In his Great Commentary on the Qurʾān, also known as Keys to the Hidden (Mafātiḥ al-Ghayb), Fakhr al-Dīn al-Rāzī says that the honorific “Lord of the worlds” in the opening ṣūra intimates that God is the “Lord of place and time, Creator and giver of existence to both.” He adds that God's “existence precedes that of the created, and this being the case, His essence exists before the occurrence of space, emptiness, and location (faḍāʾ, farāgh, ḥayyiz), and transcends all location.”Footnote 1 This is a passage that an Aristotelian might find puzzling. For Aristotle and his followers, there would be no need for God to create time or place, or at least not directly. Rather, God would bring the physical cosmos into being, with both time and place arising as supervenient phenomena. For time is, according to the famous definition in Aristotle's Physics book 4, the “number of motion in respect of ‘before’ and ‘after’” (Phys 4.11, 219b2), so that time will arise once there are bodies capable of motion. In the same book, place (topos) is just as famously defined as the “first unmoving limit of what surrounds” (Phys 4.4, 212a20).Footnote 2 Again, this suggests that place depends on bodies: whenever one body is surrounded by another, the inner boundary of the containing body will be the place of the body that is contained. For example, the place of water in a vessel would be the interior surface of the vessel that is in contact with the water.
Fakhr al-Dīn's remark in the Commentary is not, strictly speaking, in contradiction to this conception of place and time. Using standard kalām terminology, he later says that the things God creates are “located (mutaḥayyiz),” though spiritual creatures may be an exception.Footnote 3 Perhaps, then, he is speaking loosely when he implies that God directly creates time and place. He might admit that these in fact come about only because God has created located, temporally changing bodies. That impression would be borne out by a perusal of Fakhr al-Dīn's early work, al-Mabāḥith al-mashriqiyya.Footnote 4 There, he dutifully reproduces Avicenna's arguments for a broadly Aristotelian conception of time and place. Regarding time, he even repeats Avicenna's remark that the “truth about time” is that it is the magnitude of motion.Footnote 5 And as we will see, his discussion of place in the Mabāḥith is just as faithful to Avicenna's Aristotelianism.
But things look very different in his later work, al-Maṭālib al-ʿāliya.Footnote 6 In an extensive discussion spread over the fifth volume of the printed edition, Fakhr al-Dīn assesses a bewildering range of arguments concerning the existence and the essence, or quiddity (māhiyya), of time and place. The contrast between investigating the existence of time or place, and investigating its essence, is faithful to Avicenna, and for that matter to Aristotle.Footnote 7 But Fakhr al-Dīn's conclusions are not. His overview of the arguments for time's existence concludes that the most persuasive way to establish the reality of time is to say that moments are “stipulated” so as to coordinate other events, as when I agree to meet you at the moment when the sun rises – an idea from the kalām tradition that Avicenna had dismissed.Footnote 8 Fakhr al-Dīn's disagreement with the Peripatetic account of time as supervenient on motion is even more forthright, as he develops and defends a conception of time as “self-subsisting” and thus independent of bodies. He claims that this conception can be traced back to Plato, though it is strikingly similar to the theory of “absolute time” put forth by an earlier thinker of Rayy, Abū Bakr Muḥammad Ibn Zakariyyāʾ al-Rāzī.Footnote 9
In this paper, I will show that Fakhr al-Dīn adopts the same approach in the Maṭālib’s treatment of place. Whereas Fakhr al-Dīn thought it worthwhile to devote lengthy discussion to the question of whether time exists, he deals with the existence of place in relatively short order (faṣl 2, at 115–17). His attention focuses instead on two rival accounts of the essence of place. As with time, one account is ascribed to Plato, while the other is the position of Aristotle as filtered through Avicenna. Throughout the Maṭālib discussion, and in sharp contrast to the Mabāḥith, Fakhr al-Dīn argues in favor of the Platonic theory that place is three-dimensional extension that may be occupied by body.Footnote 10 Fakhr al-Dīn makes it clear that such extension should be understood as self-subsistent. It does not supervene on body, as the “limit” or “containing surface” view of Aristotle implies. It is however a further question whether space is ever actually unoccupied by body. If so, then such an empty space would be void (khalāʾ). Fakhr al-Dīn will go on to consider void in three further fuṣūl, but this exceeds the remit of the present paper.Footnote 11 We will have enough to deal with just looking at his arguments in favor of conceiving of place as “space (faḍāʾ),” “extension (buʿd),” or “location (ḥayyiz),” words he employs as synonyms. Characteristically, he presents a profusion of arguments and counter-arguments on all sides of the question, in what amounts to a detailed dialectical exchange with Avicenna. I will highlight those arguments that raise issues of particular philosophical interest, such as the identity of indiscernibles and the possibility of defining motion and rest in relative terms. A sense of the overall discussion can be gleaned from an appendix included below, which provides an outline of the whole treatment of place in the Maṭālib. My citations of the text include references to the section numbers of the outline in the appendix as well as page numbers from the printed edition.
1. THE RIVAL VIEWS
Much as he did with the question of time's essence (Maṭālib 51), Fakhr al-Dīn embarks upon his treatment of place by providing an overview of the competing positions (Maṭālib 112–13, §1.3). They will be measured against a set of criteria already listed by Avicenna, which any plausible theory of place must satisfy: “in general, place is something in which a thing is, from which [the thing] separates through motion, which does not accommodate it and something else at the same time, and into which moving things can come successively” (Maṭālib 111, §1.1; cf. Avicenna, Healing: Physics, §2.6.2 and 2.9.1, cf. Aristotle, Physics 210b34–211a7).Footnote 12 Broadly speaking, there have been two ways of trying to define place in a way that would fulfill these requirements. On the one hand, place might be a space or extension that is pervaded by the thing that occupies it. On the other hand, there is the Aristotelian position that place is the innermost boundary, limit, or as Fakhr al-Dīn usually says, “surface (saṭḥ)” of the containing body.
The first view can be distinguished into several sub-theories. On the one hand, there are some who think that space is “pure and unmixed (maḥḍ, ṣirf)” and in fact lacks existence. Then there are those who think that space does indeed exist: it is “self-subsisting extension” and becomes a place when it is occupied by bodies.Footnote 13 Thus we have the following set of possibilities: either (A) place is space that can be pervaded by body, whether (A1) as “pure” and non-existent or (A2) as self-subsisting extension; or (B) place is the inner surface of the containing body. This is not just a list of abstractly possible views but a mini-doxography on the topic of place; Fakhr al-Dīn identifies the respective proponents. Theory (A1), which actually denies real existence to place, is that of “the mutakallimūn.”Footnote 14 An interesting datum concerning his own intellectual allegiance is that he is going to distance himself from what he identifies as the kalām theory and instead embrace (A2), which he says is “the view of Plato and many philosophers.” He could have mentioned Abū Bakr al-Rāzī as a proponent of this view, but does not do so despite having named him in the preceding section of the Maṭālib on time. Finally, of course theory (B) is the Aristotelian one, but understood through the lens of Avicenna, and in particular the Physics of the Healing.
The Healing already served Fakhr al-Dīn as a primary source in his Mabāḥith, which adheres closely to the Avicennan text throughout its seven fuṣūl on the subject of place and void, often reproducing the arguments and conclusions verbatim.Footnote 15 For the most part the Maṭālib critiques the Avicennan material rather than simply reproducing it, as does the Mabāḥith. Yet when it comes to the question whether place even exists, Fakhr al-Dīn is happy to use Avicenna's arguments against the skeptical kalām position. On this view (A1), place or space is apparently being understood as a nothingness in which bodies can be created. But this flies in the face of common sense. For example, as Avicenna argues, we differentiate between up and down, which presupposes a distinction between an upper and a lower place. But how can two non-existing things be distinct?Footnote 16
Things are not quite this simple, though. Fakhr al-Dīn offers, on behalf of the mutakallimūn, a skeptical argument that is again based on Avicenna (Healing: Physics, 2.5.2). According to this argument, really existent place would have to be a substance or an accident (Maṭālib 117–18, §2.2).Footnote 17 This would lead either to a regress (since as a substance, place would need a further place), or absurd mutual dependence (since the body is accidentally in the place, and the place accidentally in the body). The upshot is that place is only something “posited by the mind,” not a real existent. This parallels skeptical arguments given earlier, which showed that time is only mentally existent.Footnote 18 Fakhr al-Dīn replies on behalf of the philosophers that place must be somehow really existent, to serve as a “vessel (ẓarf)” for body and to account for place (Maṭālib 119, §2.3). This by itself would leave open the question of whether place is substance or accident. But Fakhr al-Dīn already indicates here his preference, which is to say that place is not a mere accident of body but self-subsistent (qāʾim bi-nafsihi) and some particular thing (mushār ʿalayhi).
This leads us to the real dispute, which is between (A2) and (B). Since it is (A2) that will claim Fakhr al-Dīn's allegiance, it is worth dwelling on the provenance and meaning of this account. It can be traced back to Aristotle, who articulates the theory in order to reject it. In his Physics, he defends his own theory of place by considering and rejecting three other proposals: that place is form, matter, or extension (diastêma). He associates both the second and third incorrect theories with Plato, thinking here of the receptacle in the Timaeus. His idea is that Plato makes place the “extension of the magnitude” of a body, which is tantamount to making place the matter of the body (hê de dokei ho topos einai to diastêma tou megethous, hê hulê, Phys. 4.2, 209b6–7).Footnote 19 In effect, then, Plato is asserting that “matter (hulê) and space (chôra) are the same” (209b11–12). For, on his view, bodies would be the result of forms (or better, images of Forms) being received in spatial extensions.
The implied accusation is that Plato was simply confusing extension, matter, and place, whereas in fact all three are to be distinguished. Aristotle has no real use for extension in accounting for place, as he explains somewhat later in the Physics (Phys. 4.4, 211b14–29). He also has a good reason for rejecting an equivalence between matter and place: the same place can be occupied successively by different bodies made of different matter (Phys. 4.2, 209b22–32). The charge of confusion was known in Arabic, as we can see already from al-Kindī’s brief treatise On the Five Essences, which actually says that Plato confused place with body.Footnote 20 Fakhr al-Dīn is aware of the problem too, but frames it differently: on his interpretation Plato wants to say that place is extension, but he sometimes calls it “form” and sometimes “matter.”Footnote 21 This may sound contradictory, but Fakhr al-Dīn wants to show that Plato's manner of speaking can be vindicated. Place is not identical to matter, but it is analogous to matter because it is something that “receives” bodies, that is, when a moving body comes to occupy a certain stretch of spatial extension. Nor is it identical to form, but it is like form in that it has three dimensions – which are “like the formal part of the quiddity of body” (Maṭālib 111–12, §1.2).
The upshot is that for Fakhr al-Dīn, the “Platonic” theory of place is that it is three-dimensional extension. A given region of space can receive different bodies in succession. Thus, to take an example that appears already in Aristotle (Phys. 4.4, 211b14), there is an extension between the limits of a vessel, like a jug. This extension could be first occupied by air and then by water – the case of replacing one body with another in “the same place,” which Aristotle used to rule out the form and matter accounts. On Fakhr al-Dīn's understanding this place is not the extension of a body that is in place, for instance the extension of the water, as Aristotle suggests when he alludes to the Timaeus. Rather, it is an extension that subsists in its own right. So when space comes to be occupied by a body, we actually have two extensions that are “overlapping” or “interpenetrating.” To take our example of a jug filled with water, the three-dimensional space in which the water is located coincides with the three-dimensional extension of the water. As we'll see, Avicenna questioned the coherence of this doubling of extension, and Fakhr al-Dīn is going to mount a spirited defense in reply.
It would take us too far afield to chart the whole reception of Plato's theory of place between Aristotle and Fakhr al-Dīn.Footnote 22 But it is worth noting that among previous thinkers of the Islamic world, comparable views were adopted by Abū Bakr al-Rāzī and Abū al-Barakāt al-Baghdādī. We know from Abū Bakr's dispute with yet another al-Rāzī, the Ismāʿīlī philosopher Abū Ḥātim al-Rāzī, that he took himself to be following Plato's lead in postulating “absolute place” as one of the eternal principles that must exist in order for our non-eternal universe to be created.Footnote 23 He took this absolute place to be infinite in extent, and also called it “void.” Though Fakhr al-Dīn does not mention Abū Bakr by name in the section on place, it seems likely that he has him in mind when he discusses the idea that place-as-extension is immediately evident and needs no proof (Maṭālib 143–6, §4.1). This parallels an identical epistemic claim about time, which Fakhr al-Dīn explicitly ascribes to Abū Bakr (Maṭālib 21).Footnote 24 We find similar ideas in Abū al-Barakāt al-Baghdādī, who asserts that the reality of place is known to the general population, grasped through a kind of knowledge one may compare to eyesight and embedded in “common parlance (fī al-lugha al-mutadāwala).”Footnote 25 He explains the Aristotelian and Avicennan account of place as the inner surface of the containing body, but points out that this is not the only possible definition. Place can also be conceived of as an emptiness that can be filled by bodies that move into it, and vacated by bodies that leave it. If such a space indeed exists, then it is the best candidate to be identified with place.Footnote 26 Thus his famous defense of the possibility of void is also a defense of place as space.
Finally, a few words about position (B), which is that of Aristotle and Avicenna. As Abū al-Barakāt points out, this account denies that place “immerses itself (ʿamuqa)” in the body that occupies it, in the sense of penetrating the body through-and-through.Footnote 27 In fact, Aristotelian place does not spatially coincide at all with the body that is placed. Rather, it is in contact with the outer surface of that body, with the two surfaces remaining distinct. This may seem strange, but position (B) can claim to ratify common sense in other respects. As already mentioned, it easily handles cases of replacement, as when water displaces air in a vessel. Sadly for the Aristotelian, position (A2) seems to fare equally well on this score.Footnote 28 Replacement can only be persuasively invoked against the claim that a body's place is its form or its matter. A stronger point in favor of (B) is that a thing is said to be “in” its place: the water is in the vessel and, in Greek at least, a man may be “in (en)” the earth in the sense of standing upon the earth's surface.Footnote 29 As mentioned above, Fakhr al-Dīn too seems to find it plausible to describe place as a “vessel (ẓarf),” though this usage is probably rather metaphorical (he also applies it to the time at which something occurs). In his usage, the extension occupied by a body can also be thought of as a certain sort of vessel. A further, though less obvious, strength of (B) is that if place is only a limit or surface residing in a body, it need not have a further place, thus blocking regress arguments.Footnote 30 By contrast, Aristotle and Avicenna thought that position (A2), where place is taken to be extension, would fall foul of such arguments.
2. OUR IMMEDIATE GRASP OF PLACE AS SPACE
Let us take this as our cue to turn to the intricate dialectical arguments of the third and fourth fuṣūl of the section on place in the Maṭālib. The purpose of the third faṣl is to explain, and then respond to, five Avicennan arguments against making place self-subsistent extension or, as I shall following Fakhr al-Dīn in saying, “space (faḍāʾ).” The fourth faṣl observes that if place is space, then this is either immediately obvious, or requires proof. So Fakhr al-Dīn first gives six considerations meant to draw our attention to the self-evident fact that place is space (§4.1). Since these considerations are precisely not proofs, he describes them as mere “admonitions (tanbīhāt)” (Maṭālib 145). The six admonitions are not subjected to any critique, which suggests that Fakhr al-Dīn finds them convincing. If so, then offering proofs for place as space, as he goes on to do, is not strictly necessary. It would serve only to confirm what we already grasp with “immediate (badīh)” and “necessary (ḍarūrī)” knowledge (note the use of kalām terminology in defense of what he presents as a rival to the kalām view of place). It's worth noting also that all but one of the five arguments in this second part of the fourth faṣl are in fact not positive arguments for place as space, but rather arguments against place as containing surface.Footnote 31 Hence we can say that Fakhr al-Dīn follows the precedent established by Aristotle and Avicenna: he argues for his preferred definition of place not so much by giving positive proofs, but rather by eliminating rival accounts and meeting objections to the preferred definition. The addition of appeals to self-evidence is an important difference, though. Effectively, his strategy is first to point out that place is just obviously space, and then eliminate the only plausible account that can challenge this obvious conception.Footnote 32
To understand more deeply what Fakhr al-Dīn means when he says that place is “space” or “self-subsisting extension,” it is best to begin with the six “admonitions” of space's self-evidence. Here is the first:
Maṭālib 143–4, §4.1.1: We see there is a hill present right here. If we suppose it to be removed from this spot (jiha) and location (ḥayyiz), then after the removal of the hill from here, that spot will remain, as will those places, just as they were, without being eliminated or rendered non-existent. So that if we were to build a house on that location, every sound mind will judge that this house is present in the spot where the hill was. This indicates that the location and spot are distinct from the body which was present in it.
The second “admonition” is similar: jurists agree that the qibla (the direction faced in prayer) is the Kaaba. But what if the Kaaba were removed? Then the qibla would be the space (faḍāʾ) previously occupied by the Kaaba (Maṭālib 144, §4.1.2). These two thought experiments may seem to be little more than picturesque versions of the replacement cases already found in Aristotle and Avicenna. But a closer look shows otherwise. In the first example, Fakhr al-Dīn insists that the place of the demolished hill survives regardless whether anything replaces the hill or not. He mentions the possibility of erecting a house there just to draw our attention to the naturalness of saying that this is “the same place.” This is even clearer in the case of the Kaaba, since Fakhr al-Dīn mentions that if the Kaaba is gone, the air filling its previous location is definitely not the qibla (for one thing, new air is constantly flowing in and out, whereas the qibla is not constantly changing).
What these examples show, then, is that the survival of a place is not dependent on the survival of any particular body. In a sense, the Aristotelians can say so as well, since they hold that the same place can be filled by different bodies. But according to them, the place will only be the same so long as the containing surface is the same. And in cases where a body is removed and not replaced, there simply is no containing surface after the removal. For there is no inner surface of air where the hill or Kaaba used to be, yet we intuitively want to say that the place persists, just as when water is swapped for wine in a jug. With these cases (and other examples considered in §4.1.5–6 have a similar function), Fakhr al-Dīn has implicitly introduced what we might call a “survival test” for determining whether or not one thing is dependent on another. We carry out the test by considering whether X can survive without Y. If so, then X is not dependent on Y but is either self-subsistent or dependent on some other thing Z.Footnote 33 This seems uncontroversial, or even tautologous.
But Fakhr al-Dīn employs another sort of test which is far more contentious. We can call it the “conceptual independence” test. Consider the fourth “admonition”:
Maṭālib 145, §4.1.4: We can conceive of a body that has no [other] body touching it or surrounding it, but we cannot conceive of a body that cannot truly be said to be “here” or “there.” It follows that the particular thing we mean when we say “here” or “there” is something distinct (mughāyir) from the body's being in contact with another body, or its being surrounded by another body.
The point here is that we should “think away” anything other than one single body. This imagined situation may be impossible, but it is intelligible, and in such a situation the isolated body would still have a place.Footnote 34 One might see this as a mere variant on the survival test, in which the test involves an impossible rather than possible procedure. But a more subtle strategy is suggested by the immediately preceding admonition:
Maṭālib 144, §4.1.3: Indicating that something is “here” or “there” is something understood by necessary affirmation (amr maʿlūm al-thubūt bi-al-ḍarūra), whereas the body's actually being (ḥuṣul) here or there is not so understood. For unless proof is offered for the impossibility of void, there is no necessity that there is actually body here or there. But what is understood by necessary affirmation is distinct from what is not so understood.
This ingenious argument exploits the very fact that void's existence is controversial. Fakhr al-Dīn does not need to insist here that void is possible, only to observe that argument is at least needed to disprove its possibility. Since it is obvious that there is a place here, but contested whether the place is occupied by body, place must be independent of body.
The reason I've said that this test is more contentious should itself be obvious. Whereas it is undeniable that X must be really independent of Y if it can actually survive while Y does not, it is far from clear that X must be really independent of Y if it is conceptually independent of Y. Indeed, one might suppose that the distinction between intensional and extensional identity is needed precisely to block this sort of fallacious inference. Consider for instance that this paper could conceivably have been written by someone other than me, and I might even be asked to prove that I wrote it. The author and I are thus conceptually independent. It does not follow that I am really distinct from the author of this paper, so that one of us could survive while the other does not.
To this, Fakhr al-Dīn could have two replies. One would be ad hominem: Avicenna notoriously uses the same test in his Flying Man argument. It asks us to suppose someone who does have cognitive access to his self, but not to his body, and infers from this that there is a real distinction between the self and the body. Whether Avicenna actually makes this mistake is a much disputed question.Footnote 35 But at the very least, the Flying Man encourages the use of the conceptual independence test, which may help explain its use in post-Avicennan philosophy. A second reply would be to recall that we are in the context of exploring the deliverances of necessary and immediate knowledge. In such a context, it makes sense to appeal to conceptual independence as a way to distinguish between that which is immediately intuitive and that which is not. To put it another way, the thought experiments draw our attention to the fact that when, as Abū al-Barakāt suggested, we simply “see” that there is such a thing as place, what we are grasping is space.Footnote 36
3. COINCIDING EXTENSIONS AND THE IDENTITY OF INDISCERNIBLES
But asserting the self-evidence of place as space is not enough; we must also show that this notion of place can withstand objections. This is the goal of the third faṣl, to which we turn now. It considers five objections to the notion of space. Of these, the one that receives the lion's share of Fakhr al-Dīn's attention has to do with “interpenetration (tadākhul)” (Maṭālib 121–35, §3.1). The challenge is taken straight from Avicenna, who argued as follows (Healing: Physics §2.7.6–9).Footnote 37 If the place occupied by a body were an extension equal in magnitude to the extension of that body, then we would have two overlapping, or interpenetrating, extensions. But what makes it possible for these two extensions to overlap? After all, we find that the extensions of two bodies are not able to interpenetrate. Avicenna argues that this is not because of the matter of which the bodies are made, but is rather a feature of the extension itself (§2.7.7).Footnote 38 In cases where two extensions do come together, we see that they aggregate to become one larger extension, whereas the advocate of space is imagining that the body's extension comes to overlap with a spatial extension, without adding to that extension (§2.7.4).
Furthermore, we can ask what makes the two overlapping extensions distinct from one another:
Healing: Physics, §2.7.8 (McGinnis trans., modified): It is well known that things agreeing in nature that are not divided into species by differences in their substance are not multiplied in respect of their being (fī huwiyyātihā). They are multiplied only through the multiplicity of the matters of which they are predicated. But if there is only one matter for them, they will not be multiplied at all, and so there will not be two intervals.
The point is that since the spatial extension occupied by the body is not individuated by matter, there is no way to distinguish it from the extension of the body itself. Fakhr al-Dīn's challenge is to show that, on the contrary, it is possible for the extension of a body to overlap with a second extension of space, which is occupied by that body. He must show that the two extensions would not aggregate to form a larger overall extension; he must prove that what prevents two bodies from overlapping is not that their extensions cannot overlap; and he must explain how the two extensions remain distinct despite having exactly the same boundaries.
He makes short shrift of the claim that two interpenetrating extensions would aggregate (Maṭālib 122–5, §3.1.1). When one extension overlaps with another there is an increase in number, but not necessarily in measure (miqdār). Indeed, it is only when two extensions fail to interpenetrate that their combination yields an extension larger than either of the two. The Aristotelian too is committed to this possibility. For he must admit that, when two surfaces or lines coincide, they are able to overlap without aggregating. Why then can't the same hold for three-dimensional extension? The second claim, that bodies resist interpenetrating precisely because they are extended, is also easy to deal with (Maṭālib 125–7, §3.1.2). What prevents this is rather the density of bodies, as we can see from the fact that subtle bodies can indeed commingle. And of course, space is not dense, so there is no reason to think it would resist being interpenetrated by a body. Finally, Fakhr al-Dīn again uses the ad hominem argument concerning lines and surfaces: if extension as such resisted interpenetration, how is it that one line or surface can perfectly coincide with another?
These issues are, however, only a prelude to the more formidable difficulty that it seems otiose to posit a spatial extension in addition to the extension of the occupying body. Fakhr al-Dīn admits that this is the most powerful point against conceiving place as space (Maṭālib 129). In setting out the argument, he contrasts “distinctness (imtiyāz)” and “otherness (taghāyur)”: “if distinctness is eliminated, then so is otherness eliminated” (Maṭālib 128, §3.1.3.2). Here he is invoking, on Avicenna's behalf, the principle we now call “the identity of indiscernibles.”Footnote 39 This states, roughly, that if two items share all their attributes, then they are in fact one and the same item. In Avicenna's system, there are three sorts of attributes that could be relevant: quidditative attributes, concomitants (lawāzim) of quiddity, and accidents. But in the case of two overlapping extensions, none of these will differ. They are both extensions, so they have the same quiddity; or as Fakhr al-Dīn puts it, they are “equal in respect of their complete essence (fī tamām al-māhiyya).” But this means they will share their concomitants, since concomitants are determined by essence. Finally, their accidents are the same. Thus there is no basis for distinguishing (mayyaza) them.
Fakhr al-Dīn rightly finds this a fruitful philosophical puzzle, as shown by the fact that he offers no fewer than five responses to it. The last is the least interesting: he simply repeats the ad hominem challenge that the same argument could be used in the case of lines and surfaces (Maṭālib 133, ad §3.1.3–5). The first three are more intriguing. Here Fakhr al-Dīn tacitly accepts the identity of indiscernibles but raises doubts as to whether the two extensions really need to share all their attributes. The three doubts, as one might expect, respectively concern essence, concomitants, and accidents. On the first score, while the essence of spatial extension and of bodily extension do share some features, such as three-dimensionality, it is far from clear that their essences are identical (Maṭālib 129–30, ad §3.1.3–1). Fakhr al-Dīn mentions as a parallel case the fact that black and white are both essentially colors, despite being distinct in essence. What would differentiate the essences of our two extensions, though? Well, for one thing, spatial extension is place, whereas body is in place. We might rephrase this by saying that the extension of a body is not suitable to be the place for anything, whereas this is exactly the role played by spatial extension. This may sound question-begging, but Fakhr al-Dīn could rightly say that the move is supported by the intuitions solicited in faṣl 2. The onus is on Avicenna to show the incoherence of space; against him, establishing the theory's internal coherence suffices.
But what if their essences are indeed identical? We have been assuming that then the two extensions would have to agree in their concomitants. This seems not just reasonable, but fundamental to Aristotelian epistemology. For example any two humans, since they share the same essence, should share all the features that are concomitant to that essence. This is why concomitants count as necessary and universal features, and thus as possible objects of scientific demonstration. But Fakhr al-Dīn offers six counterexamples (Maṭālib 130–1, ad §3.1.3–2):
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(1) God and a contingent thing exist are equal in respect of existence, but God's existence has different concomitants.Footnote 40
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(2) Celestial and sublunary bodies share the nature of body but differ in their concomitants.
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(3) Human souls are the same in essence but attach to different bodies.
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(4) One person's head is the same as another's in respect of being a head. If they differed only in accidents, then a head could survive when it is detached from one body and joined to another!
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(5) One and the same genus is made into different species through concomitant differentia.
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(6) When accidents are present in a body, a single sort of existence belongs to both the body and all the accidents.
The examples vary widely, which in itself makes his point hard to refute; one would need to explain how his reasoning fails in all six cases. In each case, we have things that are on a par essentially (God's existence and a created thing's existence; two bodies; two souls, etc.) but differ in terms of their necessary properties, rather than in respect of accidental attributes. Cunningly, Fakhr al-Dīn appeals to God and the heavenly bodies in cases (1) and (2), exploiting the fact that for Avicenna all features of these entities are necessary. But he also thinks that he can make the point work with contingently existing things. To take the most amusing example, case (4) has it that each head has a necessary connection to its body – it cannot be attached to some other body – and that this connection is not something it has in virtue of being a head.
We might suspect that Fakhr al-Dīn is equivocating on the term lāzim, which can mean “necessary” or “inevitable” but also has the more technical notion of a feature that is “concomitant” to an essence. Assuming that Avicenna accepted that heads have a quiddity at all, he would surely deny that the connection between a given head and its body is lāzim for the head in the technical sense of an essential concomitant. Still, let us give Fakhr al-Dīn credit for putting his finger on a difficult issue: some properties necessarily inhere in a thing, while being absent from other things that have the same essence. We might say that they appear to be lāzim without being lāzim in the technical sense. The Aristotelian is thus forced into a difficult choice. He must either admit that such properties are mere accidents, despite being ineliminable; expand the technical sense of lāzim to accommodate such properties; or admit that the classification of attributes into essences, concomitants and accidents is not exhaustive.
So much for the questions whether our two overlapping extensions would agree in both their essences and their concomitants. Now let us ask whether they could differ in terms of their accidents, the way souls are essentially the same but have different virtues and knowledge (Maṭālib 132, ad §3.1.3–3). Surprisingly, Fakhr al-Dīn makes no attempt to explain how this could happen with the two extensions. Instead, he makes a far more ambitious move. He grants for the sake of argument that the two extensions share all their attributes – essences, concomitants, and accidents. Nonetheless, once they have “entered into existence” they could have their own “specification (taʿayyun)”Footnote 41 and “particularity (tashakhkhuṣ).” This remark stands in need of some clarification, and he obliges:
Maṭālib 132: We also mention here that the space that is place doubtless has specification and particularity, in light of the fact that it receives the succession of bodies. These bodies, which are things that receive motion and rest, doubtless [also] have specifications and particularities, in light of the fact that they receive motion and rest. If this is so, then in the case where one permeatesFootnote 42 the other, why can't one say that there remains with each of them its individual specification and particularity? Furthermore, it is accepted that the particularity of one of them is not exactly the same as the particularity of the other. This is a sufficient basis for the occurrence of distinctness and otherness between the extension that is place, and the extension that is that which is placed.
The proposal seems to be that each of the two extensions is just primitively an individual. Other differences between the two extensions, such as the fact that space receives bodies whereas bodily extension receives motion and rest, do not constitute the difference between the two extensions, but presuppose their primitive distinctness.
Of course, this tends to undermine a principle that has been assumed thus far: that indiscernible things are identical. For, even though Fakhr al-Dīn suggests that specification could suffice to ground distinctness and hence otherness, such specification has been explicitly said to be compatible with at least initial indiscernibility in respect of all attributes. So it is no wonder that in his fourth response to Avicenna's argument, he puts the principle itself in doubt:
Maṭālib 132–3, ad §3.1.3–4: Granted that each of the two extensions is not individuated by anything on account of which it is distinguished from the other, why do you say that this excludes the occurrence of otherness and distinction? For, if the specification of a thing were something added to it, then specifications would agree in this feature (mafhūm), that is, the fact that they are specifications. Then each of them would be distinguished from another by something additional, and a regress would follow.
Here we have a positive argument for the primitiveness of specification or individuality. No matter what explanatory factor we might invoke, that factor would itself need to be specified. To put it another way, any candidate individuator would in turn have to be individuated. This is a good point, indeed one that has bedeviled many attempts to ground individuation. If we say that matter individuates, as is standard in the Aristotelian tradition, then what individuates each given parcel of matter? Or if we say that accidents individuate, then how is it that the accident of one substance is distinct from an accident of the same type in another substance?
Fakhr al-Dīn's suggestion is that all such attempts are wrong-headed. Instead, we should simply assume that each entity comes into the world, so to speak, with its specificity already secure. As often with Fakhr al-Dīn, it is hard to say just how seriously he means this proposal. Nor is it clear whether it is meant to apply with complete generality, or only to regions of space. After all, if we wanted to be more parsimonious and grant primitive specificity to only a restricted range of entities rather than to all individuals, spaces and times would be good candidates. Matter, or substances, could then be individuated by spatio-temporal location. Fakhr al-Dīn develops no such proposal here. But it would fit well with the passage in his Commentary on the Qurʾān with which we began this paper. God could create time and space as a framework within which to place other created entities, and these other entities would have individuation by being situated within that framework.
4. AGAINST THE ARISTOTELIAN ACCOUNT
Having responded to Avicenna's critique of space in the third faṣl, in the fourth and final faṣl devoted to place Fakhr al-Dīn moves to the offensive and tries to establish that place really is space. As we've seen, he first offers “admonitions” to show that this is self-evidently the case. Next come five full-blown arguments (Maṭālib 146–53, §4.2), all but one of which are criticisms of the rival conception of place as the inner boundary of a containing body. The exception is the third argument (Maṭālib 149–50, §4.2.3), which positively contends that the spatial extension within a cup must be distinct from the extension of the body in the cup. So here Fakhr al-Dīn goes beyond his claim in the third faṣl that these two exceptions could be distinct, to the claim that they must be distinct. But his remarks add little to what has already been said. He invokes the possibility of replacement (§4.2.2.3), as when air is replaced by water in a cup. As we've seen, the Aristotelian theory not only can accommodate this phenomenon, but was designed in part to deal with it, so this would seem to carry little force. Fakhr al-Dīn further suggests that, whereas it is obvious that there is extension within the cup, it is not obvious that there is bodily extension there, since void's impossibility stands in need of proof (§4.2.2.2). This is just a variant on the flying-man style arguments already used in the first half of the fourth faṣl. Still, there is one advance in this section. Fakhr al-Dīn now makes so bold as to assert that void – that is, unoccupied place – can indeed exist (§4.2.2.1). For this he simply refers us forward to the next section of the Maṭālib.
His attack on the Aristotelian theory, by contrast, adds considerably to what we have seen so far. As often, he begins with the argument with the farthest reaching philosophical consequences. He points to a supposed absurdity with Aristotle's position, namely that if place were containing surface, then something could be in rest while its place is in motion, or vice-versa. His examples of something being at rest while its place is in motion are taken from Avicenna,Footnote 43 who proposed the following on behalf of the critics of the Aristotelian account:
Physics: Healing §2.6.4 (McGinnis trans., modified): If place is a surface that meets the surface of the thing [that is in place], then motion would be to depart from one surface while advancing towards another. Then the bird standing still in air and the rock standing still in water, where both [the water and air] are changing around them… must be in motion. For what they have made the place of [the bird or stone] changes around it. If it is resting, then in which place is it resting?
To this, Avicenna later suggests that we could escape the difficulty by understanding “rest” in a different way. We could say that things are at rest when their relation to certain fixed points (umūr thābita) is unchanging (§2.9.10). He does not apply this proposal to the examples, but his meaning is fairly clear. If we imagine a bird hovering with air streaming around it, then even though its proximate containing surface is moving, there is something else against which it can be judged to be at rest.Footnote 44 This could be, for instance, a nearby tree, relative to which its position is remaining the same. Or, more in the spirit of the Aristotelian account, the bird is at rest relative to the nearest containing surface that is not moving, which would probably have to be the lowermost celestial sphere.Footnote 45
The reader will be unsurprised to learn that Fakhr al-Dīn is not satisfied with this appeal to “juxtaposition (musāmata).”Footnote 46 Consider the different case of an object in a moving container (Maṭālib 147, §4.2.1.1). Let's say it is a gemstone in a box that is being carried down the street. In such a case, the gemstone remains at rest relative to the box, but in fact both are moving. A similar thought experiment is subsequently used to show that the Aristotelian must not only admit that what is at rest is moving (like the bird hovering in flowing air), but also that what is moving is at rest. Imagine that we take something – again, let's say a gemstone – in a bag from Rayy to Khurāsān (Maṭālib 148, §4.2.1.2). Since the inner surface of the bag is the supposed place of the gemstone, the gemstone stays in the same place throughout its journey! To this objection, Avicenna might simply reply that the gemstone does indeed stay in the same place, namely the bag; it is a further question whether the bag is moving.Footnote 47 An Aristotelian could also say that Fakhr al-Dīn is simply picking the wrong reference point against which a thing is moving or at rest. We should instead look to the nearest unmoving (akinêton) containing surface, as Aristotle says when discussing the example of the boat in a river: its place is not the moving water around it but the river as a whole, which does not move (Physics, 4.4, 212a20).Footnote 48 But this solution is, in some cases at least, rather forced. To say that the place of a gemstone in a traveling bag is the lowest celestial sphere is hardly to preserve our pre-philosophical intuitions.
Fakhr al-Dīn draws a different conclusion, namely that it is just wrong to define motion and rest in terms of relations to other bodies. He mentions further examples, such as two raindrops that are falling side by side. They are certainly moving, yet they are at rest relative to one another (Maṭālib 147, §4.2.1.1.1–2). The moral of the story is:
Maṭālib 148, §4.2.1.1.4: We can understand something to be at rest in itself (fī dhātihi) on the basis of the location (ḥayyiz) in which it resides, even while we are ignoring everything else. By contrast, its being juxtaposed to something else cannot be understood without also understanding something else. Thus, we know that its being at rest in itself is different from its remaining juxtaposed to something else.
It's well worth dwelling on the implications of this. Fakhr al-Dīn has, extrapolating from Avicenna's consideration of problem cases for his theory of place, attributed to the Aristotelian a relativistic theory of motion and rest. On this theory, a thing could only ever be said to be in motion or at rest in relation to other bodies. Against this, Fakhr al-Dīn upholds an absolute conception, according to which a thing moves just in case it changes its region of space.Footnote 49 On this theory, an object could meaningfully be said to move even if it existed alone in infinite space. So rest and motion are not relational, but intrinsic to bodies (they belong to things fī dhātihā). An extrinsic relation (nisba ilā al-ghayrihi) like juxtaposition is posterior to such intrinsic features (Maṭālib 147–8, §4.2.1.1.3).
On the basis of this remarkable line of argument alone, Fakhr al-Dīn's demolition of the Aristotelian theory of place should be recognized as a significant milestone in the history of science. But he's not done. The arguments that conclude the fourth faṣl heap further unwanted consequences on the proponent of place as a containing surface. In the third argument of the section, we learn that a thing's volume is not proportional to the size of its Aristotelian place (Maṭālib 150–1, §4.2.3). The extent of a thing's Aristotelian place is, of course, just the area of its own surface (since this is equal to the area of the containing surface). But a mass of wax can increase its surface area while remaining the same in volume, when it is changed from a ball into a cube. Surface area can even increase while volume shrinks, for instance if a shallow hole is scooped out of each side of a cube. By contrast, the “Platonic” place occupied by something behaves as we would expect: its size varies in proportion with the size of what is placed, since a volume of space is equal to the volume of whatever occupies that space.
These mathematical examples are not original with Fakhr al-Dīn. An important precursor of his discussion is the brief but pioneering treatise On Place by Ibn al-Haytham.Footnote 50 We know that Fakhr al-Dīn was aware of it: his Mulakhkhaṣ cites Ibn al-Haytham by name as a source for the same thought experiments, e.g. that a cube and sphere of the same volume have different surface area.Footnote 51 In light of this, we may wonder whether Ibn al-Haytham was an inspiration for Fakhr al-Dīn's view more generally. In his treatise, Ibn al-Haytham defends a notion of place as “imagined void, which is to say imagined dimensions (abʿād), in which there is no matter.”Footnote 52 While the association of place with void and dimension or extension is clearly an anticipation of Fakhr al-Dīn's view, the emphasis on the role of the imagination (takhayyul) is not. Ibn al-Haytham reiterates this role several times, writing for instance, “although the dimensions that are filled by body do not exist on their own (ʿalā al-infirād) without matter, prior to being filled by body, still body may fill imagined dimensions. For the dimensions are imagined as being on their own, abstracted from matter.”Footnote 53 Ibn al-Haytham is not really interested in the question of place as a physical or metaphysical principle: the sort of place he has in mind can, indeed, exist on its own only in his mind, abstracted from bodies. This is especially important because it has to be used in mathematical reasoning.Footnote 54 Of course, the reverse is the case for Fakhr al-Dīn. For him, place is space not as an imaginary, mathematical construct, but as a self-subsisting principle independent of both the mind and the body.
What might an Aristotelian like Avicenna say to the thought experiments that Fakhr al-Dīn takes from Ibn al-Haytham? I suppose he would just bite the bullet, and deny our intuition that the magnitude of place needs to co-vary with the magnitude of the volume of what is placed. Again, though, that might be a good enough result for Fakhr al-Dīn. It becomes increasingly evident that with these final arguments, he is simply trying to show that the Aristotelian account is less intuitive than the Platonic one. The fourth and fifth arguments seek to show this by appealing to cases where something lacks a surrounding surface (Maṭālib151–3, §4.2.4–5). If we conceive of a body with nothing surrounding it, claims Fakhr al-Dīn, we still think of it as being “here or there,” that is, as having a location. It almost goes without saying that the Aristotelian will yet again have to deny this intuition. Indeed, Aristotle himself denied this in the actual case of the universe, which (for him) is surrounded by nothing whatsoever, not even void. Aristotle's associate Theophrastus already noted the awkward implication that the universe would have no place.Footnote 55 Fakhr al-Dīn's point is related, but not exactly the same. He wants to argue that even on the Aristotelian cosmology which denies any body or void outside the cosmos, it is still irresistible to suppose that there are places outside the cosmos. He offers several thought experiments to show this.Footnote 56 For instance, if we imagine the axis of the cosmos to be extended infinitely, the part of the line extending from the north pole is clearly going to be distinct from the part extending from the south pole; that is, they are in different places. And if we imagine a man standing on the surface of the outermost sphere, he will still be able to distinguish between what is in front and what is behind him.
5. CONCLUSION: THE ROLE OF INTUITION
As Fakhr al-Dīn concludes his discussion, we get a final indication that his arguments have turned on the question of whether the Aristotelian account is counterintuitive. Fakhr al-Dīn anticipates an objection, to the effect that all these thought experiments may be misleading. They all solicit judgments from our “estimation and imagination (al-wahm wa-al-khayāl),” but such judgments are notoriously unreliable (Maṭālib 153, ad 4.2.5). This is an authentically Avicennan way of responding. Avicenna admitted that the estimation may lead us to think that there is such a thing as self-subsisting extension, as when we imagine a body being removed and replaced with nothing at all.Footnote 57 But this just shows that estimation is untrustworthy, not that there is really such a thing as space.Footnote 58 The problem is that we easily confuse leaving something out of consideration with real elimination (Healing: Physics, §2.9.10). This diagnosis could certainly be applied to some of the thought experiments we've seen Fakhr al-Dīn offering. Ibn al-Haytham, the source of some of those thought experiments, would be particularly vulnerable to such a response, since he explicitly grounds his notion of space in the activity of the imagination.
The issue arises explicitly in Fakhr al-Dīn's Muḥaṣṣal, which also contains a passage on the question of place (here “direction [jānib]”) outside the universe. Here he is contrasting the approaches of the mutakallimūn, who as proponents of void would be happy to admit extracosmic place, and the philosophers who reject any such conception:
As for the claim that there would be no difference in directions [outside the cosmos], this is false, as is immediately evident to the intellect, for the sound intellect sees that the region (ṭaraf) adjacent to the north pole, for instance, is different from the one adjacent to the south pole. Someone who denies this denies the immediately evident. Response: the mutakallimūn agree that there are distinct locations outside the cosmos, to infinity, but they claim that they are merely postulated (taqdīriyya), not existent. This is unpersuasive, because the postulated is what has no existence except in the mind (dhihn) but what has no existence except in the mind either lacks correspondence with external [reality], and then is posited falsely, or does correspond, in which case it follows that locations would in fact (fī nafs al-amr) exist… The philosophers (ḥukamāʾ) insisted that in a void outside the world there would be no distinction of one side (jānib) from another, and that supposing there to be such a distinction is estimation (wahm) not intellect; and we should not accept the judgment of estimation.Footnote 59
Notice that here too, what one side sees as “immediately evident” is condemned by the other side as a figment of the estimation. In the Maṭālib, though, Fakhr al-Dīn is not content merely to report this stalemate. He tries to resolve it by saying, in effect, that we have to start somewhere:
Maṭālib 153–4, ad §4.2.5.2: If you say that affirming some [intuitions] counts as intellect, and is thus true, whereas in other cases it counts as estimation, and is thus false, then on this view we will no longer know the difference between intellect and estimation. Secondly, we will not know of a given judgment whether it is one made by the intellect or made by the estimation. Thirdly, we will not know that intellect is true and estimation false… But if these three things are matters of immediate knowledge, that will prevent conviction arising for false judgments, given that one will have immediate knowledge that they are false. If however they are reached by argument (istidlāliyyan), then immediate premises will be based on proofs, and vice-versa, which gives us a circle.
In a sense, this is just what an Aristotelian would say. If we are to get the enterprise of demonstrative knowledge off the ground, we need primary, self-evident premises to serve as foundations for further proofs.
The difference is that Fakhr al-Dīn seems far readier to admit that the class of self-evident premises includes judgments that are, as the Aristotelians would say, “primary to us”: they simply strike us immediately as true. All the arguments of the fourth faṣl appeal to such judgments. At first, Fakhr al-Dīn tried to show that the existence of space is immediately obvious and stands in no need of argument at all. Then he offered some arguments nonetheless, mostly to undermine the Aristotelian account. While these arguments do not beg the question by reasserting the obvious existence of space, they do appeal to other items of immediate knowledge (e.g. the contrast between north and south, or front and back, outside the cosmos). At best, an Aristotelian might admit such judgments as dialectically valid because they are widely shared. On this concession, they would count as endoxa – like the criteria for place mentioned by Avicenna, such as that place is that in which something is, from which it can move, and so on. At worst, they are figments of wahm. For Fakhr al-Dīn, by contrast, they offer the only basis for a truly adequate account – or perhaps the best basis available to human reason, whatever doubts may linger.Footnote 60
APPENDIX
I here provide an analytical overview of the discussion of place in the Maṭālib. This corresponds to the first four fuṣūl of the eighth Maqāla of the fifth volume, at pages 109–54 in the printed edition. Page numbers are given in square brackets.
Faṣl 1 [111–14]: Various views on place.
1.1 [111]: In general, place is something in which there is something, from which it departs through motion, which does not accommodate it and something else at the same time, and into which moving things can come successively. This is accepted on all sides; the question is whether as Plato holds place pervades body and is extension (buʿd) or space (faḍāʾ), or as Aristotle holds place is the inner surface of the containing body.
1.2 [111–12]: Discussion of whether Plato thinks of place as both matter and form.
1.3 [112–13]: Classification of theories of place:
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(A) Place is space
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(A1) Space is “pure” and is nothing existent
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(A2) Space is self-subsisting extension
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(A2a) This extension can persist without bodies
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(A2b) This extension cannot persist without bodies
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(B) Place is the inner surface of the containing body
Faṣl 2 [115–19]: Refutation of those who say that space or void is sheer non-existence.
2.1 [115–17]: Six arguments that space is not sheer non-existence:
2.1.1: The extension of space can be divided in half, thirds, etc. which is impossible for sheer non-existence.
2.1.2: One can point out space to sensation e.g. by saying “from here to there.”
2.1.3: Body occupies space, and can depart from it and move to a difference space. This would not be possible if space were sheer non-existence.
2.1.4: By differentiating “here” and “there” we are using the same kind of expression for space that we do for a surface (“a surface from here to there”). This implies that space exists, like the surface does.
2.1.5: Spaces are numerically different (because some spaces are adjacent and others not) and the mutakallimūn admit that numerically different things must exist.
2.1.6: We contrast “above” and “below”; attributes must apply to existing things. Above means not below and vice-versa. If both are non-existent we lose this asymmetry.
2.2 [117–18]: Response by the mutakallimūn: void has only conceptual, not concrete, existence. If it did exist it would be either independent (bi-al-istiqlāl) or dependent (bi-al-tabaʿiyya) but both can be ruled out:
2.2.1: If independent, space would itself be a body and thus would need a further space, leading to a regress.
2.2.2: If dependent it would be an accident, but the body is only accidentally in the place, so they are accidental to one another which is absurd.
2.3 [119]: Response from the philosophers (ḥukamāʾ) defending the judgment that bodies exist in locations that are externally real:
2.3.1: The place is a ẓarf for the body and this cannot just be non-existence.
2.3.2: Motion is from one place to another, so the places must exist and be distinct.
Faṣl 3 [121–42]: Is place to be understood as self-subsistent extension? “Aristotle and his followers” argue that it is not, and give five proofs (3.1–5).Footnote 61
3.1: If place were self-subsistent extension then the extension of a body and the extension of the place it occupies would interpenetrate. But this is impossible, for five reasons:
3.1.1 [122–5]: The two extensions would come together without increasing in size.
ad 3.1.1–1: One must prove that two extensions couldn't interpenetrate without being identical, whereas the opponent is merely asserting this.
ad 3.1.1–2: The Aristotelians do accept coinciding extensions in the case of two surfaces that are in contact.
3.1.2 [125–7]: Bodies cannot interpenetrate without becoming a single body, and this must be because of the dimensions, rather than the matter, of the bodies, because:
3.1.2.1: Matter lacks determination, so cannot be the basis for the distinction of two bodies.
3.1.2.1: When two bodies (e.g. portions of water) are joined, the matter becomes one.
ad 3.1.2 [126–7]: This argument fails for two reasons. First, it is only dense bodies that cannot interpenetrate and density does not belong to body as such. (Indeed the division proposed in 3.1.2 may be incorrect: we should perhaps ask whether density causes the impossibility of interpenetration.) Second, when two surfaces come into contact they become coextensive; if dimensions excluded interpenetration this could not happen (cf. ad 3.1.1 above).
3.1.3 [127–9]: If there were an extension of space as well as of body, then when the two coincide either both would persist as distinct, or become indistinguishable. But both are ruled out:
3.1.3.1: They cannot persist because they will be identical in quiddity, and in respect of the concomitants and accidents of the quiddity. So there there is no principle of individuation available.
3.1.3.2: It cannot be that the two become indistinguishable.
ad 3.1.3 [129–33]: Five responses:
ad 3.1.3–1: While the dimension of space and of body may share concomitant features, this does not prove that they are identical in quiddity.
ad 3.1.3–2: Things may agree in quiddity while differing in concomitants, as shown by six examples.
ad 3.1.3–3: Accidents could also serve to differentiate the two extensions, as shown by the case of rational souls.
ad 3.1.3–4: Even if the extensions lack individuating factors, they may still be distinct; after all, if we add a distinguishing factor to each, the two distinguishing factors must themselves be distinguished, which yields a regress.
ad 3.1.3–5: The argument would apply equally well to lines and surfaces. If two things in contact have only one limit, then there is in fact no contact at all.
3.1.4 [133]: If interpenetrating extensions were possible, then we could not rule out that the whole world could be packed into the place of a mustard seed.Footnote 62
ad 3.1.4 [133–5]: Three responses:
ad 3.1.4–1: Is this supposed possibility real or only an abstract mental one? If the former, then proof needed that this is actually possible. If the latter, then we can distinguish the two cases: the mustard seed case is self-evidently impossible, whereas for the case we are arguing about it is not obviously possible.
ad 3.1.4–2: Again, the same argument could be applied to lines and surfaces.
ad 3.1.4–3: It's agreed that it is possible to make a body more or less dense, so in principle one could rarify the seed to the size of the cosmos, or condense the cosmos to the size of the seed.
3.1.5 [135]Footnote 63 : If we admit the presence of two extensions when only one is perceptible, this undermines our confidence that any single perceptible entity is one; how could we rule out that a single perceptible man is in fact 1000 men or more?
ad 3.1.5: Refers us to the responses to 3.1.4.
3.2 [135–36]: The extension, if it exists, must either inhere in matter or not. Neither is possible:
3.2.1: If it did, it would be the same as body, since body is precisely “extension inhering in matter.”
3.2.2: If not, then in general extension needs no matter. But then the extension of bodies would need no matter, but that is false.
ad 3.2: This argument makes the already discussed assumption (see 3.1) that all extensions as such are equivalent.
3.3 [136–8]: Extension as such is either receptive of motion or not:
3.3.1: If receptive of motion, then when extension moves it will go from one place to another, and will need a second-order extension to make this possible: regress.
3.3.2: If not receptive of motion, then the extension of a body could not move, which is absurd. If someone says that extension must be in matter in order to move, we respond that extension is not an attribute in a subject (maḥall), as will be shown later. Even if it were, then that subject would need either to occupy space or not: if so, the subject would already have extension before having the attribute of extension; if not, the supposed subject of extension has no location, so how can it receive motion?
ad 3.3: This assumes that what is true of the extension of body is true of the extension of space, an assumption already challenged above.
3.4 [138–40]: Consider an extension divided in two. The two parts are either equivalent in quiddity or not:
3.4.1: If equivalent in quiddity, then anything true of one is true of the other, but then the top part will be the bottom part and vice-versa. This implies that they swap places, in which case the parts of the extension need to be in place; regress.
3.4.2: If not equivalent in quiddity, then space is composed of parts with differing quiddities. Still, if we take a simple part of space and divide it, the resulting sub-parts should be the same in quiddity; then we can apply argument 3.4.1 to these sub-parts.
ad 3.4: If this were right, then one could likewise divide the simple celestial sphere into parts that would need places, implying a void outside the cosmos.
3.5 [140–2]: If space existed, then it would either be infinite or finite. It cannot be infinite, as will be shown later. If it is finite, it is surrounded by a limit, which would be a shape. What gives rise to the shape is either the very nature of the extension, a feature (ḥāll) that inheres in that nature, the subject (maḥall) for that nature, or something that is neither a feature nor a subject for that nature. By process of elimination, it is concluded that it is the matter that accounts for its specific shape.
ad 3.5: Matter is no more suitable to determine a shape than extension; and the nature of the extension could already give it the specifying attributes that make it suitable to have a certain shape.
Faṣl 4 [143–52]: Place as extension
4.1 [143–6]: Some hold that place in the sense of extension is self-evident, because it is obvious that when a body occupies a place or moves, that place is not the same as the body. Six “admonitions (tanbīhāt)” to this effect:
4.1.1: If a mountain is demolished the location it occupied remains, and could be the location for a new body, such as a mansion.
4.1.2: If the Kaaba were dismantled, the space left behind would be the qibla.
4.1.3: Whereas it is self-evident that something in particular is here or there, it is not self-evident that body is here or there, since one needs to prove that void is impossible. But the self-evident is not identical to the non-self-evident, so the particular here or there is not the body.
4.1.4: We can imagine a body with no body around it, but not a body that is not in place. So the surrounding body must be distinct from the place.
4.1.5: The space inside a jug remains the same whether it is occupied by water, air, or (assuming void is possible) nothing at all, so the space is distinct from the body that occupies it.
4.1.6: “Here” cannot travel to be “there,” but it is possible for the body here and the body there to switch places. So the particular “here” and “there” are distinct from the bodies that occupy them.
4.2: Others hold that spatial extension can be proven to exist:
4.2.1 [146–9]: If place were surface and not extension, then things at rest would be in motion and things in motion would be at rest.
4.2.1.1: Why what is at rest will be in motion on the Aristotelian theory: Avicenna's examples of a bird in the air and stone in water. It is no solution to say the bird and stone are at rest by remaining juxtaposed to other things, for an object in a moving box is at rest relative to the box but still in motion.
ad 4.2.1.1: It would be obstinate to deny the obvious fact that the bird and stone are at rest in this situation.
Further discussion of the idea of being juxtaposed:
4.2.1.1.1: Two identical objects dropped from a height will remain juxtaposed while falling.
4.2.1.1.2: Two celestial spheres remain juxtaposed even while revolving.
4.2.1.1.3: Rest is intrinsic to a body, and explains the extrinsic relation of being juxtaposed, not the other way around. Since rest is therefore prior to juxtaposition the two cannot be the same.
4.2.1.1.4: Whereas we can understand something to be at rest while ignoring all other objects, this is not true for juxtaposition, so the two are not the same.
4.2.1.2: Why what is in motion will be at rest on the Aristotelian theory: imagine an item in a bag, transported from Rayy to Khurāsān. Then despite the long journey it will be at rest, since it will remain in contact with its “place” which is the inside of the bag.
ad 4.2.1.2: The item does not move in itself (bi-dhāt) but only on a supposition (bi-al-farḍ). But it would be obstinate to insist that something can go from Rayy to Khurāsān without moving in itself.
4.2.2 [149–50]: The extension within a cup is distinct from the body contained in the cup, because:
4.2.2.1: As will later be shown, void is possible, so there can be extension in the cup without any body being in the cup.Footnote 64
4.2.2.2: Even if void is impossible, the requirement for a plenum has to be proven. So it is self-evident that there is extension in the cup and not that there is bodily extension in the cup, so the two are distinct.
4.2.2.3: The extension in the cup remains as one and the same individual (shakhṣ) while the bodies change (since e.g. water can replace air in the cup), which shows they are distinct.
4.2.3 [150–1]: If place were containing surface, then one would have to say that place can grow while that which is place stays the same, that the thing in place can shrink while the place stays the same, and even that place can grow while that which is in place shrinks.
4.2.3.2: The place can grow while the thing in place stays the same in the case where the thing is chopped into parts, since the measure (miqdār) of the parts will be the same as that of the whole but the surrounding surface will be bigger. Also, if the same wax is changed from a sphere into a cube, its surrounding surface will get bigger while the amount of wax stays the same.
4.2.3.2: The thing in place can shrink while the place stays the same: the supposed place of water in a waterskin is the inside of the skin, and this remains as it was when some of the water is squeezed out.
4.2.3.3: The thing in place can shrink while the place grows in the case where we take a cube and hollow out a hole in each of its sides.
4.2.4 [151–2]: We are able to conceive a body all by itself without imagining surrounding bodies, and when we do so we inevitably imagine it as having spatial presence (ḥuṣūl). This shows that location is not the same as having a surrounding surface.
4.2.4.1: A confirmation of this: motion and rest can be conceived without any involvement of surrounding surfaces.
4.2.5 [152–3]: Since bodies are finite, they must have location without having a surrounding surface; one cannot say that the universe has no location, for every body must have a location. This is confirmed with three examples:
4.2.5.1: Extending the cosmic axis to infinity: one side of the line would be distinct from the other.
4.2.5.2: A man standing on the north pole of the cosmos will distinguish between what is in front of him and what is behind him.
4.2.5.3: A point on the outermost surface of the sphere will move from one location to another as the heavens turn.
ad 4.2.5: Someone might say this judgment is a product of estimation and imagination. But it is not, for three reasons:
ad 4.2.5.1: This judgment is as convincing as any other immediately evident premise, and we need such premises to argue at all.
ad 4.2.5.2: To throw immediately evident things into doubt is to undermine the very distinction between intellect and estimation.
ad 4.2.5.3: The judgment involved in 4.2.5.1 is a good example of immediate, primary knowledge.
