 3 Xenos. mian men tn eikastikn horn en auti technn. esti d' haut malista hopotan kata tas tou paradeigmatos summetrias tis en mkei kai platei kai bathei, kai pros [235e] toutois eti chrmata apodidous ta proskonta hekastois, tn tou mimmatos genesin apergaztai. 4 Athnaios: ti oun ei tis kai en toutois agnooi tn memimmenn hoti pot' estin hekaston tn smatn; ar' an pote to ge orths autn eirgasmenon gnoi; leg de to toionde, hoion tous arithmous tou smatos kai

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4. In sum. whether [the statue] has the proportions of the body [= symmetry] and the positions and arrangements of each of the parts [= order] how many [parts] there are and how they fit next to one another in the appropriate order [also = order] the colors and shapes [= the limited] or whether all the things have been put together in a confused way [= lack of order]

Cf. Plato, Laws II (668d 669b) (tr. R. G. Bury):Ath. He who does not know what is done correctly would never be able to know what is done well or badly, would he? But I have not put this very clearly. Perhaps it would be clearer if put this way Kl. How? Ath. There are of course myriad images which are visible to our eye. Kl. Yes. Ath. What then, if someone doesnt know what each of the bodies of the things imitated is? Would he ever know what is correctly executed in them? What I mean is something like this: doesnt he have to know whether the imitation captures the number and the arrangement [668e] of each of the parts, how many there are and how they fit next to one another in the appropriate order, and also the colors and shapes, or whether all the things have been put together in a confused way? Do you think someone can ever know these things if he is completely ignorant of what the living thing is that has been imitated? Kl. How could he? Ath. What if we were to know that the thing that has been painted or sculpted is a human being, and that all his own parts [669a], colors, and shapes have been captured by the art? Does it follow necessarily that whoever knows about these things also readily knows whether the work is beautiful or just where it is deficient in beauty? Kl. That would mean, stranger, that all of us, so to speak, know what is beautiful in any paint-ings of living things. Ath. What you say is very correct. Isnt it the case, then, that with regard to each image, in painting and music and in all the rest, the person who is going to be a prudent judge must have three kinds of knowledge? He must know [669b] first what the thing is, and then know how correctly, and thenthe third thinghow well, any of the images of it in words, melodies, and rhythms are produced. Kl. Thats likely, anyway.

hekastn tn mern [668e] tas theseis ei echei, hosoi te eisin kai hopoia par' hopoia autn keimena tn proskousan taxin apeilphenkai eti d chrmata te kai schmata panta tauta tetaragmens eirgastai: mn dokei taut' an pote diagnnai tis to parapan agnon hoti pot' esti to memimmenon zion.

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Cf. Plato, Timaeus 87c-88c (tr. B. Jowett):There is a corresponding inquiry concerning the mode of treatment [c] by which the mind and the body are to be preserved, about which it is meet and right that I should say a word in turn; for it is more our duty to speak of the good than of the evil. Everything that is good is fair, and the animal fair is not without proportion, and the animal which is to be fair must have due proportion. Now we perceive lesser symmetries or proportions and reason about them, but of the highest and greatest we take no heed; for there is no proportion or disproportion [d] more productive of health and disease, and virtue and vice, than that between soul and body. This however we do not perceive, nor do we reflect that when a weak or small frame is the vehicle of a great and mighty soul, or conversely, when a little soul is encased in a large body, then the whole animal is not fair, for it lacks the most important of all sym-metries; but the due proportion of mind and body is the fairest and loveliest of all sights to him who has the seeing eye. Just as a body which has a leg too long, or which is unsymmetrical [e] in some other respect, is an unpleasant sight, and also, when doing its share of work, is much distressed and makes convulsive efforts, and often stumbles through awkwardness, and is the cause of infinite evil to its own selfin like manner we should conceive of the double nature which we call the living being; and when in this compound there is an impassioned soul more powerful than the body, that [88a] soul, I say, convulses and fills with disorders the whole inner nature of man; and when eager in the pursuit of some sort of learning or study, causes wasting; or again, when teaching or disputing in private or in public, and strifes and con-troversies arise, inflames and dissolves the composite frame of man and introduces rheums; and the nature of this phenomenon is not understood by most professors of medicine, who ascribe it to the opposite of the real cause. And once more, when a body large and too strong for the soul is united to a small and weak intelligence, then inasmuch as there are two desires natural to [b] manone of food for the sake of the body, and one of wisdom for the sake of the diviner part of usthen, I say, the motions of the stronger, getting the better and increasing their own power, but making the soul dull, and stupid, and forgetful, engender ignorance, which is the greatest of diseases. There is one protection against both kinds of disproportionthat we should not move the body without the soul or the soul without the body, and thus they will be on their guard [c] against each other, and be healthy and well balanced. And therefore the mathematician or any one else whose thoughts are much absorbed in some intellectual pursuit, must allow his body also to have due exercise, and practice gymnastic; and he who is careful to fashion the body, should in turn impart to the soul its proper motions, and should cultivate music and all philosophy, if he would deserve to be called truly fair and truly good.

5. On being perfect and whole according to Plato. Cf. Plato, Timaeus 32d-34b (Loeb tr.) (excerpts):[32d] ...first, that it might be, so far as possible, a Living Creature, perfect and whole, with all its parts perfect; and next, that it might be One,... [33a] He fashioned it to be One single Whole, compounded of all wholes, perfect and ageless and unailing. [33b] And he bestowed on it the shape which was befitting and akin. Now for that Living Creature which is designed to embrace within itself all living creatures the fitting shape will be that which comprises within itself all the shapes there are; wherefore He wrought it into a round, in the shape of a sphere, equidistant in all directions from the center to the extremities, which of all shapes is the most perfect and the most self-similar, since He deemed that the similar is infinitely fairer than the dissimilar. And on the outside round about, it was all made smooth with great exactness, and that for many reasons. [34a] He spun it round uniformly in the

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same spot and within itself and made it move revolving in a circle. [34b] He made it smooth and even and equal on all sides from the center, a whole and perfect body compounded of perfect bodies, And in the midst thereof He set Soul, which He stretched throughout the whole of it, and therewith He enveloped also the exterior of its body; and as a Circle revolving in a circle....

Cf. Plato, Timaeus 32d-33b (tr. B. Jowett):Now the creation took up the whole of each of the four elements; for the Creator compounded the world out of all the fire and all the water and all the air and all the earth, leaving no part of any of them nor any power of them outside. His intention was, in the first place, [d] that the animal should be as far as possible a perfect whole and of [33] perfect parts: secondly, that it should be one, leaving no remnants out of which another such world might be created: and also that it should be free from old age and unaffected by disease. Considering that if heat and cold and other powerful forces which unite bodies surround and attack them from without when they are unprepared, they decompose them, and by bringing diseases and old age upon them, make them waste away1 for this cause and on these grounds he made the world one whole, having every part entire, and being therefore perfect and [b] not liable to old age and disease. And he gave to the world the figure which was suitable and also natural.

Cf. Plato, Phaedrus 264a-e ff. (tr. B. Jowett):SOCRATES: Read, that I may have his exact words. PHAEDRUS: You know how matters stand with me, and how, as I conceive, they might be arranged for our common interest; and I maintain I ought not to fail in my suit because I am not your lover, for lovers repent of the kindnesses which they have shown, when their love is over. SOCRATES: Here he appears to have done just the reverse of what he ought; for he has begun at the end, and is swimming on his back through the flood to the place of starting. His address to the fair youth begins where the lover would have ended. Am I not right, sweet Phaedrus? PHAEDRUS: [b] Yes, indeed, Socrates; he does begin at the end. SOCRATES: Then as to the other topics are they not thrown down anyhow? Is there any principle in them? Why should the next topic follow next in order, or any other topic? I cannot help fancying in my ignorance that he wrote off boldly just what came into his head, but I dare say that you would recognize a rhetorical necessity in the succession of the several parts of the composition? PHAEDRUS: You have too good an opinion of me if you think that I have any such insight [c] into his principles of composition.1

Cf. Alcmaon Fr. 4, from Atius V30,1: Health is conserved by equal balance (isonomia) among the powers wet and dry, cold and hot, bitter and sweet, etc., disease being produced by the sole dominance (monarchia) of one among them, for the sole dominance of either one of them would be destructive [of the other]. And illness comes about by an excess of heat or cold, from too much or too little food, and in the blood or marrow of the brain . . . health is the proportionate mixture (symmetron krasin) of the qualities. (Alcmaon, or Alcmeon, of Croton was a physician who flourished in the early fifth century.) Observations such as this lie at the root of traditional philosophys understanding of beauty as a hexis or disposition. See further Aristotle, Topics, III. 1 (116b 19-23) and associated texts, quoted below.

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SOCRATES: At any rate, you will allow that every discourse ought to be a living creature, having a body of its own and a head and feet; there should be a middle, beginning, and end, adapted to one another and to the whole? PHAEDRUS: Certainly. SOCRATES: Can this be said of the discourse of Lysias? See whether you can find any more connexion in his words than in the epitaph which is said by some to have been inscribed on the grave of Midas the Phrygian. PHAEDRUS: [d] What is there remarkable in the epitaph? SOCRATES: It is as follows: I am a maiden of bronze and lie on the tomb of Midas; So long as water flows and tall trees grow, So long here on this spot by his sad tomb abiding, I shall declare to passers-by that Midas sleeps below. [e] Now in this rhyme whether a line comes first or comes last, as you will perceive, makes no difference. PHAEDRUS: You are making fun of that oration of ours.

Cf. the following from a web site (quoting Plato, Phaedrus 264c, tr. Harold N. Fowler):Socrates gives the speaker specific instructions: Every speech must be put together like a living creature, with a body of its own; it must be neither without head nor without legs; and it must have a middle and extremities that are fitting both to one another and to the whole work (264C).

6. The meaning of symmetry according to The Oxford English Dictionary:Symmetry 1. Mutual relation of the parts of something in respect of magnitude and position; relative measurement and arrangement of parts; proportion. 2. Due or just proportion; harmony of parts with each other and the whole; fitting, regular, or balanced arrangement and relation of parts or elements; the condition or quality of being wellproportioned or well-balanced. In stricter use (approaching or passing into 3 b): Exact correspondence in size and position of opposite parts; equable distribution of parts about a dividing line or centre. (As an attribute either of the whole, or of the parts composing it.) 3 b. Geom. etc. Exact correspondence in position of the several points or parts of a figure or body with reference to a dividing line, plane, or point (or a number of lines or planes); arrangement of all the points of a figure or system in pairs (or sets) so that those of each pair (or set) are at equal distances on opposite sides of such line, plane, or point.

N.B. The first two definitions given here show the appropriateness of translating summetria by proportion. They also show that symmetry pertains first of all to size and order. But for the way in which these attributes enter into the consideration of a work of art, cf. the following:

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Cf. M. Bill. The Mathematical Way of Thinking in the Visual Art of Our Time, The Visual Mind: Art and Mathematics, M. Emmer, editor, Leonardo Books-MIT Press, Cambridge, 1993:Now in every work of [visual] art the basis of its composition is geometry or in other words the means of determining the mutual relationship of its component parts either on plane or in space.... And again, since it is mathematics which lends significance to these relationships, it is only a natural step from having perceived them to desiring to portray them. This, in brief, is the genesis of a work of art.

7. Plato on beauty in sum. (a) beginning and end (order as consisting in a before and after; transposition of parts should make a difference to the nature): for he has begun at the end, and is swimming on his back through the flood to the place of starting Then as to the other topics are they not thrown down anyhow? Is there any principle in them? Why should the next topic follow next in order, or any other topic? Now in this rhyme whether a line comes first or comes last, as you will perceive, makes no difference. (b) a body, head, and feet (a middle, beginning, and end) (parts adapted to one another and to the whole):1 every discourse ought to be a living creature, having a body of its own and a head and feet; there should be a middle, beginning, and end, adapted to one another and to the whole (c) succession or connection (continuous and one): but I dare say that you would recognize a rhetorical necessity in the succession of the several parts of the composition See whether you can find any more connexion in his words than in the epitaph which is said by some to have been inscribed on the grave of Midas the Phrygian On these observations, cf. Aristotle, Parts of Animals (641b 21-24) (tr. William Ogle): Yet there are some who, while they allow that every animal exists and was generated by nature, nevertheless hold that the heaven was constructed to be what it is by chance and spontaneity; the heaven, in which not the faintest sign of haphazard or of disorder is discernible! Cf. ibid.: Absence of haphazard and conduciveness of everything to an end are to be found in natures works in the highest degree, and the resultant end of her generations is a form of the beautiful. Note: The form of the beautiful at issue here is that of taxis or order; for the parts of an integral whole cannot be put together in just any way; such an orderliness importing an absence of haphazard. Cf. nature is not episodic,1

Such a thing being a whole having size, hence an order in its parts (= position as dispositio).

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like a bad tragedy. Cf. a whole is what has a beginning, a middle, and an end. Cf. St. Thomas Aquinas, In V Meta., lect. 8, n. 3 (tr. B.A.M.): For some things are called one not by reason of indivision or solely by reason of continuity, but because they are whole and perfect insofar as they have some one species, not in the sense of a homogeneous subject, but that which consists in a certain totality requiring a determinate order of parts. Cf. also St. Thomas Aquinas, In V Meta., lect. 21, n. 21 (tr. B.A.M.): For when it is so that in a quantity there is an order of parts, because there is a beginning, a middle, and an end there, in which the account of position consists, every such continuous whole must have position in its parts. Cf. Plato, Timaeus 29d-34a (tr. B. Jowett):Tim. Let me tell you then why the creator made this [e] world of generation. He was good, and the good can never have any jealousy of anything. And being free from jealousy, he desired that all [30] things should be as like himself as they could be. This is in the truest sense the origin of creation and of the world, as we shall do well in believing on the testimony of wise men: God desired that all things should be good and nothing bad, so far as this was attainable. Wherefore also finding the whole visible sphere not at rest, but moving in an irregular and disorderly fashion, out of disorder he brought order, considering that this was in every way better than the other. Now the deeds of the best could never be or have been other than the fairest; [b] and the creator, reflecting on the things which are by nature visible, found that no unintelligent creature taken as a whole was fairer than the intelligent taken as a whole; and that intelligence could not be present in anything which was devoid of soul. For which reason, when he was framing the universe, he put intelligence in soul, and soul in body, that he might be the creator of a work which was by nature fairest and best. Wherefore, using the language of probability, we may say that the world became a living creature truly endowed with soul and intelligence by the providence of God. [e] This being supposed, let us proceed to the next stage: In the likeness of what animal did the Creator make the world? It would be an unworthy thing to liken it to any nature which exists as a part only; for nothing can be beautiful which is like any imperfect thing; but let us suppose the world to be the very image of that whole of which all other animals both individually and in their tribes are portions. For the original of the universe contains in itself all intelligible beings, [d] just as this world comprehends us and all other visible creatures. For the Deity, intending to make this world like the fairest and most perfect of intelligible beings, framed one visible animal comprehending within itself all other animals of a kindred nature. Are we right in [31] saying that there is one world, or that they are many and infinite? There must be one only, if the created copy is to accord with the original. For that which includes all other intelligible creatures cannot have a second or companion; in that case there would be need of another living being which would include both, and of which they would be parts, and the likeness would be more truly said to resemble not them, but that other which included them. In order then that the world might be solitary, like the perfect animal, the creator made not [b] two worlds or an infinite number of them; but there is and ever will be one only-begotten and created heaven. Now that which is created is of necessity corporeal, and also visible and tangible. And nothing is visible where there is no fire, or tangible which has no solidity, and nothing is solid without earth. Wherefore also God in the beginning of creation made the body of the universe to consist of fire and earth. But two things cannot be rightly put together without a third; there must be some bond of union [e] between them. And the fairest bond is that which makes the most complete fusion of itself and the things which it combines; and proportion is best adapted to effect such a union. For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the [32] first term as the last term is to the

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meanthen the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one. If the universal frame had been created a surface only and having no depth, a single mean would have sufficed to bind together itself and the other terms; but now, as the [b] world must be solid, and solid bodies are always compacted not by one mean but by two, God placed water and air in the mean between fire and earth, and made them to have the same proportion so far as was possible (as fire is to air so is air to water, and as air is to water so is water to earth); and thus he bound and put together a visible and [c] tangible heaven. And for these reasons, and out of such elements which are in number four, the body of the world was created, and it was harmonised by proportion, and therefore has the spirit of friendship; and having been reconciled to itself, it was indissoluble by the hand of any other than the framer. Now the creation took up the whole of each of the four elements; for the Creator compounded the world out of all the fire and all the water and all the air and all the earth, leaving no part of any of them nor any power of them outside. His intention was, in the first place, [d] that the animal should be as far as possible a perfect whole and of [33] perfect parts: secondly, that it should be one, leaving no remnants out of which another such world might be created: and also that it should be free from old age and unaffected by disease. Considering that if heat and cold and other powerful forces which unite bodies surround and attack them from without when they are unprepared, they decompose them, and by bringing diseases and old age upon them, make them waste awayfor this cause and on these grounds he made the world one whole, having every part entire, and being therefore perfect and [b] not liable to old age and disease. And he gave to the world the figure which was suitable and also natural. Now to the animal which was to comprehend all animals, that figure was suitable which comprehends within itself all other figures. Wherefore he made the world in the form of a globe, round as from a lathe, having its extremes in every direction equidistant from the centre, the most perfect and the most like itself of all figures; for he considered that the like is infinitely fairer than the unlike. This he finished off, making the [c] surface smooth all around for many reasons; in the first place, because the living being had no need of eyes when there was nothing remaining outside him to be seen; nor of ears when there was nothing to be heard; and there was no surrounding atmosphere to be breathed; nor would there have been any use of organs by the help of which he might receive his food or get rid of what he had already digested, since there was nothing which went from him or came into him: for there was nothing beside him. Of design he was created thus, his own waste providing his own food, and all that he did or suffered taking [d] place in and by himself. For the Creator conceived that a being which was self-sufficient would be far more excellent than one which lacked anything; and, as he had no need to take anything or defend himself against any one, the Creator did not think it necessary to bestow upon [34] him hands: nor had he any need of feet, nor of the whole apparatus of walking; but the movement suited to his spherical form was assigned to him, being of all the seven that which is most appropriate to mind and intelligence; and he was made to move in the same manner and on the same spot, within his own limits revolving in a circle. All the other six motions were taken away from him, and he was made not to partake of their deviations. And as this circular movement required no feet, the universe was created without legs and without feet. Such was the whole plan of the eternal God about the god that was to be, to whom for this reason he gave a body, smooth and even, having a surface in every direction equidistant from the centre, a body entire and perfect, and formed out of perfect bodies. And in the centre he put the soul, which he diffused throughout the body, making it also to be the exterior environment of it; and he made the universe a circle moving in a circle, one and solitary, yet by reason of its excellence able to converse with itself, and needing no other friendship or acquaintance. Having these purposes in view he created the world a blessed god.

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8. On good harmony, good rhythm, and good color. Cf. Plato, Laws II (655a-b) (ed. Perseus; tr. Thomas Pangle):It should be noted, though, that music includes postures and tunes, since music involves rhythm and harmony; now one can speak of good rhythm and good harmony, but one cannot correctly apply to either tune or posture and image good coloras the chorus teachers, speaking in images, do. On the other hand, with regard to the posture or tune of the coward and the courageous man, it is correct to call what pertains to cowards ugly. To avoid our getting involved in a very lengthy discussion of all these things, lets simply let all the postures and tunes that belong to virtue of the soul or of the body (whether they belong to virtue itself or to an image of it) be beautiful, and those belonging to vice be entirely the opposite.

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III. THE BEAUTIFUL ACCORDING TO ARISTOTLE. 1. The three greatest forms of the beautiful. Cf. Aristotle, Metaph., XIII. 3 (1078a 311078b 6) (tr. W. D. Ross, rev. B.A.M.):Now since the good and the beautiful are different (for the former always implies conduct as its subject, while the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do [35] not expressly mention them, but prove attributes which are their results or their definitions, it is not true to say that they tell us nothing about them. The chief forms of beauty are order and symmetry [1078b] and definiteness, which the mathematical sciences demonstrate in a special degree. And since these (e.g. order and definiteness) are obviously causes of many things, evidently these sciences must treat this sort of causative principle also (i.e. the beautiful) as in [5] some sense a cause. But we shall speak more plainly elsewhere about these matters.1414

Apparently an unfulfilled promise. (emphasis added)

Cf. Aristotle, Metaph., XIII. 3 (1078a 311078b 6) (ed. W. D. Ross; tr. Hugh Tredennick):epei de to agathon kai to kalon heteron (to men gar aei en praxei, to de kalon kai en tois akintois), hoi phaskontes ouden legein tas mathmatikas epistmas peri kalou agathou pseudontai. And since goodness is distinct from beauty (for it is always in actions that goodness is present, whereas beauty is also in immovable things), they are in error who assert that the mathematical sciences tell us nothing about beauty or goodness;

legousi gar kai deiknuousi malista: [35] ou gar for they describe and manifest these qualities in ei m onomazousi ta d' erga kai tous logous the highest degree, since it does not follow, deiknuousin, ou legousi peri autn. because they manifest the effects and principles of beauty and goodness without naming them, that they do not treat of these qualities. tou de kalou megista eid taxis kai summetria kai to hrismenon, [1078b][1] ha malista mathmatikai epistmai. deiknuousin The main species of beauty are orderly arrangement, proportion, and definiteness;

hai [1078b][1] and these are especially manifested by the mathematical sciences. And inasmuch as it is evident that these (I mean, e.g., orderly arrangement and definiteness) are causes of many things, obviously they must also to some extent treat of the cause in this sense, i.e. the cause in the sense of the Beautiful.

kai epei ge polln aitia phainetai tauta (leg d' hoion h taxis kai to hrismenon), dlon hoti legoien an kai tn toiautn aitian tn [5] hs to kalon aition tropon tina.

mallon de gnrims en allois peri autn But we shall deal with this subject more eroumen. explicitly elsewhere.

Cf. Aristotle, Metaph., XI. 3 (1061a 29-b 3) (tr. W. D. Ross): 24

As the mathematician investigates abstractions (for before beginning his investigation he strips off all the sensible qualities, e.g. [30] weight and lightness, hardness and its contrary, and also heat and cold and the other sensible contrarieties, and leaves only the quantitative and continuous, sometimes in one, sometimes in two, sometimes in three dimensions, and the attributes of these qua quantitative and [35] continuous, and does not consider them in any other respect, and examines the relative positions of some and the attributes of these, and the commensurabilities and incommensurabilities of others, [1061b] and the ratios of others; but yet we posit one and the same science of all these thingsgeometry)the same is true with regard to being.

Cf. Aristotle, Metaph., XI. 3 (1061a 29-b 3) (ed. W. D. Ross; tr. Hugh Tredennick):kathaper d' ho mathmatikos peri ta ex And just as the mathematician makes a study of aphaireses tn therian poieitai abstractions (perieln gar panta [30] ta aisthta therei, hoion baros kai kouphotta kai sklrotta kai tounantion, eti de kai thermotta kai psuchrotta kai tas allas aisthtas enantiseis, monon de kataleipei to poson kai suneches, tn men eph' hen tn d' epi duo tn d' epi tria, kai ta path ta toutn hi posa esti [35] kai sunech, kai ou kath' heteron ti therei, kai tn men tas pros allla theseis skopei kai ta tautais huparchonta, [1061b][1] tn asummetrias, de tas summetrias (for in his investigations he first abstracts everything that is sensible, such as weight and lightness, hardness and its contrary, and also heat and cold and all other sensible contrarieties, leaving only quantity and continuity sometimes in one, sometimes in two and sometimes in three dimensions and their affections qua quantitative and continuous, and does not study them with respect to any other thing; and in some cases investigates the relative positions of things and the properties of these,

kai [1061b][1] and in others their commensurability or incommensurability,

tn de tous logous, all' homs mian pantn kai and in others their ratios; yet nevertheless we tn autn tithemen epistmn tn gemetrikn ), hold that there is one and the same science of all ton auton d tropon echei kai peri to on. these things, viz. geometry), so it is the same with regard to Being.

2. Comparison of texts.Aristotle, Meta., XIII. 3 (1078a 371078b 1) (tr. W. D. Ross) The chief forms of beauty are order [taxis] and Aristotle, Meta., XI. 3 (1061a 36-b 1) (tr. W. D. Ross) and [as the mathematician] examines the relative positions [tas pros allla theseis] of some and the attributes of these,

symmetry [or commensurability, summetria] and the commensurabilities and incommensura[1078b] and bilities [tas summetrias kai asummetrias] of others, [1061b]

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definiteness [or the limited, to horismenon], and the ratios [tn de tous logous] of others. which the mathematical sciences demonstrate in a special degree. [the relation of ratio to limit being indicated by De Anima, II. 4 (416a 15-20) (tr. H. G. Apostle): [B]ut a thing which is composed by nature of all [the elements] has a limit and a [certain] ratio [of elements] with respect to both size and growth, and these [i.e. limit and ratio] belong to the soul and not to fire, and to the formula rather that to the matter of the thing.

Cf. Aristotle, Metaph., XIII. 3 (1078a 37-1078b 2) (ed. Tredennick; tr. Duane Berquist):tou de kalou megista eid taxis kai summetria The greatest forms of the beautiful are order and kai to hrismenon, [1078b][1] ha malista deik- symmetry and the limited, which the mathenuousin hai mathmatikai epistmai. matical sciences especially show.

3. In sum. Symmetry has to do with the parts of an integral whole being commensurate that is, possessing their due measure with respect to quantity. Cf. the analogy with health: just as there must be a proper balance of humours in a body for it is to be healthy (for if one humour were to be excessive, the animal would be ill), so also for a body to be beautiful there must be a proper measure of the parts with respect to quantity; for if a limb were too large, the animal would be ugly (Cf. Plato, Timaeus 87 d-e: Just as a body which has a leg too long, or which is unsymmetrical [e] in some other respect, is an unpleasant sight.). How does the notion of admitting (or not admitting) a common measure arise? Inasmuch as it is most proper to quantity to be either or equal or unequal, the consideration of the relative sizes or ratios of magnitudes in geometry will necessarily make this notion manifest to the understanding. Note that color and lustre have no place in a consideration of the beauty pertaining to mathematicals, which are abstracted from sensible matter, and so their surfaces have no color. 4. On the notion of the limited. Cf. Aristotle, Metaph., V. 17 (1022a 5-14) (tr. Joe Sachs; rev. B.A.M.):Limit means the extremity of each thing, understood as the first thing outside of which there is nothing to find and the first thing inside of which everything belonging to it is, which is also the form of a magnitude or of something that has magnitude; and it means the end of each thing (and of this sort is that toward which its motion or action tends, but not that from which it starts, though sometimes it is both and consists of that from which as well as that toward which), and that for the sake of which it is, and the substance of each thing, and what it is for each thing to be; for the latter is a limit of knowledge, and if of [10] the knowledge, also of the thing. It is evident, then, that in however many ways beginning is said, limit too is said, and in yet more ways; for a beginning is a limit, but not every limit is a beginning. (emphasis added)

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5. The four ways in which limit is said: the form [or end, or terminus] of a magnitude or of a thing having magnitude: i.e. the end points of a line, or the shape or figure of a surface or body, coming under the fourth species of quality [the last thing taken in respect of quantity] the end [or extreme] of a motion or operation; e.g. being as the limit of coming to be [the last thing taken in respect of virtue or power] that for the sake of which it is; e.g. the final cause (and form) [the last thing in intention] the substance of each thing [the essence or definition] [the last thing in knowledge]

where a quantity comes to an end: a point, a line, a surface where a virtue or power comes to an end: coming to be where an intention comes to an end: that for the sake of which, which is also the form where knowledge comes to an end: the substance or what it is of a thing 6. On limit and ratio. Cf. Aristotle, De An., II. 4 (416a 14-20) (tr. Hippocrates G. Apostle):Now fire is in some way a joint cause; however it is not the cause without qualification. [15] Rather is it the soul which is the cause. For the growth of fire proceeds indefinitely, as long as there is fuel to be burned; but a thing which is composed by nature of all [the elements] has a limit and a [certain] ratio [of elements] with respect to both size and growth, and these [i.e. limit and ratio] belong to the soul and not to fire, and to the formula rather that to the matter of the thing.1

Cf. St. Thomas Aquinas, In II De Caelo, lect. 20. n. 7:LB2 LC20N.-7 manifestum est autem quod continens est But it is obvious that the thing containing is honorabilius contento, et finis quam finitum: more honorable than the thing contained, and the limit [more honorable] than the limited, quia contentum et finitum pertinent ad rationem the reason being that the contained and the limimateriae, ted pertain to the notion of matter, esse autem continens et finiens, ad rationem but to be containing and limiting, to the notion formae, quae est substantia totius consistentiae of form, which is the substance of the whole rerum. consistence of things.1

Cf. St. Thomas Aquinas, In V Meta., lect. 18, n. 5 (tr. B.A.M.): For each thing is perfect when no part of the natural magnitude, which belongs to it according to the species of its proper virtue, is lacking to it. Now just as any natural thing possesses a determinate measure of natural magnitude according to continuous quantity, as is said in the second book of the De Anima [II. 4, 416a 15ff.], so also any thing possesses a determinate quantity of its natural virtue. But, as Aristotle states, the possession of a determinate quantity of magnitude is a function of the ratio of the elements composing the thing. Consequently, inasmuch as a thing composed of elements is marked by a limit and a certain ratio with respect to those elements, it will possess those forms of the beautiful called symmetry and order. From the foregoing, one sees how definiteness arises from symmetry, which in turn involves order.

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Cf. St. Thomas: a thing is determinata when it has attained that to which it is ordained, which is itproper term. Cf. St. Thomas Aquinas, In X Ethic., lect 3, n. 8 (tr. B.A.M.):LB10LC-3N.-8 sed tamen neque etiam delectationes quae secundum se recipiunt magis et minus ratione suae mixtionis, oportet non esse determinatas, neque bonas. nihil enim prohibet quin delectatio recipiens magis et minus sit determinata, sicut et sanitas. huiusmodi enim determinata dici possunt, For things of this sort may be called deterinquantum aliqualiter attingunt id ad quod mined insofar as they somehow attain to that to ordinantur, licet possent propinquius attingere. which they are ordained, although they may get nearer to it. sicut commixtio humorum habet rationem In the same way a mixing together of humours sanitatis ex eo quod attingit convenientiam has the character of health by reason of the fact humanae naturae; that it attains an agreement with human nature et ex hoc dicitur determinata, quasi proprium for from this a thing is called determined as terminum attingens. attaining its proper term.

Cf. St. Thomas Aquinas, In II De Anima:[80612] Sentencia De anima, lib. 2 l. 8 n. 6 Deinde cum dicit videtur autem ponit aliam positionem. Et circa hoc duo facit. Primo ponit eam. Secundo improbat, ibi, hoc autem concausa, et cetera. Sciendum est autem, quod haec opinio differt in hoc a prima, quod prima attribuebat causam augmenti et alimenti diversis elementis, scilicet igni et terrae: haec autem attribuit eorum causam igni tantum. [80613] Sentencia De anima, lib. 2 l. 8 n. 7 Et movebantur ad hoc hac ratione. Quia illud videtur esse principium alicuius passionis vel motus in aliquo, secundum quod se habet illam passionem vel motum: sicut ignis, qui secundum se calidus est, est causa caloris in rebus mixtis; et terra, quae secundum se est gravis, est causa gravitatis in eis. Inter autem elementa videtur solus ignis nutriri et augeri, si superficialiter de nutrimento et augmento loquamur. Solus igitur ignis videtur esse faciens augmentum et alimentum in plantis et animalibus. Utrum vero ignis nutriatur et augeatur, inferius erit manifestum. [80614] Sentencia De anima, lib. 2 l. 8 n. 8 Deinde cum dicit hoc autem improbat praedictam positionem. Sciendum tamen est, quod praedicta positio aliquid habet veritatis. Necesse est enim omne alimentum decoqui: quod quidem fit per ignem: unde ignis aliquo modo operatur ad alimentum, et per consequens ad augmentum: non quidem sicut agens principale, hoc enim est animae; sed sicut agens secundarium et instrumentale. Et ideo dicere, quod ignis quodammodo concausa est augmenti et alimenti, sicut instrumentum concausa est principalis agentis, verum est; non tamen est principaliter causa ut principale agens, sed hoc modo causa est anima: quod sic probat.

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[80615] Sentencia De anima, lib. 2 l. 8 n. 9 Illud est principale in qualibet actione a quo imponitur terminus et ratio ei quod fit; sicut patet in artificialibus, quod terminus vel ratio arcae vel domui non imponitur ab instrumentis, sed ab ipsa arte. Nam instrumenta se habent differenter ut cooperentur ad hanc formam vel quantitatem, vel aliam. Serra enim quantum est de se, apta est ad secandum lignum, secundum quod competit et ostio, et scamno, et domui, et in quacumque quantitate; sed quod sic secetur lignum, quod sit aptum ad talem formam et ad talem quantitatem, est ex virtute artis. Manifestum est autem, quod in omnibus quae sunt secundum naturam, est certus terminus, et determinata ratio magnitudinis et augmenti: sicut enim cuilibet speciei debentur aliqua accidentia propria, ita et propria quantitas, licet cum aliqua latitudine propter diversitatem materiae, et alias causas individuales; non enim omnes homines sunt unius quantitatis. Sed tamen est aliqua quantitas tam magna, ultra quam species humana non porrigitur; et alia quantitas tam parva, ultra quam homo non invenitur. Illud igitur quod est causa determinationis magnitudinis et augmenti est principalis causa augmenti. [Now it is obvious that in all things that are according to nature there is a certain term, and a determinate ratio of size and growth; for just as in any species certain proper accidents are due, so also proper quantities, although there is some latitude by reason of a diversity of matter. But there is nonetheless a certain quantity beyond which the human species cannot go; and there is another quantity so small beyond which a man cannot be found. That, therefore, which is the cause of the determination of size and growth is the principal cause of growth.] Hoc autem non est ignis. Manifestum est enim, quod ignis augmentum non est usque ad determinatam quantitatem, sed in infinitum extenditur, si in infinitum materia combustibilis inveniatur. Manifestum est igitur, quod ignis non est principale agens in augmento et alimento, sed magis anima. Et hoc rationabiliter accidit; quia determinatio quantitatis in rebus naturalibus est ex forma, quae est principium speciei, magis quam ex materia. Anima autem comparatur ad elementa, quae sunt in corpore vivente, sicut forma ad materiam. Magis igitur terminus et ratio magnitudinis et augmenti est ab anima, quam ab igne. [It is therefore obvious that fire is not the principle agent in growth and nutrition, but rather the soul. And this happens reasonably, the reason being that the determination of quantity in natural things comes from the form, which is the principle of the species, rather than from the matter. But the soul is compared to the elements, which are in the living body, as form to matter. Therefore the limit and ratio of size and growth is more from the soul than from fire.]

7. The greatest forms of the beautiful in sum. Cf. Aristotle, Metaph., XIII. 3 (1078a 361078b 1) (tr. W. D. Ross, rev. B.A.M.):The chief forms of beauty are order and symmetry [1078b] and definiteness , which the mathematical sciences demonstrate in a special degree.

8. On order and definiteness. Cf. Aristotle, On the Parts of Animals, I. 1 (641b 16642a 30) (tr. William H Ogle):And that the heaven, if it had an origin, was evolved and is maintained by such a cause, there is therefore even more reason to believe, than that mortal animals so originated. For

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order and definiteness are much more plainly manifest in the celestial bodies than in our own frame; while change and chance are characteristic of the perishable things of earth. [20] Yet there are some who, while they allow that every animal exists and was generated by nature, nevertheless hold that the heaven was constructed to be what it is by chance and spontaneity; the heaven, in which not the faintest sign of haphazard or of disorder is discernible! Again, whenever there is plainly some final end, to which a motion tends should nothing stand in the way, we always say that such final [25] end is the aim or purpose of the motion; and from this it is evident that there must be a something or other really existing, corresponding to what we call by the name of Nature. For a given seed does not give rise to any chance living being, nor spring from any chance one; but each seed springs from a definite parent and gives rise to a definite progeny. And thus it is the seed that is the ruling influence and fabricator of the offspring. For these it is by nature, the offspring being at [30] any rate that which in nature will spring from it. At the same time the offspring is anterior to the seed; for seed and perfected progeny are related as the developmental process and the result. Anterior, however, to both seed and product is the organism from which the seed was [35] derived. For every seed implies two organisms, the parent and the progeny. For seed or seed is both the seed of the organism from which it came, of the horse, for instance, from which it was derived, and the seed of the organism that will eventually arise from it, of the mule, for example, which is developed from the seed of the horse. The same seed then is the seed both of the horse and of the mule, though in different ways as here set forth. Moreover, the seed is potentially that which will spring from it, and the relation of potentiality to actuality we know. [642a] There are then two causes, namely, necessity and the final end. For many things are produced, simply as the results of necessity. It may, however, be asked, of what mode of necessity are we speaking when [5] we say this. For it can be of neither of those two modes which are set forth in the philosophical treatises. There is, however, the third mode, in such things at any rate as are generated. For instance, we say that food is necessary; because an animal cannot possibly do without it. This third mode is what may be called hypothetical necessity. Here [10] is another example of it. If a piece of wood is to be split with an axe, the axe must of necessity be hard; and, if hard, must of necessity be made of bronze or iron. Now exactly in the same way the body, which like the axe is an instrumentfor both the body as a whole and its several parts individually have definite operations for which they are madejust in the same way, I say, the body, if it is to do its work, must of necessity be of such and such a character, and made of such and such materials. It is plain then that there are two modes of causation, and that [15] both of these must, so far as possible, be taken into account in explaining the works of nature, or that at any rate an attempt must be made to include them both; and that those who fail in this tell us in reality nothing about nature. For primary cause constitutes the nature of an animal much more than does its matter. Th