[matter as principle of multiplicity]

For the multiplicity (takaththur) of things is in respect of either quiddity and form, or relation to the element (ʿunṣur) and matter, which [in its turn] is multiplied due to the places which surround all matter in space (jiha), and the times that are specific to each one of them [sc. material substrates] in its origination, and the causes which divide them. But [souls] do not differ in quiddity [224] and form, for their form is one. Therefore they differ only with respect to the recipient of the quiddity, or that to which the quiddity is specifically related, namely the body. As to whether it is possible for the soul to be existent without a body, [in that case] it would be impossible for one soul to be numerically distinct from another. This applies absolutely to everything. For things whose essences are mere notions, and whose species have been multiplied through their individuals, can be multiple only on account of their subjects (ḥawāmil), recipients, effects (munfaʿilāt), or through some relation to them and to their times.

[individuation through direct reference/indication]

The individual becomes an individual only through the conjunction of accidental properties (khawāṣṣ), both necessary and non-necessary, with the nature of the species, and the assignment to it of designated (mushār ilayhā) matter. It is impossible for intelligible properties, however many they be, to be conjoined to the species so that the individual would thereby subsist in the intellect, without there being in the end [also] a reference to an individuated notion (ishāra ilā maʿnā mutashakhkhaṣ). For if you were to say: Zayd is the tall, handsome writer, and so on, [giving him] as many descriptions as you wish, Zayd’s individuality would not become determinate for you in the intellect. Indeed, it is possible for the notion assembled from the totality of all these [descriptions] to belong to more than one individual. Instead, what so specifies it [as an individual] is existence (al-wujūd) and reference (ishāra) to a notion that is individual. For instance when you say that he is the son of a certain person, that he exists at a certain time, that he is tall, and that he is a philosopher, and furthermore it so happens that no one at that time exists sharing these descriptions, and you have had previous acquaintance (maʿrifa) with this happenstance, this thanks to perception of the kind that indicates [the particular individual] through sensation, by way of indicating a determinate person himself (bi-ʿaynihi) and a determinate time itself (bi-ʿaynihi)—it is then that the individuality of Zayd is established, and this statement would indicate his individuality.

[against individuation through a combination of universal attributes]

There is, however, no definition of the singular in any respect,⁶ although the composite does have definition in a way. For definition is composed of characterizing (nāʿita) names that cannot possibly indicate (laysa fīhā ishāra) any concrete thing. For, if these did indicate [something concrete], this would be nothing but naming, or reference by making a motion, pointing (ishāra), and the like, and would not make the unknown understood through characterization. Since every name confined to the definition of a singular thing indicates a characterization, and since characterization may be applied to a number [of things], with composition not excluding this possibility from it, then [it follows that] if A is a universal meaning and B, another universal meaning, is added to it, then there could be some specification (takhṣīṣ mā). But if [this is] specification of one universal by another universal, then the thing that is both A and B would remain universal, and sharing in common may still apply to it. For example, if you define Socrates here by saying, “he is the philosopher,” then this can be still shared in common. If you say, “he is the pious philosopher,” this can be shared in common. If you say, “he is the pious philosopher unjustly put to death,” this can still be shared in common. If [189] you say, “he is the son of so-and-so,” there is still the possibility of sharing in common, besides which, so-and-so [i.e. the father] is an individual that [needs] to be understood (ṭaʿrīf) just like Socrates does. If that individual is then understood by indication (ishāra), or by a proper name (laqab), then we are back to indication and proper names, and we have failed to give a definition. Even if one goes further and says, “he is the one put to death in such-and-such city on such-and-such day,” this description, despite having been made individual by artifice, is universal and can be said of many, unless it is [somehow] tied to an individual.

[prime matter and motion as the causes of multiplicity]

The multiplicity of blackness, or of anything that has multiple individual [instances], is thus due to a cause. Conversely, the existent that has no cause cannot be made multiple, given that if it were many, there would be a cause for the existence of that multiplicity. Also, because this multiplicity would happen through division (qaṭʿ), and division can occur only by cause of the receptacle (qābil), since [division] is a notion extrinsic to the true reality of the thing. So division occurs only insofar as there is the receptacle. The receptacle is matter (mādda), so division occurs only to body. Therefore, the reason for multiplicity is prime matter (al-hayūlā).

From the foregoing you have learned that motion is the cause of everything originated. So divisions that occur to bodies are due to the multiplicity of the dividers, and the multiplicity of the dividers is by cause of motion. For multiplicity must be traced back to something that is multiple in itself, and this is motion. Thus, if there were no motion, then by this rationale there would be no multiplicity. As for the multiplication of motion, its cause is [motion] itself, since motion entails [multiplication] and it is according to the existence [of motion] that it comes to be and occurs in sequence.⁷

[matter, time, position, and motion as individuating factors]

You should know that the very conceptualization of an individual prevents its being anything else. Sharing in common cannot apply to the concept [that corresponds to an individual]. By contrast, the essence of a thing and its constituents do not exclude the application of sharing in common. So this must be due to some accident. But the concomitant accident (al-ʿaraḍ al-lāzim) is shared in common. So it must be due to some accident that attaches (lāḥiq) [to the essence] without changing, given that the reason for a thing’s being concrete cannot be eliminated while the effect remains, as you will learn. So [the individuating accident] must be attached, but not concomitant (lāḥiqan lā lāziman). Now, what is attached comes to be attached by means of matter. So the multiplication of individuals, of whatever sort, must be material. Furthermore, what is attached must come to be attached with a temporal beginning. But whatever has a temporal beginning is originated, and everything originated is preceded by matter. So [again] what is attached comes to be attached by means of matter. And what is attached at two different times does not exclude sharing in common, so the unity of time must [also] be a condition for individuation.

If you consider the nine categories, [you will see] that nothing that [falls under] them is individuated through itself so as to exclude common sharing, with the exception of position (al-waḍʿ). For “where” is not individuated through itself until it is specified by some position. Therefore, what individuates is position together with unity of time. Anything that has no position, or does not happen in time, has a quiddity [506] that is in no way divided among [multiple] individuals in existence. On this basis, you may know that motion is the reason for the multiplicity of the individuals of a species. As for the unity of position—like that of the human being from the start of his existence until the end—this is like the unity of time, and is the unity of the connection of positions that are multiple in potentiality.

[individuation is essential when it is not through matter]

Furthermore, some things have individuation through themselves, as in the case of the Necessary Existent in itself. Some have individuation through the concomitants of their essences, like the Sun. For in this case, position is among their necessary concomitants. Or like the active intellects, as we will show. Then there are those [whose individuation is] through something attaching accidentally from the beginning of [their] existence: we have shown that this is the class [of things individuated by] occupation of space (taḥayyuz) and time, not by anything else.⁸

[concretization requires no additional factor]

As for concretization (taʿayyun), it means simply the distinction (tamyīz) of one thing from another. Whatever is distinct from anything else, so that one can indicate it (with either a sensory or intellectual indication), is concrete. It need not be the case that distinction occurs through some existing item (amr wujūdī) that is additional to the essence of the thing. Various quiddities differ from one another through themselves, not through some other item additional to them. If they are existent, then each of them is a concrete object and its concretization is not through an item additional to it.

[arguments that individuation is something positive]

There are two ways to argue that these concretizing and individuating [factors] are something positive (thubūtī). [165]

First, the concretization and specificity of a thing are equivalent to its concrete being (huwiyya). The individual, insofar as it is what it is, is positive. Concrete being is intrinsic to it insofar as it is what it is. And whatever is a part of something positive, insofar as it is something positive, must also be positive. So concrete being is positive.

Second, if concretization were something privative (amran ʿadamiyyan), then it would be equivalent to either (a) the privation of not-being-concrete, without qualification, or (b) the privation of being concretized as something else (ʿadam taʿayyun ghayrihi). (a) If it is equivalent to the privation of not-being-concrete, without qualification, since it is self-evident that the latter is something privative, then concretization would be the privation of a privation. Therefore it is [after all] something existing (wujūdiyyan). (b) But if it is equivalent to the denial of concretely being something else, then concretely being that other thing might be (b1) itself privative, so that its privation would be something positive. But one thing’s concretization should be like another’s concretization, so anything else’s concretization should be positive too. (b2) If, on the other hand, concretely being something else is something positive, and one thing’s concretization is like another’s, then it should be positive for it to be concrete as well.

[arguments against the same position]

One may say that concretization (taʿayyun) cannot be something positive, relying on the following arguments:

First, if concretization were something positive and additional to the quiddity, then [this addition] would also have to be concretized, and this concretization would have a third concretization, yielding an infinite regress.

Second, the specification of that additional [first-order concretization] with that [second-order] concretization, to the exclusion of any other, can happen only once that concretization is distinguished from another. Otherwise its being specified by that [concretization] would be no more fitting than its being specified by any other, nor would it be more fitting than something else being specified by that [concretization]. Hence the specification of that distinguishing factor by that distinction (tamayyuz) would come only after it is already distinct from everything else. Therefore it would have to be distinct before it is distinct, which is absurd.

Third, if the individuation of the individual that shares in a species along with something else were something additional, then there would need to be a further factor involved. (a) It cannot be that quiddity [itself], since otherwise its species would be in this individual [alone]. (b) Nor can it be the agent cause, since the agent’s role is only to bestow existence, and bestowing existence does not entail that the result is that concrete object. (c) Nor can it be the formal cause, since its existence is posterior to the existence of the subject of inherence, so it cannot be the cause of its concrete being. (d) Nor can it be a final cause, since its existence is [likewise] posterior to the thing’s existence. (e) Nor can it be a receptive [i.e. material] cause, since the problem of the concretization of that receptacle will be the same as the problem of the concretization of this thing. [The receptacle would become concrete] either due to the concretization of the thing, resulting in a vicious circle, or due to the concretization of [a further] receptacle, resulting in an infinite regress. Alternatively, [the receptacle might be concrete] due to the very quiddity of this receptacle, which would imply that each type of receptacle will be for [just one] individual. But this is absurd, given that bodies have corporeality in common. Either there is nothing that receives it, in which case we have discovered items that are one in quiddity as individuals, without this being explained by receptacles; or [their corporeality] does have something that receives it. But if these receptacles share their quiddity, then the whole argument can be run again. If on the other hand it is not like this [sc. they do not share their quiddity], then in that case [166] the receptacles of the parts that one may assume in what is corporeal would need to be actually distinct. But the parts that can be assumed in it are infinite. So these receptacles, which are distinct in terms of quiddity, are infinite, and the corporeality that inheres in each one of those receptacles would be different from the corporeality that inheres in another. So body would be composed out of an actually infinite number of parts, which is absurd.

Thus it has been established that when individuation is claimed to be additional [to quiddities], these absurdities follow, so this is false.

[solutions to arguments against a positive principle of individuation]

Response. Regarding the first argument: the solution has been presented in the chapter on existence, namely that if concretization meant anything other than being-made-concrete (taʿayyuniyya), in that case the meaning of being-made-concrete would have to be connected to some other meaning. Otherwise, concretization is concretized through itself, and its concretization is identical to itself, not additional to it, so no infinite regress follows.

Regarding the third⁹ argument: whenever the concretization of anything is not an effect of its quiddity, so that its species would be in [one] individual, then it must inevitably be in matter. Its matter will inevitably be specified by individual accidents. The individuation of the matter through these accidents is the cause of the individuation of that originated thing. It is impossible for any other instance of that species to be connected with that matter at that time, so that the problem [about how it is individuated] would arise. Nor do we say that that thing exists, and only then the concretization exists, and then after both have occurred, they come to be connected. Rather the occurrence of that thing in that specific matter just is its concretization. Recall what we have presented to you in the chapter on existence, as it provides an escape from many problems.

[the senses do not perceive concrete objects as such]

Perception of a concrete individual, insofar as it is an individual, is either through immediate feeling (bi-l-wijdān) (as when each person knows his concrete self, as such) or through sense-perception (as when we observe Zayd and indicate him).

This calls for further investigation. For sense-perception either connects to [the individual] as such, or to something that is common to both it and something else. The common view is that it is the former, but this may be doubted. For, if we posit two bodies equivalent to one another in shape, color, magnitude, and other sensible attributes, and each of the two is like the other, then if we see one of them and thereafter it is hidden from us, and then we see it once again, we will not know whether the one we saw first is the one we see on the second occasion, or [32] the other, which looks just like it. Obviously that which distinguishes one from the other is distinct from that which they share, since what is shared cannot be that which distinguishes. So if, when sense-perception connects to the concrete individual, it were connected to the item on account of which [the individual] is what it is, then it could not resemble something else, since it would be impossible for this [individuating] item to belong anything else. So, since [such] resemblance does occur, we know that sense-perception does not connect with [the individual] as such, rather [only] to an extent (al-qadar) that may be shared [with others]. Or, if sense-perception does connect to it as such, one could not confirm this in imagination. Now that you understand this, it should be clear that whatever each of us indicates about ourselves when we say “I” is distinct from whatever we indicate by [saying] “it.”¹⁰

[another infinite regress argument]

If these concretizations were something positive, then (a) if the quiddity to which these concretizations are related is existent, one individual would be two existents, not just one. Furthermore, in this case, the same problem would arise for each [of these two existents, the quiddity and the concretization] as arose before, and then each of them would be two existents as well. It would follow that everything is an infinite number of things, which is absurd. And even if one admitted this, there would need to be unity in it, since no multiplicity can be realized without unity. (b) If on the other hand [the quiddity] is not existent, then something existent [that is, the concretization] would be added to something non-existent and would inhere in it, which is absurd.

[matter as the principle of individuation]

You should know that the concretization of a quiddity is either (a) one of its necessary concomitants or (b) not. (a) The first option implies that this species is in only one individual. (b) On the second option, individuation [167] would call for a cause that is distinct from this quiddity, and the cause of individuation would need to be prior to the occurrence of this individuation. This cause will be either (b1) separate from that individual or (b2) connected to it. (b1) The former is absurd, since the relation of this separate [cause] to this individual is the same as its relation to another individual, so it cannot be the cause of the individuation¹² of that individual. (b2) If however it is connected to it, then either (b2a) it is inhering in the individual or (b2b) the individual is inhering in it. (b2a) The first option is absurd, since the subject of inherence is prior to what inheres in it, but the cause of individuation cannot be posterior to the individual. Therefore (b2b) the individual must be what inheres in it [the cause of individuation]. Thus, whenever the species of anything exists in many individuals, the multiplicity occurs only by reason of matter.

So everything whose species does not consist in its individuality, must be material. This may happen in two ways. First, individuation may be through a mere relation to matter without [matter] being anything within the object itself, as with the individuation of simple things and accidents. For their individuation takes place only by their occurring in their matter and in their subjects of inherence. Second, there may be [material] states additional to relations.

[accidents do not individuate]

Whatever the individuating factor may be, when we assume it to be non-existent and eliminated, there follow the non-existence and elimination of the individual, since when the cause is non-existent the effect’s non-existence is necessary. By contrast, this would not follow from the non-existence of any accident or property belonging to the individual. Therefore [accident or property] are not among the individuating factors. Rather they occur accidentally, only after individuation has already been realized. They are not constituents of the individual, but rather are constituted by it.

[problems with individuation and universality]

The qualification of one universal by another universal does not yield individuality. For if you say that Zayd is a human, this is something that is shared; and if you say he is a knowledgeable, pious human, this is still shared; and if you say that he is a son of so-and-so, who was talking today about this-and-that, at such-and-such a place, still none of this excludes being capable of being predicated of many.

Someone might say: the item that is added to the quiddity so that it is individuated is either (a) a quiddity or (b) not. (a) On the first option, quiddity as such is universal as well, but whenever one universal is qualified by another universal, it does not become particular, according to you. Hence, quiddity does not become concrete by reason of adding whatever is added; but it was assumed that it does, which is a contradiction. (b) But the second option is absurd, since what has no quiddity cannot be added to anything else.

One may respond as follows: why can’t it be that, although each quiddity (I mean, both the one that is individuated and the one that individuates) is in itself universal, each of them is the cause for the other’s becoming particular?

The questioner may respond: the particularity that you make out to be the effect of the two essences is universal too, since the true reality of “particularity” is univocally predicated of this particularity and that particularity. And if the particularity itself is a universal nature, how can the particularity come to be?

In order to solve these problems, some of them came to think that the particularity of each particular differs in quiddity from the particularity of any other. But this raises problems of its own.

[identity of indiscernibles]

A universal nature can occur as multiplied in extramental reality only through a distinguishing factor (bi-mumayyiz). For instance two blacknesses, or two whitenesses, must be distinguished from one another through an item apart from being blackness, which will be either the subject of inherence or something else. If neither is distinguished from the other, then the multiplicity will arise through blackness or whiteness itself, so that the quiddity of blackness would in itself imply that it is multiple. But we have already demonstrated that no quiddity can be realized that would imply multiplicity through itself. Furthermore, if this blackness is distinguished from unqualified blackness, then there occurs something together with it that distinguishes it, and the distinction is through some item additional to [its] being blackness. But if [this blackness] were unqualified blackness, and that blackness is also [unqualified blackness], then this blackness will be identical to that blackness.

Whenever a quiddity has a number of things falling under its species, it must be possible to indicate one of [these instances] separately, whether by sense-perception, estimation, or intellect. The one who indicates this [instance] is aware of it, and aware that it is distinct from another [instance]. But whenever one recognizes that one of them is not the other, one has already distinguished between them. So one has recognized something in [this instance] by which one recognizes it and distinguishes between it and another. This [distinguishing feature] is additional to the shared quiddity.

[against individuation through matter]

Some of the people of knowledge said: the very conceptualization of the individual excludes sharing in common. This is not by reason of its constituents, since the constituents in themselves do not exclude sharing, nor by reason of a necessary concomitant, since [things may] agree [in having this concomitant] and sharing is not excluded. Nor is it by reason of a separable accident, since this does not exclude sharing either. So it is determined to be by reason of matter (al-mādda).

Investigation and critique: this is wrong, for two reasons. First, when features and forms of one and the same species occur in a single matter at two different times, this results in two different individuals. The distinction [335] of one of them from the other is due not to matter, but to time. Second, prime matter (al-hayūlā), which is [supposedly] what individuates and excludes sharing, relates to the exclusion of sharing in just the same way as anything else. For its very conceptualization does not exclude sharing either: prime matter applies with one and the same meaning to multiple things. Given that none of the attributes of a thing exclude sharing, and nor does the very conceptualization of prime matter exclude sharing, and an aggregate of universals is universal, there is no benefit in what they go on to say.

[individuation vs. distinction; individuation through huwiyya]

Now that you understand this, you should know that a distinguishing factor (al-mumayyiz) is not the same an individuating factor (al-mushakhkhiṣ). Sharing in concrete quiddities is not excluded by reason of the distinguishing factor; we have already indicated an aspect of this in the principles of logic. Rather the concrete being (huwiyya ʿayniyya) of prime matter excludes sharing because of its being a concrete being. Likewise with blackness and whiteness. We have already shown that sharing in a true reality means nothing but correspondence (al-muṭābaqa). This is not just any correspondence, but the correspondence of something whose essence or true reality consists in being a perceptual representation of something else, without [this essence] itself being a fundamental concrete being. So sharing is excluded for things by their concrete being, whereas they are distinguished by their specifying [features]. The individuation of a thing just belongs to it in itself, whereas distinction is only relative to what shares [with it] some common character (maʿnā), and the aspect of multiplicity. So if there is nothing [that shares a character with it] then it requires no distinguishing factor in addition; yet it still has individuation. Otherwise, [given that] the aggregate of [features] that do not exclude sharing itself fails to exclude sharing, all particulars would be universals. But in fact two things can be distinguished, one from the other.

[individuation through huwiyya]

The only judgment to make is that individuation happens in light of the concrete being that occurs concretely (bi-iʿtibār al-huwiyya al-wāqiʿa ʿaynan). Any concrete being that occurs concretely is individuated, and excludes sharing. The distinction between distinguished things, though, is through attachments (lawāḥiq).

[kinds of distinguishing features]

A single species of features is distinguished numerically either through numerous subjects of inherence or through time, if the subject of inherence is the same. As for the case of perfection and deficiency, this can also serve to distinguish; we will mention this case in what follows.

Investigation and reminder: some followers of the Peripatetics, having admitted that when we see something and its image reflected in a mirror, the forms of both are in one and the same subject, distinguished [between the two forms] on the basis of their relation to their sources. For one of the two is due to the bearer of the form, the other through the mediation of the mirror. We however force them to acknowledge that many numerically distinct things belonging to a single species, and found in a single subject of inherence, may differ in relation to [their] sources and efficient causes. In light of this, their argument fails, which was meant to establish that the soul is not based in a bodily organ (ghayr āliyya). [Their argument was] that if it were in an organ, and it were to grasp its organ intellectually through the occurrence of a form other than the form that belongs to the bearer in itself, then two different forms of a single species would occur in one and the same matter. But one may say to them: the two forms do differ, since one of the two is in the thing itself without the meditation of a faculty, whereas the other is representational, and occurs through the mediation of a faculty.

[distinction and time]

Another investigation: you objected by saying that two features of a single species are distinguished from each other, if the subject of inherence is the same, in virtue of time, but time itself (if it is the measure of the motion belonging to the celestial sphere¹⁴) is in a single subject of inherence. So how is each of its parts distinguished from the others?

Response: the parts of time are distinguished from one another through themselves.

But this does not show anything, since if this were possible, then one could say of any two things within a single species that they are distinguished through themselves, without any distinguishing factor. The parts of time share in the quiddity and the subject of inherence, so they cannot do without a distinguishing factor.

To which it might be responded: time is one not just in species, but also as an individual. For it is one and the same continuous item (amr muttaṣil wāḥid).

But this is not a successful response either, because even if time is one and continuous, it is still divisible into distinct parts.

The truth is that the parts of time never coincide with one another in such a way that one of them would [need to] be distinguished as a concrete individual. But with regard to conception and intellection, some parts may be distinguished from others in terms of priority and posteriority, and in terms of proximity to, or distance from, what imagination (wahm) takes as a beginning. They are also distinguished by relations to various celestial bodies, like the stars, in terms of their oppositions, conjunctions, and interrelations.

Problem: you said that time is one of the factors that distinguishes between two features that have a single subject of inherence. But they might coincide in a single subject of inherence, in such a way that one of them originates at one time and another at a second time. Then they would remain together, while differing in the time of their origination.

[339] Response: if the time of the origination of both has passed, the relation they each bear to it no longer remains, so there is no distinction in terms of a relation to time, [this relation] having passed by means of the passing [of time]. The factor that distinguishes between two things must occur while they both still exist and are distinct.

[against individuation through position]

Another investigation: it is worth noting here that some people allege that the only category that is individuated through itself is position (al-waḍʿ), and that “where (ayn)” is not individuated through itself in the absence of position. But this is a mistake. For the case of position is no different from that of the [other] categories, since nothing excludes that two bodies may be in one and the same position at one and the same time, or that both (or just one body) are in one and the same position and in one and the same “where,” but at two different times. For that which exists at one and the same time, two positions may be distinguished through two subjects of inherence and two “wheres.” Also, what is in one and the same “where” may be distinguished through two times. But individuation in the sense of excluding sharing belongs to position to the same extent as to anything we have explained above.

[individuation is distinct from quiddity as such, but not from quiddity in concrete individuals]

Every thing has a true reality through which it is what it is. [The true reality] is distinct from its individuation, since the mere conceptualization of the quiddity as such does not exclude that sharing applies to it; whereas the mere conceptualization of the individual as such does exclude that sharing applies to it. Thus quiddity is distinct from being an individual, so the individuation is not the quiddity. On the other hand, its concrete being (huwiyya) cannot be separate from the concrete being of the quiddity in concrete individuals. Otherwise the quiddity in concrete individuals would [have to] receive individuation, and whatever receives anything has an individuation that is distinct from that which is received. So the quiddity would have an individuation distinct from its individuation, which is a contradiction. Therefore, individuation cannot be separate from quiddities in existence.

[identity of indiscernibles and the need for an individuating factor]

Whenever a universal nature is multiplied in concrete individuals, then its multiplication in concrete individuals must be additional [to it]. For this human is other than that human. If his being so were in virtue of unqualified humanity, then [this human] would be the same as that [human]. So they must differ in some respect. If that which two things share is merely accidental, then the distinction lies in the quiddity to which the accidents occur. If [what is shared] is a genus, the distinction lies in the specific differences. If [what is shared] is a species, then the distinction lies in separable accidents. For in the case of quiddities that have the subject of inherence, their difference is due to the difference between their bearers. But if their subject of inherence happens to be one and the same, then they differ in time, like two cases of blackness that occur in one and the same subject of inherence, one after the other has perished. On this basis, it is clear that two different similar things cannot co-occur in one and the same subject of inherence, since they would not be distinct.

[return of the non-existent]¹⁵

For this reason, there can be no return of the non-existent, since whatever occurs at the second moment of time is distinct from what occurred at the first moment; it would be absurd that it should return together with the returning of its [first] time at the second time.

[analogical distinction]

If something is predicated analogically (bi-al-tashkīk), distinction may result in it due to intensity and weakness, like in the case of existence. Or it may result through these and through other distinguishing factors as well, for instance that which is more intensely white.

[subject of inherence as the principle of individuation]

Differing accidents occur to a quiddity only by reason of the receptacle. Otherwise the reason would be either (a) the quiddity or (b) some separate thing. The (a) first option is absurd, since otherwise a separable accident would be a necessary concomitant, which is a contradiction. (b) The second option is absurd as well, since otherwise specifying certain instances to the exclusion of others would be specification without any specifying factor (takhṣīṣ bi-lā mukhaṣṣiṣ).

[individuation through combination of quiddities, not universals]

You should know that particularity does not necessarily arise from the qualification of one intelligible universal by another. For, when the universal human in the intellect is qualified with the universal black in the intellect, the universal black human results in the intellect, without becoming anything that would exclude sharing in common. However, when the natural universal—that is, the quiddity as such—has another quiddity added to it in extramental reality, namely the quiddity of concretization (māhiyyat al-taʿayyun), then it does become a concrete individual that excludes sharing.

[individuation is not privative]

Concretization cannot happen through something privative (ʿadamī), as non-existence (al-ʿadam) has no concrete being (huwiyya) in concrete individuals, so nothing can be concretized by it. Also because concretization is a part of the concrete, and the concrete is existent; but [any] part of the existent is existent. So concretization is existent.

[arguments that individuation is not positive]

First, if concretization were something positive, then it would have a quiddity that the concretizations would share in common. Then their concretization would require a further concretization, yielding a regress. [38r] Or we may say: if that which renders things concrete were affirmative, then it would have a universal quiddity. Inevitably it would need a further concretization, yielding the regress.

Second, if [concretization] were something positive, then its being added to a quiddity would presuppose [that quiddity’s] being distinct from other [quiddities]. So [that quiddity] would have a concretization before this concretization. So it would be concretized before being concretized, which is a contradiction.

Third, if [concretization] were something positive, the concretization of an individual that shares the same quiddity as others would be either in virtue of (a) the quiddity itself, (b) an agent, (c) the receptacle, or (d) something else. (a and b) The first option is wrong, as is the second. Otherwise its species would be restricted to its [one] individual. (c) The third option is wrong too, since if [concretization] were due to the receptacle, then (c1) if the concretization of the receptacle were through another receptacle, this would yield a regress. (c2) But if it were through that which is received, a vicious circle would follow. (d) The fourth option is wrong as well, since concretization is only conceivable in these three ways.

[responses]

But all this is unconvincing. As for the first, we do not concede that if it were positive, it would have a quiddity that the concretizations would share. Why can’t every species of concretization be restricted to an individual? As for their argument that if concretization were something additional, it would have a universal quiddity, we say: if you mean by this the natural universal, we do not concede that it has a [second order] concretization. This would follow only if other [concretizations] shared in [the quiddity of this concretization] in external reality. But if you mean by it the intelligible universal, we do not concede that this must have a universal quiddity [either]. This would follow only if it occurred in the intellect in such a way that universality applied to it. Furthermore we can ask, why do you say that this sort of regress is wrong? You need to provide a demonstration for this.

As for the second, we say: we do not concede that if the adding of the concretization to a quiddity presupposes that the latter is [already] distinct, it follows that [the quiddity] requires another concretization. This is because the quiddity is distinct from other quiddities through itself (bi-dhātihā).

As for the third, we say: we do not concede that if the concretization of the receptacle were due to that which is received, a vicious circle would follow. For the quiddity of each of them would be the cause of the concretization of the other, rather than the concrete being of each of them being the cause of the concretization [of the other]. So, no vicious circle follows. And even if we granted this, why do you deny that the fourth option is intelligible? Why couldn’t the agent ensure the concretization, but on the condition of some disposition that has occurred to the receptacle, by reason of something originated? This originated [factor] would depend on another originated [factor], and so on to infinity.

[another version of the regress argument]

If concretization were something positive (thubūtī), and if it were caused by the quiddity, then the quiddity would be prior to it in terms of concretization, given that the cause must be concrete before the effect is concrete. So the quiddity would have another concretization; that concretization would have another concretization, and so there would be an infinity of concretizations between the concretization and the quiddity, which is absurd. If, on the other hand, [concretization] were caused by a separate cause, then, if a given quiddity were specified by occurring as many concrete individuals, as opposed to others [that might have realized the same quddity], then this would be preponderation without a preponderating factor (tarjīḥ bi-lā murajjiḥ), which is absurd. […]

[response: matter and a separate cause combine to individuate]

[268.15] We do not concede that if [concretization] were caused by the quiddity, the quiddity would be prior to it in terms of concretization. Why can’t it be prior to the [concretization] in terms of existence alone? For existence might occur to the quiddity, and this existence could entail the existence of the concretization, and the conjunction of the two existences would be the existence of the individual. And even if we did concede this point, why have you said that, if it were caused by a separate cause, then the specification of the quiddity with multiple individual [instances] by certain concretizations and not others would be preponderation without a preponderating factor? Why can’t [269] concretization occur by reason of certain dispositions that occur to the receptacle, by some different cause?

So it should be known that, when individuation is caused due to the quiddity, the species of [the quiddity] is [uniquely] in its [one] individual. But if its species is not restricted to its [one] individual, then concretization happens by reason of the receptacle together with a disposition that occurs to [this receptacle] through causes external to it.

[against arguments in favor of privative individuation]

The first argument, which [al-Rāzī] ascribes to the theologians (al-mutakallimīn), holds only on the supposition of affirming that there is some universal “concretization,” which different concretizations share in common. But if this were so, then the quiddity of concretization would be shared by them, and it would not be concretization. Here “concretization” means simply that through which similar things are differentiated; it is not something shared in common. “Concretization” or “that through which there is differentiation” is applied accidentally to different instances of concretization. Every instance of [concretization] is distinct from any other through itself, not through a further concretization. So it does not follow from this that the concretization has a further concretization.

As for the second argument, which says that if concretization were positive, then it could not be added to a quiddity unless the quiddity already existed, this is not right. For concretization is that which, because it is added to the quiddity, the quiddity exists. No circle follows from this, nor does concretization need to be affirmed twice.

As for the third argument, which says that the existence of the quiddity is different from the existence of the concretization, and they are two, or even an infinite number of things, this isn’t right either. For existence is attributed to the quiddity by reason of the attribution of concretization to it. Just as the quiddity that is different from existence does not have existence as an attribute, insofar as it is distinct from existence, so likewise concretization does not have existence as an attribute insofar as it is concretization. As for the concretized quiddity, it is just one existent.

[individuation is merely conceptual, and is explained by matter]

Individuation is among the items that are conceptual (min al-umūr al-iʿtibāriyya). When we consider it insofar as it is an intelligible (ʿaqlī) item, we find that other individuations share in it. But this yields no regress: the regress is stopped as soon as one stops [adding] consideration.

As for [the principle of] individuation, it may be the quiddity itself, in which case there is no multiplicity [i.e. there is only one thing that has this quiddity], or it may go back to the matter that individuates by means of the specific accidents that inhere in it.

[Ibn Kammūna: can incorporeal matter individuate?]

They showed that the individuation of things that agree in species can only be because of matter. Yet in all the cases where they actually put this premise to use, they make it more specific than what they have shown. For matter without qualification is more general than the corporeal [matter] and other [kinds of matter]. Nor have I found them giving a demonstration indicating that this [individuating] matter is the corporeal one, specifically. A number of passages in their books show that they do allow incorporeal matter, like what they have mentioned about the afterlife of the soul, etc. What then is the demonstration that things agreeing in species are specified by corporeal matter, as opposed to any other [kind of matter]? […]

[al-Ṭūsī’s response]

[31.4] The matter that is mentioned when explaining the individuation of that which agrees in species is nothing but the prime matter (al-hayūlā al-ūlā) that belongs to bodies. For the division of something into parts that are all equal and agree in species, is conceivable only in the case of bodies that are put together out of a form and the aforementioned matter, not in any other case. No objection can be raised against this, since if something is divided into two parts that are equal in species, that division must be in terms of measure. But measure occurs only to natural bodies whose forms inhere in matter. What we have mentioned on this issue suffices.

[individuation through matter, place, and position]

He [al-Mūsawī] said that individuation in extramental reality comes down to the occurrence of specific accidents to the essence, such as form, color, shape, and the like.

I say: these things are not individuation. For individuation is that through which something becomes such that it cannot be applied to many. But these things he has mentioned do not exclude being applied to many, whether or not they are taken together. Individuation is only through concrete corporeal matter, which belongs to nothing but this individuation. The “where” that is specific to it follows upon [the matter], which is the reason why no other [individual] can occupy that same place. The same goes for the position specific to it, that is, the indication available to sense perception that refers to it and to nothing else. These are the causes of individuation.

[refutation of al-Rāzī’s arguments for positive individuation]

Concretization cannot be privative (ʿadamī), since non-existence (al-ʿadam) has no concrete being (huwiyya) in concrete individuals, so nothing else can be concretized through it. Also, because it is part of the concretized existent, so it is existent [too].

[15] This calls for further inquiry. Regarding the first argument, because it is question begging. Regarding the second argument, we do not concede that [concretization] is a part of the concretized, if “the concretized” means that to which concretization occurs accidentally. But if it means the composite of both [concretization and what is concretized], we do not concede that it is an existent.

[response to regress argument: concretization is equivocal]

You argue on the assumption that the concretization of every quiddity in a species is a positive item additional to it. In this case, there can be no doubt that the concretization would be a specific, positive quiddity as well, so its concretization would also be something positive and additional to it, yielding a regress, in the way we have explained.

But obviously one can also refute what has been mentioned here. Namely by saying: we do not concede that, if concretization is an item positive and additional to the quiddity of a species, then the concretization would also be a positive specific quiddity, predicated of the individual instances of concretization. Why can’t concretization be predicated of whatever falls under it equivocally, not univocally?

[defense of individuation through bundled universals]

Why do you say that upon the association [of a universal quiddity and the quiddity of particularity], if one, or both, of two universal quiddities implied the particularity of the other, then it would follow that no individual results? He [al-Rāzī] says: for in this case there occur [even] three or four universals, since being particular is a universal as well, but the association of one universal with another does not yield an individual even if there are thousands of them.

We say: we do not concede that particularity is a universal. This would follow only if it were truly predicated univocally of what falls under it. But this is denied. Rather, according to us, the particularity of every particular is different in its true reality and quiddity from the particularity of any other particularity. This being so, what occurs upon the association of some of those things with others is particular, since the association of a universal with a particular or of one particular with another certainly does yield a particular.

[individuation and essence are distinct only in the mind]

If it is said: if concretization were additional to the quiddity, then in extramental reality the quiddity would be the subject of inherence for the concretization, but the subject of inherence must be concretized before the existence of that which inheres in it. So the quiddity would have concretization before its concretization, and it would have [another] concretization before that concretization, so there would need to be an infinite number of distinct ascriptions from the quiddity and its concretization, which is a contradiction.

Then we say: we do not concede that if concretization were additional to quiddity, then the quiddity would be the subject of inherence for the concretization in extramental reality. This would follow only if the extramental quiddity and the concretization were not united in extramental reality. Why do you deny this? On our view, the extramental quiddity and the concretization are one and the same thing in concrete individuals. But when the extramental quiddity occurs in the intellect, the intellect divides it into two things: a quiddity and a concretization, in the same way as previously stated concerning quiddity and existence.

[individuation as the joint result of material disposition and the Giver of Forms]

If the concretization (methyaqqnānawth: lit. “coining”) of a quiddity takes place through either the quiddity, the agent, or the receptacle, then the species of that quiddity is limited to one [individual] substance (qnūmā) alone, in that, so long as the quiddity, the agent, and the receptacle remain the same, there may be a cause for one concretization alone. Yet it is the Giver of Forms that gives rise to multiple concretizations, through which a multiplicity of [individual] substances belong to one and the same species. He bestows them upon matter, in accordance with the different dispositions that occur to it. For instance, if the concretization of Socrates were through humanity or the Active Intellect or prime matter [alone], then humanity would exist only in his [individual] substance. But this is not so. So [his concretization] is not through any of them by itself. Rather it is through the agent, the receptacle, and the effects [in the matter], taken together. Indeed, different forms emanate upon prime matter from the Active Intellect in accordance with diverse dispositions, which come about through celestial motions. The individual concretizations of humanity take place through these forms, and it is likewise that multiple individual [substances] exist for every species.

[individuation of the divine Persons]

We say: it is not necessary that if the material ways [of subsistence] are responsible for plurality in making up [different] hypostases [usually], then all plurality of hypostases would be in virtue of [those] material ways. […] [140.22] Moreover, we say that rational souls too are equal in terms of nature, but they do not fail to be distinct from each other without those material ways [of subsistence]. [They are distinct] after their separation from bodies, according to the view of Aristotle, and both before their connection to bodies and after their separation from them, according to the opinion of Plato. Likewise, the hypostases of the divine nature are distinct from each other without any material ways [of subsistence].

[the need for a distinguishing factor]

A universal nature is multiplied in concrete individuals only through something that distinguishes. For instance, there can be no two blacknesses unless by reason of two bodies that render them multiple, or by reason of two states. For if it were just because it is blackness [92] that it is required to be multiple, then each of [its instances] would require whatever the nature of blackness requires; but if every blackness is similar to any other, not differing in anything at all, they are one and the same (fa-huwa huwa). Also, if [blackness’] being blackness requires it to be this blackness, and it is a condition for it is that it be this one, then there must be no other [blackness]. So it is by some cause (bi-sabab) that it is rendered multiple, and that there is multiplicity for anything that becomes multiple in its instances. If something has no cause, multiplicity cannot apply to its universal nature. For if it were multiplied, there would be some cause for the existence of that multiplicity, but we supposed that there is no cause for [the multiplicity], which is a contradiction. Furthermore, when someone indicates a number of things [belonging] to the species of that nature, whether in a way suitable for sense-perception, estimation, or intellection, he is aware that [one] is distinct from another. He has already recognized in it something through which it is recognized, and which distinguishes it from any other. That [distinguishing feature] is additional to the shared quiddity.

[distinction by intensity]

Among distinguishing factors there is being more perfect and being more deficient, like perfect and deficient magnitude, since one exceeds the other only in terms of being a magnitude.

[difference between distinction and individuation]

It should be known that a distinguishing factor (al-mumayyiz) is not the same as an individuating one (mushakhkhiṣ). Sharing in common is not prevented for concrete quiddities by reason of the distinguishing factor, but by their concrete beings (bi-huwiyyātihā al-ʿayniyya), whereas their being distinct (imtiyāz) is by whatever specifies them. [93] The individuation of a thing belongs to it in itself, whereas its distinction is simply through [its] relation to [other things] that share a common feature (maʿnā ʿāmm) [with it]. If something had nothing that shares [a common feature with it], then it would not need any additional distinguishing factor, but it would be still individuated.

[intrinsic individuation through perfection and deficiency]

Having understood this, you should know that unqualified extension applies in common to both the particular [extension] C, which is three cubits long, and B, which is two cubits long, just as C applies in common to its concrete particular instances [i.e. whatever is three cubits long], and B [214] to its concrete particular instances. The distinction between the longer extension of three cubits and the shorter extension of two cubits, subsequent to their commonly sharing in unqualified extension, is through nothing apart from being an extension; rather, it is through themselves. This kind of distinction is called “by perfection and deficiency” or “by intensity and weakness.” For we have already shown that multiplicity only is by way of mental consideration. There is no multiplicity in extramental reality. Rather, [these lengths] are simple. There is no need to give a demonstration for the simplicity of [these lengths] and what is like them, though there may be a need for a reminder and calling to mind.¹⁶

[definition of individuation]

Whenever a quiddity is realized in extramental reality, various features (maʿānī) occur to it, which are specific [to it] either by quiddity or by relation, and which cannot belong to anything else. [The quiddity] is specified through them, so that no possibility remains for sharing them in common. That through which there is specification is called “concretization” and “individuation.” That which is composed from it and from the quiddity is “concrete being (huwiyya).”

[the principle of individuation is positive]

The verifiers said that [individuation] is something affirmative, but some people said it is privative. The truth is the first position. For if it were privative, then it would need to be either (a) the privation of being unqualified [that is, universal], or (b) [the privation] of something else, whose privation is not the same as the privation of being unqualified. Otherwise it would not be like this [sc. privative].

(a) In the first case, it would follow that all individuals would share this feature in common, and none of them would be distinct from the others. So this is not how concretization works. (b) But if it is not [the privation of being unqualified], then one privation could differ from another. In which case either (b1) the privation of being unqualified does not exist together with that privation, or (b2) it does. (b1) The first option implies that one and the same thing is not unqualified, but at the same time nor concretized. (b2) The second option [implies] that something is unqualified and concretized at the same time. Both are absurd. This is an unprecedented demonstration.

[refutation of al-Rāzī’s argument against individuation as privative]

The Imām [al-Rāzī] said: if [individuation] were privative, it would be either (a) the privation [110] of a further concretization or (b) [the privation] of being not-concretized. (b) On the second option, it would be affirmative, since being not-concretized is privative, and the privation of a privation is affirmation. (a) On the first option, if that [other] concretization were [likewise] privative, then [this one] will be affirmative; but if [the other concretization] is affirmative, and this one resembles it, then it will be affirmative too.

But this calls for further inquiry. For if, by “being not-concretized,” he meant nothing but this notion, then we do not grant the division [of options], since [concretization] could be the privation of something else, neither of [a further] concretization nor of being not-concretized. If however by [being not-concretized] he meant that of which being not-concretized can be truly predicated, then the division is granted, but we will not concede that it is privative. Even if we did concede this, we have already shown that the opposite of something privative need not be something existing, for instance blindness and not-blindness.¹⁷

[against the bundle theory of individuation]

If you say: when we qualify a universal with a universal, and every qualification makes it more specific than it was before, why could this not reach the point (ḥadd) of being specific for just one thing, so that there could occur no sharing of it in common? Also, why couldn’t each of two or more universals provide concretization and specification for the other? Then the aggregate could be specific for one thing alone, jas in the case of a composite property.

I say: the mind can posit an unlimited number of individual instantiations for any universal notion, since positing an individual is nothing but positing that feature as existent and individuated, and this reaches no limit. […]

[113.3] True, [a universal feature] may happen to be specific for just one extramental existent, but this does not prevent the mind from conceptualizing another individual [that has this feature].

[individuation is caused by the realization of a quiddity]

The truth is that the cause of concretization is the realization of the quiddity in extramental reality. For we know necessarily that, whenever a quiddity is realized in extramental reality (regardless whether this involves matter, or a relation, or neither) this becomes a discrete, specified thing which cannot be counted or shared in common. This is the only meaning of concretization. Thus may one know that just the realization of a quiddity suffices for its concretization, and it is the cause of concretization. Individuals are counted only by counting the existences of a quiddity. But God knows best.

[discernibility through time; cf. T16]

Some have allowed that distinction comes down to time, as we have said before. Against them, it has been objected that time is a measure of motion that inheres in a single subject of inherence: how then can one of its parts be distinguished from another? To which it has been responded that the parts of time are in themselves distinct from one another. But then some hold the view that this is invalid, because if the parts of time are different in themselves, there will need to be a sequence of “nows.” Whereas, if they form a unity, then one [may as well] allow for every species that its individual instances are distinct in themselves. It has been also responded that the parts of time do not co-occur in a way that [there would need] to occur something that distinguishes them as concrete individuals; in conceptualization, though, some differ from others in terms of priority and posteriority. To this it is objected that if two [parts] of time are distinct in terms of priority and posteriority, then one of [502] two individual instances of a species could be distinguished from the other by occurring at an earlier time. But in this case two individual instances [of a species] may be in a single subject of inherence at the same time. They responded: if the time of the creation of the universe has passed, the relation of [the universe] to it does not remain either. So no distinction arises in consideration of its relation to the time that has passed. The distinction between two things must arise while both exist and are distinct from one another.

[distinction vs individuation]

I say: when [al-Ṭūsī] mentions that individuation and distinction are two different things, he explains that commonality does not hold of them in an unqualified sense. For one may hold true of something without the other doing so, and they may also both hold true of a third thing. For any two things of this sort, it is the case that they have something common in a certain respect [but not in an unqualified sense]. Individuation may hold true without distinction, which applies to that which is individuated and is not considered as sharing in common with anything else, even though in fact (fī nafs al-amr) it will inevitably share something in common, even if [only] in respect of common accidents. Or, distinction may hold true without individuation, which applies to the universal, when it is particular relative to another universal under which it is subsumed: it is distinguished from everything else, but not individuated. As for both holding true of a single thing, this applies to that which is individuated and subsumed under something else, when it is considered insofar as it is subsumed. Then it is both individuated and distinguished.

[an argument against individuation as something positive]

The fact that this additional [individuating factor] is specific to that concretized object, and not for anything else, presupposes [179] the distinction of that concretized object from everything else. Otherwise its being specific to it would be no more appropriate than its being specific to anything else, or anything else being specific to it. It follows that the specification of that concretization to that concretized object presupposes the concretization of the latter, so it is concretized before being concretized, which is a contradiction. […]

[response: individuating accidents in matter]

[181.6] Whenever the concretization of something is not an effect of its quiddity, such that it is one of a kind, it must inevitably have matter, and its matter must inevitably be specified by individuating accidents. The individuation of matter by these accidents is the cause for the individuation of that originated thing. It is impossible for another individual instantiation of that species to be attached to that matter at that time, given the problems that would follow from this. Nor do we say that this thing exists, and its concretization exists, and that once both have occurred, they attach to each other. Rather, the occurrence of the thing in that specified matter just is its concretization.

But this calls for further inquiry. For we reject matter, as will be explained. Even supposing we granted it, if those accidents are the individuating factors, the issue [of individuation] would arise for them just as it did for quiddities. So the mediating role of matter would be fruitless, and one may as well allow that quiddities are individuated through themselves.

The most eminent among the verifiers [Naṣīr al-Dīn al-Ṭūsī] responded: natures are concretized either through specific differences, as with species which are composed from genera and differences; or through themselves, as with species that are simple. Furthermore, insofar as they are natures, they are suitable to be either common and intelligible, and to be specific and individual. Just as [182] they become common through the addition of the feature of commonality (maʿnā al-ʿumūm), likewise they become individuals through the addition of concretizations to them, with no need for a further concretization. Even if it were supposed that concretization were something negative, it [still] would not be the absolute privation of something (ʿadam al-shayʾ muṭlaqan). Rather it would be something privative (shayʾ ʿadamī). There are many examples of such privative [attributes] that are suitable as differences, to say nothing of the fact that there [can] be accidents.