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
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