Timaeus' Receptacle: A Search for Coherence

Prabhu Venkataraman Abstract: The Receptacle of Plato’s Timaeus has long been considered one of the most mysterious

objects that appear in Plato’s corpus. Numerous papers have attempted to tackle the question of

what the Receptacle is, its structure and function, and the difficulties with Timaeus’ account of it.

Verity Harte has published an essay in which she attempts to explicate the structure of the primary

bodies in the Receptacle. Kenneth Sayre has published an essay in which he raises four, highly

problematic issues with Timeaus’ account. In this paper I argue, using Harte’s theory as a

foundation, how one can better understand and deal with the difficulties concerning the structure of

the Receptacle that Sayre raises.

I. Introduction

In his essay titled “The Multilayered Incoherence of Timaeus' Receptacle” 1, Kenneth Sayre lists four

anomalies in Timaeus' description of the Receptacle, which, in his view, renders Timaeus' account of

the Receptacle “incoherent from start to finish”. The four anomalies2 that Sayre explores in his

paper are:

1. Conflicting Descriptions of the Receptacle,

2. The Status of the Traces before the Universe Was Made,

3. Unaccountable Relations between Shape and Quality, and

4. Regrouping Triangles and Changing Qualities.

1 Kenneth Sayre, “The Multilayered Incoherence of Timaeus' Receptacle” in Gretchen Reydams-Schils, eds.,

Plato's Timaeus as Cultural Icon (South Bend: University of Notre Dame Press, 2003)

2 The titles for the listed anomalies are taken from Sayre's paper.

In this paper I examine Sayre's account and respond to his criticisms using a picture of the

Receptacle put forth by Verity Harte3. In particular, in the following sections I will provide a brief

description of Sayre’s arguments for each of these anomalies, followed by a way of possibly dealing

with them.

II. Conflicting Descriptions of the Receptacle

Sayre's Critique Sayre raises the question as to why Timaeus does not employ the analogy of a mirror to describe the

Receptacle. Since the Receptacle shows the images of the forms, it is curious that, among the

numerous analogies and metaphors employed by Timaeus in describing the Receptacle, that the

analogy of a mirror is not present. Sayre suggests that this could be because “the Receptacle also

plays the role of space, and that being reflected in a mirror is a spatial relation. It makes little sense

to think of space itself as participating in spatial relations.”

Sayre then explains that the same problem arises when Timaeus describes (52e-53a) how the traces

of the elementary particles shake the Receptacle, and cause the Receptacle to shake in turn. Timaeus

compares the shaking of the Receptacle and the corresponding dispersion of the traces to “particles

shaken and winnowed out by sieves and other instruments used for purifying grain”. But, as Sayre

notes, “shaking is a form of motion that takes place in space,” hence “the thought of Space itself as

shaking is literally unintelligible.”

3 See Verity Harte, “The Receptacle and the Primary Bodies” in R. Mohr and B. Sattler, eds., One World, The Whole

Universe: Plato's Timaeus Today (Las Vegas: Parmenides Publishing, 2010); see also Verity Harte, Plato on Parts and Wholes:

The Metaphysics of Structure (Oxford: Oxford University Press, 2002), Section 4.4.

A Response

Recall from passage 33a of the Timaeus that the demiurge does not want to leave anything outside of

the cosmos so as to prevent its decay by elements that are outside of it that might wear it down. The

Receptacle is the nurturer of all things and so contains the cosmic animal. If the cosmic animal were

a proper subset of the receptacle, then the Demiurge would not be able to accomplish the task of

leaving nothing outside of the cosmos4. So we may deduce that the limits of space are spherical, and of the

same radius as the cosmos that the demiurge constructs.

This claim that the Receptacle is a spherical medium5 needs to be reconciled with Timaeus'

statements that the Receptacle “both always receives all things, and nowhere in no way has it ever

taken on any shape similar to the ones that come into it” (50c), and that “if the imprints are going to

be sufficiently various with every variety to be seen, then that in which the imprints are fixed

wouldn't be prepared well unless it's shapeless with respect to all those looks that it might be going

to receive from elsewhere” (50d). But these statements imply that the Receptacle is only shapeless

“with respect to all those looks that it might be going to receive from elsewhere” i.e. as long as it is

invisible and so can receive, nurse, and show images without distorting them in any way, it is

shapeless with respect to the images received. The fact that the limits of space (according to our

interpretation) are spherical does not, given that the Receptacle is not detectable to the senses

4 Even if the Demiurge used up all the traces from the Receptacle in his construction of the cosmos, the receptacle,

while not capable of being perceived by any sense organs, is not nothing.

5 Our use of the word “medium” should not be taken to mean that the Receptacle is just “space.” As Scott Hemmenway

points out, and John Sallis argues extensively in John Sallis, Chorology (Bloomington: Indiana University Press, 1999), the

Receptacle is more than space; it is what allows images of the forms to partake in being.

(especially of sight), contradict the property of shapelessness of space with respect to the “looks”

that it will “receive from elsewhere”.

Once we accept this, we can make sense of how the Receptacle might shake (prior to the building of

the cosmos by the Demiurge) even if it is all of space. A sphere centered at a point can rotate every

which way without the center moving; indeed the cosmos comes to have a rotation of this sort

caused by the circuits of the “Same” and “Other”. So one would have to conclude, given the

unintelligibility of space itself shaking, that what Timaeus means here is that the Receptacle is

induced by the traces to rotate in arbitrary directions, similar to all the ways in which a sphere can

rotate with the constraint that its center be fixed. Timaeus' comparison of the dispersion of traces to

“particles shaken and winnowed out by sieves and other instruments used for purifying grain” is

more a reference to the kind of sorting that occurs from the use of a sieve or winnowing basket,

rather than the shape of the sieve or basket itself. 6

III. The Status of the Traces before the Universe Was Made

Sayre's Critique

In the precosmic state of the universe, prior to the actions of the Demiurge, the receptacle contained

the traces of fire, air, water, and earth. Sayre raises two questions under this anomaly:

1. How did the traces come to be in the Receptacle initially?

2. How can we explain their ability to shake the Receptacle, and of the Receptacle to shake them?

6 Scott Hemmenway points out to me that one can go further and say that shaking itself is a kind of spatial metaphor for

a non-ordered mixing and sorting of the trace elements.

In 52d-e, Timaeus says: “[The] wet-nurse of becoming, being liquefied and ignited and receiving

shapes of earth and air, and suffering all the other affections that follow along with these, appears in

all sorts of ways to our sight.” Sayre argues that these appearances are sensible qualities; by this he

means that the traces are “qualitative in character” as opposed to “having configurational (hence

quantitative) features before being endowed by the Demiurge with ‘forms and numbers’ (53B5)”. He

presents the views of two interpreters--Taylor7 and M. L. Gill8--who take the view that the traces are

quantitative in character, before explaining why their views are problematic. Taylor thinks of the

traces as having the rough shape of the precise geometrical figures that the Demiurge will

subsequently assign to them. Gill has a related view; she suggests (according to Sayre) that “there are

principles more ultimate than Timaeus' triangles, which, though constantly in motion, are simple and

unalterable in character” and “the Receptacle contains many such simples combining and separating

by chance, now and then forming ‘random compounds’ that produce likenesses of the four kinds

which are the traces”. Sayre finds these approaches (and others like them) problematic because they

both, rather than thinking of traces as that which follows in the wake of something, view traces as

“pre-configurations--that is, as anticipations--of the shapes” that are assigned by the Demiurge to

them, and the text of the Timaeus does not suggest the presence of “configurational properties”

prior to the appearance of the Demiurge. For these reasons, Sayre argues, it is more natural to think

of the traces and their affections, as quoted above in 52d-e, as referring to sensible qualities.

To further bolster his view that the traces and their affections should be thought of as referring to

sensible qualities, Sayre reminds us of Timaeus' words in 48b, when he discusses the necessity for a

second beginning: “In this way, then, we must retreat, ... [and] we must begin again from the

7 A. E. Taylor, A Commentary on Plato’s “Timaeus” (Oxford: Clarendon, 1928), p. 357

8 M. L. Gill, “Matter and Flux in Plato’s Timaeus,” Phronesis 32 (1987), p. 50-53

beginning. We must get a view of the nature itself of fire and water, and air and earth, before the

birth of heaven, and of their affections before this.” In this sentence, we may assume that Timaeus

is referring to the traces of the four elements in their precosmic state, before the Demiurge gives

them “forms and numbers” (53b). Sayre points out that prior to assigning to the traces “forms and

numbers”, the traces were “without ratio and measure” (53a), and it therefore falls to the Demiurge

to give these traces their quantitative properties in order to “array” them (53b). Thus, concludes

Sayre, the traces “are appearances (albeit faint) of the qualitative features traditionally associated with

the elements”.

Sayre now takes up question 1 above: How did these traces come to be present in the Receptacle in

the latter's precosmic state? The traces are presumably images of the forms of the elements, and

they are present in the Receptacle prior to any action by the Demiurge; yet, throughout the text of

the Timaeus, when images of entities in the world of Being are produced in the Receptacle, the

Demiurge is the cause. So how do these images (i.e. the traces) come to be in the Receptacle? Sayre

considers two answers to this question. First, perhaps the traces are present due to ``Necessity'' i.e.

the errant cause. But according to Timaeus, the nature of the errant cause is to “sweep things

around” (48a-b). Sayre notes (convincingly) that “[T]o move things here and there, however, is

quite different from producing images of the Forms; and it seems unlikely that a disorderly cause

should have anything to do with the Forms at all, inasmuch as Forms are the ultimate source of

order”. Second, Sayre considers the possibility that the traces are part of the “primitive nature” of

the Receptacle. Indeed, Sayre notes that for the Receptacle to “have something to ‘nurse,’ after all,

there must be something already undergoing generation within it.” In 52d, Timaeus says that “Being

and Space and Becoming, three in a threefold way, are before the birth of heaven” and Sayre notes

that, by this second answer, the traces (as part of the Receptacle) are part of this “threefold”. But

Sayre finds this answer problematic as well. For recall Timaeus' remarks in 48c: “[I]t would not at all

be suitable for [fire, air, water, and earth] to be likened with any degree of likelihood even to the

forms of ‘syllable,’ at least not by a man who was even the slightest bit prudent.” So Timaeus does

not think it “prudent” to treat the elements as “primitive” (Sayre's term). Sayre also references

Timaeus' statement in 49b about how, in order to speak distinctly about the Receptacle, it's first

necessary to raise perplexities about fire and its fellows, and according to Sayre, “what an account

takes as primitive should not pose such problems”.

Sayre then takes up question 2 above: What are the powers that are possessed by the Receptacle and

the traces that enable them to shake each other? According to Sayre, the Receptacle is neither

capable of motion (see previous section), nor does it possess any characteristics whatsoever (he

refers to 50c-e), so the notion that it can impart motion to the traces (or anything else) makes no

sense. The traces, on the other hand, do possess characteristics, but not the sort that would allow

them to impart motion. Sayre notes that traces of fire, for example, may possess properties of

“brilliance and heat” but “not any quantitative features that would enable them to impart motion of

any sort to their containing medium”.

For these reasons, Sayre finds the precosmic presence of the traces in the Receptacle, and the ability

of the traces and the Receptacle to shake one another completely “unintelligible”.

A Response

Despite Sayre's claims to the contrary, the passages in the Timaeus do explicitly connect the

affections of the elements to their geometric (i.e. quantitative) structure. For example, in 61e,

Timaeus explains why fire is hot as follows: “[L]et's see why we call fire ‘hot,’ investigating as

follows--by having noted the dividing and cutting that arises from it in relation to our body. That

fire's affection is somehow sharp, all of us pretty much sense; but as for the fineness of its sides and

the acuteness of its angles and the smallness of its portions and the swiftness of its course, for all of

which reasons fire is intense and keen and always acutely cuts what it encounters--all this must be

reasoned out by recollecting the birth of its figure, how that nature most of all, by dividing up our

bodies and mincing them up minutely, provided, as is likely, both that affection we now call ‘heat’

and the name.”

So if the affections of the elements are a result of their geometric configurations, how do we explain

their presence in the Receptacle, parts of which are “liquefied and ignited and receiv[e] shapes of

earth and air, and suffe[r] all the other affections that follow along with these” (52d-e), in its

precosmic state? The affections must be the result of the traces of the elements, and these traces

must have, as Taylor and Gill have argued, some quasi-configuration prior to any action of the

Demiurge. Sayre finds this problematic because according to him “the text of the Timaeus does not

suggest the presence of “configurational properties” prior to the appearance of the Demiurge”. But

in fact, there are at least two passages that do suggest such pre-configurations. The first one is in 53b

and bears quoting at length:

“[W]hen the attempt was made to array the all, at first fire and water and earth and air--although

they had certain traces of themselves--were yet altogether disposed as is likely for everything to be

whenever god is absent from anything; and since this was their nature at that time, god first of all

thoroughly configured them by means of forms and numbers. On the other hand, that the god

constructed them as far as possible to be beautiful and best, from a condition that was not so before--

let this above all be granted by us as that which is always said.” (All emphasis are mine.)

The words italicized above suggest that there was some kind of pre-configuration in place, albeit not

so precise as to allow “ratio and measure”, that the god made more thorough by precise geometric

shaping9. This pre-configuration may not have been mathematically so exact as to be “beautiful and

best” to the maximum extent possible (so the pre-configured shapes may have been irregular or

asymmetrical or incommensurable); the actions of the Demiurge maximize this possibility.

Verity Harte has described the primary bodies in the Receptacle (after the actions of the Demiurge)

as configurations of space10. Her description11 bears quoting at length here:

“[Each primary body] is a configuration of space, as distinct from a configuration in space.

Configurations in space have the space they are in as a separate container. The regular solids could

be configurations in space, like objects in a container, if they were made of some material distinct

from that which contains them; one could make them out of paper, for example. However, the

regular solids that the demiurge constructs are identified with earth, air, fire, and water, and these are

the material constituents of everything bodily. So it is hard to see what (other) material these regular

9 This point is made in an essay by Alan Code, “Aristotle on Plato on Weight” in R. Mohr and B. Sattler, eds., One World,

The Whole Universe: Plato's Timaeus Today (Las Vegas: Parmenides Publishing, 2010), p. 210

10 See Verity Harte, “The Receptacle and the Primary Bodies” in R. Mohr and B. Sattler, eds., One World, The Whole

Universe: Plato's Timaeus Today (Las Vegas: Parmenides Publishing, 2010); see also Verity Harte, Plato on Parts and Wholes:

The Metaphysics of Structure (Oxford: Oxford University Press, 2002), Section 4.4.

11 See Harte, “The Receptacle and the Primary Bodies”.

solids could be made up of. Further, there is nothing in what Timaeus says that suggests that the

regular solids are made up of some sort of material, unless space itself is that material. This latter is

certainly possible but should not be misunderstood. Since the regular solids that the demiurge

constructs are configurations of space, space as such—the three dimensions considered in

abstraction from any specific configuration—may be viewed as the matter of the four

configurations. But, if we so view it, we should not be misled into thinking of space as bodily stuff.”

This brings us to the second passage that suggests pre-configurations of the elements in the

Receptacle prior to the appearance of the Demiurge. In 51b Timaeus says of the Receptacle “that

the part of it that's been ignited appears each time as fire; the part that's been liquefied, as water; and

both earth and air appear to the extent that it receives imitations of these”. Harte points out12 “that it

is a part or region of the receptacle that is made fiery and appears as fire. This identification of

specific parts or regions of the receptacle is parasitic upon that (portion) of space being somehow

configured. We must, then, suppose that, even in the absence of demiurgic activity, the receptacle is

somehow configured.”

Given these arguments for the traces of the elements having some sort of pre-configuration prior to

the actions of the Demiurge, how can we respond to Sayre's points that (a) the traces, under such an

account, appear to be something that anticipates the configuration, which goes against what the

word “traces” signify--namely, something that follows or appears in the wake of something, and (2)

that Timaeus tells us of the perplexing nature of the elements, and so the notion that the elements

are part of the primitive nature of the Receptacle is problematic, since what is primitive should not

pose such problems of complexity?

12 See Harte, “The Receptacle and the Primary Bodies”.

We can deal with point (a) by following Harte13, who explains that the pre-configured traces do

follow in the wake of something--they are the result of the existence of the forms of fire, air, water,

and earth. This is the only possible explanation, given Timaeus' statement (50c) that the Receptacle

“appears different at different times; and the figures that come into it and go out of it are always

imitations of the things that are, having been imprinted from them in some manner hard to tell of

and wondrous” (first emphasis mine). And in this sense, the pre-configuration of the traces serve as

the footprints (or traces) that the Demiurge can follow so as to properly configure and create the

elements. In other words, the traces are images of the forms of the elements, and the Demiurge

perfects or improves the extent to which they represent the forms. As for point (b), it suffices to

observe that when Timaeus remarks in 48c that “it would not at all be suitable for [fire, air, water,

and earth] to be likened with any degree of likelihood even to the forms of ‘syllable,’ at least not by a

man who was even the slightest bit prudent”, he is referring to the elements themselves, and not to

their precosmic traces. The latter, while having some kind of pre-configuration, are not geometrically

structured to the extent necessary for their orderly interaction and inter-transformations; in this

sense they are more primitive, and require the actions of the Demiurge to obtain their full structure.

The traces are part of what the Demiurge has to work with when he decides to create the cosmic

animal; their simplicity/complexity is just a necessary condition that the Demiurge has to tackle as

he sets about completing his task.

IV. Unaccountable Relations between Shape and Quality

Sayre's Critique

13 See Harte, “The Receptacle and the Primary Bodies”.

Sayre raises two problems under this section: (a) the question of which forms give fire and the other

elements their distinctive characteristics, and (b) the way in which the “qualitative traces” are

“associated with their 3-dimensional shapes”.

To expand on problem (a), we may posit that the traces of fire have certain qualities such as “hot”

or “white” (50a) that allows them to make the Receptacle appear as “ignited” (52d). It is safe to say

that the traces of fire receive these characteristics from the Form of Fire (51b). But, according to

Sayre, “sensible fire does not become fully what it is in the rational order of things until it becomes

capable of orderly interaction with the other elements; and it does not become capable of orderly

interaction until it receives its distinctive geometric shape”. Therefore “fire does not become fully

what it is until it is made to participate in the Form Tetrahedron”. As Sayre notes, it's strange that an

entity does not fully become “what it is” before participating in a form “other than that after which

it is named” 14. Thus the Form of fire does not provide the “distinctive features” that characterize its

instantiations in a “rationally ordered universe”. And clearly, this issue of whether a form provides

its instantiations with their distinctive characteristics can also be raised with respect to air, water, and

earth.

14 Sayre points out in footnote 17 of his paper that this issue cannot be resolved by “identifying the Forms after which

the elements are named with those of their geometric shapes, or by simply “retiring” the former in favor of the latter”

because there are “instantiations of the Form Fire, for instance (those in the precosmic Receptacle), that are not

tetrahedral, and instantiations of the Form Tetrahedron (classroom models, etc.) that are not fiery.” And this problem is

exacerbated by “the need to augment the trace's firelike qualities with quantitative overlays to bring that element to its

full interactive potential.”

To understand problem (b), let us again grant that the traces of the elements have certain qualitative

properties, as in fire is hot and bright, water is damp, etc. The Receptacle in its precosmic state

consists of the traces of the elements, and hence these qualitative characteristics occur throughout

the Receptacle. Now take brightness and heat--qualitative features of every trace of fire. Presumably,

in the precosmic situation, if a tiny portion of the Receptacle appears bright and hot, that portion

does not necessarily form some regular geometric solid shape like a tetrahedron. So when the

Demiurge shapes the traces of fire into tetrahedrons, how does he ensure that brightness and heat

stay confined within the boundaries of the tetrahedron? Or, as Sayre puts it, “How could it come

about that the qualitative traces appearing initially in amorphous locales become subsequently

confined within distinct spatial boundaries?”

Sayre considers two possible answers to this problem, and explains why these answers are

problematic. One answer is that, given a certain location of the Receptacle that is occupied of a trace

of fire, the Demiurge “change[s] the shape of that locale into a precise geometric figure”. But this is

not feasible since, as Sayre points out, “any portion of space before the universe is set in order is

likely to contain traces of more than one element”. And while the shaking of the Receptacle may

disperse the traces to different regions of the Receptacle, this dispersion is never complete. Thus,

despite any attempts by the Demiurge to shape a locale into a precise Platonic solid, the locale will

contain traces of more than one element, rendering the Demiurge's attempts at shaping that region

incomplete.

Another answer is that, while engaging in the shaping of a certain locale into a Platonic solid-shaped

enclosure based on the dominant trace that it contains, the Demiurge also removes from that region

the traces of any other elements. But this is problematic because “[i]n order to serve as containers in

this fashion, the boundaries of the enclosures would have to be impervious to the things they

contain.” And according to Sayre, “geometric figures by themselves (regardless of the nomenclature

‘regular solid’) do not have impervious boundaries”. He also reminds us that the material properties

that allow an object to serve as a container (i.e. by being impervious) do not appear until 60d and

hence cannot be ascribed to the figures of the elements themselves.

So we have the problem of certain forms not giving their instantiations their distinctive

characteristics, and the problem of how the qualitative properties of the traces can be contained

within the boundaries of Platonic solids.

A Response

In passages 106b-c of the Phaedo, Socrates points out that the Form of Fire is invariably

accompanied by the Form of Hotness. Since it is safe to posit that heat is an intrinsic characteristic

of fire, the idea that the Form of Hotness falls under the Form of Fire in the hierarchy of forms

makes sense. In a similar manner, we may accept, based on Timaeus’ account, that the Form

Tetrahedron also falls under the Form of Fire, so Sayre’s concern that “fire does not become fully

what it is until it is made to participate in the Form Tetrahedron” is not really problematic, at least no

more so than that it must participate in the Form of Hotness15. Sayre makes the point that there are

“instantiations of the Form Fire, for instance (those in the precosmic Receptacle), that are not

15 I am assuming here that the Form of Hotness and the Form of Tetrahedron are related to the Form of Fire in similar

ways. But, as Scott Hemmenway points out, one could interpret Timaeus’ metaphysics as an attempt to say what the

Form of Fire is, namely, the tetrahedron. Under this interpretation, Timaeus is attempting to give a mathematical

metaphysics of the elements.

tetrahedral, and instantiations of the Form Tetrahedron (classroom models, etc.) that are not fiery.”

But Timaeus makes very clear that the affections of the elements are due to their geometrical

configuration (see 61e, for example, for the case of fire), so the traces of the elements in the

precosmic Receptacle must have some kind of related pre-configuration before the action of the

Demiurge. This is what makes Harte’s account attractive--since there is nothing in the dialogue

suggesting that some substance is configured into geometric shapes, she makes the plausible

conclusion that the substance must be space itself. This is in keeping with Timaeus’ identification of

the Receptacle as Space in 52a. So it is not the case, as Sayre claims, that there are “instantiations of

the Form Fire, for instance (those in the precosmic Receptacle), that are not tetrahedral”, and while

there are certainly instantiations of the Form Tetrahedron that are not firelike, this is no threat to the

coherence of Timaeus’ account, anymore than the instantiations of the Form of Hotness that are not

fiery threaten the coherence of Plato’s theory of forms.

We now turn to Sayre’s second objection in this section: How is it that the qualitative properties of

the traces can be contained within the boundaries of the Platonic solids? Our response, in keeping

with Harte’s picture, is that the “qualitative” properties of the traces such as heat, fiery-ness, and

moistness are the result of the geometric (and hence quantitative) structure of the traces. To be clear,

we are not saying that the Receptacle was already in a perfect condition of geometric ordered

structure prior to the actions of the Demiurge. Indeed, Timaeus points out in numerous places that

the task that the Demiurge takes on for himself is precisely the imposition of order in a disordered

pre-cosmos. But we are supporting Harte’s account that “in the absence of the Demiurge, portions

of the Receptacle are configured in ways that closely resemble, but do not precisely correspond to,

the configurations of the regular solids”16. The Demiurge, in order to create the perceptible elements

of fire, air, water, and earth (and not just their traces) so as to construct the cosmos, makes these

configurations precise “as far as possible to be beautiful and best--from a condition that was not so

before”. Sayre’s objection arises from a conception of the regular solids as configurations in space,

where space acts as their container. Under his conception, the regular solids are not, as in Harte’s

view, “configurations of space, where space ... is the medium that takes on and displays the

configuration in question. Viewed as configurations of space, the regular solids are not empty, not

empty of space, that is, for they are three-dimensional”.17 So it is with the traces themselves. In

short, the answer to the question of how the qualitative properties of the traces can be contained

within the boundaries of the Platonic solids is that the qualitative properties of the traces are the

result of the pre-cosmic geometric structure of the traces, (which one may reasonably posit are the

result of the associated forms,) in the pre-cosmos inherited by the Demiurge.

V. Regrouping Triangles and Changing Qualities

16 See Harte, “The Receptacle and the Primary Bodies”. Harte also points out another possibility, that “by some

precosmic accident, portions of the Receptacle take on precisely those configurations which the demiurge imposes, but

do so only fleetingly or in some other unstable fashion”.

17 According to Harte in “The Receptacle and the Primary Bodies”, the “regular solids are made of plane surfaces, which

are in turn made up of triangles. … [The triangles] too are configurations of space, now in two, rather than three

dimensions.” An objection that one may raise about Harte’s account is whether it entails that fire, for example, is a

tetrahedron of space that isn’t made of any material. It is precisely this objection that Harte tackles in her paper—

whether, by her account, we are getting something from nothing. I will not get into the details of her (in my view,

convincing) response; the reader should refer to her essay “The Receptacle and the Primary Bodies”. But her point is

that the Form of Fire (and that of the others) is, according to Timaeus, geometric in nature. So the geometric shaping

that the demiurge imposes is where “the reality of something being fire comes” from.

Sayre's Critique

Under this heading, Sayre takes up the topic of how the elementary triangles, produced by the

decomposition of particles of the elements, recombine to produce tetrahedrons, octahedrons,

icosahedrons, and cubes again; and also the status of the qualitative features of the elements

produced by such reconfiguration.

As we know from Timaeus' account, the reconfigurations of the 30-60-90 triangles are what explain

the cyclical nature of fire, air, and water, while the 45-45-90 triangles produced by the breaking up of

earth particles can reconfigure themselves only into cubes again. Sayre asks why. In particular, why is

it that these elementary triangles can recombine only in the specific ways described by Timaeus? Why

can't the 45-45-90 triangles recombine to form rectangles rather than cubes? Why is it that the 30-

60-90 triangles can only reconfigure themselves to produce tetrahedrons, octahedrons, and

icosahedrons, and no other solid? Why can't the triangles combine, for instance, “in the shape of a

sundial (face to face)”, or stack together “in the shape of a wedge”? Also, during the reconfiguration

process, do “these objects ‘float’ in space for a while before reassembling, or do they ‘snap’ into

place instantly to form other regular solids”? And why can't the triangles remain “unattached

indefinitely within the space of the Receptacle”?

The other question Sayre raises here is how the particles (of the elements) formed from a

reconfiguration of elementary triangles acquire their qualitative features. Setting aside any problems

with how the Demiurge initially associated the qualitative features of the traces with the geometric

shapes he made for them, the question now is where, after dissolution and recombination, do the

qualitative features come from18? The traces, after initially acquiring their shape from the Demiurge,

might possess their qualitative characteristics, but upon dissolution into elementary triangles, what

happens to those features? “Are they ‘set free’ to wander erratically throughout the Receptacle, in

effect reverting back to their preconfigured state”? Or do “they remain closely bunched together in

the immediate vicinity, but lose their power of interacting with the other elements”? “Or do they

simply disappear, snuffed out with the dismantling of the figure that once hosted them?” Sayre does

offer a couple of possible answers, after which he explains why they are problematic. His passage

here bears quoting at length:

“Are we to assume that some of [the] traces were passed over in the initial shaping and remain

available for ‘capture’ by the newly formed particles? Another possibility, of course, is that there are

‘second-hand’ traces conveniently lurking nearby, set free by the breakup of previous particles of

fire. In this case, we would have to assume that the Demiurge has somehow contrived to maintain a

working balance between traces released and traces assimilated as a result of transformations

occurring in any given vicinity. In either case, we have the problem of accounting for the

assimilation of appropriate traces by newly formed particles. Because any subsequent geometric

shaping of traces would be a repetition of the original act of ordering, this would seem to require

that the Demiurge remain on the scene indefinitely. And we are told at 42D that, after distributing

human souls among the stars, the Demiurge in effect retires, leaving the formation of mortal bodies

to the lesser gods.”

18 Note that Timaeus’ account (56c) would imply that the elementary triangles would be too small for us to be able to

sense their qualitative properties. Sayre is presumably referring to what we can perceive when the particles of the

elements are en masse.

Thus in Sayre's view, the question of how the reconfiguration of elementary triangles occurs, and the

related question of how the Platonic solids which are the products of such reconfiguration acquire

their respective qualitative characteristics add further credence to his thesis that Timaeus' account of

the chora is unintelligible.

A Response

As indicated in the responses to the other objections above, we are approaching Sayre’s objections

from the standpoint of Harte’s account that the traces in the Receptacle were (unstable) pre-

configurations of space. The demiurge improves on this pre-configuration to the greatest extent

possible, but making it as precise as he can via “forms and numbers”. This results in the creation of

the four elements. Given that the demiurge is improving to the maximal extent possible

configurations already in existence, it is reasonable to conclude that the only pre-configurations of

space present in the Receptacle were those corresponding to the four elements and no other “element”,

and therefore, by necessity, the only elements that the Demiurge could produce via his efforts were

those whose pre-configurations were inherited with the Receptacle--namely fire, air, water, and

earth. Therefore, after the geometrization of the traces and the production of the four elements, if

the faces of the regular solids corresponding to elemental particles were to become unhinged, they

could only recombine into one of the four configurations of space permitted by the inherited

structure of the Receptacle. Any other configuration, or floating of the elementary triangles, would

not be permitted by the structure of the ordered cosmos, whose receptacle can only be made up of

spatial configurations corresponding to the four elements. I would employ the analogy would be that

of a jigsaw puzzle, where the pieces of the puzzle only come in the shapes of triangles and squares,

and the board on which the pieces of the puzzle must be placed (i.e. the receptacle) has grooves cut

into it which only allow the placement of triangles and squares in it, and stacking pieces one on top

of the other results in pieces jutting out from the board, which is not permitted.

As to the second question of how the qualitative features appear after the elementary triangles

recombine to give a regular solid, we have already made the point that the qualitative features of the

elements are inextricably linked to their geometric structure; hence creation of the structure through

configurations of space would necessitate the appearance of the relevant qualitative features.

VI. Conclusion

We have argued that Verity Harte’s picture of the Receptacle allows us perceive and comprehend it

in a way that can help meet at least some of Sayre’s objections. While profound difficulties still lie in

Timaeus’ account of the Receptacle, to declare his account as “incoherent from start to finish” is, in

our view, simply not the case.19

VII. References

A. E. Taylor, A Commentary on Plato’s “Timaeus” , Oxford: Clarendon, 1928

Alan Code, “Aristotle on Plato on Weight” in R. Mohr and B. Sattler, eds., One World, The Whole

Universe: Plato's Timaeus Today, Las Vegas: Parmenides Publishing, 2010

19 My thanks to Scott Hemmenway for additional comments.

Verity Harte, “The Receptacle and the Primary Bodies” in R. Mohr and B. Sattler, eds., One World,

The Whole Universe: Plato's Timaeus Today, Las Vegas: Parmenides Publishing, 2010

__________, Plato on Parts and Wholes: The Metaphysics of Structure, Oxford: Oxford University Press,

2002

M. L. Gill, “Matter and Flux in Plato’s Timaeus,” Phronesis 32 (1987), p. 50-53

John Sallis, Chorology, Bloomington: Indiana University Press, 1999

Kenneth Sayre, “The Multilayered Incoherence of Timaeus' Receptacle” in Gretchen Reydams-

Schils, eds., Plato's Timaeus as Cultural Icon, South Bend: University of Notre Dame Press, 2003