Christopher Buckels* Making Room for Particulars: Plato's Receptacle as Space Not Substratum DOI 10.1515/apeiron-2016-0006 Received January 22, 2016; accepted February 4, 2016 Abstract: The "traditional" interpretation of the Receptacle in Plato's Timaeus maintains that its parts act as substrata to ordinary particulars such as dogs and tables: particulars are form-matter compounds to which Forms supply properties and the Receptacle supplies a substratum, as well as a space in which these compounds come to be. I argue, against this view, that parts of the Receptacle cannot act as substrata for those particulars. I also argue, making use of contemporary discussions of supersubstantivalism, against a substratum interpretation that separates substratum and space in the Timaeus. Keywords: Plato's Timaeus, space, receptacle, substratum, particulars I Introduction The entity introduced halfway through the Timaeus is shrouded in mystery; the Receptacle of all Becoming, as it is called, is "obscure" and "difficult to explain". It is called space (χώρα, 52a8), place (τόπος, 52a6), a seat (ἕδρα, 52b1) for Form images, that "in which" things come to be, and a mother which, together with the Forms as father, have things that come to be as their offspring.1 It is also compared to some gold in which shapes are molded, a wax tablet in which images are stamped from the Forms, and the unscented base of a perfume. Between these descriptions and analogies, two prominent conceptions of the Receptacle emerge, first, that it is a space in which things come to be, and, second, that it is, in addition to space, a substratum that *Corresponding author: Christopher Buckels, Department of Philosophy, University of the Pacific, 3601 Pacific Avenue, Stockton, CA 95211-0110, USA, E-mail: cbuckels@pacific.edu 1 Unless otherwise noted, all references are to the OCT text of the Timaeus and translations are my own. apeiron 2016; aop Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM underlies things. The second, labeled the "traditional" interpretation, maintains that the Receptacle is divided into parts that act as substrata to ordinary material particulars such as dogs and tables. Thus, it takes particulars to be form-matter compounds – like Aristotelian substances – to which Forms supply properties and the Receptacle supplies matter, i. e., on this interpretation, a substratum for the properties. In addition, the Receptacle is the space in which these compounds come to be. The main alternative is to assign it only this second role: it is the space in which particulars appear, but its parts are not substrata for particulars. My primary aim is to show that parts of the Receptacle cannot act as substrata to particulars; my secondary aim is to show that the Receptacle functions as the space in which particulars come to be, although I leave open several questions about the ontological status of space, each of which beg separate treatment: for instance, whether the Receptacle is absolute or relative space, whether it is dependent on Forms or independent of the Forms, whether there is any relation between it and time, and whether it is possible to call the Receptacle "matter" in some carefully-construed sense. For now, I seek primarily to clear the way for further investigations by showing that the traditional interpretation is untenable. We will begin, in Section II, by examining how Timaeus motivates his introduction of the Receptacle. In Section III, we will discuss the nature and capacity of the Receptacle, focusing on several analogies Timaeus gives. I argue that the nature of the Receptacle, as revealed in the analogies and surrounding text, is to serve as the space in which sensible particulars, as images of Forms, come to be. Section IV examines the contrasting view, endorsed most prominently by Donald Zeyl, which holds that parts of the Receptacle act as substrata for particulars. I criticize this interpretation on a philological as well as a philosophical basis, since several absurdities arise if parts of the Receptacle can move and change as the traditional interpretation requires. In Section V, I will consider a view whereby we posit two Receptacles, one to provide space and the other to provide substrata; in particular, we will investigate a view in this vein which has been advanced by Dana Miller. Section VI relates this two-entity view with discussions of substantivalism in contemporary metaphysics. On the basis of these contemporary discussions, I also find the two-entity view lacking for general philosophical reasons; for example, the two-entity view unnecessarily duplicates entities and properties, and we have the added complication of relations between sensible particulars and the two entities and between the two entities themselves. On balance, the evidence favors a space interpretation over these forms of the substratum interpretation. 2 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM II A Puzzle Concerning the Elements Timaeus introduces the Receptacle in his "second beginning" (48e2ff), apparently adding it as a third kind to the other two kinds he has discussed, Being and Becoming (Forms and images of Forms).2 Up to this point, he tells us, two kinds sufficed for our cosmogony, "but now the argument compels me to make clear in words a difficult and unclear kind" (49a3-4). The natural capacity of the third kind, Timaeus reveals, is to receive all coming to be; it is the Receptacle of all Becoming. But before we can understand this enigmatic utterance further, Timaeus says that we must detour through a puzzle about fire and the other socalled elements. This puzzle motivates our theoretical posit of a Receptacle that receives all genesis. The problem, in brief, is how to identify the elements in a stable way, since they seem constantly to change into one another. The Receptacle provides the necessary ground for the designation of particulars: only it, we will see, is constant, while what comes to be in it – the elements and the particulars composed of the elements – is ephemeral, continually coming to be and perishing and never providing a stable referent for language. For the purposes of this paper, I will initially adopt a reading of this "much misread passage" (49b2-50a4) that is sometimes called the "traditional translation", exemplified by Zeyl,3 according to whom Timaeus tells us "not to apply the term 'fire' to this (i. e., some particular bit of phenomenal fire or water we might point to), but rather to things that are such."4 Think about it this way: when we put some water on the stove to boil, the stuff in the pot seems to turn 2 Cf. Silverman 1992, 91–92 and 2002, 260, who argues that "the receptacle is not some third primitive (ἀρχή) merely added to Timaeus' previous account. When viewed as a mere addition to the account, the receptacle functions simply as space or, at best, as providing a place in which the four traditional elements are located" (Silverman 2002, 261). For the purposes of this paper, it does not matter whether the Receptacle is a new primitive or not, but I take it still to be an open question whether or not the Receptacle functions "simply as space." While the elements are certainly not merely the traditional elements the Presocratics employed, Silverman does not offer much in the way of direct criticism of the "simply space" view. 3 Zeyl 2000, lvi–lix, compares the "traditional translation" and the "alternative translation" wherein we are told not to call fire, or water, or anything to which one can point, "this". Instead, the alternative translation continues, fire and such things are "this-suches", i. e., qualities or property-instances. Gill 1987, among others, also defends the traditional interpretation. For more on the alternative interpretation, see Cherniss 1954 (who gives the "much misread passage" its name) and Lee 1966, 1967. Although I elsewhere defend the alternative translation, here I follow the traditional translation to show that, even according to it, the Receptacle's parts cannot serve as substrata to particulars. 4 Zeyl 2000, lvi–lix. Making Room for Particulars 3 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM into air. One and the same stuff, it seems, can be both water and air at different times. The same point can be made with our modern elements, since radioactive decay can turn one element into another. Water, then, is not a this, i. e., something that is "whatever it is in its own right rather than by virtue of something else."5 Instead, water is a such, since "its being [water] is at best a temporary characteristic of" the stuff in the pot.6 Water is more like a phase sortal than a stuff, since it only applies to some stuff for a certain amount of time.7 The "stuff" water applies to, Zeyl suggests, is a part of the Receptacle. At this point, I will interrupt our discussion of the text, for Zeyl's reading is already leading us, or misleading us, from translation into interpretation. In particular, it is leading us into thinking that Timaeus rather obviously puts forward a substratum theory. In fact, Timaeus never says that water and fire are characteristics of the Receptacle. Instead, he says that they come to be in the Receptacle and perish from it. The "in which" locution is repeated several times – the Receptacle is that "in which" material particulars come to be (ἐν ᾧ, 49e7, 50d1, 50d6; cf. ἐν αὑτῷ, 50e5). The further point that water and fire are properties of the Receptacle does not immediately follow from the fact that they are in the Receptacle; water and fire could be properties of a substance that comes to be in the Receptacle, or they could be property instances (tropes) that come to be in the Receptacle. Going on in the text, Timaeus generalizes his claim about water to anything to which we point and try to call this or that (49d7-e4), and anything that is "some 'such' or other," such as hot or white (50a2-4). Anything to which we can point and call that is not really a that, i. e., something that stably retains the same properties, never altering into something else. Everything we encounter through sensation is mutable. Can we, then, use the terms "this" and "that" at all? Timaeus tells us that we can, but not to designate the ordinary objects presented through sensation. Instead, when we point to something and say "that", we are actually indicating the only stable, unchanging thing there – the Receptacle (49e7-50a2). In each case, the Receptacle is the "this or that", while everything else is a characteristic or property. I submit that the "this or that" we can designate is the location itself, the space occupied by the thing, the place that underlies it. This particular space does not change, no matter what occupies it, whether a trope (or bundle of 5 Zeyl 2000: lvi–lix. 6 Zeyl 2000: lvi–lix. 7 Water cannot, of course, be a sortal in the grammatical sense, since water is not a count noun. But the elements are nonetheless treated like sortals, so we might think of water as "water molecules." 4 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM tropes) or a substance. Its nature always remains the same, as well, since it always has the capacity to receive anything into itself. This, I will argue, is the function of the Receptacle: to provide a place for coming to be. III Textual Support for the Substratum Interpretation Let us first turn to the textual evidence for the view I am criticizing, that the Receptacle is a substratum. Timaeus explains the Receptacle largely by analogies which seem to support such an interpretation, since these analogies involve some basic stuff receiving properties. My purpose in this section is to show that the analogies need not be read to support a substratum interpretation. The point of the analogies is not that the Receptacle is a stuff that receives properties, but rather that the Receptacle cannot itself have any of the properties it is supposed to receive, for then it could not properly receive those properties. If there are philosophical problems with substrata interpretations, as I will argue in the following sections, and if the text does not explicitly support a substratum interpretation, as I argue in this section, then we should look for an alternate interpretation, namely that the Receptacle is space and not substratum. Timaeus first compares the Receptacle to some gold in which a sculptor is continually molding different shapes (50a5-b6). If someone should ask "what is that?" while pointing to one of the figures, Timaeus says it would be safest just to reply, "gold". The idea is that the figures are being changed so rapidly that it would be incorrect to say "triangle" or any other shape, since the sculptor can be flattening out the tips of the triangle, busily forming a square, even as one gives the answer. So it is safest to say, "it is gold."8 With regard to the triangles and other shapes appearing in the gold, we can never say that these transitory figures are real.9 The same account goes for the Receptacle, Timaeus tells us. We have just been told (49e7-50a4) that fire is not a this, something to which we can point, but a such. Likewise, "that is a triangle" is false when one points to a triangular piece of gold, because the gold can be molded into many other shapes; it is not a triangle, but triangular. In other words, a triangle is not a that but a such. 8 For the purposes of the analogy, we have to pretend that gold is a basic substance – unlike water or fire, at least as Timaeus has just explained them – which is, of course, false. 9 Cf. Zeyl 1975, 143, according to whom this passage tells us that it is both true and false to say "triangle" in response to the question, "what is it?" If we mean by "triangle" a τοῦτο, then we have spoken falsely. If we mean by "triangle" a τοιοῦτον, we have spoken truly. Cf. Cherniss 1954, 125–8, and Mohr 2005, 101–10. Making Room for Particulars 5 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM We should, then, say "that is gold", since it will still be gold however one molds it. Thus, according to the analogy, it seems the only true "that" statement we can make is, "that is the Receptacle", for the Receptacle is what is always the same, however it may appear.10 Timaeus gives us more images later in the text to help us understand the receptivity of the Receptacle. Because of everything we have just discussed, the Receptacle, which is to receive all forms (γένη) in itself, must be without any of the forms (πάντων ἐκτὸς εἰδῶν), just as the base of a perfume must be made completely scentless, so that one can impose any scent upon it one wishes; similarly, any soft substance – let us take molding clay – must be, in and of itself, without shape, so that one can impose any shape upon it (50e4-51a1). In the first image, the base of the perfume is designated by the same terms as the Receptacle, "this very thing" (τοῦτ' αὐτὸ), so in the analogy the perfume base is a this, not a such. The perfume base is also said to be the foundation (ὑπάρχον) that will receive scents. This foundation must underlie the scents without imposing any scent of its own; the scent is the such, and the base is bare of suches. Likewise, in the second image, it is said that the craftsmen who mold the clay do not permit any shape at all to stand out in the clay, i. e., to underlie the shapes that they try to mold into it. Any shape already in the clay would obscure the shapes the craftsmen superimpose upon it. Finally, in connection with the gold analogy, which likens the Receptacle to gold that is being constantly reshaped, Timaeus calls it something "in which" impressions are made, like a block of wax. The things coming into the Receptacle, then, are stamped into it, like seals into wax (50c2-6).11 While helpful for illustrating the receptivity of the Receptacle, these images have their limitations. The clay and the wax cannot have any particular shape essentially, since they are supposed to receive all shapes, and the perfume base cannot have any scent, since it is supposed to receive any scent. All of them may, of course, have many other properties. In fact, they must have many other properties; the perfume base must be a liquid, the clay must be malleable, the 10 As I point out in detail below, we have to be careful to avoid being misled by the analogy and thinking that the Receptacle is too much like gold, i. e. that it is some kind of material "out of which" material particulars are made such that it remains a part of each material particular. Cf. Prior 1985, 112, Johansen 2004, 122, n. 8, and Harte 2002, 255–8. 11 Cf. Mohr 2005, 91: "So Plato while setting forth the philosophical functions of the third thing uses metaphors which, if read literally, would, when taken together, assign incompatible properties to the contents of the receptacle." Harte 2002, 255–8, actually argues that the gold and wax analogies support taking the Receptacle as a spatial medium. It bears mentioning that the Theaetetus likens the soul to a wax block, even though the soul is not material. 6 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM wax must be soft. The Receptacle, however, is to receive all things into itself. It can not be like any of those things it receives. Its nature is, in fact, to be like none of them, but to receive all.12 If, for example, it is to receive immaterial things such as souls, it cannot be material.13 It must underlie all things without imposing anything upon them or contributing anything to them; Forms provide characters to things that come to be in the Receptacle, which are thus images of those Forms. What the Receptacle provides is not a character but rather a place or space for these characters; it is some sort of medium in which appearances come to be.14 The main point of the images, then, is to convey the fact that the Receptacle must be, in itself, characterless so that it can receive all characters, in just the same way as the perfume base, the clay, and the wax must not, in themselves, have the characters that they will receive. There is a particular difficulty with reading the image of the wax block literally, namely, a difficulty with the mechanism of stamping impressions into the block.15 The difficulty is as follows: there are three kinds of thing: Forms, the Receptacle, here imagined as a wax block, and that which comes to be, here imagined as impressions in the block of wax. The Forms would presumably be stamps, the ideal models that cause the impressions. But this role seems closed to them, since a Form does not "itself come into another thing anywhere" (52a3). 12 The Receptacle cannot, in itself, share in any Forms, but it does have properties, contra White 1981, 327 & 339, n. 9, since it has a nature; cf. Miller 2003, 90. It should, at least, have the property of being able to receive Form images. White 1981, 319, seems to hold that the Receptacle is given properties later in the dialogue, though it is initially described as having none. It has properties, White explains, in order to account for Form images coming to be in a certain place at a certain time. But the Receptacle need not, in fact, have properties for this reason; Timaeus has already brought in the demiurge to explain how Form images come to be at a certain time in a certain place. McPherran 1988, 535–42 characterizes the Receptacle as "Form-bare," saying that it possesses no properties essentially for which there are Forms. 13 Timaean souls are made of "stuff," but it seems to be an immaterial stuff (35a1-b4; 41d4-7). While souls are not made of the elements, which are discussed in detail later (53c f.), there is no reason to think they are not in the Receptacle, since they are matched with, and seem to be the same size as, the particulars of which they are souls (e. g., the cosmos and its soul, 36d8-e5), and these particulars are in the Receptacle. 14 Cf. Cherniss 1954, 128. On media in general, cf. Broadie 2012, 63–4. Cf. Mohr 2005, 92: "It is clear from our passage Timaeus 49b-50b that it is the metaphors of space as a medium for receiving images which are meant to be taken at face value and that the reading of the other metaphors must be brought into accord with the conception of space as a medium." 15 White 1981, 316, also points out that the wax block image is misleading if taken too seriously, as it can lead us to believe that images of Forms are fairly stable, since impressions and stamps are fairly long lasting compared, at least, to reflections in a mirror. Making Room for Particulars 7 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM How would the Forms stamp impressions into the Receptacle without coming into it to form impressions? One would have to hold that the Forms are ideal stamps, and that there are intermediaries that are actual stamps, and these, in turn, form impressions, i. e., whatever comes to be. But this interpretation would introduce a fourth ontological category into the Timaeus, which should be avoided, since Timaeus explicitly lists three kinds of thing.16 We should not, then, read the wax block image as an accurate portrayal of the Receptacle's properties. Although the wax block image should not be taken literally, it is still a valuable image for how things come to be in the Receptacle. Like stamps impressed into wax, Forms give their characters to the Receptacle, shaping it in a certain way. The character of the Form that comes to be in the Receptacle is an image of that Form. Where we must modify the analogy, however, is where it leads us to believe that the Receptacle is some underlying material, like a hunk of gold that is constantly reshaped. These – wax and gold – are merely images for a thing which is difficult to imagine, something that must be grasped by "bastard reasoning". If material particulars are, in some way, images of Forms, in what are those images? Must they not be somewhere or in something? This is "bastard reasoning" because we do not reason about the Receptacle directly, but instead we see a need for it in reasoning about other things. We see it as a necessary posit, something for which we have no direct evidence but which explains the phenomena. Thus, the Receptacle explains how material particulars have some place and space in which to move. Let us look at two more brief passages that bear upon the ontological status of the Receptacle. First, Timaeus says that the Receptacle is not earth, or air, or fire, or water, nor is it anything composed of these or out of which these were composed (μήτε γῆν μήτε ἀέρα μήτε πῦρ μήτε ὕδωρ λέγωμεν, μήτε ὅσα ἐκ τούτων μήτε ἐξ ὧν ταῦτα γέγονεν, 51a4-6). We should not call the Receptacle one (or all) of the elements, since these all have determinate characters, and it must exist without any particular character that comes to be in it. Recalling the 16 The charge of introducing a fourth kind is a common attack against Cherniss (see Cherniss 1954, 129, and 1957, 246) and Lee (see Lee 1967, 27): cf. Zeyl 2000, lx; 1975, 134; Miller 2003, 27. But see Zeyl 2013: § 6, whose interpretation seems to require a "fourth thing" if Forms cannot stamp impressions directly into the Receptacle: "What is missing from that analysis [into three kinds], however, is any mention of character types or tokens, and while later philosophers might see a use for such concepts in elucidating the metaphysical scheme of the Timaeus, it is far from clear that Plato himself makes any use of them there." Algra 1995, 102, appears to endorse a four-kind ontology for the Timaeus similar to that of Cherniss. 8 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM gold example, we cannot call the gold a triangle or a square or any other shape, since it is not really any of these, and it is not even temporarily any of these for any determinate length of time, since it is being constantly remolded. If we want to be safe, we should call it only "gold". Since the Receptacle cannot have the character of any of the elements, we also cannot call it any of the thingsmade of the elements, because anything made of the elements will have their characters. Thus, we cannot call the Receptacle any bodily, sensible thing, since all bodily, sensible things are composed out of the elements (31b5-32b2). Finally, we should not call the Receptacle anything "out of which" the elements are made (51a6), since those things, too, must have characters. This prohibition keeps us from calling the Receptacle constitutive matter, since matter would presumably be that out of which the elements are made.17 Indeed, although Timaeus explicitly rules out the Receptacle being that "out of which" Form images come to be, it is common for scholars to call it the "out ofwhich", since the Receptacle is compared to gold, as we saw above, which is, explicitly, that "out of which" shapes come to be.18 Wemust, I repeat, take the analogies for what they are – metaphors – and take seriously Timaeus' explicit denial that the Receptacle is an "out of which"; it is, again, only the "in which" for images of Forms. Thus, although Timaeus has not pursued the project of naming the "elements of the elements" (cf. 48b5-d1, 53d6-7), we can definitively rule out naming the Receptacle as the ultimate material element or constituent of any material thing.19 In the second passage, Timaeus tells us that we are unable to discern that it is fitting for an image, which is always a transitory appearance (φάντασμα) of something else, clinging precariously to being on pain of being nothing at all, to come to be in another thing, since it does not have the very thing for which it 17 In particular, the Receptacle should not be identified with matter that is stuff-like. "Matter" can mean many things, so it may be that on some conceptions of matter, the Receptacle is matter; but cf. Cratylus 389c5, where the "out of which" is clearly the matter (in which a craftsman puts the form he sees). If the "out of which" is matter, and the Receptacle is not that out of which the elements are made, then it is not their matter. The position I am rejecting here is that the Receptacle acts as a kind of matter or stuff that is contained by the geometrical shapes rather than the view that there is some primitive matter in the Receptacle (and distinct from it), as found, e. g., in Gill 1987; cf. McCabe 1994, 180. I find Gill's view implausible, too, as well as unmotivated by the text; for fairly definitive criticism of it, see Silverman 2002, 267–73. 18 E. g., Algra 1995 , 91; Harte 2002, 250; Miller 2003, 189. 19 Interestingly, much of the opposition I have encountered in discussion to my interpretation of the Receptacle seems to stem from a conviction that everyday objects are "made of stuff," coupled with a belief that Plato shared this conviction and thus must have tried to explain the "stuff" of everyday objects with the Receptacle. I see little basis for this conviction in the dialogues, however, and one might speculate that it is a particularly Aristotelian prejudice. Making Room for Particulars 9 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM comes to be (ὡς εἰκόνι μέν, ἐπείπερ οὐδ' αὐτὸ τοῦτο ἐφ' ᾧ γέγονεν ἑαυτῆς ἐστιν, ἑτέρου δέ τινος ἀεὶ φέρεται φάντασμα, διὰ ταῦτα ἐν ἑτέρῳ προσήκει τινὶ γίγνεσθαι, οὐσίας ἁμωσγέπως ἀντεχομένην, ἢ μηδὲν τὸ παράπαν αὐτὴν εἶναι, 52c2-5). This is a complicated sentence, but, as Cherniss points out, its meaning is relatively straightforward: an image is always an image of something, so it is not itself what it depicts.20 It is dependent on something external to it for its generation and continued existence, and, therefore, it must come to be in something, since it cannot exist on its own. For example, a mirror image is completely dependent on the mirror and the thing imaged in the mirror – if either of these were taken away, the image would perish, too. In the context of the Timaeus, a Form image is what it is because of the Form of which it is an image, and it comes to be in the Receptacle.21 It is dependent on both Form and Receptacle for its continued existence, although in different ways.22 IV The Incompatibility of Space and Substratum We have seen that the textual basis for identifying the Receptacle as a substratum to particulars, or as the matter out of which particulars are made, is at best inconclusive and at worst quite dubitable. The "much misread passage," along with the passages about the relation of the Receptacle to the elements and about the ontological status of images, do not give us reason to take the Receptacle as a material substratum, and the analogies only give us reason to take it so if we read them quite literally. The case for the space interpretation, however, seems quite good, especially if we read the analogies as just that, images that reveal some aspects of the Receptacle's nature and obscure others. Let us now turn to philosophical reasons for denying the role of substrata to parts of the Receptacle; if there are philosophical reasons as well as textual reasons to identify the Receptacle as space rather than substratum, then a charitable interpretation of the Timaeus should do so. 20 Cherniss 1957, 264–6. 21 Regarding images, see Mohr 2005, 93–95, esp. n. 24, and Lee 1966, 353–4, who distinguishes substantial and insubstantial images; I agree with Lee (357) that Form images are insubstantial images. 22 I do not propose, in this paper, to settle exactly how Forms images depend on Forms and on the Receptacle. In the latter case, one may hold that Form images depend on the Receptacle as on an independent entity, or Form images may depend on the Receptacle while it itself depends, in some way, upon the Forms. The mirror analogy favors the first option – a Receptacle independent of Forms – but Plato does not use the mirror analogy himself. 10 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM Donald Zeyl is one of the most recent supporters of the substratum interpretation. According to his reading, Plato's particulars are substratum/property compounds: Since the Receptacle takes on a rapid succession of imprints (cf. the "gold example" at 50a4-b5), a particular will change rapidly over time without, however, necessarily ceasing to be that same particular. Its identity over time is preserved by virtue of the fact that it remains the same part of the Receptacle, its neutral, self-subsistent substratum.23 The parts of the Receptacle thus play the role of substrata, while Form imprints play the role of properties.24 The Receptacle-parts provide a basis for identity over time, so that a particular is the same particular so long as it has the same part of the Receptacle as its substratum. We can even account for flux without endangering identity over time, since a particular's properties can change as that part of the Receptacle takes on new Form imprints. That same particular can change location, too, and still be the same particular, since it retains its substratum. We have, in sum, a very Aristotelian sounding analysis of particulars into a subject that serves as the ultimate subject of predication and properties that inhere in and depend on the subject. These properties will be, of course, non-essential to the identity of the particular, since its identity over time depends on its being the same part of the Receptacle, rather than being the same rhinoceros or the same rhododendron. While an Aristotelian reading the Timaeus might appeal to some, it is impossible to reconcile with the stated role of the Receptacle in the text, namely that the Receptacle is space (52a8-b5). Zeyl contends that it can fulfil both roles, but there are immediate obstacles for this reading. First, since particulars can increase in size or decrease in size, and particulars are parts of the Receptacle, i. e., parts of space, 23 Zeyl 2000, lxi, Zeyl's italics. An immediate objection might be that Zeyl's conception of particulars is more substantial than Plato would want; these particulars seem to have independent existence once they have their properties, rather than being continually dependent upon the Forms for their existence. This objection could also take the form of a question for Zeyl: how is such a substance an image of a Form? 24 Cf. Algra 1995, 91: the Receptacle may "conveniently be described as the substratum for the eventual phenomenal bodies (i. e., 'instances' of the Ideas) and, as such, as an ex hou." Algra admits that the roles of matter and space are inconsistent and so may not object to philosophical arguments against the Receptacle as substratum. Algra's defense of the Receptacle as a constitutive factor of bodies relies, however, on the passages treated above, which, I have shown, support taking the Receptacle to be space. Algra admits, 99–102, that an interpretation such as mine is possible but feels that "one might expect this unfamiliar position to be explained in a more unambiguous manner" (101). Indeed, if only Plato had explained all his positions in a more unambiguous manner! Making Room for Particulars 11 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM space must increase and decrease in size. But it seems ridiculous to claim that space can get bigger or smaller; when something gets bigger, it takes up more space, but space does not expand to "make room" for it.25 A similar argument may be run for particulars changing shape, since parts of space must also have some shape: when a thing changes shape, it occupies a differently-shaped region of space, rather than the space it occupies changing shape to accommodate it. These objections may not be fatal, since one may hold that size and shape are provided for by Forms of Size and Shape; substrata would not, then, have sizes. But this is a somewhat awkward reply, since the substratum in this case is also space, which is, presumably, measurable and, thus, of some determinable size and shape. Second, and more seriously, material particulars can change place with other material particulars; but material particulars are parts of the Receptacle, i. e. parts of space, which also serves as place. The Receptacle would not be, it seems, on Zeyl's view, a stable, unified thing with regions or parts, but a collection of discrete parts that can change order, direction, and place. But then places can change place, which is absurd. We would have to have a second, distinct notion of place to make sense of this claim, so that places can be in places; this has the ring of a regress to it, and there is no hint of two notions of place in the text.26 One might object that the Receptacle does move; thus, even if it is absurd to say that places change place, Timaeus says it! But Timaeus makes clear that the shaking and moving of the Receptacle is the moving of the whole of the Receptacle, and it is the things in the Receptacle that change place, i. e., change location in the Receptacle, moving from one part of the Receptacle to another. Recalling that earth, air, fire, and water are separated into different areas of the Receptacle like grain in a winnowing basket (52e6), we know that the parts of a winnowing basket do not change places with other parts, even though the pieces of grain in the basket do change places. Thus it is absurd to say that place changes place. Zeyl does not think that this objection is insurmountable. He tells us to imagine the Receptacle as a container filled with liquid.27 There could be currents in the liquid, so that parts of it are moving through other parts and changing place with other parts. The Receptacle is like this liquid-filled 25 Plato and Timaeus have, of course, no inkling of the modern notion of an expanding universe, where it may indeed make sense to speak of space "getting bigger." 26 For example, my place on the couch can change place if I move the couch, but there are two distinct notions of place in use, one of places on the couch and one of places in the room. 27 Zeyl 2010, lxii. 12 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM container, both a material substratum and a space. While this is an ingenious image, there is no textual evidence for Zeyl's position that parts of the Receptacle can change place with other parts of the Receptacle or for his comparison to a liquid-filled container. We do, as I said above, get the image of the Receptacle shaking and being shaken, but this only suggests, again, that the Receptacle as a whole can move. There is no reason to think that the individual parts of the Receptacle – parts of space – can change space with other parts of space. Perhaps, then, we should not take the Receptacle to be divided into regions that are substrata but, rather, as one substratum for the kosmos as a whole. Material particulars would, then, move around in the Receptacle without changing it, since regions of the Receptacle would not change place along with the moving particulars. It seems that Zeyl holds such a view in a later work, where he offers another image of the Receptacle.28 In his words, it is "simultaneously the special matrix for all becoming and the material 'filling' of that matrix."29 He uses the image of a liquid-filled container – in this case, an aquarium – for the Receptacle, but there is a substantial difference in how he portrays particulars (in this passage, the fish): If we now think of [the fish] as a three-dimensional image in water, the product of a projection into the water by realities outside the aquarium, we can understand what it means for the fish to move from one place to another. The fish is nothing other than a series of water places that successively come and cease to bear a particular configuration of colors and outlines, and it is that configuration that moves, not the water places into which that configuration is projected.30 According to this picture, particulars are combinations of Receptacle and Form projections, but the key difference is that a particular does not involve any particular part of the Receptacle. The projections glide over the surface of the Receptacle, not really having any effect upon it. They only seem to affect it. This makes Zeyl's new conception of the Receptacle and the particulars in it much closer to my own view: the key difference is that the Receptacle is material, and this material – though not any particular part of it – is tied to the existence of particulars. 28 This image is not, however, mentioned in his latest treatment of the Receptacle, in Zeyl 2013. 29 Zeyl 2010, 119. 30 Zeyl 2010, 124, Zeyl's italics. Making Room for Particulars 13 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM Zeyl offers this image to illustrate how the Receptacle can serve as a "primarily spatial, but also material hypokeimenon for the images that subsist in it."31 But it is not apparent to me how it fills the role of material substratum; as Zeyl presents the Receptacle in other treatments, its parts act as individual material substrata, thereby offering a means to track the identity of particulars over time. But now the Receptacle cannot fulfill that role, since no particular part of the Receptacle is a substratum to any given particular. The Forms are projected on different parts of it, and thus the particulars move. The substratum or matter does not seem to be playing any role in the makeup of each particular; any given substratum or matter is accidental to the particular, and it is really defined by its "colors and outlines", i. e., the Forms projected upon the Receptacle. In fact, I cannot see what role the material substratum is playing at all. Since, then, we do not have strong textual evidence that the Receptacle is a material substratum – the strongest evidence is in the analogies, which we have already discussed – why should we burden Plato with a Receptacle that unnecessarily fills two roles – space and substratum – rather than one that is just spatial? Since the material substratum does not seem to serve any purpose, I propose that we discard it: we are left with a Receptacle that is space. In fact, let us look at Zeyl's own explanation of his image of the aquarium and fish: The account of Platonic space that I am trying to develop is that of a neutral threedimensional material medium or field within which spatio-temporal particulars, as images of Forms, come into and pass out of being. These images are the products of the Forms' "projecting" their various natures into the field. Space as the material medium "receives" these projections.32 If we delete the two instances of "material" from this paragraph, I concur. Zeyl even uses the language of the Receptacle as a medium, a term which is favored by those who take the Receptacle to be only space, an interpretation Zeyl has roundly criticized.33 Since, then, neither matter nor substratum, as put forward by Zeyl, serve a purpose in this picture of the Receptacle, we should discard them. Another interpretation of the Receptacle that seems to render it a material substratum is Verity Harte's view, which describes it as that out of which particulars are constructed; she holds that sensible particulars are constituted by configured regions of the Receptacle, where the Receptacle is understood as the matter of the configurations, though it is not bodily matter or stuff.34 First of all, this 31 Zeyl 2010, 124, Zeyl's italics. 32 Zeyl 2010, 124. 33 Zeyl 1975 passim; cf. Zeyl 2000, lvi–lxiv. 34 Harte 2010, 135 & 139, Harte 2002, 250 f. Cf. Miller 2003, 186–95. 14 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM interpretation seems to violate Timaeus' admonition, discussed in the previous section, that we should not call the Receptacle anything "out ofwhich" the elements come to be (51a6), since the elements, on Harte's reading, come to be out of space.35 Furthermore, although the Receptacle is called that "in which" Form images come to be, it is never called that "out of which" anything comes to be.36 If all Harte means, however, is that sensible particulars are spatial, it may not matter much whether we say they are in space or of space.37 But if Harte means that particulars are spatial in some other sense when she says that they are "of space", then her position would be open to the arguments above against taking the Receptacle to be a material substratum. She suggests another sense when she writes, "At least when configured in the form of the regular solids, then, space, so configured, does indeed have features, including perceptible features" (2002, 260). She goes on to say that "the specific configuration of space involved and its geometrical character are constitutive of the features in question" (260). If the claim is that the space appears a certain way because there is a property-instance (a Form image) in that space, then I have no qualms with it. But if the space itself takes on the features, thus becoming part of the particular – if a specific region of space is configured, rather than a specific configuration that can be applied to any region of space – then we run into problems. If particulars are composed of a certain space, as in Zeyl's first account, then, again, space must change space, because the space that 35 Harte 2002, 250. 36 Contra Algra 1995, 85–6. The closest Timaeus comes to calling the Receptacle an "out of which" is in the gold analogy, where figures are said to be formed out of gold (πάντα τις σχήματα πλάσας ἐκ χρυσοῦ, 50a5-6). Above, I discussed the gold analogy and why we should not be misled by the image into thinking the Receptacle is a moldable material substratum out of which material particulars come to be. Cf. Cratylus 389c5, where the "out of which" is clearly the matter; the craftsman puts the form he sees into matter. Additionally, Algra, 80, calls the Receptacle an out of which because "it is an ekmageion" (50c2). This is, however, merely to compare the Receptacle to a wax tablet, and I address this comparison above. For more on the difference between an "in which" and an "out of which," see Algra 1995, 90–91. 37 Cf. Harte 2002, 250: "The regular solids are ... configurations of space, and not configurations in space – at least not if we think of the space they are in as a separate container. They are configurations of space because the three dimensions of which they are configurations are space. The regular solids could be configurations in space, like objects in a container, if they were made of some (other?) material ..." (Harte's emphasis and parentheses). First, Timaeus does speak of the Receptacle as a container – a receptacle is something into which one puts stuff. Second, even if the Receptacle is a container, the regular solids need not be made of any material. It is a container for images, just as a mirror is a container for images, even though mirror images are not composed of the mirror or of any other material (excluding their relation to the original, i. e., light waves). Making Room for Particulars 15 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM composes a particular would move (in space) when the particular moves. Or, if particulars are composed of just any space, and their composition changes as they move, as in Zeyl's second account, then it is not apparent what the configuration claim is contributing; would a particular be composed of entirely different matter from one moment to the next, because the particular has moved to an adjacent place? We have little reason to call that particular the same thing, rather than saying that it has gone out of existence, only to be replaced with an adjacent, exactly similar particular. Such a view would certainly be in tension with Timaeus' implication that some objects persist through time, e. g., a molecule of fire evidently persists until it is broken up to be re-formed into molecules of a different sort. So, again, if Harte merely means that particulars are spatial insofar as they are in space and thus space is a "matter" of sorts for particulars, then I see no problem with the view, even though I would prefer to stick with Timaeus' language of the Receptacle as the "in which". V Receptacle and Chora In the last section, I argued against taking the Receptacle, as a single entity, to be both space and substratum. But we might think that these two functions should be assigned to two different entities, at least on a charitable interpretation of the text. Receptacle1 would function as space and place, while Receptacle2 would be divided into substrata. The substrata of Receptacle2 occupy regions of Receptacle1, but they can freely change place by moving into other regions, and they can increase or decrease in size by occupying larger or smaller regions as appropriate.38 In fact, this position is similar to one defended by Dana Miller, who argues, although for different reasons than I have just discussed, that there are two members of the third kind, the Receptacle and chora (χώρα), which he translates as "place" and I have hitherto translated as "space". Chora, he contends, is introduced in a digression which functions as an argument against materialism. Accordingly, it fulfills the function of what I call Receptacle1, while the Receptacle fulfills the function of what I call Receptacle2. 39 This position avoids 38 In this section and the next (in contrast to the rest of the paper), I take Receptacle1 (chora) to be absolute space and independent of the Forms, since it must be part of the same ontological kind as Receptacle2 (substratum); both, then, exist independently. 39 Miller 2003 does not frame his view as I frame the two-entity view here, and his Receptacle and chora do not precisely fit the roles of Receptacle1 and Receptacle2 as I have set them out. He is, however, the only recent advocate of a two-entity view, as far as I can tell, so I consider his arguments for such a view. 16 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM some of the difficulties I have demonstrated for the substratum interpretation, for it keeps space and substrata separate. In this section, I will examine and argue against such a view, employing primarily textual arguments. In the next section, I will continue to argue against this view, although I will introduce and borrow from a similar debate in contemporary metaphysics in order to give philosophical arguments why we should, for reasons of charity, avoid attributing the two-entity view to Timaeus. First, however, let us consider Miller's main argument against the space interpretation, namely, that it cannot account for a passage in which the Receptacle is said to "shake".40 But a substratum or matter interpretation has no better grounds for explanation: what is it for unformed matter (rather than material things) or a bare substratum (rather than something with a substratum) to shake? It seems just as likely that space could shake, especially if it is conceived as a kind of container in which all things come to be; it shakes like any other container. Miller's own explanation of the shaking evokes the movement of bodies in the Receptacle; since bodies are parts of the Receptacle, the parts move when bodies move, and this can be called shaking.41 There is, however, no support for this reading in the text, as I mentioned above in response to Zeyl's view that parts of the Receptacle move. The Receptacle as a whole shakes like a winnowing basket: the grain in the basket moves, but parts of the basket do not, relative to one another. Just as the basket as a whole shakes, and, as a result, the grain in the basket moves this way and that, so the Receptacle as a whole shakes, and, as a result, the bodies in the Receptacle 40 Miller 2003, 140 & 154–5. Miller also argues (1) that Plato's "third kind" should have more than one member, i. e., not merely the Receptacle, since it is an ontological "kind" or class. In addition, he argues (2) that the space interpretation conflicts with Plato's conception of relative location and (3) that it is anachronistic. First, we need not maintain that an ontological kind has more than one member. Even in ancient times, the third kind was thought to consist of one entity, so a kind (γένη) need not have multiple members – an entity can truly be sui generis. Even though there is only one entity in the third kind, namely, the Receptacle, it is still a different kind of thing from Being and Becoming. Second, Miller suggests that the space interpretation is untenable because "Plato explicitly denies that the place of the elemental bodies in the world is established on an absolute locational grid" (Miller 2003, 151). But this is not quite true; Timaeus denies that "up" and "down" can be determined absolutely (63e5-7), but that is completely compatible with location being determined absolutely. "Up" and "down" are simply determined relative to one's orientation in absolute space. Finally, the notion of "space" that we require is not anachronistic (cf. Miller 2003, 141); we need only the notion of the "space" in a room. Such a space can receive things (or images) into it, and those things are thereby located in it, and this is all we require of the Receptacle. 41 Miller 2003, 152–3. Making Room for Particulars 17 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM move this way and that. The Receptacle's parts must be stationary relative to one another, just like parts of a basket. It seems that it would be better for a two-entity view to locate the shaking in chora, so that it, as a whole, shakes, while the bodies in it, which are parts of the Receptacle, are free to move this way and that. Unfortunately, this move is prohibited by the text, which explicitly locates the shaking in the Receptacle, not in chora. This fact seems to be evidence against separating the Receptacle from chora, since Plato could have located the shaking in a different entity if he actually endorsed a two-entity view. Let us now turn to textual arguments against the two-entity interpretation. First, when Timaeus describes chora, he uses language that is very similar to what he uses to describe the Receptacle. Both receive whatever comes to be and both are an "in which"; both are, in addition, difficult to grasp and imperceptible. The text gives no indication that we are introducing a new, extremely similar entity, even if we grant that the section of text that introduces chora is a self-contained argument against materialists.42 Furthermore, immediately after discussing chora, Timaeus resumes discussion of the Receptacle with no obvious change of topic (52d4). The best explanation for why Timaeus makes it so difficult to distinguish the Receptacle and chora is, I submit, that he did not himself distinguish them; they are the same thing. Second, Timaeus gives a summary of the three kinds at 52d4, listing them as Being, chora, and Becoming. But it seems he should use some neutral term for the third kind as a whole, i. e., one that includes the Receptacle, in this list. The fact that he lists "chora" strongly suggests that it exhausts the third kind and is, thus, identical to the Receptacle. Third and finally, Receptacle2 is an "out of which", and Miller claims that the Receptacle is the "out of which" for the triangles' physicality.43 As I have pointed out above, the Receptacle is never called the "out of which", and there is no need to take it as such. Putting this aside for the moment, though, Miller claims that the Receptacle is both an "in which" and an "out of which", but in different ways.44 As an "in which", it is separate from the triangles, but as an "out of which", it is not; it is separate from the forms it receives but not separate from the physicality of the triangles. It would seem, however, that a two-entity view should take chora as providing the "in which" and the Receptacle as providing the "out of which". This functional division would seem the main reason for having distinguished the 42 See Miller 2003, 116–145. 43 Miller 2003, 189. 44 Miller 2003, 193–4. 18 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM two in the first place. But, as it is, the Receptacle performs both functions, while chora performs only the "in which" function. Miller does, of course, distinguish the two "in which" functions: the Receptacle is the "in which" for forms, while chora is the "in which" for bodies.45 So Timaeus must distinguish two kinds of "being in" and two kinds of "receiving," one each for the Receptacle and chora, although he does notmake either of these distinctions explicitly. Again, the simpler explanation, and the one that avoids attributing confusion or inadequate explanation to Timaeus, is that the Receptacle and chora are identical. VI The Receptacle and Supersubstantivalism46 I want, in this section, and somewhat parenthetically, to indicate how the debate about the status of Plato's Receptacle – space versus substratum – can usefully be linked with a recent debate in contemporary metaphysics on the status of spacetime. I will be referring to and borrowing from the debate addressed to the question whether material particulars are substances in addition to spacetime or, on the contrary, spacetime is the only substance. Contemporary supersubstantivalists, particularly Jonathan Schaffer, have offered arguments against a dualism of spacetime and material particulars, and many of these arguments can be modified to work against a dualism of Receptacle and chora. Allow me first to discuss the relation between supersubstantivalism and the space interpretation. Afterward, I will examine some arguments for supersubstantivalism and against dualism. According to one version of the space interpretation, Timaeus has some sympathy with supersubstantivalism, the position in contemporary metaphysics that spacetime is a substance and that material particulars are not separate substances. This can be spelled out in different ways, with particulars being 45 In distinguishing between the reception of bodies and the reception of forms, it seems that Miller requires a "fourth thing," in addition to bodies (Becoming), Being, and the third kind. Since the Receptacle receives forms but cannot receive Forms themselves, since they do not enter into anything, it would have to receive immanent forms, conceived as a fourth category of thing, if anything. But Miller criticizes some versions of the space interpretation for precisely this reason, namely, for introducing a fourth thing into the Timaeus' ontology. The space interpretation does not, in fact, need a fourth thing, since space provides a place for bodies, leaving us with Being (Forms), Becoming (bodies), and Space (the Receptacle). 46 This section may be safely skipped by anyone who is not interested in the contemporary debate on the metaphysical status of spacetime and its relevance to the Timaeus. Making Room for Particulars 19 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM identical with regions of spacetime, composed of regions of spacetime,47 or eliminated completely in favor of regions of spacetime. As may be obvious already, the Receptacle differs from spacetime in an important regard: it is only space, not time. Space and time appear to be distinct in the Timaeus, since time is said to be a moving image of eternity (37d5-7). On the version of the space interpretation that is quite similar to supersubstantivalism, the Receptacle is absolute space and a substance in a way that material particulars are not; it exists independently, with its own unchanging nature, while they are dependent on Forms. The difference between the Receptacle and spacetime introduces some complications for taking Timaeus to be a supersubstantivalist. For example, if Timaeus employed a notion of spacetime, it would be much more likely that his particulars would be property-substratum compounds, for spacetime points could underlie properties as bare particulars.48 There would be no problem for movement and change of size, because a certain spacetime region would be a particular's substratum. Thus the substratum would be "stretched" over the spatiotemporal region that the particular occupies over its entire lifetime. Since the Receptacle is not spacetime, however, a particular would have to have a different substratum from one moment to the next when it moved or changed in size, since its substratum would not change or move with it; this is one of the reasons that we rejected the substratum reading above. Now, then, let us turn to general arguments against endorsing both a Receptacle and a chora (space), one to provide substrata to material particulars and the other to provide places for those particulars to come to be. The first two arguments Schaffer offers against such a dualism, the arguments from parsimony and from harmony, complement each other.49 Not only are we positing two entities that perform the same function, since regions and substrata each bear properties, but we are also duplicating sets of properties that always happen to coincide, namely, geometrical and mereological properties. Such properties are mirrored in regions and particulars: my hand exactly occupies a hand-shaped region, and it is part of my body just as the hand-shaped 47 Perhaps Harte, based on the interpretation discussed above, would endorse something like this composition view. 48 Cf. Sider 2006. 49 Schaffer 2009. The only argument for dualism that Schaffer considers and that is relevant to the Timaeus is the argument from plenitude. One might think that space and substrata must be distinct because there can be empty space. This might be a non-starter in the Timaeus, however, because Timaeus denies the possibility of void (58a7), so that the Receptacle is always filled. For a reading of the text that allows for a kind of void (empty space), cf. Gregory 2000. 20 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM region is part of a body-shaped region. Why can my hand not occupy a differently-shaped region of space, if both it and space are substances, i. e., independent entities, with distinct mereological and geometrical properties? The supersubstantivalist can discard one type of entity – substrata – and one type of such properties – those of material particulars, since space bears those properties and all others. My hand is simply a hand-shaped region with all the properties appropriate to a hand – no substratum or duplicate properties are needed. The dualist, in contrast, must tolerate duplicate entities and duplicate properties whose coincidence is brute fact. Similar arguments can be marshaled against a two-entity view in the Timaeus. First, the two entities perform overlapping roles, especially on the view sketched above, where both chora and the Receptacle act as an "in which." But there is a reply to such an argument: chora supplies the place in which particulars move, and parts of the Receptacle (acting as substrata to those particulars) move within chora. Thus there is a reason to posit two entities instead of one. Such a reason stands, however, only if there is independent reason to endorse substrata and space. Since the space interpretation suffices, there is no reason to endorse substrata. Although the two-entity view has a response, albeit one that is ultimately unsatisfying, to the first objection, it does not have a similar response to the argument from harmony, i. e., that geometrical and mereological properties inexplicably coincide. In the Timaeus, material particulars are composed of geometrical solids – the elements – which have elemental triangles as parts. The triangles must occupy triangular regions of chora. Thus, we have a doubling of properties between chora and the substrata of particulars, i. e., parts of the Receptacle, and we have an inexplicable coincidence of those duplicate properties: both substrata and spaces are triangular.50 The dualist cannot reply that space, but not a substratum, has the geometrical properties – or, similarly, that substrata inherit geometrical properties from space – since material particulars are, in the Timaeus, literally composed of geometrical properties. While the dualist has a weak reply to the doubling of entities, then, given a previous commitment to substrata, there is no such explanation for the doubling and coinciding of properties. Let us examine three more complementary arguments Schaffer offers against a dualistic view, the arguments from materialization, exhaustion, and monopolization. They proceed from the facts that a material particular must 50 See Silverman 2002, 282, who acknowledges a similarly inexplicable coincidence of geometrical and "traditional" Forms on his account. Silverman offers a bundle theory of particulars on Timaeus' behalf, rather than a substratum theory, but he thinks that the Receptacle is more than just space; it contributes a material aspect to particulars, as well. Making Room for Particulars 21 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM occupy at least one region, must occupy at most one region, and must exclude other material objects from its region. If material particulars and space are distinct substances, however, these facts are inexplicable. Why must one substance occupy another? One would think that substances can exist independently, so that material objects could exist without being in a space. And if material objects have to occupy spaces, why can each occupy only one? One would think it possible that a material object could bear the located at relation to several different spaces. Finally, why can material objects not coincide? One would think that, if two substances, a material object and space, can coincide, surely many more substances could coincide, too. These arguments equally apply to a two-entity interpretation of the Timaeus whereby parts of the Receptacle occupy regions of chora. First, the dialogue's namesake observes, in discussing chora, that we think everything must occupy some space and be in some place. But, if parts of the Receptacle exist independently, there seems no need for them to bear a relation to another distinct entity, a second member of our third kind. Those parts should be able to exist independently of chora. As it is, though, the parts of the Receptacle, themselves clinging precariously to chora, seem to be no more independent than Form images, which cling to the Receptacle for their precarious existence. Second, given the (apparently brute) fact that parts of the Receptacle must bear some relation to regions of chora, why must they bear that relation to only one region? Forms can bear relations to many parts of the Receptacle, it seems: the Form of Fire casts an image onto many distinct portions of the Receptacle. Why cannot portions of the Receptacle bear the located at relation to many regions of chora? In fact, it seems that locating the same fire in many different regions would save Plato from any need for Forms at all, and the two-entity view could allow him a two category ontology: the Receptacle and immanent universals. But this is obviously precluded by the rest of the Timaeus, which contains an explicit argument for the existence of transcendent Forms (51d3-52a4). Finally, Timaeus assumes that elemental bodies force one another out of spaces, making it obvious that only one body can occupy one region at one time. But why does he assume this fact, if he thinks that parts of the Receptacle and the regions of chora are independent of one another? Again, we already have two coinciding independent entities, so there seems no harm in allowing multiple portions of the Receptacle to bear the located at relation to a single region of chora. Yet Timaeus assumes, without explanation, that this coincidence of entities is impossible. From a general philosophical perspective, then, the two-entity view attributes confusion and a serious lack of explanation to Timaeus. The space 22 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM interpretation, however, explains the lack of explanation: one region is exactly one region, so none of the above problems arise. We need no entity to be located at another entity, i. e., for one entity to "enter into" another, which is desirable anyway, since Timaeus explicitly (52c6-d1) denies that such a thing is possible! VII The Receptacle as Space: The Mirror of Becoming Now that we have dismissed the two main interpretations according to which the Receptacle is a substratum to particulars, let us turn briefly to the space interpretation. Here I give no more than a rough characterization of it, as there are several versions of the space interpretation.51 The natural capacity of the Receptacle, we recall, is to receive all things – all images of Forms, in Timaeus' terms – into itself without interjecting anything of itself into what it receives. Let us recall the passage about fire and water being "suches," while only the Receptacle is a "this." Timaeus generalizes his claim about the elements to anything to which we point and try to call "this" or "that" (49d7-e4), and anything that is "some 'such' or other," such as hot or white (50a2-4). Anything to which we can point and call "that" isn't really a "that," i. e., something that stably retains the same properties, never altering into something else. Everything we encounter through sensation is mutable. The only thing that can be designated, the only "this" or "that," is something stable and unchanging – the Receptacle (49e7-50a2). In each case, the Receptacle is the "this or that," while everything else is a characteristic or property. As I said above, I submit that the "this or that" we can designate is the location itself, the space occupied by the thing and the place that underlies it. This particular space does not change, no matter what occupies it, whether a substance, a trope (property-instance), or a bundle of tropes. Its nature always remains the same, as well, since it always has the capacity to receive anything into itself. This, then, is the function of the Receptacle: to provide a place for coming to be. Since the things appearing in it are imitations of real things (τῶν ὄντων ἀεὶ μιμήματα, 50c5), we might think of the Receptacle as a kind of mirror.52 Like reflections in a mirror, Form images are completely dependent on the things that 51 For analytical discussion of prominent interpretations of the Receptacle, see chapter 1 of Miller 2003. 52 Cf., for example, Mohr 2005, 90–2, Lee 1966 passim, and Gill 1987, 48–50. Making Room for Particulars 23 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM cast the reflections (cf. 52c2-5).53 Images of Forms are "reflected" in a sort of Mirror of Becoming; the mirror analogy also emphasizes the fact that the images are radically dependent on Forms, just as mirror images are wholly dependent on whatever casts reflections in the mirror. Opponents of this interpretation often point out, however, that Plato nowhere makes this comparison himself. What would be more natural than for him to compare it to a mirror, they point out, if that is what he was thinking? After all, he discusses mirrors as they relate to vision just a few pages before introducing the Receptacle, so mirrors should be a convenient analogy.54 It may be that Plato avoids this obvious analogy merely because ancient mirrors – burnished metal surfaces – were unable to reflect images without significant distortion. The Receptacle is supposed to contribute nothing of itself to the images it contains, but an ancient mirror imposed something of itself upon the image. Reflections in metal or water – although used by Plato in other places to represent material particulars – do not give us clear representations of the things reflected therein. Interestingly enough, although Plato avoids the mirror analogy for the Receptacle, he employs it for the liver, which he describes in very similar language. In fact, the liver receives images like "a mirror receives impressions and presents images for seeing" (ἐν κατόπτρῳ δεχομένῳ τύπους καὶ κατιδεῖν εἴδωλα παρέχοντι, 71b4-5), just as, in the wax block analogy, the Receptacle receives impressions for seeing. A disanalogy between the liver and the Receptacle is that images appear on the surface of the former, while images in the latter will be three-dimensional. Since the same disanalogy holds between the Receptacle and a mirror, this may be a further reason Plato avoids explicitly comparing the Receptacle to a mirror. One further worry about the mirror analogy, which is used in service of the space interpretation, is that it does not seem to represent space very well – mirrors are things that have reflective properties, representing reflected items in certain ways, while space seems to be entirely different. Space does not, after all, provide a place for images, but for things. Since Timaeus calls the Receptacle space (χώρα), 53 Cf. White 1981, 315–6. Cornford 1937, 177, comments that "the [Form] copy is not selfsubsistent; it needs the support of a medium, just as a reflection requires a mirror to hold it." Lee 1966, especially 353–57, explores the distinction between substantial and insubstantial images; Form images are insubstantial images, dependent upon the Receptacle but not made of it, more like a mirror image than a statue. 54 Mohr 2005, 91, suggests that Plato avoids this explicit comparison because it would imply the presence of a perceiver, in accordance with his earlier analysis of mirror images (46a-c), and because a mirror distorts its image by flipping it, while the Receptacle is supposed to impose nothing upon the image. Cf. Lee 1967, 357, n. 32. 24 Christopher Buckels Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM place (τόπος), and a seat or spot (ἕδρα) for images of Forms to come to be (52a6-b5), wemust determine if themirror analogy reflects Timaeus' use of these terms. But we may be imposing our own notion of space too much upon Plato's use of chora (space).55 The Receptacle would have to be a space that receives images – images of Forms. We normally think of things in space, not images in space, so Plato's space differs from our intuitive notion of space. But his notion is like ours insofar as these images must take up space, i. e., they are located in certain parts (regions) of the Receptacle, just as images are located in certain parts of a mirror. Thus we may cautiously employ the mirror analogy ourselves, even though Plato avoids it, as long as we keep in mind its limitations.56 VIII Conclusion On the basis of philological evidence and philosophical argument, then, we should not attribute to Timaeus the position that the Receptacle and chora are distinct, and on the same basis we should not assign both roles, of space and substrata, to a single Receptacle and its parts. The analogies do not necessitate a reading whereby parts of the Receptacle act as substrata to material particulars, nor does the "much misread passage" necessitate such a reading. Moreover, the substratum interpretation entails several absurdities, such that the parts of the Receptacle (which are also places) must change place with one another and must be able to change size and shape. Likewise, the text does not necessitate the reading whereby the Receptacle and chora are distinct, and, in fact, it tells against such a distinction, and the two-entity view piles extra ontological commitments on Timaeus without a corresponding increase in explanatory power. We are left, then, with the function that Timaeus explicitly assigns to the Receptacle: it is the space in which Form images come to be, a place or seat for such images. Since there is no indication that Timaeus thought it necessary for material particulars to have substrata, we should not import such things into the dialogue. There is already plenty of room for particulars in the Receptacle.57 55 For more on the Receptacle as space, cf. Algra 1995 passim and Johansen 2004, 129. 56 See Lee 1967, 366–7, for more on the limitations of the mirror analogy. 57 I would like to thank Vasilis Politis, Peter Larsen, Jan Szaif, Thomas Chance, and Cody Gilmore for comments on previous drafts and discussion of the topics herein. I am also grateful for comments from an audience at the Understanding Matter conference at the University of Palermo in April 2014. Making Room for Particulars 25 Brought to you by | University of the Pacific Authenticated | cbuckels@pacific.edu author's copy Download Date | 4/7/16 10:24 PM References Algra, K. 1995. Concepts of Space in Greek Thought. Leiden: Brill. Broadie, S. 2012. Nature and Divinity in Plato's Timaeus. Cambridge: Cambridge University Press. Cherniss, H. 1957. "The Relation of the Timaeus to Plato's Later Dialogues." The American Journal of Philology 78 (3):225–66. 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