The role of spatial position in individuation

798 Mubāḥathāt, 337–339 [1044–1057].

ﺭﻭﻣﺃ things

ﺕﻻﺎﺣ states

ﻰﻟﺇ ﺭﺎﻘﺗﻓﺍ ﻥﻭﺩﺑ ﺓﺭﻭﺻﺗﻣ ﺔﺑﺳﻧ

conceptualized without need of a

relation

ﺔﺑﺳﻧﺑﺔﻘﻠﻌﺗﻣ depending on a

relation

ﺏﻭﺳﻧﻣﻟﺍ ﻰﻟﺇ ﺱﺎﻳﻘﻟﺎﺑ related to something

ﺏﻭﺳﻧﻣ ﻰﻟﺇ ﺱﺎﻳﻘﻟﺎﺑ ﻝﻭﻘﻟﺍ ﺩﺭﺟﻣ ﻥﻭﻛﻳ ﻥﺃ ﺭﻳﻏ ﻥﻣ ﺔﺑﻭﺳﻧﻣ

related but the statement [describing it] is not [such that it needs] a relation to something

ﺕﺍﻭﺫ

"essences"

189 This little chart recalls the division of accidents from the Maqūlāt of the Shifā’. Things are either in themselves (substances), or states (accidents). Accidents may be divided according to a relation. On the one hand, there are accidents the conceptualization of which requires something else, external to the subject, and, there are accidents the conceptualization of which does not. Into the latter category fall the category of position (waḍʽ), quantity (kamm), and quality (kayf). It is obvious that quantity and quality are indeed such that they are not related to something else, apart from their subject. The color or being one and the like do not need any external point of reference in their concept formation. However, the position is more curious:

it is always related to something, but in this case not to something external, but to itself. Here, it represents the spatial relation of the parts to the whole. In another passage in the Maqūlāt Avicenna attributes three interpretations to the category of position:

1. Position may be predicated of everything that may be indicated [by finger] (mushār ilayhi). The indication is the determination of direction (taʽyīn al-jiha) that specifically falls upon it from among the directions of the cosmos.

2. Position may relate to the quantity⁷⁹⁹

3. The position is the state of the body inasmuch as its parts have a relation to the other parts, but this reading applies only to substances.⁸⁰⁰

The second and third readings are close to each other, it is as if the second was derived from the third: body, subsumed under the category of a quantity means simply that a body, be it a line or a surface is continuous and potentially have parts. According to Avicenna’s division in the Maqūlāt, the category of position is placed above quality and quantity. In this reading position is taken in meaning (3): insofar a body is potentially divisible and has parts, their parts have a relation to each other. As Avicenna adds, these differences, that is, the differences of their parts adhere to the body in itself.⁸⁰¹ However, in another work, in the Dānishnāmayi ʽAlā’ī, a similar division may be found, but here, the position is subsumed under relation: taken this way, it reflects meaning (1) that is, position to something else. ⁸⁰²

This consideration roughly follows the Late-antique commentary tradition. The commentators generally distinguished between those categories that are in themselves (καθ αὑτό, ἀσχετοί) and

799 This is the traditional Aristotelian division that quantity is continuous or incontinuous, and positional and non-positional. Aristotle, Cat., 4b21–22: καὶ τὸ μὲν ἐκ θέσιν ἐχόντων πρὸς ἄλληλα τῶν ἐν αὐτοῖς μορίων συνέστηκε, τὸ δὲ οὐκ ἐξ ἐχόντων θέσιν.

800 Maqūlāt, 127, 10–16.

801 Maqūlāt, 84, 6–17.

802 Ilāhiyyāt-i Dānishnāma, 29.

190 those that are in relation (ἐν σχέσει). ⁸⁰³ For Simplicius, the non-relational accidents are quality and quantity, and relational ones are all subsumed under relation: position is labeled as the relation to the body, which corresponds to the classical interpretation of κεῖσθαι. ⁸⁰⁴ Elias and Olympiodorus held a quite similar view. ⁸⁰⁵ In other words, the classification of the categories in virtue of relation seems to be a common commentary practice that also appears in Avicenna.

In this context, however, this classification helps him to find those features that explain individuality. In this context again, the crucial question is which category means an unshareable element. Ultimately, this inquiry is guided by what he meant by individuation. The answer lies in the passage [1045]:

The conceptualization of the individual, insofar as it is an individual, rules out that another [individual] be it.

Thus, it must be such that no commonness may fall into its concept.⁸⁰⁶

This description of individuation follows the Porphyrian unshareability criterion. This is the so-called logical understanding of individuation, where the starting point is the concept of an individual. As we have seen, this involves the epistemic approach: it raises the issue into a conceptual level, where the question is about which feature explains unshareability. The whole discussion is about the distinction between common and non-common features, and in this respect, an individual element is that which prevents that two things share all the properties.

In the following passages, Avicenna follows this way: he examines all the possibilities throughout the division, whether it may be shared or not. Just like in the Madkhal, he insists that all the universals are shareable: thus, substances and the non-relational states (ḥālāt ghayr mansūba). As for the relational concepts, he divides them further: there are those that depend on extension and sense-perception, and those that do not: they are the intellectual relations. The latter is either simultaneous (nisba maʽiyya) or diverse (mubāyina). Simultaneous relations are either homologous (mutakāfi’a) or different (mukhtalifa), as the relation between cause and effect. The example of the diverse relation is the horse and the human. That is, that they intellectually share some features, like animality, but they are different by their differentia specifica. All the intellectual relations, including the simultaneous, homologous ones (the concept of brother that applies to two brothers as well) are common. They are all shareable,

803 Olympiodorus, in Cat., 54, 7; Simplicius, in Cat., 67, 33–34.

804 Simplicius, in Cat., 67, 26–68, 13.

805 Olympiodorus, in Cat., 54, 4; Elias, in Cat., 159, 9–33.

806 Mubāḥathāt, 337 [1045].

191 because – as all universals are applicable to many, they do not prevent the thing from being shared in any feature. Therefore, the only possibility left is the extensional relation.

Why would the extensional relation be unshareable? The author here comes up with an interesting example:

1052: The individual double (al-mithl al-shakhṣī) is separated by an existential thing, which is concomitant to the individual or it is a non-constitutive accident to the distributed quiddity. As for the extensional relation, if it exists, it is impossible for it to have an individual double that exists with it.

1053: If we supposed two extensional relations, with an individual similarity (al-tamāthul al-shakhṣī) between them, it is necessary that everything that is in one direction from one of them be in that direction from the other. However, this is not possible; thus, there is no individual similarity between them that has no difference in individual [cases].⁸⁰⁷

Passage [1052] is not easy to interpret, but our proposal is the following: we shall suppose two absolutely identical instances of a quiddity, like two Zayds as if he was perfectly cloned and reduplicated. This is an individual double, which is separated from its counterpart by an existential thing (amr wujūdī) that is concomitant to its quiddity, namely, existence.

There is another interesting point here, namely the technical term tamāthul – similarity. This is what we have seen in kalām texts as well, referred back to as early as Abū Qāsim al-Balkhī (d.

319/931). It is also striking that here, the criterion of difference during sense-perception is also extension (taḥayyuz).⁸⁰⁸ Although the work is written by a later author, Abū Rashīd al-Nīsābūrī, who is a contemporary of Avicenna, as he admits, he is about to report earlier views, actually the debated points between Abū Hāshim al-Jubbā’ī and the Baghdadian mutakallimūn.⁸⁰⁹ Here, he deals at great length with the question of the similarity of substances.

Turning back to the text, it means that if we suppose that a certain individual exists, it has a double: this is the starting point. On the conceptual level, two otherwise absolutely identical instances may differ only in their spatial relation to each other. However, what Avicenna says is not exactly this. If we suppose two extensional relations, as two identical instantiations of the quiddity “spatial relation,” they cannot be but different. If we suppose two points for the sake of simplicity, and posit a third a one, their spatial relations to this third point must be necessarily

807 Mubāḥathāt, 338 [1052–1053].

808 al-Nīsābūrī, al-Masā’il fī khilāf, 29–36.

809 al-Nīsābūrī, al-Masā’il fī khilāf, 28.

192 different, because two individual points cannot occupy the same location. In other words, two spatial relations are per definitionem different.

As we saw above, this is the same argument that Avicenna used in the argument against the existence of the void and immaterial dimensions. ⁸¹⁰ If two things interpenetrate, they have the same relation to an external object. This idea also entails that it is not a place that differentiates, because place, taken in the Aristotelian sense that Avicenna equally accepts, means the inner surface of the surrounding body. In this description, there is nothing that would entail any kind of specificity. If we take two identical instances of a thing, be it a quiddity or an individual, their place, meaning the inner surface of the surrounding body, is the same, even if they are at several spatial points in the universe. However, this meaning is something superadded to the simple concept of place: actually, this is what may be described by spatial position.

However, the story does not end here. As we have seen elsewhere, a spatial position also may be reduplicated at two different moments. Thus, the temporal condition is equally important:

1057: One extensional relation may fall on two things in two times. That very relation does not exclude [the possibility of] a double existent until time or moment is not attached to it. Thus, the thing that is not temporal essentially or by a state, its quiddity is not said of many.⁸¹¹

This actually is the spatio-temporal reading of differentiation, but here Avicenna or his pupil notes that it is spatial position on a temporal condition, which necessarily differentiates between two instances of the same species. Time is equally necessary because the spatial position does not contain any indication of time in itself: in other words, a spatial relation in itself, between two points, A and B, may be the same at two different instants.

A similar division with the same conclusion appears in the Kitāb al-Taʽlīqāt: ⁸¹² there are essences, states, and relations. Every one of them that may be intellectual is shareable; it is only the extensional relation on the condition of time that is unshareable. Then, as the author of the passages adds, it is spatial position that is individuated in itself (mutashakhkhiṣ bi-al-dhāt).⁸¹³ Just like here, however, the text supplies it with the temporal reading:

810 Samāʽ, 121, 7–10.

811 Mubāḥathāt, 339 [1057].

812 Taʽlīqāt, (B) 86; 98–99, (M) 233–234 [376]; 275–276 [467].

813 Taʽlīqāt, (B) 50, (M) 119–120 [158–159]; (B) 86, (M) 233–234 [376]; (B) 98–99, (M) 275–276 [467]; (B) 106, (M) 300 [524]; (B) 107, (M) 303 [529]; (B) 120, (M) 348 [622]; (B) 138, (M) 408–409 [725–728].

193 The individuated in itself is the position. Then, the time is also individuated by position, and likewise all general thing. And position also is not individuated until the unity of time is not postulated in it. Everything that is individuated, it is such that its position is one, I mean that its time is one.⁸¹⁴

In this spatio-temporal reading, time, and position play a mutual individuating role. It is position that ultimately individuates time, because time attaches to motion, and heavenly motion moves from spatial position to spatial position. On the other hand, time, in general, depends on the movements of the celestial substances. At the same time, spatial position, inasmuch as it is the spatial position of something, is unshareable, only if the unity of time is taken into consideration A spatial position is unique only as taken in an instant time t’, which, taken Avicenna’s theory of motion, is that which spatially corresponds to a given instant. In Avicenna’s physical universe, it is this constellation that is ultimately unique. This clear-cut spatio-temporal understanding equally appears in Bahmanyār’s Kitāb al-Taḥṣīl ⁸¹⁵ and Lawkarī’s Bayān al-ḥaqq.⁸¹⁶ Bahmanyār goes even further:

The unity of position, like [in the case of] “the human,” from the beginning until the end of [its] existence, is like⁸¹⁷ the unity of time and the unity if continuity of the potentially many positions.⁸¹⁸

Bahmanyār understands spatio-temporal reading as a unity. From the beginning until the end of existence, all the continuously changing spatial positions are taken as one unity of positions as if it denoted a distinct spatial extension from time A to time B. Bahmanyār admits in the introduction that he relied on Avicenna’s works, his discussions with him, but adds his own deductions as well.⁸¹⁹ Therefore, this statement corroborates that the idea of spatial position as the individuated-in-itself feature is indeed Avicenna’s tenet. The unity-reading is hard to be found in the Mubāḥathāt material; therefore, it easily can be Bahmanyār’s addition, but no one can tell it for sure. This idea, however, implies that accidents are indeed spatio-temporally

“earmarked.”⁸²⁰ If the spatio-temporal accidents individuate in the sense of distinction, as a cause, they must last until the effect lasts. Thus, this individuating bunch of features should

814 Taʽlīqāt, (B) 99, (M) 275–276 [467].

815 Bahmanyār, Taḥṣīl, 505–506.

816 Lawkarī, Bayān al-ḥaqq, 176–177. Lawkarī’s chapter follows Bahmanyār’s text verbatim.

817 This is Bahmanyār’s reading, whereas the Lawkarī edition offers another reading: fa-li-waḥdati l-zamān, is because of the unity of time.

818 Bahmanyār, Taḥsīl, 506; Lawkarī, Bayān al-ḥaqq, 177.

819 Bahmanyār, Taḥsīl, 1.

820 This is Jari Kaukua’s term and suggestion that he made in his review of this dissertation. This is actually a tenable option, but, in light of this I cannot but add that it appears in Bahmanyār and probably it might have appeared in Avicenna’s discussions with his pupils.

194 accompany the subject and should not change as such. ⁸²¹ It is only possible if we take it to form a unity, a temporally defined spatial extension.

In document Individuation of Material Substances in Avicenna’s Philosophy (Pldal 188-194)