Here is chapter 12 of Modern Thomistic Philosophy by R.P. Phillips (despite its title, the book was published in London in 1934). Caution: it is a neo-scholastic work (the nihil obstat is by George Hayward Joyce, censor deputatus). However, I have used this book for many years and it is generally an accurate summary of scholastic positions, in spite of the occasional eccentricities and anachronisms. The references are particularly good.
The topic of the chapter is individuation. Phillips covers the origin of the problem in Aristotle - who only touches upon it in a handful of places, its treatment by Avicenna and Averroes, and S. Thomas. Sadly, the views of Scotus and Ockham are only given a paragraph each.
London, September 2010
Its Nature—Opinions—Explanation of the Thomist View—Reasons in its Favour—Meaning of 'Materia Signata'—Some Difficulties Considered.
So far, we have been concerned with general natures ; first of material substances, and then of its various species and accidental characteristics ; and we now have to turn to the individuals which belong to these species, It is with such individuals that our knowledge begins, and the whole process of generalisation has as its object and end the understanding of them. It will, however, only allow us to have knowledge of them with regard to those features which they possess in common with other individuals, leaving us still in ignorance as to what it is that constitutes them as individuals, or as differentiated from other concrete substances; for the individual, while undifferentiated in itself, is yet distinguished from others, as S. Thomas says. [151.1] If what has been said about the essential unity of the atom and molecule be true, these bodies, at least, when taken singly, will be true individuals ; even if we are obliged to deny or doubt the individuality of larger masses of inanimate matter ; [151.2] and we wish to discover what it is precisely which is the root of their unity and of their distinction from other bodies of the same nature as themselves. This question as to the root of numerical unity is known as the problem of the principle of individuation, and is one of the most recalcitrant and obscure of the many difficult problems discussed in mathematical philosophy.
The history of the consideration of this problem may be  said to begin with Aristotle who regarded the individual as containing reality in itself, in contrast to Plato, who looked upon the subsisting Forms as constituting reality. The former finds in the individual two kinds of unity, a unity of nature, which it shares with other individuals, and a unity which is all its own. The first is specific, and the second numerical, unity. Specific unity is, in his view, derived from form, since form is that which makes the substance to be determinately what it is. What, then, is it which is the source of the numerical unity of individuation ? Few passages, and those ambiguous, can be cited in which individuation seems to be ascribed to form; [152.1] while there are numbers in which it is distinctly attributed to matter. So he says : ' The whole thing, such and such a form in this flesh and these bones, is Callias or Socrates; and they are different owing to their matter (for this is different), but the same in species, for the species is indivisible.' [152.2] So it is no doubt true to say that Aristotle thought that things which differ numerically within the same species do so in matter only, and so by reason of it.
The question does not make much progress till we come to the Arabian philosophers of the Middle Ages; though Boethius, in touching on it incidentally, seems generally to ascribe individuation to accidents. 'Ea vero quae individua sunt et solo numero discrepunt, solis accidentibus distant.'
Passing then to the Arabians, Avicenna (980-1037), or rather his translator, first introduces us to a term which was to become famous in discussions of this question, by using the word ' signatum ' as synonymous with ' determinate individual,' which thence comes to be applied to any determinate reality. Thus we hear both of ' forma,' and of ' materia,' ' signata.' Since a nature, he contends, is not of itself individual, the relation between it and individuality is an accidental one, and therefore we must look for its source not in essence, but among the accidents, such as quantity, quality, place, and time. Nevertheless, a definite theory of  individuation is not worked out by Avicenna, though his dicta about it should logically lead to the conclusion that its source lie's in matter which is determined by spatial dimensions. No doubt this latent conclusion was perceived by the penetrating mind of S. Thomas: who, however, was also much influenced in this question by another writer of the same race—Averroes (1126-1198). According to Averroes, known in the Middle Ages as the Commentator, from his exhaustive commentaries on Aristotle, matter is in itself numerically one, since being undetermined, it cannot be many. Nevertheless, it is divisible, and that which makes it so must be quantity, i.e. the three dimensions of the continuum. Hence matter must be conceived as carrying with it, not this or that three-dimensional extension, but extension in general—' unterminated extension or dimensions.' So first matter is in potency to a determination by three dimensions in general, which potency is logically prior to that which it has for being determined by a specific form.
The theories of Avicenna and Averroes seem to have had a predominant influence on the thought of S. Thomas (1224- 1274) ; which vacillates in a remarkable fashion between their explanations. He never, as it seems, had the least doubt with regard to the Aristotelean theory of individuation by means of matter ; but he hesitates for some time as to the way in which this general theory should be understood. After accepting, at first, the expressions and theory of Avicenna that the principle of individuation is matter designated by determined dimensions,[153.1] he abandons it in favour of the Averroist opinion that it is matter affected by unterminated dimensions which is this principle. [153.2] He makes considerable use of this second theory, only in the end to throw it over and return once more to the view that the dimensions are determined ones. [153.3]
The reason of this change of opinion is almost certainly to be found in S. Thomas' keener realisation of all the consequences which flow from the strict acceptance of the doctrine of the uniqueness of substantial form: since the Averroist theory really implies some real priority of the unterminated dimensions to substantial form. A few words must be added with respect to the subsequent history of this discussion in the Schools, though it is impossible to treat it fully, or to examine non-Scholastic views of individuation.
Scotus (1265(?)-13o8) held that the source of individuation is the numerical determination of the form and matter of the compound, by which they become this form and this matter. He maintains, further, that it is distinguished from the nature of the thing by a formal distinction a parte rei, i.e. it is not wholly identified as a reality with the nature. He says it is the 'ultima realitas entis' ; [154.1] and though not substantial form is yet of the nature of a formality as determining the thing to be ' this.' He calls it ' haecceitas ' or ' thisness '; so that a thing is this by its thisness, it is an individual by means of the last reality of its being: a conclusion which is not very illuminating.
Ockham (c. 1300-1348), and the Nominalists generally, necessarily regard the question as to the principle of individuation as meaningless, since they do not admit as realities independent of the mind any universal or specific natures, but only individual things or phenomena. Hence the individual is distinct of itself, and not multiplied in the species, the latter being either a mere concept or a group name.
Suarez (1548-1617) considers, in opposition to Scotus, that the principle of individuation can only be logically distinguished from the individual being. Every being, even an incomplete one, is individual of itself, by reason of its entity. He is particularly determined in his opposition to the Thomist thesis which would see in a part of the nature only, viz. matter affected by quantity, the principle of individuation. [154.2]
It is essential to notice that in this enquiry we are not  looking for the proximate cause of individuation, but its root or first cause ; nor yet do we wish to discover how individuals are to be distinguished by it, how we recognise them as distinct individuals, but how they are distinguished from one another in themselves. [155.1]
The Thomist school all answer this question by saying that the principle is matter signed or sealed by quantity : which at this stage we may take as meaning matter which has a relation to quantity—Wicksteed describes it as ' earmarked by quantity '[155.2]—though later we will examine this phrase more closely. It is necessary to discuss this question fairly fully since S. Thomas' view on this subject is at the very heart of his metaphysical system, to such an extent that its abandonment would seem to involve the abandonment of his whole conception of the universe; and conversely a real grasp of it will greatly help to an understanding of the whole of his philosophy. We have already had occasion to notice that the theory of matter and form is a particular case of the Aristotelean division of being into potency and act—though almost certainly not a derivative of it—and this thesis is another special case of that theory. For multiplication implies a distinction, and so a restriction or limitation, which limitation implies, in its turn, some imperfection or potency ; from which it follows that an act which is complete and perfect in its own order, both as a substance and as a species, cannot be multiplied in that order; and also that if any form or act is multiplicable, this cannot come about from the form or act itself; since this in itself implies no limitation. The multiplication must therefore come from potency or matter.
To prove their contention that the principle of individuation must be matter determined by quantity, the Thomists argue in the first place that no other principle can be discovered which will satisfy the necessary conditions, viz. to multiply substantial individuals within the species ; since in any material substance we can distinguish four, and only  four, elements : matter, form, subsistence (i.e. that by which the thing is put in the category of substance, and made self- supporting or existing per se, or on its own account), and existence. The last two cannot possibly be the principle of individuation, since they both belong to the existential order, and so presuppose, as a necessary condition of their own individuality, an individual nature already constituted. The reason of this is that existence being, in itself, all of a kind, must, if it is to be differentiated and made individual at all, be so differentiated by something other than itself, i.e. by nature. Moreover, we are, in fact, asking how we can have an individual nature, so that the question is concerned with the order of nature or essence, not existence. Neither can form be the principle we are looking for, since form differentiates things specifically, for the very conception of form implies that it is form which makes a thing to be of a determined species: so that when form varies, the species varies. Consequently, matter, as the only remaining element in the thing, must be the principle of individuation. Matter, however, does not seem to be capable of filling the role required of it, for it is, as we have seen, altogether potential and undetermined in itself, so that it could not determine, or differentiate, anything else. If, then, it is to do this, it must be in some way determined. Such determination as is required evidently cannot come to it from substantial form, since we are looking for numerical, not specific, determination : while the very word ' numerical' suggests that it does come from that accident, which is most closely united to it, and which is numbered, viz. quantity ; which is also, as we saw, individual of itself (cf. p. 65). In so far, then, as matter has a relation to this quantity rather than that, it can be, and is, the principle of individuation.
Again, [156.1] if we look at the question directly we see that two things are required for the principle of individuation ; first, that it should be an intrinsic substantial principle of incommunicability of form ; and, second, that it should be the principle whereby one body is made distinct from all others. Now, that matter is an intrinsic substantial principle is clear,  and moreover, being the basic and primary substratum of bodies it is unable to be received in anything else; from which it follows that any form which is received in it will likewise be unable to be received over again, and so will be rendered incommunicable so far as reception in a subject is concerned. The principle of distinction from others, on the other hand, is not matter, since this is in itself undifferentiated ; while the source of differentiation and division is extended quantity, for a thing is rendered naturally incapable of existing in several things if it is undivided in itself, and divided from all others. It is clear, moreover, that it is extension which divides substance, and so is a kind of individuating principle, inasmuch as forms are numerically differentiated by being in different parts of matter. That quantity is indeed, in this way, a principle of individuation can be seen in the order of pure quantity, inasmuch as we can imagine several lines of the same species, differing only by their position in space : and the same is true of other geometrical figures. Such difference in position, however, belongs to quantity. Hence a double principle of individuation is required, matter and quantity, or matter determined by quantity. From this we can see the way in which the phrase ' materia signata quantitate ' ought to be understood : a much controverted question.
Sylvester of Ferrara held that materia signata is a compound of matter and the quantity which actually informs it. This idea is perfectly clear and acceptable if we consider an existing individual; which, of course, has a particular quantity; but it is not satisfactory if we consider the individual in the process of coming into existence, and attempt to determine how it came to be individualised; since the matter could not be actually informed by a particular quantity until it had already received a substantial form. Now, it is precisely with the individuation of this form that our enquiry is concerned; and so we cannot ascribe such individuation to actually informing quantity, since being posterior to form it cannot be, in the same order, prior to it, and so cannot make the matter to be this rather than that, and thus individuate form.
 In order to meet this and other difficulties in the opinion of Ferrariensis, Cajetan and the majority of Thomists say that materia signata must be explained as first matter which has a radical requirement for this quantity rather than that: for first matter, being the potential principle of bodies, requires quantity.
First matter in general requires quantity in general, and so this or that determined matter requires this or that determined quantity. Hence the radical requirement for a determined quantity is considered as prior to the coming of substantial form, and actual quantity, to the body. This, perhaps, lessens the difficulty, but does not clear it up ; for how can matter which is altogether undetermined have a determinate requirement ? To answer this an appeal is made to the Aristotelean principle of reciprocal, priority of mutual causes. [158.1] According to this principle, causes, which are causes of one another are in different genera of causality ; and in this case, quantity, being an accidental form, is posterior to substantial form in the genus of efficient causality, but, since it is at the same time a disposition which disposes matter to receive this form, it is prior to it in the genus of material disposing causality. So the matter in which the new form is about to appear, being disposed to receive this form, is also disposed to receive the quantity which goes along with it. This explanation, however, seems only to give us matter with a requirement for some quantity within the limits of the quantities which are suitable to the form in question, as e.g. the quantities suitable to elephants as opposed to those suitable to mice. Such quantity, it is plain, cannot be said to be individually determinate ; in fact, the very idea of it is of that quantity outside whose limits we should not find a member of the species, and within whose limits we might find any individual of it, not a particular one. Now, as we have seen, quantity essentially consists in a plurality of parts, and one quantity is differentiated from another, and is this quantity as opposed to that, by a different  order of parts in the whole. So, in a homogeneous body one part differs from another by its position in the whole body, and having thus once acquired an individuality it retains it, even if its position in the whole be changed. If we apply this idea to a body which is about to undergo a substantial change, we see that at the instant before the change it has a determinate order of parts, and occupies a determinate ' situs ' or position with respect to all the other bodies in the universe. Then comes the change, and the new form is drawn out of matter under the action of the agent, the matter having been so modified as to be disposed to receive just this form and no other, among such predispositions in it being that it requires to occupy a definite situs, viz. that of the corrupted body. Thus the new body also has a requirement for occupying this same situs, and so is made individual. Having once gained such individuality it can retain it, i.e. it can remain divided from every other body by reason of its actual quantity at any given moment, and remain unable to be subjected in any other by reason of its matter. Being thus an individual, if, as in the case of living things, it takes up new matter into itself and grows, thus altering its quantity, it does not thereby lose its individual identity, since it makes the new matter part of itself, both specifically and individually, by a continuous process.
If this theory be correct, it is evidently in accord with S. Thomas' requirement, in the last phase of his thought on this question, for a determinate quantity as a co-principle of individuation with matter ; and avoids the difficulty which he eventually found in accepting the Averroist theory of matter affected by unterminated quantity, viz. that such quantity must be conceived as prior to substantial form in the matter. According to the view just outlined, there is no real priority of quantity, whether determined or undetermined, to form, but merely a requirement in the matter for the occupation of a determinate situs or position, owing to the fact that the body at the instant of corruption actually occupied that situs. Thus, no actual quantity remains through the change, but the matter has been predisposed to receive a form accompanied by a determined quantity. The [16o] quantity in the generated substance will not be numerically the same as that in the corrupted one, since, like all other accidents, it will be individuated by its subject: even though, as we saw, it possesses a certain distinction and individuation of its own. Its actual dimensions, qua dimensions, remain the same, but they are now the dimensions of the body B, whereas before they were those of A. The fact, however, that they are the same ; in other words, that the generated body occupies the same situs as the corrupted one, and that the matter which is in each has therefore a requirement for this situs, enables us to say that this matter remains the same under the change. ' This ' matter, which is marked out as ' this' by the requirement for a definite position and quantity, is found both in the corrupted and generated body: a state of affairs which seems to be demanded by our common way of talking about such changes, as, for example, this wood has turned into this ash ; this dead body is the body of such and such a man, and so on. [160.1]
It seems, then, that there can be no doubt that matter is the principle of individuation, since, as S. Thomas says : ' Differentia qua ex forma procedit inducit diversitatem speciei ' (Contra Gentiles, Lib. II, Cap. 93), which, as we noticed before, is a consequence of the principle that act, if it is to be limited and multiplied must be so limited by potency.
Nevertheless, certain further difficulties arise with respect to the theory, for it seems that if first matter has a requirement for a definite quantity, it is already determined to a certain extent, or actuated, and so does not lose all its actuation in substantial change, in contravention of what we have already seen is necessarily required in such change. This, however, is not the case, for just as first matter in general is not a capacity for receiving all forms of whatsoever kind, but only material ones, so that it is determined extrinsically, though not intrinsically, similarly' this ' matter has a great deal of its capacity taken away from it, but nevertheless, what remains is a sheer capacity, not any positive determination. The Scholastics express this by saying that it has a transcendental relation to ' this ' quantity, i.e. a relation which is not something added to it, but is its very self; just as matter as such has a transcendental relation to material form as such. They are correlatives, one implying the other. The matter remains purely potential, but its capacity is limited ; as in the case of two vessels of different sizes, the smaller one's actual content would be less than that of the larger, and yet both may be equally empty ; so, in the case of our two ' matters,' both may be equally potential. The matter which has a transcendental relation to a definite quantity is no less potential than matter in general, but there is less potentiality.
Again, it might seem that our principle, though sufficient to account for the individual distinction of two bits of inanimate matter, such as two stones, is hardly sufficient when we come to things of a higher order, such as two dogs, and still more two men. This difficulty arises, partly, from the fact that we often confuse individuality with personality; but we can hardly insist too much on the distinction between them, for they are, in fact, at the opposite ends of the scale. Quite apart from this theory of individuation, consideration shews, as we shall presently see, that personality is the highest and most perfect thing in nature, whereas individuality is almost the lowest. [161.1] Further, it is to be noticed that by individuality we mean something negative : this thing is not that, whereas, as we ascend in the scale of beings, we get, along with this negative character, a gradual increase of a positive character as the things become more and more masters of themselves. Such self-mastery is in proportion to the capacity for action on one's own account, by and for oneself; in other words, in proportion to the capacity for immanent action. Now a plant has immanent activities which inanimate things have not, being able to nourish itself, grow, and reproduce its kind; animals have still more of such immanent activity, for they direct themselves by sense, and men most of all, being able to determine their own  actions both by sense and reason. Thus we have a growing centralisation and self-control, but the negative division from other bodies which is characteristic of individuality remains the same ; and we can legitimately attribute individuation to matter, while recognising a growing unification in the thing itself as we ascend the scale. [162.1]
As to the way in which we distinguish one individual from another, there is no doubt that we do so by remarking their different accidental characteristics, such as position, dimensions, shape, colour, etc.; but though individuality is known to us by means of these, it would be a confusion of thought to conclude that they are therefore its principle.
If, then, the principle of individuation be matter affected by a transcendental relation to a determined position, it follows that material substances are not individuated absolutely in themselves, but in relation to other individuals, from which they are separated ; and consequently that the principle of individuation, though intrinsic, cannot be, as Suarez maintains, the entity of the thing considered absolutely. For, if this were so, the matter of one thing, considered absolutely, would be different from the matter of another, and so would not be common matter. This would lead us to conclude that any two substances differ essentially or specifically of themselves. Such a conclusion, however, is definitely Nominalistic, since there could, in this case, be nothing universal in nature. All things would be essentially different, and no essential concept could apply to several of them. On the other hand, if, with Scotus, we make individuation something added to the nature of the thing, we equivalently assert that nature without such addition is universal; and since such nature is found in individuals, the universal as such will be found in individuals. This view, therefore, tends towards an extreme form of Realism. In saying this our intention is only to point out the tendencies which seem to be implicit in the views of these two great thinkers, not to suggest that Suarez was a Nominalist, or Scotus an advocate of an extreme form of Realism. In any case, the balance  between an extreme Realism and Nominalism is undoubtedly preserved in the theory of S. Thomas, in which the individual neither absorbs the universal, nor is absorbed by it. Such a moderate realism avoids both scepticism, which is the outcome of Nominalism, and Monism, from which extreme Realism cannot escape. From this point of view, therefore, this thesis may be said to be a postulate of the Thomist theory of knowledge. Indeed, whether we look at the change and motion in the material world, or at the multiplication of individuals in it, or at our knowledge of it, the facts force us to say that the only intelligible explanation which can be given of them is that this world and all things in it are composed of two elements, one of which is actual and the other potential, and of which the latter limits the former.
[151.1] Summa Theol., Pars I, Q. 29, a. 4.
[151.2] For a full discussion of this question see Nys, Cosmologie, Vol. II, pp. 281-294.
[152.1] Cf. Met., 1038b14 ; 1071a27-29 ; Phys., 412a6-9.
[152.2] Met., 1034a5-8 ; cf. 1016b32 ; 1035b 27-31 ; 1054a 34 ; 1074a 31-34 ; Phys., 278a7-b3.
[152.3] In Isagogen Porphyrii, ed. Brandt, pp. 241, 9 ; cf. De Trinitate, I.
[153.1] De ente et essentia. Cap. 2.
[153.2] In Boethium de Trinitate, Q. 4, A. 3, et ad 3um.
[153.3] e.g . Quodlibet, XI., a. 6, ad 2um.
[154.1] Opus Oxoniense, II, dist. III, Q. 2, No. 15.
[154.2] Disp. Metaph., V. Sect. 3. Cf. Mahieu, Francois Suarez, pp. 112 ff. The greater part of the foregoing account of the history of this problem is derived from Fr. Roland-Gosselin's masterly analysis in his edition of the De Ente et essentia; particularly with regard to S. Thomas' opinions.
[155.1] Cf. Salmanticenses, Cursus Theol., Vol. I, Tract. I, Disp. I, Dub. 2. No. 45 f.
[155.2] The Reactions between Dogma and Philosophy (1926), p. 368.
[156.1] For the following argument cf. Summa Theol., Pars III, Q. 77, a. 2.
[158.1] Cf. S. Thomas in V Metaph., Lect. 2 ; de Veritate, Q. 28, Arts. 7 and 8. John of S. Thomas, Cursus Phil. Phil. Nat., P. II, Q. 1, A. 7, and Q. 9, A. 4. Salmanticenses Cursus Theologicus, Tom. I. De Principio Individuationis, Disp. I, Dubium 5, Sect. 3.
[160.1] This theory of individuation, in so far as it attributes an important role to situs,was proposed by Fr. Geny, S.J., Gregorianum, April 1921, pp. 290 ff., with acknowledgements to the Venetian Province of the Society.
[161.1] Cf. Maritain, Three Reformers, pp. 19 ff., where this distinction is shown at length with many of its applications.
[162.1] Cf. M. C. D'Arcy, S.J., Thomas Aquinas, pp. 148 ff., where this difficulty is discussed and the notion of immanence emphasised.
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