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ONTOLOGICAL SYMMETRY IN PLATO: FORMLESS THINGS AND EMPTY FORMS.

1. Introduction

This paper explores the evidence for ontological symmetry in Plato's metaphysics. (1) The symmetry in question is that between Forms and things: (2) never one without the other. Is such symmetry necessary? Is it possible? Is it justified? Is it there? Is there anything outside the reciprocal ontology of the Forms from which things draw their essence (or get their name) and the things of which they are Forms? (3)

Imagine the relationship between Forms and things in terms of the admittedly imperfect metaphor of a river. What can we say about the water alone? What about the channel through which the water flows? We can reasonably say that the water can exist without the channel and the channel without the water. We may find each useless or incomplete without the other, but we do find each without the other. What about Forms and things? Are they ever found alone, one without the other, or are they useless, perhaps meaningless, possibly even inconceivable, without one another? (4)

To put it in philosophical rather than practical terms, must we hold with Kant that "concepts without percepts are empty, percepts without concepts chaotic" and with Taylor that this is exactly what Plato had anticipated with Forms and particulars (1926: 188)? (5) Taylor's position is that we must indeed hold this with Kant and that we must therefore reject both Formless things and empty Forms in Plato. (6) Is he right? Does Plato allow nothing without a Form and no Form without a thing?

The questions have been with us for a while. But the answers have yet to inspire a consensus. (7) This is partly because the questions are not as clear as they might seem and partly because the evidence is not as strong as would be desired. The combination can be a formidable obstacle, especially when the questions are taken up not as focused studies but as possibilities to be considered in the course of addressing other issues, usually concerning the relationship between Forms and particulars as opposed to the correspondence or correlation between them. (8) But even with clear questions and complete dedication, the nature and extent of the evidence remains a problem. The direct evidence, limited to the Platonic corpus, is inconclusive at best, arguably not even there at all. We get some help from Aristotle but not enough to make up for what is missing in Plato. The purpose of this paper is to determine and demonstrate the best we can do with the evidence we have.

The best we can do begins with the least we can do: clarifying the questions. There are two: one concerning Formless things, the other concerning empty Forms. A preview now of the answers formulated in due course may help follow the clarification process building up to them.

The answer to the first question (section 3) is that Formless things are a matter of what we mean by "Form," a matter, that is, of what counts as a Form. To elaborate, working out the possibility and reality of Formless things requires accounting for fundamental differences among types of Forms, the variegation in which precludes a single answer covering all the reified universals familiar from the canonical corpus. The examples in the dialogues come with differences in kind admitting of categorization, and, in fact, requiring it. The question of Formless things depends ultimately on whether we are prepared to count all of these as Forms. The answer developed here happens to draw on my earlier work on the relevant differences and the proper categorization, but no familiarity is presumed or required. (9)

The answer to the second question (section 4) is that empty Forms are possible, with the possibility, either practical or conceptual, being determined by factors other than the nature of the Form in question. Instantiation could, for example, be interrupted by accident or prevented by necessity. (10) The reality of empty Forms, however, beyond the bare possibility, depends on whether Forms that would be empty if they existed actually do exist. This is different from the more basic question of the existence of Forms. This one is specifically about whether circumstances that point to a vacancy in a certain Form, whether by accident or by necessity, suggest at the same time, and therefore instead, that there is no such Form.

Serving the aim of clarification, a preliminary section on the evidence precedes the two sections on the questions. To avoid any misunderstanding, it bears reiterating that both the questions and the answers are concerned with what Plato thought about the matter, or given the dearth of evidence, with what he may have thought about the matter, not with what we might be able to make of it invoking what we now take to be Forms (or any modern counterparts we may find more appealing).

2. The Evidence

One Form for everything of the same kind (Republic 596a). This is the extent of the guidance we get from Plato on the correspondence between Forms and particulars. There is plenty more on the relationship, but this is it for the correlation. We are told, for example, of a separation between the Forms and the things of which they are Forms, each residing in a different region of the world (Republic 509d, 517b; Phaedrus 247c-d, 248b; Parmenides 134d). (11) We are told also of Forms inhering in things, and of things participating in (or partaking of) Forms, and of the two being in a communion of sorts (Phaedo 100b-102b; cf. Parmenides 130a-135d). We are told even of Forms being recollected upon sight of particular things (Phaedo 72e-77a). (12) As vague as some of these details may be, they add up to quite a bit of information on the relationship between Forms and particulars, but they have no bearing on the numerical correspondence. (13) Nothing about the mechanics of the relationship tells us whether there is a Form for everything and a thing for every Form. Neither does the general rule, however loosely intended, that there is a Form for each multitude of things with a common name (Republic 596a). (14) The rule is confirmed in other words in other places, and illustrated elsewhere with examples, but not in a way that expands, explains, or enriches the information we already have in this statement. (15)

What does the rule say? Does it express a perfectly reciprocal correlation such that Forms are never without things, and things never without Forms? Or does it affirm only that Forms are never without things and not necessarily that things are never without Forms? Or does it do just the opposite, affirming that things are never without Forms, while remaining silent on whether Forms are never without things? Is it perhaps merely a limiting condition whereby at most one Form (and, in fact, exactly one Form, if any at all) corresponds to a multitude of things of the same kind, which does not rule out whether there are any cases where no Form corresponds to a multitude of things of the same kind, and is altogether silent on whether there are cases where no things correspond to a given Form? (16)

The apparent absence of a unifying answer in the Platonic corpus is often a motivation, both in general and in this particular case, to turn to Aristotle for any insight he might be willing and able to offer in regard to Plato's actual answers. But the evidence there is mixed as well. Aristotle can be helpful on specific points of interest, some of which come up in the course of this paper, but he cannot settle the debate for us. Regarding the general rule just mentioned (Republic 596a), Aristotle seems, on at least one possible reading, to interpret Plato's concern to be specifically with natural kinds, not with types in general: "And so Plato was not far wrong when he said that there are as many forms as there are kinds of natural things (if there are forms at all)" (Metaphysics 1070a17-19). (17) This would then seem to rule out, on Plato's behalf, Forms for artifacts (if for nothing else besides).

Yet Aristotle's praise can be taken either way. Another interpretation, as suggested by Bluck (1947), is just the opposite: Aristotle's acknowledgment that Plato was not wrong in saying there are as many Forms as there are kinds of natural things could have been a foil for Aristotle's (presumable) conviction that "'but of course he was wrong in saying there are Forms of artificial products'" (1947: 75). This is the reading Bluck favors. Together with other clues, it shapes his conclusion: "Plato did not reject Forms of any artefacta, and I do not think Aristotle ever intended to suggest that he had" (1947: 76). Fine, in contrast, is inspired to go in the other direction with the same facts: "If Plato recognized forms in both cases [natural kinds and artifacts], Aristotle would not commend him as he does" (1993: 83).

Both commendations work, though the Plato in Fine's scenario is somewhat more commendable than the one in Bluck's scenario from the perspective of Aristotle in either scenario. It may not seem less fitting to commend Plato for recognizing one thing while condemning him for recognizing another (as Bluck has it) than to commend him for recognizing the first thing and rejecting the second (as Fine has it). But the distinction is more properly between commending Plato for recognizing a truth while condemning him for recognizing a falsehood (Bluck's scenario) versus commending him for recognizing that same truth and rejecting the corresponding falsehood (Fine's scenario). The achievement or distinction to be commended seems greater in the latter case without making commendation altogether inappropriate in the former case.

This is just the periphery of the interpretive quagmire in an appeal to Aristotle on this matter. Even if we could confidently discard Bluck's reading in favor of Fine's, we would have to contend with opposition from other things Aristotle says as well as from some things Plato says. To return to the example on hand, finding a Platonic rejection of artifacts in Aristotle's commendation of Plato contradicts the way Plato's thoughts run to Forms for beds and tables (Republic 596b, 597c-d), if only in an exploratory dialectical effort, immediately after introducing the generalization of one Form for each kind of thing. Curiously, Aristotle demonstrates a sensitivity to the evidently familiar and controversial (Platonic) supposition of Forms for artifacts, as he invokes the analogous example of the Form of table as a reason why he does not find the "theory" (of transcendent Forms) reasonable (Metaphysics 988a1-5). (18) This, in turn, seems to undermine Aristotle's separate testimony that Plato rejected Forms for artifacts, as related in two different passages (Metaphysics 991b3-8, 1080a3-10), both citing houses and rings as examples of things (Plato found to be) without Forms (or, less decisively, of things thought to be such either by the author of the Phaedo or by the proponents of that work, or possibly by both). (19)

There are no easy answers, whether within Plato or without. No matter what we are supposed to do with Aristotle's report, Plato's general rule could have been intended (even on its own evidence) without a restriction beyond types, broadly construed. It would thus rule out nothing more than arbitrary multitudes (those to which we would not be able to assign a "common name" as required by the original statement): e.g., the random things accumulating inside my desk drawer over time, or better yet, those remaining outside my desk drawer (comparable to "barbarian" at Statesman 262e). More important, this "general rule" is not the only relevant consideration here. Even if the generalized guidance provided through it could be trusted as a precise formula for sorting out the correspondence between Forms and things, and even if we were clear on what was actually being said in that regard, we would still have plenty to talk about (though the "rule" as properly deciphered would certainly help with those talks).

To parse the logic of the problem, by way of recapitulation, there are only two distinct questions here: (1) The question of Formless things: Is there anything without a Form? (Is there a Form for everything?) (2) The question of empty Forms (uninstantiated Ideas): Are there any empty Forms? (Is there a thing for every Form?) (20) We cannot look up the answers. There is nowhere to look. Plato does not tell us anything either way regarding either question. Had he done so, neither question would have come up in the first place. Whatever the answer, we have to reason it out instead of looking it up. Still, this does not mean we will have no use for the dialogues. We have to extrapolate from what Plato does say of Forms and of things (other than Forms).

A notorious exception to the absence of a direct answer in the canonical corpus is the apparent availability there of an answer to the first question, the question of Formless things. This is where Socrates the character declares with great confidence that there are no Forms for hair, for mud, or for dirt (Parmenides 130c-d). (21) This is an unequivocal answer to the question whether there is anything without a Form. The answer is yes. There is at least hair and mud and dirt. (22) And the answer would be definitive save for the attendant dramatic conflict: First, the speaker himself confesses in the same breath as he rules out Forms for these things (hair, mud, dirt) that he is troubled by the inconsistency of attributing Forms to some things but not to others (130d). Second, the answer meets with disapproval from the character Parmenides, whose assessment of the matter is that the young Socrates is not yet a proper philosopher and that, once he is, he will no longer consider such things (hair, mud, dirt) unworthy of attention (130e). Given that the answer by the protagonist is undermined both by his own misgivings (paradoxically, perhaps ironically, coupled with his certainty about the matter) and by protest from another major character, there really is no answer. (23) And this goes beyond the usual difficulty of attributing the views of Plato's characters to Plato himself. (24) In this case, the character whose views are in question is troubled by the inconsistency of his own views, and troubled or not, he is opposed by another character, one more advanced in both years and experience if not also in wisdom. Hence, there is no solution in the work itself, regardless of whether the answer, such as it is, may reasonably be attributed to Plato.

This is not the only conceivable reading, nor even the only reasonable reading, of the conflict between the young Socrates and the elderly Parmenides. Patterson (1985a: 126), for one, presents a respectable alternative. He contends that making room for hair and mud and dirt would still be consistent with a restricted population for Forms, as the Forms countenanced in the process represent natural kinds, already recognized as Forms, rather than arbitrary predicates constituting an aberration in the mutually accepted ontological platform. In other words, neither Socrates's misgivings nor Parmenides's intervention is about assenting to a Form for everything. The conflict is instead about acknowledging a Form for everything already qualified to have a Form (as natural kinds seem to be) (25) but denied one only out of inexperience on the part of the young Socrates.

This is believable. So is the interpretation here. Both are consistent with the facts of the matter. The fact that making room for hair and mud and dirt among the Forms would continue to be consistent with a restricted population for Forms (as Patterson rightly points out) does not mean that it is inconsistent with a push toward a Form for everything (which Patterson does not deny). If this is a tie or standstill of some sort, note that Patterson's reading makes the drama do less work than one where the young Socrates is confused about truly philosophical problems. If there is no qualitative difference (for there will certainly be a quantitative difference) in the population of Forms with and without Forms for hair and mud and dirt, then the misgivings of Socrates and the intervention of Parmenides are both insignificant--or at least less significant than (dramatic backdrop for) a philosophical question regarding the range of Forms, or what is the same, (dramatic backdrop for) a philosophical concern over the possibility of Formless things. This is what Patterson's interpretation amounts to, leaving us with a Socrates hesitating, and a Parmenides wincing, for no better reason than the detection of prejudice against the dignity (value) of things like hair or mud or dirt. This is not a bad reason, but it is not as compelling as the recognition of a philosophical problem. My reading allows the author of the Parmenides to be a better philosopher than does Patterson's alternative.

As for the second question, Plato does not even give us a conflict to work out. In the case of Formless things, we know at least that he is thinking about the matter. In the case of empty Forms, we know next to nothing. (26) The reason we have not been able to get very far with the conflicting evidence for Formless things is not just that the conflict precludes a definitive solution but also that it attracts some of us to one perspective and some to the other instead of inspiring us to unite around a consensus regarding the uncertainty, namely, around an agreement that the uncertainty of the matter is itself a conclusion, possibly the most reasonable conclusion under the circumstances. (27) We may, ironically, be able to do more with empty Forms, where there is hardly any evidence either way as opposed to clear evidence both for and against. The greatest conflict we have in discussing empty Forms will be with one another, which is usually easier to negotiate than a conflict with Plato, the unavoidable result of a positive or negative answer to whether there is a Form for everything.

3. Formless Things

It is only natural that both the evidence for and the evidence against Formless things should command attention and find support. There is, to be sure, clear if sparse evidence in either direction. But what does it mean, as suggested above, to embrace the uncertainty as opposed to adopting one position or the other? It means that the uncertainty need not silence us, instead showing us where to look for a solution. The problem is that the evidence is mutually inconsistent, thus supporting contradictory positions. But what if there were a way to remove the inconsistency in the evidence and thereby the contradiction between the positions?

It is possible to do just that under any interpretation of Plato that recognizes meaningful variation in Forms. The one here happens to be my own, developed in collaboration with Holger Thesleff. (28) I interpret Plato's ontology in terms of a monistic stratification of a unitary reality into levels (as opposed to a dualism of worlds), including a division of Forms into three categories at the upper level: Ideal Forms; Conceptual Forms; Relational Forms. (29) This model originated as a thought experiment (Alican and Thesleff, 2013: 14, 17, 43), but what it says is more important than what it is. The basic idea is that the entities (or constructs) traditionally identified as Forms (or Ideas) in Plato are not, one and all, the same kind of thing, simply a Form, undifferentiated in any way and fungible in every way. (30) Instead of interchangeable representatives of a homogeneous collection, there are Ideal Forms, such as the just itself and the beautiful itself (Phaedo 57d; Parmenides 130b), Conceptual Forms, such as strength (Phaedo 65d; Meno 72d-e) and shape (Meno 73e-76e; Philebus 12e), and Relational Forms, such as rest/change, same/different (paired contrasts as exemplified by the megista gene [[phrase omitted]] at Sophist 254d-e). (31)

The examples may be telling enough on their own, but a clarifying narrative will help: Ideal Forms correspond to value paradigms (moral, aesthetic, religious, etc.), Conceptual Forms represent types and properties, and Relational Forms constitute the building blocks of reality as ontological categories in pairs of complementary contrasts. (32) Strictly speaking, they are not these things but the Forms of these things. (33) In other words, they are not themselves these things (at least not nothing more than these things), though they represent these things as the Forms of these things. And as Forms, they are all more than concepts or universals as we understand them today. (34) They exist outside the mind (as well as within). (35)

The divisions are underpinned by a stratification of reality into levels, two basic levels, and an untold multitude of subdivisions. (36) The stratification scheme ranges from the good at the highest level of reality to images (not just physical things) at the lowest. Hence, it is not a binary division between Forms and the things of which they are Forms. (37) The simile of the divided line (Republic 509d-511e) is a good model for the structure envisaged. (38) The two main levels of the layout contemplated here correspond roughly to the top two and bottom two segments of the divided line, but the subdivisions here, an indefinite many, allow greater flexibility than explicitly recognized in the original line. All three categories of Forms belong to the top level, though Ideal Forms rank higher than the other two divisions. The most important difference is that Ideal Forms possess intrinsic value whereas the other two do not (Alican and Thesleff, 2013: 21, 29, 43). (39)

The proposed classification has the advantage of simultaneously accommodating the rejection of trivial Forms by the young Socrates and the acceptance of the same by the elderly Parmenides. More accurately, it makes sense and use of three elements in mutual conflict: the young Socrates's rejection of Forms for trivial things; the same character's misgivings regarding the generalizability of that rejection; the elderly Parmenides's warning against rejecting them. The vision of Plato's world adopted here points to a way out of this conflict: Trivial things may have Conceptual Forms. Even if they lack Ideal Forms, they are not necessarily Formless.

This means that everything, or well near everything, could have a Form insofar as each of the three divisions may be counted as Forms. But that possibility also raises a question, as these divisions are not different varieties of a single thing identifiable as a Form. They are instead different answers Plato has come up with in his own thought experiments exploring (discovering or inventing) abstraction. An Ideal Form is something quite different from a Conceptual Form, and both, in turn, are altogether different from Relational Forms. The question is whether they are similar enough that there being an Ideal Form for one kind of thing, a Conceptual Form for another kind, and a Relational Form for yet another, counts as there being "Forms" for those kinds of things (and so on to the conclusion that there is a Form for everything for which there is some "Form" or other).

This is a fair question. (40) But the answer is not as important as it may seem. The point is not that there is a Form for everything in a sense that says exactly the same thing of everything to which it attributes a Form but that there is room for it all in Plato's lifelong experimentation with abstraction--an experiment that ends up with three different divisions in the things traditionally regarded, without further differentiation, as Forms. This reading of Plato has the additional advantage of making sense of both the young Socrates's misgivings and the elderly Parmenides's intervention (and subsequent encouragement). The question of the precise balance of similarity and difference between the three categories of Forms reflects a more manageable problem than pretending that knowledge and mud, for example, are the same sort of thing, and then wondering why the young Socrates is fascinated by one and not by the other. The interpretive model here not only removes that inconsistency but also explains why the young Socrates is bothered by it and why the elderly Parmenides interprets it as a lack of philosophical insight and development. (41)

The emphasis in this classification of Forms is on what is valuable, significant, important, or at least interesting--all from Plato's perspective. The possession of Forms is indicative of value assignments by Plato. (42) This contingency, with its emphasis on value, is the same contingency whether the result is a genuine Form or an ambiguous abstraction, perhaps halfway between a concept and a Conceptual Form. (43) The distinctions we are able to make, with the conceptual and linguistic apparatus available to us, between a concept and a Conceptual Form, cannot be confirmed by anything to be found in the dialogues, where concepts and Conceptual Forms from our perspective may remain undifferentiated from Plato's perspective. (44) But that does not undermine the conclusion that there is room in Plato both for affirming and for denying that there is a Form for everything.

This conclusion is also consistent with the dramatic nature and position of the underlying conflict. We need not take the uncertainty regarding Formless things as a mid-career crisis, an association often made in textbook characterizations of the Parmenides. (45) The developmentalist tradition ignores the explanatory power of the dramatic chronology connecting the dialogues in the Platonic corpus. (46) This perspective, the corpus as drama, has been gaining support as an alternative to seeking out the most likely production order of the dialogues. (47) The young Socrates of the Parmenides is the youngest Socrates in all the dialogues. (48) At the other extreme, the oldest Socrates in the corpus, in fact, the oldest Socrates possible, is in the Phaedo, going through his last day on earth. Even without agreement on what goes in between, and in what order, it should give us some pause to note that Plato could easily have avoided dating these two dialogues so far apart dramatically. He could instead have used an ageless Socrates, as often done with characters in serialized fiction, whereby we would have had to rely on other dramatic clues, if any, to ascertain the relative dramatic dates of these two dialogues. (49) Given that he has not done so, there is possibly something to be gained from considering the reason and even more from figuring it out. (50)

An immediately relevant possibility is that of a deliberate effort to emphasize the personal, intellectual, and philosophical growth of the character Socrates. (51) The ambivalent young Socrates of the Parmenides could well have matured into the confident old Socrates of the Phaedo. (52) Indeed, the last Socrates we know is neither ambivalent nor hesitant nor confused. The best explanation for the transformation of conflict and uncertainty into sagely serenity is growing satisfaction with the subject matter, in this case, the Forms. (53) The end result need not be precisely like the classification adopted here. However, if it makes sense to speak of an end result at all, especially one that stands in contrast to a correlative beginning, this alone favors a comprehensive explanation in the spirit if not the letter of the one provided here. (54)

4. Empty Forms

The scarcity of evidence is not the only obstacle to consensus on empty Forms. A prior obstacle is the absence of a standard interpretation of the question. We do not agree on what the question is, so we keep coming up with different answers. We might still have different ideas on what to say even if we agreed on what was being asked, but we would then be in genuine disagreement, which is the proper starting point of dialectic.

The question of empty Forms is rarely discussed apart from those of transcendence and immanence. (55) These, in turn, can be addressed either separately or jointly, but they are usually taken up together, even in studies devoted primarily to one or the other (as in Fine, 1984, 1986). Aristotle often turns up in such discussions, and rightfully so, as he seems to have initiated them. (56) Specifically, transcendence tends to be discussed in relation to what Aristotle reports Plato to have said or thought about separation (Metaphysics 1078b30-32, 1086a30-b11), while immanence is typically examined through Aristotle's understanding of the place Plato assigned to the relationship between Forms and particulars among the variety of ways one thing can be said to be in another (Physics 210a14-24; cf. Metaphysics 991a9-19, 1079b12-23), with additional relevance to the ways one thing can be construed as part of another (Metaphysics 1035b32-1036a13). (57) Hence, any metaphysical tension between transcendence and immanence also shows up as a contrast between the separation of Forms from particulars and the presence of Forms in particulars. (58)

The general presumption against the compatibility of separation and immanence, though by no means universal, is a reflection of how each of these concepts is understood. The variety of interpretations makes the presumption, where it exists, far from uniform. Some combinations work against the presumption, perhaps even overturning it.

Suppose that separation came in degrees, immanence in modes. As a rough illustration of possible combinations, suppose further that degrees of separation were to be mapped onto modes of immanence. What would the result look like?

Degrees of separation might range from numerical distinctness, under the weakest interpretation, to transcendence, under the strongest, with ontological independence as a possibility somewhere in between. (59) The two extremes probably mean just about the same thing to everyone, but ontological independence is best spelled out. (60) I take one thing to be ontologically independent from another if the existence and essence of that thing do not depend on the existence and essence of the other. This is to define ontological independence in terms of both existential and essential independence. (61) The existential dimension can be elucidated in modal terms (though this is not necessary): (62) One thing is existentially independent from another if that thing can exist even if the other does not, and if it need not and does not exist just because the other does. Essential independence is clear enough as it is: One thing is essentially independent from another if that thing is what it is (the way it is) regardless of what may be the case with the other thing.

As for modes of immanence, the relevant range might extend from a shared property, at the weakest end, to numerical identity, at the strongest, with instantiation falling somewhere in between. (63) The distribution of actual viewpoints, for both separation and immanence, may well have a different range or median or both. This breakdown should nevertheless suffice for the discussion in progress.

Even those who oppose mixing separation with immanence will find some combinations more appealing than others. One option is to combine a strong interpretation of separation with a weak interpretation of immanence. Another is to do the opposite, combining a strong interpretation of immanence with a weak interpretation of separation. The optimal solution, if the path of least resistance qualifies for that designation, may indeed be to pair the strongest sense of one with the weakest sense of the other. (64) Depending on where the resistance originates, however, a viable alternative may be to take a moderate interpretation of each concept.

My own view falls outside the range of optimal solutions. On the matter of degrees of separation, I come down on the side of transcendence. (65) On the matter of modes of immanence, I am satisfied with the admittedly vague notion of instantiation. A position outside the optimal range is not automatically wrong. The point of going through possible combinations of views on separation and immanence is not necessarily to adopt or recommend the path of least resistance but to show where that path is, thereby facilitating the reader's assessment of where the present position is in relation to that.

I take the Forms to be transcendent. (66) And I take them to be instantiable. (67) One does not preclude the other. (68) The Forms are transcendent by nature, that is, as a part or aspect of what they are. They are immanent by chance. They are, in other words, transcendent essentially but immanent accidentally. Their transcendence is a part of their nature, but their immanence is a reflection of our own insight into their existence and essence. The question is whether there is room for empty Forms in this combination of transcendence and immanence.

As already mentioned, there is no particular conflict of evidence in the case of empty Forms as there is with Formless things. Here, the evidence, at least the direct kind, is lacking rather than contradictory. At the same time, we must recognize that the problem of empty Forms is not entirely a matter of neglect or reticence on the part of Plato. It is not as if the only thing missing were an express commitment by Plato regarding a perfectly clear question. The problem itself is unwieldy, difficult even to express, let alone to resolve.

For instance, is an empty Form one that does not, at the moment, happen to correspond to anything in particular, or is it one that does not, has not, and will not ever correspond to anything at all? To illustrate, is there a Form of mastodons, and is it an empty Form? And if there is no Form of mastodons, is this because there are no mastodons anymore? The difference here is temporal. But perhaps the question should be expressed in modal instead of temporal terms. Is an empty Form one that does not (but could) correspond to anything, or is it one that cannot correspond to anything? Are empty Forms a temporal phenomenon or a modal phenomenon? Is instantiation a physical relationship (because it is a temporal one) or is it a metaphysical relationship? Or is it perhaps a logical relationship (or even a psychological one)?

We need to distinguish at least between "past emptiness" and "present emptiness" --and perhaps also between either or both of these and "future emptiness." All three can be relevant:

* Past emptiness (backward vacancy): Was there a Form of mastodons before there were mastodons? Was the Form of mastodons empty before it came to be instantiated, namely, at a time before there were mastodons?

* Present emptiness (forward vacancy): Is there a Form of mastodons at present? Is the Form of mastodons now empty or is it still in some sense instantiated by the fossil evidence confirming both existence and extinction?

* Future emptiness (forward vacancy): Switching from actual to possible extinction: Will there be a Form of elephants when there are no longer any elephants in existence?

This is just to lay out some of the options. (69) What we should be looking for is probably not past, present, or future emptiness, but timeless or unqualified emptiness. Likewise, what seems most relevant is not a backward or forward vacancy but a permanent vacancy. Armstrong (1989: 75-76), for one, understands instantiation without temporal restrictions. (70) A universal is instantiated if it is instantiated at any time in the past, present, or future. It need not be instantiated forever. It need not even be instantiated "right now." An uninstantiated universal, on this interpretation, is one that is never instantiated. Armstrong rejects uninstantiated universals, defined as such, which thus amounts to denying permanently empty Forms but not temporarily empty Forms. Yet he does, albeit with some hesitation, attribute permanently empty Forms to Plato (1989: 76). (71) I agree with Armstrong that instantiation need not be either current or permanent to count as instantiation. But I do not see Plato's Forms failing to fulfill such a liberal conception of instantiation.

Neither does Armstrong. He does not claim that justice and beauty, for example, or any of the other Forms we regularly encounter in the Platonic corpus, are permanently empty, or even that they ever are. He merely suggests, without citing examples from the text, and relying instead on hypothetical cases, that Plato seems to be open to Forms that are permanently empty. One such instance is his discussion of "travelling faster than light" as a candidate for an empty Form, or for an "uninstantiated property" as he has it (1978: 64-65). Our best theories tell us that traveling faster than light is not something to be realized in practice. But does that mean that the corresponding Form is empty ("uninstantiated") or does it mean that there is no such Form ("property")? Armstrong himself rejects the property, but he takes Plato to accept the Form--not, of course, this specific one (traveling faster than light) but those representing uninstantiated properties (or universals) in general (1989: 75-82). (72)

We may need to distinguish not just between Forms that are temporarily empty and Forms that are permanently empty but also between Forms that are not instantiated and Forms that cannot possibly or conceivably be instantiated (and perhaps even between Forms that cannot possibly be instantiated and Forms that cannot conceivably be instantiated). We already have some idea, from questions concerning mastodons and such, what a Form that does not (but could) correspond to anything might be like. What might a Form that cannot correspond to anything be like? Is the Form of unicorns perchance such a Form? (73) Or to break up the loaded question: Is there a Form of unicorns, and if there is, is it an empty Form?

A question of this sort naturally comes to mind, but it may not be the right question to ask. Plato does not countenance Forms for fictional things. (74) Hence, the relevant question about unicorns is not whether their Form is empty but whether there is such a Form in the first place. And the answer to that is negative. Had Plato allowed Forms for fictional entities, the question about unicorns would have been closer to that of mastodons, the main difference being their animation, irrelevant to their instantiation at present since neither one currently exists. Moreover, it is not clear whether the case of unicorns constitutes an example of a Form that cannot possibly correspond to anything in our experience as opposed to that of a Form that simply does not happen to correspond to anything of that sort. One reason for hesitation might be that an actual animal answering to the present conception of a unicorn could someday either come into existence through evolutionary processes or be brought into existence through genetic engineering.

What about things that are not fictional but are still not instantiated? Consider, for example, the cases of the chiliagon and the ideal state (city), both brought up by Vlastos (1969: 301), the latter also (and earlier) by Maula (1967: 35). Plato would presumably classify them both as empty Forms. (75) Each would be empty because nothing in our experience corresponds to either Form, provided that there are such Forms to begin with. (76) But just because we cannot in practice tell the difference between a chiliagon and, say, a myriagon, as suggested by Descartes in his Sixth Meditation, does not mean that nothing of that sort could exist. Nor does the utopian nature of the ideal state preclude all possibility of instantiation. The chiliagon and the ideal state, if they are proper Forms, seem to be examples of Forms that are not instantiated but not necessarily of Forms that cannot be instantiated. (77) They do not expand the relevant possibilities beyond the examples of the mastodon and unicorn.

Are there no examples of Forms that cannot be instantiated? This may be a bad question--or a bad way of putting a good question. The nature of the desired exemplification remains vague. What exactly are we to assume is preventing the instantiation in question? Is the instantiation impossible or is it inconceivable? More specifically, is it inconceivable, and therefore impossible, or is it impossible in some other way despite being conceivable? And either way, if the instantiation is impossible or inconceivable, how could the Form itself be possible or conceivable? Modal reasons against instantiation should also work against reification, and even against conceptualization, the preclusion of which would then make the original question vacuous.

Is there even a difference, preferably a meaningful one, between asking for examples of Forms whose instantiation is impossible or inconceivable and asking for examples of Forms that are themselves impossible or inconceivable? And if we are really talking about impossible or inconceivable Forms, especially inconceivable ones, how are we to come up with examples? Rectangular circles, fractional integers, and liquid icebergs, to name a few, are not good examples. This is not because they are impossible or inconceivable. It is because they are, in each instance, spurious intersections of two separate Forms rather than paradigm cases of one that is empty or impossible or inconceivable. The examples can be multiplied indefinitely with the same result: eternal moments, concrete abstractions, silent sounds, and so on.

There may be counterexamples, as well as other resourceful responses, but none that rules out the instantiation while validating the Form. Eternal moments, for example, are neither instantiable nor even sensible. (78) A Hegelian, on the other hand, will be quick to nominate space as an example of a concrete abstraction, but space will then serve as the instantiation of a concrete abstraction, the Form of which, if there is such a Form, cannot consistently be considered empty. The problem with silent sounds, which present a contradiction, is the same as the problem with soothing sounds, which do not: Neither combination has a Form. One is instantiable, the other is not, but neither one counts as an empty Form, because neither one qualifies as a Form, owing to the compositional structure of the mutual reference. The presumption against the instantiation comes from the contradiction, while the presumption against the Form comes from the complexity--combination, modification, or contamination--which is no longer about the instantiability of a particular Form but about the purity and unity of Forms in general. Silent sounds will not be instantiated in our phenomenal experience, due to the contradiction, whereas soothing sounds will be instantiated, as they are consistent with the way the world works. But neither will have a Form, nor therefore, will either exemplify an empty Form. The complexity precludes it.

This emphasis on simplicity, or against complexity, appears to have certain exceptions, depending on the interpretation. One obvious objection is that even basic geometrical figures, such as circles, triangles, and squares are not simple without qualification. They are all plane figures with an intrinsic structure common and peculiar to each. They are thus composed of simpler elements in a predetermined pattern. If there are Forms for lines and angles, for example, then the Forms of circles and polygons will arguably be complex ones, if acknowledged at all. (79) Perhaps the notion of angles can be explained through that of lines, and is therefore partly redundant with it, but even lines have a derivative nature originating in points as their constituents. And we cannot do much with points alone. Or maybe we can, but we cannot afford to start from scratch, that is, at the level of points, every time we encounter a problem of geometry. We need other units even if they are relatively more complex ones. In short, our standard conceptual apparatus for making sense of the world is not restricted strictly to (partless) simplicity.

None of this, however, voids the premium on simplicity in Plato's Forms. Explicating that premium can help eliminate apparent exceptions. The simplicity here is not limited to the absence of parts. As a matter of fact, it does not even require the absence of parts. The restriction is against unstructured complexity, the kind associated with modification or contamination, as in the combination of multiple items as opposed to the composition of individual items. The complexity of the square (Republic 510d), for example, is significantly different from the complexity of, say, either silent sounds or soothing sounds. The square is a unitary whole; the other two are not. The cohesion of the square may be a matter of perception and convention, hence subjective rather than objective, but that does not make it any less significant as a distinction between things with a unitary structure and those without it. Plato's Forms are unitary wholes if not outright simple objects. An internal structure is allowed but modifications or impurities are not. (80)

This is not to say that Forms cannot instantiate other Forms, just that they do not merge into a single Form when they do. Nor do they give birth to a new Form separate from the interacting originals. There are no complex Forms, certainly not Platonic Forms, or more precisely, none in accordance with Plato's ontology. This, of course, does not preclude the possibility of empty Forms, only the whimsical combinations. All manner of empty Forms, so long as each is its own Form, may still be possible and conceivable. They could even exist without our awareness. As with many other things, the existence of an empty Form is not contingent upon our knowing about it.

Answers to what we can know in this regard should not be charged with settling the broader question whether types, properties, abstractions, or fictional entities exist. In a field where it is perfectly reasonable to claim that there are nonexistent objects (Parsons, 1982), and equally reasonable to ask where they are (Hintikka, 1984), an answer is best not attempted in passing, in the process of working out an altogether different matter, as in the possibility or reality of empty Forms in Plato. Nor should it depend upon formulating a general theory of existence, nor even merely upon establishing whether existence is a predicate. These are the best of questions. But they go the heart of philosophy itself, having no special bearing upon Plato's Forms. And even if they were to be addressed in connection with the Forms, the place for that would be in discussing whether the Forms exist at all, not in deciding what to do with the empty ones.

How do we separate the question of the possibility of empty Forms from that of the reality of Forms? Are we to determine whether, given what Plato says about Forms, there could possibly be empty ones? Or are we to determine whether, given what Plato says about Forms, he seems like he might be open to empty ones? We do not have much of a choice. Given that Plato says nothing about empty Forms, we are going to have to take what would be reasonable to conclude about them as a proxy for what Plato would have said or may have thought. This is not always the best thing to do, but it may be the only thing to do here. If we all agreed on the reasonable, we would not disagree so often. Yet so long as we take care to construe the reasonable with sufficient regard for what Plato himself would have found reasonable, based upon the things that he does find reasonable, this should be an acceptable proxy. It is, after all, not far from Plato to be reasonable.

We are not completely lacking in resources. As is often the case when we find ourselves without direct evidence, or without enough of it, we can turn to Aristotle for help. In this case, we have to reach a bit further, to an Aristotelian commentator. Alexander of Aphrodisias (In Aristotelis Metaphysica Commentaria 81.25-82.7) reports that Aristotle, in the now lost work, Peri Ideon, construed Plato as being committed by implication, though not by declaration, to the existence of Forms for (some) things that have ceased to exist, such as dead persons, as well as for (some) things that never did exist, such as centaurs and the Chimera. The point there, however, is not that, because of the alleged implication, we would be safe to assume that Plato had actually made room in his ontology for such Forms, but that we would be safe to conclude that what Plato does say about the Forms is productive of such infelicities, thereby undermining the tenability of his overall position on the Forms.

The offending implication is to be sought in the Object-of-Thought Argument for the existence of Forms, briefly, an Aristotelian reconstruction assigning, on behalf of Plato, a Form to every object of thought (see, e.g., Fine, 1988: 105-145; 1993: 120-141). Any such implication is difficult to confirm outside that context. In regard to dead persons, it would be hasty to saddle Plato with corresponding Forms, as he never mentions personal Forms even for the living. (81) In regard to imaginary things, again, there is no talk of corresponding Forms, nor any tendency on the part of Plato to recognize the reality of such things, let alone the existence of Forms for them. This, of course, is entirely consistent with the objection, where the crux of the charge is that, precisely because Plato is not open to Forms for these things, the implication that he is (through the Object-of-Thought Argument) vitiates his general outlook.

What is relevant for our purposes is not so much the implication itself as it is the silent premise that Plato did not welcome (or would not have welcomed) Forms for dead persons or fictional entities. If this were a reliable report or a reasonable assumption, either way, it would constitute evidence that Plato did not countenance empty Forms. And that is perhaps just what it is. But there is still room for doubt, or at least for confusion, because the anomaly is attributed not just to the implied commitment to the existence of Forms for things that do not themselves exist but also to a parallel commitment to the existence of Forms for things that are tokens as opposed to types. Perishable things, including those that have already perished, and individual things receive equal emphasis in the elucidation of the problem. This makes it difficult to tell whether Plato is supposed to be uncomfortable because the postulated Forms are empty or because they are individuated.

The difficulty does not apply to the example of centaurs, troublesome because centaurs do not exist, not because the example picks out a particular thing as opposed to a universal one. There is no specific centaur to speak of. The centaurs are a race or breed of legendary creatures. The Chimera, on the other hand, is a fictional individual rather than a fictional kind. It is therefore fully exposed to the ambiguity between not qualifying as a real thing and not qualifying as a type of thing. (82) The same ambiguity is present in the case of dead persons, say, a dead Socrates, which counts both as having perished and as being particular.

To be fair, there is no ambiguity in context. Both perishables and particulars are identified as problematic candidates for Forms. The ambiguity emerges only in attempting to sort out the specific examples in terms of whether they represent things that do not exist or things that do not exist as types or natural kinds. No doubt, the context of the objection would have been more enlightening in relation to the problem on hand had we been given only the example of a species that had perished instead of including that of an individual that had perished. Nevertheless, the Aristotelian scenario related by Alexander still suggests that Plato was not open to empty Forms, as we cannot explain away the example of centaurs, least of all by claiming to have detected an ambiguity of the relevant sort in it. The suggestion may or may not be compelling, but it is there.

Unfortunately, Plato himself says nothing about empty Forms. But he says enough about Forms in general to enable inferences about empty Forms. Fine (1984: 74-78), for one, considers artifacts a possibility. Her thinking can be generalized as the postulate that the Forms of artifacts can and do exist, and hence remain uninstantiated, both before and after the artifacts themselves are in existence. (83) But Fine (1984: 76) personally focuses only on their existence before the emergence of the instantiating artifacts (which is sufficient to discuss or demonstrate separation) and not additionally on their existence after the possible disappearance of those artifacts. She notes that any Forms for beds and shuttles, for example, and for artifacts in general, if there are such Forms, would have to exist not just when but also before the artifacts themselves are in existence, that is, before the first physical bed or shuttle is constructed.

This makes the Forms temporal, as does Fine's acknowledgment of the alternative (which she adds is unlikely to have been maintained by Plato) that the Forms of artifacts come into existence at the same time as the artifacts themselves (1984: 76, n. 73). We know, in contrast, that the Forms exist outside time, as evidenced by the fact that they were already in existence when the demiurge created time (Timaeus 37c-39e). (84) Time is, in fact, a creation fashioned after the Forms.

Yet making the Forms temporal is not necessarily wrong. Plato, we see, wavers between Forms that are created, unique to the Republic (597b-d), and Forms that precede creation, explicit at least in the Timaeus (30c-31a, 37c-39e). (85) We cannot be certain whether his Forms are infinitely durable (or perhaps just extremely durable) or simply atemporal. But maybe we do not have to have a direct and definitive answer in the original sources just to sort out the precedence between Forms and artifacts. Whether the Forms are atemporal or infinitely durable, the possibility of their emptiness would not be precluded by contingencies concerning artifacts, which are neither atemporal nor infinitely durable. (86)

Is it not possible for there to be empty Forms? It is indeed possible. The Timaeus confirms not just a possibility but also a reality. (87) The Forms precede the cosmos, and therefore pretty much everything, given that the cosmos is fashioned after the Forms (Timaeus 30c-31a, 37c-39e). They are thus empty until sensible phenomena come into existence. What are these primordial Forms the Forms of? Presumably, of everything. Otherwise, we would have to settle for some nebulous and mercurial batch of Form-stuff (even before there were nebulae or mercury or batches). Whatever may be the "everlasting Living Thing" serving as a model for the demiurge's creation of time (Timaeus 37c-39e), if it has anything at all to do with the Forms, then it has that to do with all Forms: "For that Living Thing comprehends within itself all intelligible living things, just as our world is made up of us and all the other visible creatures" (Timaeus 30c-d).

Fine (1984: 79) points out interesting exceptions to uninstantiated Forms in the context of the Timaeus. The Form of fire, she observes, cannot reasonably be counted among any Forms existing uninstantiated prior to the creation of the cosmos, because, so the story goes (Timaeus 53b), there were already "traces" of fire in the chaos preceding the cosmos. (88) The same may be said of air, water, and earth (Timaeus 53b), though Fine (1984: 79) focuses specifically on fire, probably not to exclude the others but to minimize clutter where one example will do just as well as four. Other exceptions include justice and goodness, which, Fine notes (1984: 79), would have been instantiated even before the creation of the cosmos, as they would have then been instantiated at least by the demiurge (before any [other] moral agents and moral acts), who is said to be just and good (Timaeus 29a, 29e-30b). (89) We do not know whether these would have been the only moral Forms that were not empty before the cosmos came into being, as we are not told very much about the demiurge, whose nature may (or may not) happen to be such as to instantiate other moral Forms as well, conceivably even all of them. The point, however, is not to explore Forms that are never without instances but to explore those that are the opposite, namely, those that are, in fact, without instances. And the Timaeus seems open to that possibility, even with a just and good demiurge preceding the cosmos.

The question of empty Forms depends, in the end, on what we want to know. We all agree, no doubt, that an empty Form is a Form that is not instantiated. There is no room for dissent there. That is the core definition. But the reasons for the emptiness, not to mention the actual circumstances, including the duration if applicable, together with any prospects for reversal, and yet other details, all stand to make a difference.

The main problem, then, is that we are not clear on what the question is. Actually, that is not entirely accurate. We usually are clear. But we are clear on different questions, and consequently, keen on different answers. This makes us clear as individuals but divided as a community of interested scholars.

A related problem is that we are regularly torn between emptiness and existence as the relevant possibilities for the Forms in question. In other words, we are never quite sure whether problem Forms are just empty or simply do not exist. The confusion is hardly ever about whether a Form already agreed to exist is or is not empty. And it is even less likely to be about whether a Form that would be agreed to exist even if it were empty is or is not in fact empty when it is not instantiated. It is instead about whether the scenario being contemplated precludes just the instantiation or the Form as well.

The two possibilities jointly present a puzzle terminating in a logical impasse. The examples we come up with invariably require, or at least invite, a judgment not just on whether the relevant Forms are empty but also on whether they exist. These do not unfold as mutually independent considerations: Does the Form exist? Check! Is it empty? Check! They turn out to be competing conclusions, with any evidence that the Form is empty also suggesting that it does not exist. This being so, they complicate matters as they provide no more inspiration to deny the instantiation of any given Form in a problem scenario than they do to deny the existence of the same Form in the same scenario. This is not because they are in every case equally plausible alternatives but because the uncertainty in any case is sufficient to leave us undecided. They thus leave us adequately inspired to do both yet unable to do either with confidence. Even more likely, they inspire some of us in one direction, others in the opposite direction.

The potential for confusion is there regardless of the complexity of the scenario. Simple scenarios come with a temporal frame of reference in which things that used to exist no longer do. In that case, the corresponding Forms, if they still exist, are most certainly empty. The Form of mastodons, as already discussed, is empty right now, as would be the Form of elephants if the existing elephants were to disappear. These are easy answers to easy questions. Yet they come with reasonable doubt. It might be reasonable, or not altogether unreasonable, to deny the existence of such Forms and thereby also the possibility of their being empty. One could object, for example, that things that do not exist do not have Forms, and further, that things that are extinct are, in fact, things that do not exist. This is not an untenable position even if there is a case to be made for the contrary view that a Form does not cease to exist just because its contents or participants do.

At the opposite end from the simple scenarios, the questions are still not difficult, just more complex, and perhaps a bit contrived. The same ambiguity awaits there. The scenarios become enigmatic as their specifications begin to stretch the imagination, as in the polygon that has too many sides, or the state that is run too well, or the object that is moving too fast. In each case, the excess is to an unworkable extreme: the chiliagon is supposed to have too many sides to imagine, the ideal state, too much justice to realize, the superluminal starship, too great a speed to subsist (retain mass and remain coherent). The common problem here is the notion of a Form that cannot possibly or conceivably be instantiated. The answers are easy here as well: The corresponding Forms, if any, will surely be empty. Yet it is not clear that there would be any Forms answering to these descriptions. Even if such Forms cannot possibly be instantiated, one could, for much the same reason, deny not just the instantiations but also the Forms themselves, especially if one is committed to keeping the discussion focused on Plato's Forms as opposed to universals from a modern perspective.

The ideal state stands as something of an anomaly among the examples considered. It seems to defy the ambiguity attributed to the others. For example, it is difficult to place the ideal state in the same category as either the chiliagon or the starship traveling at warp speed. (90) While we may be unable to decide whether chiliagons and superluminal starships lack Forms or have Forms that lack instantiations, the evidentiary context precludes the first alternative in the case of the ideal state. We could even dismiss the other two examples as irrelevant from Plato's perspective, but the ideal state is among his fondest interests. It would be almost heresy to deny that Plato would countenance a Form for it. As a matter of fact, he appears to be doing just that at the end of the ninth book of the Republic (592a-b), as Maula (1967: 35) and Vlastos (1969: 301) remind us. And the Form for this ideal state would have to be empty (for the same reason that the Forms in the other two examples would be empty if they existed).

If this is the proper reading of the related exchange between Socrates and Glaucon on the ideal state, we would seem finally to have an answer to whether Plato had a specific position on empty Forms. He evidently did, openly embracing that possibility. But the evidence is not as conclusive as it may seem upon initial inspection. Heresy becomes appealing here, perhaps even compelling, as the assignment of a Form to the ideal state contradicts the simplicity and purity of Forms. As discussed above in connection with other combinations, the ideal state is a complex or derivative notion invoking not just statehood but also ideality (however defined), and accordingly, combining two Forms rather than exemplifying one, or else tampering with a proper Form to adduce an imposter redundant with the original.

This is akin to combining a type with a property where the property is not just one of countless accidental attributes imaginable but presumably also one that cannot possibly be realized. Various kinds and degrees of complexity may be accommodated, or at least debated, in contemporary discussions on universals, but Plato makes no allowance for this in Forms. Even if there is a Form for statehood, or perhaps especially so, there should not be a separate Form for the ideal state. (91) And it is patently counterintuitive for there to be a Form for the ideal state but none for statehood. Introducing a Form for the ideal state is like reserving a Form for the longest line, or the largest circle, or the greatest pleasure (not only in the sense that these are not instantiated in our phenomenal experience but also in the sense that the longest line is still a line, the largest circle, still a circle, the greatest pleasure, still a pleasure). None of them should have its own Form. Nor should the ideal state.

Yet there it is, the Form of the ideal state, tantalizing us at Republic 592b. There is no mention throughout the canonical corpus of any other superlative Forms redundant with their ordinary counterparts, but we have to make peace with the fact that there is mention of what looks very much like a bona fide Form earmarked for the conceptually redundant and phenomenally uninstantiable ideal state.

The complexity of that Form, however, if it really is one, is not the only consideration against taking it seriously as a Form. Another is the lack of dramatic support. A significant interpretive judgment on a major philosopher is best not indexed to a hasty generalization from a single passage in his intellectual output. What is even worse in this case is that the problem is not merely with the quantity of evidence but also, and more so, with the quality. It is dramatically discordant, and therefore philosophically disconcerting, that in our best evidence for a Form of the ideal state, there should be absolutely nothing of the irrepressible confidence typically reserved for Forms. The heavenly pattern for the ideal state is suggested only as an understated possibility, with both speakers expressly affirming no more than a likelihood (Republic 592b). The thrust of the passage is that we should strive to instantiate the ideal state no matter the odds. This can, if it must, be interpreted, against the grain of the relevant ontology, as a complex (combined, modified, or contaminated) Form that happens to be empty, but the ambivalence is hard to miss.

The standard dramatic template for discussing Forms is a spectacle with fanfare. Plato provides plenty of that elsewhere: "Do we say that there is such a thing as the Just itself, or not? We do say so, by Zeus" (Phaedo 65d). That is how it is done. That is how Plato introduces a Form. That is how he prepares his audience. The passionate endorsement in this exchange is motivated not by a special devotion to justice but by a general appreciation of Forms. We find the same spirited agreement where the question is about whether we shall say that there is such a thing as the equal itself: "Indeed we shall, by Zeus, said Simmias, most definitely" (Phaedo 74b). This overly theatrical combination of conviction and enthusiasm animates the customary confirmation for the existence of Forms. Simmias conditions us to expect it in all cases: "Nothing is so evident to me personally as that all such things must certainly exist, the Beautiful, the Good, and all those you mentioned just now" (Phaedo 77a). Yet the intensity is not there in the passage brought up by Maula and Vlastos as evidence of an empty Form for the ideal state: "But perhaps, I said, there is a model of it in heaven.... Probably so, he said" (Republic 592b). The evidence itself is still there. Despite the wooden delivery, it still counts as an apparent reference to empty Forms (ignoring the aberrant complexity of the notion of an ideal state). But it is difficult to recommend this as the final word on the matter.

The final word may well be the uncertainty whether what is missing is the instantiation or the Form itself. The lukewarm confirmation ending the ninth book of the Republic, if it really confirms empty Forms, also confirms that uncertainty. But independently of the question of textual evidence, the idea of a Form that cannot possibly or conceivably be instantiated is itself overelaborate. Uninstantiated universals may be common in thought experiments, but not all universals from our perspective are Forms from Plato's perspective. Only the important ones are. (92) And those without instances could hardly have been prominent enough for him to take notice. Plato may, if pressed, have to make room for some such entries in his ontology, but we cannot responsibly or rightfully lay them all at his door just because we detected something of an affinity in the case of the ideal state.

The real threat to dialectical progress here is that our failure to confirm a phenomenal manifestation for a Form undermines its existence even if it also supports its emptiness. A mitigating factor is that it does not do so equally well. This presents an opportunity to resist the doubt, or to work with it or through it, even as it lingers as a possibility. The inherent ambiguity does not rest on a precise epistemic balance. The possibility that what is missing is the Form rather than the instantiation is merely a reasonable doubt, a nagging suspicion at most. It should keep reasonable persons from concluding with confidence that they have discovered empty Forms, but it need not keep them from pursuing the possibility.

The alternatives are not necessarily equally plausible. As indicated above, I am not in favor of disputing the existence of a Form just because its contents are emptied out or its participants are gone. There is no end to that train of thought. There might even be a slippery slope in there somewhere. To claim that the Form of mastodons is gone, just because the mastodons are, could be the first step toward the extreme result that Forms blink in and out of existence--not to mention undergoing fundamental constitutional changes (in contradiction of their supposed immutability)--to match the whimsical course of nature, including both the natural and the artificial phenomena and processes therein.

Granted, one could hold consistently that Forms do not exist at all before they are instantiated and that they cease to exist when they are no longer instantiated. This need not automatically degenerate

into a slippery slope. But the same ontological minimalist would then have to admit that Forms come back into existence upon reinstantiation, only to disappear again upon disinstantiation, thus revealing a radical metaphysical dependence of Forms on sensible phenomena. What is wanted, in contrast, is an answer to whether ontologically independent Forms can be empty and whether they ever are.

It would appear that they can be and that they sometimes are. Yes, the mastodons are gone, but it is not as if they never existed. Why not mark that difference with an empty Form? Yes, the chiliagon seems too intricately nuanced to draw or imagine, but it is not as if it were not a proper mathematical object. Why not honor that distinction with an empty Form? And perhaps we are not having much luck thinking or willing objects into motion, but it is not as if the possibility were unimaginable. Why not allow an empty Form for psychokinesis? These may or may not be Forms, but if they are, they could easily be empty ones.

On the other hand, we should not have to assent to a Form, empty or otherwise, for everything we encounter through fantasy or science fiction. Perhaps we need to answer the question of empty Forms on a case-by-case basis, especially so if we are to stick with what Plato himself would have thought. As we try, it is ultimately more important that we agree on what the question is so that we may come together on where the problem is--and ultimately on what the answer is.

5. Conclusion

The overarching aim of this paper has been to enrich the current understanding of Formless things and empty Forms in Plato. A guiding principle in the formulation and development of answers has been the clarification and refinement of the prevailing questions. There may be more to do in that regard. There always is. Yet the questions are now clear enough to adopt or reject the answers that have emerged in the process.

With respect to the question of Formless things, the answer starts with the Forms themselves. Sorting out the characteristics and implications of a thing without a Form requires reconsidering what Plato takes to be a Form and reclassifying the various constructs we have been in the habit of associating indiscriminately with his philosophical vision for Forms. They exhibit essential differences, and that, in turn, makes a difference in whether they are all the same sort of thing. No answer to the question of Formless things can be right if what we take to be Forms is wrong. Any sensible answer must accommodate pertinent differences.

The ontology attributed to Plato in this paper constitutes such an answer (cf. Alican and Thesleff, 2013; Alican, 2014, 2015). The basic profile is one of metaphysical monism in a solitary two-level world with three types of Forms--Ideal Forms, Conceptual Forms, and Relational Forms (Alican and Thesleff, 2013: 21, 26-38, 43; Alican, 2014: 26-29, 34-44)--all in the upper level of reality. What is true of one type could but need not be true of the other.

This classification not only helps clarify the question of Formless things but also provides an answer to that question. The answer is that there is an Ideal Form for everything corresponding to that definition, a Conceptual Form for everything corresponding to that definition, and a Relational Form for everything corresponding to that definition. Hence, the answer depends on what is meant by "Form": If these are all Forms, then yes, there is a Form for everything. If they are not, if only Ideal Forms count, then no, there is not a Form for everything.

This answer has the additional advantage of making holistic sense (both dramatically and philosophically) of the conflict between the main characters of the Parmenides (as well as the internal conflict of the protagonist there) on whether there is a Form for everything. It does this by explaining how Plato could be content to leave us with a protagonist associating Forms only with things that matter against an antagonist requiring a Form for everything: Not everything merits an Ideal Form, but anything that lacks this type of Form can instead be classified under Conceptual Forms or Relational Forms.

The dialogues jointly accommodate all three categories of Forms, and this suggests that everything, no matter how trivial, might have a Form in some sense or other. The implication for Formless things is that there are none, that is, that there is nothing--at least among the actual examples we encounter in the dialogues, though not necessarily among examples we might be able to conjure up--that cannot be associated with one of the three types of Forms identified here. This, we must keep in mind, is not a demonstrable solution, or verifiable observation, but a "proposal" for consideration, a label of caution employed from the outset (Alican and Thesleff, 2013: 11) to acknowledge the absence of conclusive evidence and the presence of competing alternatives (also without conclusive evidence). (93)

Note that the tripartite classification here allows but does not require everything to have a Form (in some sense or other). There might conceivably be abstractions remaining at the level of concepts (the lower level of reality) and not quite making it to the level of Forms (the upper level of reality). Hence, the solution espoused here does not strictly rule out Formless things, as the flexibility it introduces into the conception and discussion of Forms supports the possibility, but not the necessity, of a Form for everything.

This is not an oversight but insight, recognizing as it does that reification is entirely a matter of value assignments by Plato (Alican and Thesleff, 2013: 29-33, 44; Alican, 2014: 51-52). Even if hair and mud and dirt, for example, have Conceptual Forms corresponding to them, there might yet be things, perhaps even more trivial than these, that do not have any Forms whatsoever corresponding to them. This is neither to affirm nor to deny that hair and mud and dirt have Conceptual Forms: They could, and they might, but they do not have to. Both possibilities remain open. This is not a bad thing. But neither is further deliberation. We can try for greater certainty and broader agreement. That would require combing through the dialogues to identify all the actual value assignments by Plato, which, however, would be to flesh out the details of the answer already given here rather than to reject it in its essentials.

In the meantime, a good reason for preferring this solution over the traditional alternative of a homogeneous collection of Forms representing the same thing in every context is that it makes Plato a more interesting and resourceful philosopher without giving up anything to be gained by adopting the alternative instead. The solution advocated would be more compelling if we could be assured categorically that it was Plato's considered opinion instead of a reconstruction consistent with the evidence. But this is no reason to reject and no excuse to ignore the possibility. Any lack of certainty here is no greater than the prior, and indeed primary, one regarding what Plato thought about the existence and essence of Forms. Did he ever think they are real, and if so, did he always think so? If we can live with the uncertainty there, we should be able to survive the one in the tripartite classification of Forms and in the implications of that for (and against) Formless things.

Comparable gains can be claimed for the section on empty Forms. There, too, the clarification process moves the discussion forward, exposing and establishing solution prospects that seem plausible: that the Form of mastodons, given that there are no longer any mastodons, is demonstrably empty; that the Form of unicorns, given that there have never been any unicorns, is assuredly empty; that the Form of the chiliagon, given that it has too many sides to distinguish it from a circle, is apparently empty; that the Form (if allowed) of the ideal state, given that it is too good to be true, is regrettably empty; that the Form of the superluminal starship, given that no such speed can be attained, is evidently empty; and so on with any examples I may have overlooked or any that may yet come up.

These answers are only provisional. But they collectively point to one that is conclusive: Empty Forms, as it turns out, are empty either because of a phenomenal contingency, as in the case of mastodons, unicorns, and faster-than-light travel, or because of a conceptual difficulty, as in several of the other examples. The first gives us contingently empty Forms, the second, necessarily empty Forms. (94) Between Forms whose phenomenal manifestations have been destroyed or inhibited (and are therefore circumstantially empty) and those that cannot possibly or conceivably be instantiated (and are therefore categorically empty), there are no Forms that just are empty, in other words, empty despite the absence of external restrictions (physical, metaphysical, or logical) dictating such a vacancy.

The last reference is as difficult to verbalize as its referent is to visualize. A Form that is empty without reason, call it a "naturally empty Form" just to give it a name, would probably have to be something like the Form of beauty if it were never instantiated, not because of a practical or conceptual problem, such as the destruction of all things beautiful, but simply because nothing ever happens to instantiate it, as might be the case if nothing at all were ever beautiful. Naturally empty Forms, in contrast to contingently empty Forms and necessarily empty Forms, would be empty by design yet for no reason (other than the absence of instantiation). A better name for them might be "inherently empty Forms" (or perhaps even "mysteriously" or "surprisingly" or "inexplicably" empty Forms). There are no such Forms. If there are any empty Forms, not one of them is like that. (95)

This takes the mystery out of the puzzle. The rest are perfectly reasonable answers, though arguably not as exciting as they are reasonable, and perhaps even a little frustrating. It is not very interesting, for example, that the Form of mastodons is now empty, or that the Form of unicorns will always be empty unless we engineer the unicorns, or that the Form of faster-than-light travel must be empty if we are reading the universe right. It is also not particularly exciting that all Forms (perhaps with exceptions) were empty before there was anything other than Forms and a lone demiurge. As for the impossible or inconceivable instantiations, they may be more interesting, but the rigidity of the scenarios leaves no room for discussion. And all cases come with the nagging uncertainty whether what is precluded is the instantiation or the Form itself. Yet uncertainty hardly ever keeps philosophy from being worthwhile. It is probably just the opposite. And that explains any frustration that may accompany the uncertainty. Not every answer has to be exciting. All that matters is that it be right. We have to follow where reason dictates. And this is where it leads us in this case.

Perhaps we want to know something more than whether a Form that does not happen to be instantiated, or one that cannot be instantiated, is or is not instantiated. It just so happens that there is nothing more. Either kind, if it exists, is indubitably not instantiated, and is therefore empty. That is the extent of the problem. The question is not even meaningful outside the context of Forms that used to be empty, those that have been emptied out, and those that have to be empty. The answer, then, is that there can be contingently empty Forms and necessarily empty Forms but not naturally empty Forms (the elusive hypothetical correlate of a Form that is, for example, just like the Form of beauty, except that, for no reason at all, it never happens to be instantiated).

This answer is only about the possibility. It points to Forms that would be empty if they existed, but it does not, in addition, show that there are such Forms. The question whether there are empty Forms turns ultimately on whether we are prepared (with good reason) to accept or reject the Forms that would in fact be empty if they existed, or more to the point, it depends on whether Plato would accept or reject them.

Neither any lingering hesitation nor the inherent uncertainty, however, diminishes the progress made through the clarification process carried out in the corresponding sections and through the conclusions drawn on that basis. Although these question, like any others, would benefit from further thought, any initiative toward that end will be more likely to build upon the present one than to tear it down.

Acknowledgment

I am grateful to Debra Nails, Nicholas D. Smith, and Holger Thesleff for their comments on earlier drafts of this paper.

NOTES

(1.) Quotations are, except where noted otherwise, from the Hackett edition of Plato's complete works (Plato, 1997) and the revised Oxford translation of Aristotle's complete works (Aristotle, 1984).

(2.) Given that Forms are also things (at least in the sense that a Form is something rather than nothing), the reference here (as elsewhere in the paper) is to Forms and other things, specifically to Forms and the things of which they are Forms: Forms and particulars, Forms and sensible phenomena, Forms and their instantiations, and so on.

(3.) A brief discussion of the symmetry between Forms and things is available in Alican (2012: 103-104, cf. 87-110, 110-129). Relevant personal contributions also include an analysis and classification of Forms in Alican and Thesleff (2013), a follow-up to this in Alican (2014), and a psychological assessment of Plato's ontology in Alican (2015).

(4.) Imperfect metaphors abound: Another is that of a pillow. Both the casing and the filling can exist without the other, but a pillowcase stuffed with filler becomes something more than the sum of those two things taken severally, more so than might reasonably be said of the wind in my hair or the keys in my pocket. Are Forms and particulars like that in any way: Do they make an ontological pillow, or flow, perhaps, like a metaphysical river? Yet another example might be that of a fertilized egg, where the dynamics of the combination may be even more evident, with the sperm fertilizing the ovum as part of the reproductive process. Might that be analogous, then, to how Forms and particulars account for reality? Or are the constituents of Plato's world more like the hydrogen and oxygen that would still be real and abundant even if they were never to combine to make water?

(5.) This is a loose translation of Kant's famous maxim: "Gedanken ohne Inhalt sind leer, Anschauungen ohne Begriffe sind blind" (KrV A51/B75). The standard translation is: "Thoughts without content are empty, intuitions without concepts are blind" (cf. Kemp Smith; Pluhar; Guyer and Wood). Taylor comes closer to the liberal translation above but reverses it in proposing that "the theory [of Forms] does full justice to both parts of the Kantian dictum that 'percepts without concepts are blind, concepts without percepts are empty'" (1926: 188).

(6.) Taylor takes a firm stand on this in a footnote to the passage cited above: "there are no 'forms' except those which sense-experience suggests, or, to use the language which will meet us later in the dialogue [Phaedo], there are no 'forms' which are not 'participated in' by sensible particulars" (1926: 188, n. 1). This is an extension of his longstanding conviction that "Plato's fundamental problem is essentially identical with that of Kant in the Critique of Pure Reason" (1908: 37).

(7.) On the question of things without Forms, the literature reveals a broad spectrum of positions. Nehamas (1973: 461-491, especially 463; 1975: 108-109), Patterson (1985a: 123-129), and Sedley (2013: 113-137), to name a few, are open to Formless things in Plato. Cherniss (1944: 240-260, especially 244), Ross (1951: 24, 79), and Vlastos (1969: 301), in contrast, deny that Plato has any room for them. Broadie (2007: 232-253) and Fine (1993: 81-88, 97-102, 110-116), remaining sensitive to both sides, each offer an assessment of the conflict between evidence in Plato and testimony by Aristotle, particularly in regard to Forms for artifacts (the rejection of which would mean the acceptance of Formless things). As for the question of Forms without things, the prevailing perspectives tend to be more polarized, with little orientation toward anything between adoption and opposition. Proponents of empty Forms include Fine (1984: 74-85), Maula (1967: 12-50), and Vlastos (1969: 301). Opponents of empty Forms include Crombie (1963: 153-246), Lovejoy (1936: 45-55), and Rohr (1978: 268-283 [= 1981: 19-56]).

(8.) The leading issues are the separation of Forms from particulars (e.g., Fine, 1984, 1985; Morrison, 1985a, 1985b; Vlastos, 1987) and the immanence of Forms in particulars (e.g., Dancy, 1991: 9-23, 53-56; Fine, 1986; Matthen, 1984), questions that are also discussed in conjunction (e.g., Devereux, 1994; Perl, 1999; Rist, 1964).

(9.) The principal source is a collaboration: Alican and Thesleff (2013). Some of these ideas originate in rudimentary form in Thesleff's earlier work (1989: 4, n. 14, 14, n. 45, 24-25; 1993a: 17-45; 1999 [= 2009: 383-506]). My subsequent publications on the topic include Alican (2014) and Alican (2015). None of this is required reading for following the discussion in this paper. The point is not to classify Plato's Forms as I do but to take stock of their essential differences as Plato does. We may not be able to agree on exactly how he does this, but we should be able to agree that he does it. That is all the common ground required.

(10.) To illustrate: The Form of poetry, if there is such a Form, must have been empty before we started expressing ourselves in verse, and would be so again if we gave it up. But the Form of resurrection, if there is such a Form, seems to be empty now, and would have to remain so if raising the dead continued to be unworkable.

(11.) The traditional interpretation assigns two separate worlds to this dualism, often (but not always) drawing on the testimony of Aristotle (Metaphysics 987b1-13, 1028b19-21, 1078b12-17, 1078b30-32, 1086a30-b11). Allen, among others, illustrates the traditional perspective, giving a concise overview in one work (1970: 149-154) and referring explicitly to a "doctrine of two worlds" in another (1997: 115). Thesleff (1999 [= 2009: 383-506]), Alican and Thesleff (2013: 14-17, 17-19), and Alican (2014: 29-34; 2015: 307-324) reduce this dualism to two "levels" in one world. Nails (2013: 78-87) regards the division into two worlds as dogma, and rejects it, though not necessarily endorsing Thesleff or Alican in the process. Smith (2000, 2012) focuses on the epistemology rather than ontology of the problem.

(12.) This phenomenon or process, anamnesis ([phrase omitted]), is sometimes interpreted as the activation of an intellectual capacity--for "inference" in Allen (1959: 167), for "abstraction" in Schumacher (2010) expanding on Helmig (2004)--as opposed to the recollection of specific Forms. The Phaedo (72e-77a) has hardly any room for an alternative interpretation of this sort, especially not as a competing (either/or) alternative, but the Meno (81a-86c) does seem open to it. The Phaedrus (249b-c, 250a-b) can go either way.

(13.) The preceding details of the relationship between Forms and particulars are meant to be representative rather than exhaustive. A relatively recent example of an account that goes further toward exhausting the relevant details is the analysis of Rickless (2007), employing a rich set of axioms, auxiliaries, and theorems (pp. 10-52; summarized: pp. xxii-xiv; flowchart: p. xv) in a reconstruction of the argument(s) of the Parmenides (pp. 112-250).

(14.) This is because the rule is silent on whether there are things (a multitude of things with a common name) for each Form and possibly equivocal on whether the formula of one Form for each multitude is an ontological commitment (one rather than none) or a mathematical affirmation (exactly one and not any other number) or a qualitative emphasis on the importance of identifying what is common and peculiar to each kind.

(15.) A case in point is the reference to "our perpetual claim that there exists an intelligible Form for each thing" (Timaeus 51c). See also: Parmenides 130d-e, 135a-c; Republic 507b. Cherniss (1944: 244) adds several other examples. These are all partial expressions of what has traditionally been called (first by Aristotle, e.g., in Metaphysics 990b13, 1079a9) the One-over-Many Argument (of which there is no full expression in Plato, except arguably at Parmenides 132a and Republic 475e-476a). They are, more accurately, instances of a One-over-Many Principle. Commentary is endless: Fine (1980: 197-240; 1993: 103-119), Matthews and Cohen (1968: 630-655), and Sedley (2013: 113-137) are a few examples.

(16.) The interpretation of the general formula of one Form for each multitude (Republic 596a) as a limiting condition finds credence in the subsequent discussion of why there can be at most a single Form for bed (596b, 597c-d). Among those who favor this reading, see Annas (2003: 86), who claims not merely that this is what is meant but also that this is what is said. She takes the more common rendition positing an unrestricted range of Forms to be a mistranslation. Harte (2008: 200) agrees that the passage need not be translated with an unrestricted range of Forms (but not strictly that it must not be so), presenting an alternative (actually reviving an old one) that has no bearing upon the range of Forms: "for we are, as you know, in the habit of assuming [as a rule of procedure] that the Idea which corresponds to a group of particulars, each to each, is always one, in which case [or, and in that case] we call the group of particulars by a common name" (Smith, 1917: 70; original brackets). Sharma (2006: 27-32) rejects the alternative in Smith and recommends the earlier (and still current) translation suggested in Adam's note to 596a5: "for we are, as you know, in the habit of assuming a certain idea--always one idea--in connexion with each group of particulars to which we apply the same name: lit. 'an Idea, one each' i.e. each being one" (Adam, 1902: ad loc.).

(17.) Patterson (1985a: 117-145) suspects a broader connection in context between Forms and nature (expanding thereby on what it means to be "in nature" and including therein what it means to serve a "natural end") than a restriction to natural kinds. On this interpretation, even the Form of bed (couch) can be said to be "in nature" (1985a: 123-124, cf. 125-126), though Patterson reminds us that the example might be playful (126).

(18.) As is often possible and frequently done, it might conceivably, though here somewhat unreasonably, be objected that Aristotle is talking about Plato in one case and Platonists in the other. This can be especially problematic when the collective reference to Platonists is understood to exclude Plato. In this case, however, the reference to Plato is beyond question in the first passage and hard to deny in the second (where Plato is mentioned by name just before and just after the relevant portion). Fine warns that the reference to Plato may not be beyond question even in the first passage, though she personally finds it reasonable to include Plato in that reference (1993: 289-290, n. 11 to p. 83).

(19.) Fine (1993: 83-85, cf. 85-88) and Broadie (2007: 232-235) may be consulted profitably for further discussion of these two examples (houses and rings). With some reservations, they both take the examples to support the interpretation of Aristotle as reporting Plato to have rejected Forms for artifacts.

(20.) This is for the sake of parallel construction with the preceding parenthetical question. A more perspicuous way of asking the same thing may be: Must each Form correspond to something, that is, as per the rule of the Republic (596a), to some multitude of things with a common name?

(21.) If we are meant to extrapolate from here, the only thing we have to go by, other than our own intuition, is the characterization of these things as trivial (Parmenides 130c), from which we may, if we are so inclined, conclude with Socrates the character (though not with the blessing of the other characters) that trivial things ("undignified" and "worthless" things) do not have Forms.

(22.) Other candidates include man and fire and water (Parmenides 130c), which may or may not have Forms, depending on whether and how Socrates the character resolves his ambivalence in that regard. Man comes up again at Philebus 15a without any apparent ambivalence, and the hesitation regarding fire and water is evidently gone in the Timaeus, unmistakably so for fire at 51b (cf. Phaedo 103c-d, 105a, 105c, 106a-c). But hair and mud and dirt, in contrast, are ruled out with certainty (Parmenides 130d), even if that certainty (ironically?) comes with doubt, as Socrates questions the consequent coherence of the general position on Forms.

(23.) In fact, evidence to the contrary, which is to say, evidence against hair and mud and dirt as serious exceptions, starts to accumulate, as Parmenides, in the briefest of passages (Parmenides 135a-c, anticipated at 133c), thrice attributes a Form to each thing: "Only a very gifted man can come to know that for each thing there is some kind, a being itself by itself" (135a-b); "a form for each one" (135b); "for each thing there is a character that is always the same" (135b-c). Further discrepancies await outside this dialogue, where we encounter Forms for other things that seem trivial, especially in contrast to justice and beauty and goodness, though perhaps not in comparison with hair or mud or dirt: e.g., bed and table (Republic 596b, 597c-d); shuttle, awl, and tools in general (Cratylus 389a-d). Yet none of these would count as "undignified" or "worthless," which seems to be required for rejection (but not for hesitation).

(24.) The difficulty has only recently become a "usual" one. It does not trouble, for example, Diogenes Laertius (3.52), who identifies four mouthpieces for Plato: Socrates; Timaeus; the Athenian Stranger; the Eleatic Stranger. For critical perspectives, however, there is no better place to start than the collection of essays edited by Press (2000). Thesleff (1993b: 259-266; 1999: 6 [= 2009: 392]; 2000: 53-66) is a good example of interpretations taking the drama itself as speaking for Plato--as opposed to affirming or denying that the task is assigned to this or that particular character.

(25.) I am neither endorsing nor rejecting Patterson's (1985a) understanding of natural kinds. I am merely reporting what he, in this one case, counts among natural kinds (hair, mud, dirt).

(26.) More accurately, there appears to be nothing in Plato, save for a muted allusion to a Form for the ideal state (Republic 592b). The significance of that reference, together with the strength of the evidence it constitutes, is discussed in section 4 below, initially around the middle of the section but mostly toward the end. There seems to be nothing else. I could have missed something. But others would have caught it. See, for example, Perl (1999: 351): "Nowhere in the dialogues does Plato mention any uninstantiated forms, or even suggest that there could be such forms." A possible exception to the absence of evidence, in fact, a somewhat popular one, is the tendency, as in Rickless (2007: 20, n. 12), to take evidence for or against the separation of Forms as evidence for or against empty Forms. This is not to say that Rickless confuses the two cases, or the evidence for them, but that he finds the evidence in one case relevant to efforts to judge the other. In contrast, I side with Silverman (2002: 19), who divorces the two issues, including the evidence for them. This is also consistent with Fine (1984), whose interest in empty Forms is grounded in and limited by her interest in separation. The extent of the connection she makes between the two is that instantiation does not undermine separation, and, conversely, that the absence of instantiation is sufficient but not necessary for separation (1984: 44, 74).

(27.) The point here is not that we ought to judge the issue entirely on the merits of a short stretch of dialogue in the Parmenides (130a-e) but that the passage in question is rich enough (especially in combination with 135a-c, though also without it) to contradict whatever position one might take, including any other relevant evidence throughout the corpus.

(28.) See Alican and Thesleff (2013) for the original theory presenting Plato as a metaphysical monist working with various different types of Forms in a single world, Alican (2014) for elaboration both on Plato's monism and on Plato's classification of Forms, and Alican (2015) for further thoughts on just the monism.

(29.) The rationale for the classification as well as the salient features of the individual categories are laid out in Alican and Thesleff (2013: 11-47, especially 21, 43) and scrutinized further in Alican (2014: 25-55, especially 26-29, 34-44).

(30.) The characterization of Forms as "entities," with a parenthetical reference to "constructs," or any such explanation with the opposite arrangement, reflects the role of perspective. The Forms are entities if Plato discovered them, constructs if he invented them. From Plato's perspective, they are, of course, entities. This need not, however, be our view as well. A stand on this is best not taken in silence. I refrain from taking one in the passage to which this note refers and in the rest of the paper.

(31.) These are just a few examples. They can be multiplied indefinitely, as attempted in Alican and Thesleff (2013). Note in general that Plato does not give us an Ideal Form with every eidos ([phrase omitted]) or idea ([phrase omitted]), whereas he gives us nothing but that with auto kath' hauto ([phrase omitted]). This is substantiated through arguments and citations in Alican and Thesleff (2013: 23-26); cf Thesleff (1999: 53-61, 113 [= 2009: 437-445, 494]). On matters of terminology, Greek or English, see also Baldry (1934: 141-150), Else (1936: 17-55), and Taylor (1911: 178-267). For a more recent perspective, see Ademollo (2013: 41-85, especially 56-69).

(32.) Nothing short of a full reconstruction will be as informative as the original account (Alican and Thesleff, 2013). But a few details may help orient readers even without consulting the original: First, Ideal Forms (2013: 26-29) concern intrinsic value of any kind, without restriction to a specific category (moral, aesthetic, religious, etc.), thus including anything valuable in itself, whereby knowledge (Phaedo 68a-b; Phaedrus 247d; Parmenides 134a-e), for example, qualifies no less than justice or beauty or piety. Second, Conceptual Forms (2013: 29-34) cover types (including but not limited to natural kinds) and properties, but they also include other abstract phenomena, such as events, actions, and experiences. Third, Relational Forms (2013: 35-38, especially n. 54) are not pairs of Conceptual Forms that happen to demonstrate some sort of opposition relation but basic ontological categories collectively constituting a cosmic blueprint of reality. The contrast between the paired elements (rest/change, same/different, etc.) in Relational Forms points to a productive tension, an explanatory vision, as opposed to a logical contradiction or polar opposition. Alican and Thesleff, together and separately, avoid speaking of "opposites" in this context, preferring instead to refer to "contrasts," correlative albeit asymmetrical ones (one dominating the other).

(33.) To illustrate the difference (with respect to one of these categories), an Ideal Form is not just a paradigm of value but also an ontologically independent noetic reality constituting the very value (itself-by-itself) only imperfectly instantiated in our experience. The same difference, or something comparable, holds for the other two categories as well. The distinction is for our benefit: The Form of justice (the just itself-by-itself), for example, is something more than the concept of justice, but this is probably not a distinction to be taken up with Plato, who was busy at the time with the more basic distinction between justice and things that are just.

(34.) This is to say neither that we now have a common understanding of concepts and universals nor that concepts and universals are the same thing. I suggest only that Plato took abstraction more seriously than we do today. He was more excited about it, and this is perhaps why he seems to have found a greater reality in it than we tend to do. The difference between Forms and mere concepts (or mere abstractions) is not something Plato discusses, but it may still be possible to say something about it without being anachronistic: See Alican and Thesleff (2013: 29-33, 44) and Alican (2014: 44-52).

(35.) Other features include, but are not limited to, transcendence, intelligibility, para-digmaticity, perfection, immutability, simplicity, and uniqueness (Alican and Thesleff, 2013: 27-28, including nn. 33, 34; Alican, 2014: 35-38, 45-46; Alican, 2015: 322, n. 14). These are attributes of Ideal Forms (Alican and Thesleff, 2013: 26-29), though the other two types of Forms can mimic, exhibit, and eventually possess the same features (one or more or all of them) as they approximate to Ideal Forms through a process of "ontological ascent" (2013: 22, n. 21, 29-33, 42, 43-44). This is a term Thesleff and I introduced in recognition of the fluid boundaries between the three different types of Forms in terms of qualities we associate categorically with Ideal Forms but acknowledge in the other two types as well (cf. Alican, 2014: 29, 36-37, 45-46, 50-51; Alican, 2015: 322). The seven characteristics listed above (and intended to be representative of features commonly associated in the literature with all Forms) are found invariably in Ideal Forms but only arbitrarily in either of the other two types, which can, though need not, come to resemble Ideal Forms in all the relevant ways except for the possession of intrinsic value. The process, or phenomenon, of ontological ascent is thus one of approximation. The ascent in question is not so much about the Forms themselves as it is about Plato's outlook on them. This is because the dynamics of formalization and reification (the emergence of Forms from among the ranks of what are now considered concepts or universals) are a matter of value assignments by Plato, making it inevitable that ontological ascent should also proceed in conformity with such assignments, which is why Conceptual Forms or Relational Forms (especially the dominant element in Relational Forms) tend to resemble Ideal Forms in proportion to Plato's interest in them (in the ones doing the resembling). The significance of these value assignments, that is, the relationship between what Plato found interesting and what he identified as Forms, comes up again below, both in the main text and in corresponding notes, but for a sustained discussion, which is not necessary to follow anything here, see: Alican and Thesleff (2013: 29-33, 44) and Alican (2014: 44-51, 51-52). One example would be how equality, a Conceptual Form, seems to be on a par with beauty, an Ideal Form, in terms of features indicative of ontological eminence (cf. Alican, 2014: 36, 45-46), whereas bedness (the Form of bed) or shuttlehood (the Form of shuttle), also Conceptual Forms, are dwarfed in comparison.

(36.) The corresponding ontology is in Alican and Thesleff (2013: 14-17, 17-19), with critical elaboration in Alican (2014: 29-34) and a broad reassessment in Alican (2015: 307-324). My independent efforts are constructive rather than corrective. Any development is in the spirit of confirmation and explication as opposed to modification. The rudiments of the basic framework can be traced back to Thesleff (1993a: 17-45; 1999 [= 2009: 383-506]).

(37.) The key to understanding Plato's ontology in Alican and Thesleff (2013) is neither the distinction between Forms and particulars nor the division of Forms into three categories but the two-level vision of Plato. The Forms certainly have a place in that vision, but they are defined by it rather than defining it.

(38.) The analogy originates in Thesleff (1999: 453-455 [= 2009: 70-72]) and continues to appear in Alican and Thesleff (2013: 18-19, 22-23) and in Alican (2014: 33-34).

(39.) This is an essential difference (a difference belonging to the essence of the objects of comparison, essential as against accidental) persisting even through the process of ontological ascent whereby the other two types of Forms may otherwise approximate to Ideal Forms.

(40.) This is a question neither Thesleff nor I have answered directly, whether in collaboration (Alican and Thesleff, 2013) or in independent studies (Alican, 2014, 2015), primarily because we find the three categories similar enough to be categories of some one thing (as opposed to being altogether different things) and different enough to be categories of that thing (as opposed to being uniform examples of it). If nothing else, these categories are similar and different enough that they collectively exhaust what has long been understood as Forms without distinction (as in the distinction between, say, justice and beauty and goodness, on the one hand, and hair and mud and dirt, on the other).

(41.) Thesleff alone, especially in his earlier work, can alternatively be read as rejecting Forms for artifacts, where he describes the familiar examples of the bed (Republic 596b, 597c-d) and the shuttle (Cratylus 389a-b) as playful scenarios (1999: 63-65, 71-73 [= 2009: 447-448, 454-455]). But this would be misleading. It is important to keep up with Thesleff's terminology to do justice to his views: He initially rejects artifacts as "Ideas" but not as "Forms" (Thesleff, 1999: 112-113 [= 2009: 493-494]), whereas he later rejects artifacts as "Ideal Forms" but not as "Conceptual Forms" (Alican and Thesleff, 2013: 11-47, cf. 26, n. 31).

(42.) The connection between Plato's predilections and Plato's Forms is discussed in Alican and Thesleff (2013: 29-33, 44) and in Alican (2014: 51-52), with evidence and arguments linking what Plato finds important or interesting with what he takes to have Forms.

(43.) Hair and mud and dirt (Parmenides 130c-d), for example, may arguably represent a halfway category of this sort. Or they might be Conceptual Forms. The difference is not cut and dried.

(44.) See the discussion of "conceptualization and formalization" (reification) in Alican and Thesleff (2013: 29-33) and of the "continuum of abstraction" in Alican (2014: 44-52).

(45.) Any guide or companion to Plato, or even to Greek philosophy in general, will note, usually without endorsement or objection, the significance of the Parmenides as a possible turning point in the development of Plato's thought, particularly in regard to the Forms. Examples at random include (the first three volumes I consulted to test this pedagogical hypothesis): Benson (2006: 180-182, 184, cf. 184-198); Kraut (1992: 14); Shields (2003: 90).

(46.) This does not prove developmentalism wrong. Nor is that the intention. I am merely pointing out an alignment between the present perspective and one possible alternative to developmentalism, mainly for the benefit of readers who may already have an interest in the methodological analogy of the Platonic corpus at large as a dramatic unit of sorts. This is neither a refutation of developmentalism nor a proof of the alternative. The reason I avoid formal opposition here, even though I do indeed have reservations regarding developmentalism, is to acknowledge the complexity of the matter as an ongoing scholarly controversy, which I do not presume to be resolving in passing.

(47.) No effort to reconstruct the dramatic order of the dialogues can do without the prosopography of Nails (2002: see especially 307-330, 357-367). While her prosopography does not say what to do with any such reconstruction, thus remaining silent on the plausibility and merits of reading the Platonic corpus as a dramatic unit in and of itself, Nails herself does oppose developmentalism, at least the developmentalism of Vlastos, in a separate work (Nails, 1993). A good example of what to do with comparable dramatic details, especially in regard to whether they can be strung together for meaningful insight into the corpus as a whole, is Zuckert (2009: see 1-19 for an overview). A useful tabular presentation of the dramatic chronology of the dialogues is available in Press (2007: 72-73).

(48.) Zuckert (2009: 11) makes a good case for locating the youngest dramatic Socrates in the Laws rather than in the Parmenides. But even if she is right in her relative dating of the dramatic settings of the two dialogues, the author of the Parmenides goes out of his way to emphasize the youthfulness of the character Socrates, whose counterpart in the Laws receives no such attention.

(49.) An ageless Socrates would not have been possible to implement in the Phaedo, at least not without an entirely different plot, but replacing the young Socrates of the Parmenides with an ageless Socrates would have been sufficient to obscure the difference between the ages of the two protagonists.

(50.) Consider an analogy from popular culture: Batman looked to be about thirty-five years old when I was five. I have grown older. He has not. He still looks thirty-five as he thrills new generations with new adventures. Had I ever encountered a teenage Batman, or a geriatric Batman, I would have thought, even when I was five, that something out of the ordinary was going on.

(51.) We must keep in mind, as Nicholas D. Smith has reminded me through personal correspondence, that interpreting the Platonic corpus as a cohesive dramatic unit attributes a rather elaborate scheme to Plato, whose initiative would then have been conspicuous enough to merit mention both by his contemporaries and by his successors. The fact that no such report or discussion has come down to us presents a difficulty for the dramatic holism interpretation.

(52.) This scenario has no implications for the production order, as the dramatic alignment between the two dialogues can be achieved regardless of which one was composed before or after the other.

(53.) This is not to say that the Phaedo is free of doubt and uncertainty. Confidence is not certitude. Socrates exudes confidence even as he declares the arguments of the Phaedo fallible. Any doubt or hesitation in the Phaedo concerns the immortality of the soul, not the existence of the Forms. The uncertainty attached to the final argument (favored over the others) is purely technical: It is about the reliability of a conclusion based on a hypothesis (107a-b). What is to be challenged is not so much the immortality of the soul or the existence of the Forms as it is the soundness of inferring the former from the latter where the latter is nothing more than an unquestioned assumption. The soul may well be immortal and the Forms may well exist, but we cannot be sure that the former is established by the latter, until we conduct a separate inquiry into the latter. It is in this spirit that Socrates introduces the existence of the Forms as a grounding hypothesis (100a-b) for the final argument for personal immortality. The success of that argument depends ultimately on whether the Forms actually exist. Socrates fully admits this in the end (107b), having already stipulated that the hypothesis and the inference are not to be appraised together in one fell swoop (101d-e). This admission that the final argument must be studied further, so as to test the hypothesis itself, does not represent a lack of conviction. If anything, it shows confidence in the hypothesis. Socrates does not merely admit that the investigation could or should be continued. He insists that it must be continued, encouraging his interlocutors to make the effort (107b).

(54.) I am neither confirming nor denying evidence of development in Plato's lifelong experimentation with abstraction. Nor am I assuming or rejecting a correspondence between the classification scheme here and any developmental or stylometric periods (early--middle--late) in the production process of the Platonic corpus (cf. Alican and Thesleff, 2013: 14, n. 4). My divisions are not inferences from any particular order of composition for the dialogues even if they happen to coincide with such groupings.

(55.) The scarcity of evidence (in the Platonic corpus) on empty Forms does not translate into a further scarcity of evidence (in the Platonic corpus) on transcendence or immanence. There is an abundance of relevant dialectical progression in the Phaedo alone and certainly a plethora of evidence throughout the so-called middle dialogues. Yet none of it is sufficiently enlightening. We are all familiar with the equality beyond the sticks (the equal itself at Phaedo 74c1), the largeness in Simmias (Phaedo 102b5-6), and any number of other examples that illustrate transcendence and immanence without quite telling us how either one works. These, I trust, recall comparable examples without further citation. The Forms (specifically Ideal Forms), despite their transcendence, make themselves available at the edge of the cosmos where gods and souls (the disincarnate souls of philosophers) travel for a glimpse of their glory (Phaedrus 246e-249d). And immanence is what we are able to make of the same Forms and yet others in our attempt to apprehend them while we are still trapped in a physical body. The reason I move straight to Aristotle in what follows (before focusing on Plato) is not that Plato says nothing relevant about transcendence or immanence but that Plato makes no obvious commitments in regard to either one, or at least none that is strong enough to keep scholars from turning to Aristotle for his testimony regarding Plato's views. Aristotle may not cover everything missing in Plato, but whatever he does cover is free of hesitation to divulge what Plato keeps to himself.

(56.) Discussions in the Academy, as evidently shared in, say, the Parmenides, constitute an exception to initiation by Aristotle, as they indicate origination with Plato himself. While we cannot be certain Aristotle did not inspire or initiate these as well, what is meant in the passage above is that he seems to have initiated the secondary literature.

(57.) Going through Aristotle to reach Plato, even where necessary, can be messy, if only because it is not always clear whether Aristotle is talking about Plato or about Platonists in general. The two passages regularly invoked in connection with separation constitute a prime example (Metaphysics 1078b30-32, 1086a30-b11), as they refer to successors of Socrates, which may or may not be a reference to Plato. Sometimes, such passages become clearer in conjunction with those that refer to Plato by name (e.g., Metaphysics 987b1-13). When they do not, we are left with nothing more than what is in Plato. Nails (2013: 81-84) rightly emphasizes the importance of sorting out not just whether Aristotle is talking about Plato or Platonists but also whether he is talking about Socrates the philosopher or Socrates the Platonic character (see especially p. 83, including the footnotes).

(58.) Such metaphysical tension is clear in Aristotle and perhaps originates there. Fine attributes this to Aristotle's assumption that "universals cannot exist uninstantiated" (1984: 39, 45; 1986: 94-95).

(59.) As I am not trying to reconstruct Aristotle's position (on Plato's position), I do not feel compelled to explicate the results in terms of ontological or explanatory priority. Among those who do this well, see Cleary (1988), Corkum (2008), Fine (1984, 1985), and Morrison (1985a, 1985b). Here, ontological independence should suffice to capture the range between numerical distinctness and full transcendence.

(60.) Note that to place ontological independence in the middle is not to deny ontological independence in transcendence. What is intended for the middle here, by way of reviewing the possibilities, is ontological independence without transcendence.

(61.) This is just to fix the reference of the term, not to introduce a special definition to manipulate subsequent positions or arguments. A sense of separation that might fit between the two extremes of numerical distinctness and transcendence can be had with either existential or essential independence, or perhaps with something altogether different. I am open to alternatives.

(62.) Fine does it (1984: 33, 35, 43; 1993: 51, 268-269, n. 28). Corkum warns against it (2008: 76, n. 8). Fine's version is different from mine. Corkum would oppose both.

(63.) The difference in strength between instantiation and a shared property (one such property) is not clear. While it may be clear that they are not the same thing, it is not so clear why one should count as a weaker relationship than the other. My intuition is that sharing one property represents a stronger connection than sharing none at all, while falling short of instantiation, which, in turn, suggests a connection strong enough to tell that one thing is a manifestation of the other. I would be happy to defer to metaphysicians on this matter, and would, in fact, prefer to do so. All I am trying to do here is to visualize the ways in which separation may be combined with immanence and to determine whether this leaves room for empty Forms.

(64.) The resistance invoked here concerns possible perceptions rather than the mechanics of the model under discussion. What I am trying to do is not to coin a technical term ("path of least resistance") but to anticipate how (and how not) observers may be inclined to reconcile separation and immanence, which may seem less than maximally compatible both in the strongest form of each and in the weakest form of each, hence pointing to a path of least resistance in the combination of the strongest form of one with the weakest form of the other, or perhaps suggesting something in between the two extremes in either category.

(65.) I am not alone in this. McCabe (1994: 101, n. 6) and Silverman (2002: 13) also state that they take separation as transcendence in this context. Prior makes the same commitment without using the word "transcendence": "As I use the term, separation presupposes not only the numerical distinctness of the Form from its participants, its ontological independence and priority, but also the claim that the Form is not to be found in the phenomenal world" (1985: 49, n. 33). Perl uses both terms (or derivatives thereof) without personalizing his commitment like the others while still making his position clear: "As incorporeal, changeless, intelligible realities, the forms remain as transcendent to the world of physical, mutable, sensible things as the strongest proponent of separation could maintain" (1999: 361). Ademollo proposes outright to leave separation to Aristotle, focusing instead on transcendence (2013: 74-75). The fact that I am not alone, however, does not mean that I am unopposed, nor even that I am in the majority.

(66.) More to the point, I take Plato to take the Forms to be transcendent. What I mean by this is that he considers them objectively real but beyond sense perception, thus attributing to them an existence outside sensible phenomena. Yet "transcendence" can and often does take on different meanings even when the context is restricted to Plato. See, for example, the overview in Ademollo (2013: 74-83). Here, I am thinking specifically of the first sense (A) Ademollo considers, though I might be on board with a combination of his A (p. 75) and B2 (p. 83), so long as nothing there is understood as a commitment to a separate world for the Forms.

(67.) A Form's immanence means nothing to me beyond its instantiation. Elsewhere (Alican, 2014: 39-44), I deny immanence but not instantiation. The two positions are consistent. Instantiation is not in either case anything more than a phenomenal reminder of the relevant Form. The immanence denied, on the other hand, is the phenomenal presence of the Form itself. I am always open to immanence as instantiation in a representational sense that does not compromise transcendence. This, however, is not directly relevant to the question of empty Forms, which is not about whether a Form is actually in the thing as opposed to being merely represented by the thing but about what to make of either possibility (in contrast to a Form's having absolutely nothing to do with anything in phenomenal experience).

(68.) Among those who explicitly recognize the compatibility of transcendence and immanence, see: Allen (1970: 147); Fine (1986: 94-95) with some qualification; Perl (1999: 339-362, especially 339, n. 1, 361-362).

(69.) The options are not exhausted here. Consider, for example, the question whether recreating a mastodon from naturally preserved genetic material would count as "refilling" (or "repopulating") an empty Form. The extended sequence would then start with an empty Form before there were actual mastodons, followed by an instantiated Form when mastodons came into existence and during their presence on earth, followed by an empty Form upon and during their extinction, followed by an instantiated Form activated through genetic engineering, to be followed by an empty Form should they become extinct again.

(70.) Rohr (1978: 268-269 [= 1981: 20-21]) also favors an unrestricted temporal frame of reference.

(71.) Armstrong makes sure the hesitation comes through: "It appears to have been the view held by Plato" (1989: 76).

(72.) The deciding factor against ascribing this specific Form (traveling faster than light) to Plato may be not just that Einstein's theory of special relativity constitutes an anachronism here but perhaps also that the reference to traveling faster than light invokes too many separate concepts to count as a single Form. It seems to require motion, velocity, and a traveler, hence, at least three things rather than one as usual. Then again, the Form of tennis, another anachronism, also requires a combination of elements (balls, rackets, courts, players, and so on) without thereby compromising the "formalization" (conceptualization) in question. The simplicity requirement for Forms receives ample attention below, where it is defined in terms of unitary integrity devoid of impurities.

(73.) The example is only for our benefit. Unicorns may have been considered closer to fact than to fiction in Plato's day. Aristotle reports actual beasts that are comparable, at least in terms of the solitary central horn, to the unicorns we now speak of as mythological creatures (Historia animalium 499b18-19; De partibus animalium 663a20-34). A more suitable example of mythical animals for Plato (and obviously also for Aristotle) would be centaurs (Phaedrus 229d; Statesman 291b, 303c) and satyrs (Statesman 291b, 303c; Symposium 215b, 216c, 221d, 221e, 222d; Laws 815c).

(74.) Notwithstanding the notorious difficulty of proving negative claims, one may, if it helps, think of this not as an explicit rejection that can be confirmed anywhere in particular but as an implicit repudiation that is evident through and through, for example, in the divided line (Republic 509d-511e). Fictional entities are denied not just their own Forms but any representation whatsoever in the divided line. Even the lowest level, eikasia ([phrase omitted]), is reserved for images of visible things, hence for shadows and reflections, and not for wholly imaginary things, which is what fictional entities are. Plato would not be likely to assign Forms to things he did not think existed, or more accurately, to those he thought existed only by convention and not by nature.

(75.) Vlastos construes Plato as rejecting Formless things and accepting empty Forms: "For Plato nothing could exist in space and time with a definite character, F, if there did not exist a corresponding [PHI], while the converse would not be true at all. The existence of a specific Form, say, of a chiliagon, would of itself not offer the slightest assurance of its physical instantiation; not only the Form of the Ideal City (Rep. 592AB), but infinitely many other Forms as well exist which have been uninstantiated since time began and may so remain forever in Plato's universe" (1969: 301).

(76.) Both examples come up again toward the end of this section, and in the conclusion, with the case of the ideal state taken up in greater detail, particularly in relation to the requisite simplicity, or unitary integrity, of Forms.

(77.) In the case of the ideal state, we know for a fact that we are dealing with something merely difficult, and not impossible, to realize: "Then we can now conclude that this legislation is best, if only it is possible, and that, while it is hard for it to come about, it is not impossible" (Republic 502c). This is because the ideal state is the just state, not the perfect state, unless justice is sufficient for perfection. Any justice to be achieved in this regard must be modeled after the Form of justice. That is why philosophers are best suited to the task of helping the state live up to its potential: "the city will never find happiness until its outline is sketched by painters who use the divine model" (Republic 500e).

(78.) The notion of eternal moments may work as a metaphor, and there may be a Form for metaphors, but there would be none for literal metaphors, because there would instead be two (literality and metaphors), as is the case with eternal moments (eternality and moments).

(79.) Plato's interest in geometry is the stuff of legend (cf Alican, 2012: 41-43). Whether he regards geometrical figures as Forms, however, remains an open question. Aristotle portrays Plato as giving mathematical objects (both numbers and shapes) an intermediate position between Forms and particulars (Metaphysics 987b14-17, 1059b5-14). This would mean that such objects are not Forms. Yet even if we are inclined to take Aristotle's word for this, he complicates matters by describing Plato as holding all Forms to be numbers (Metaphysics 991b9, 1081a12), which not only contradicts his own report (that Plato does not take numbers to be Forms, because he takes them instead to be intermediates) but also transposes the original question whether numbers (and shapes) are Forms (cf Alican, 2012: 105-107). This last bit of testimony is not directly relevant to geometrical figures anyway, since no such figures can be Forms if all Forms are numbers, unless all geometrical figures are also numbers. Plato himself is not clear about the matter. Even where he mentions the "square itself and the "diagonal itself (Republic 510d), the reference is ambiguous between invoking a Form and calling attention to a shape as distinct from the particular illustration of it under discussion. This is a matter of longstanding controversy among Plato scholars. See Yang (1999) for a short list of notable references, together with a brief presentation of his own position (which challenges what he calls the "critical view" that the references in question are to Forms, without insisting that they are not, instead noting the ambiguity in context).

(80.) Plato's favorite Forms, if we may judge the matter by where he focuses his efforts, have no internal structure at all: justice, piety, beauty, temperance, knowledge, and so on. Those that do are unitary wholes with a cohesive structure: beds and tables (Republic 596b, 597c-d); shuttles, awls, and tools in general (Cratylus 389a-d); and evidently therefore all artifacts, including houses and rings, as reported by Aristotle (Metaphysics 991b3-8, 1080a3-10), though not mentioned by Plato.

(81.) Dead persons continue to exist as souls, presumably until they are reborn with an earthly body, but it is not clear whether individual souls have Forms. I have not seen a case for it in any of the relevant places: Phaedo 70c-72e, 72e-77a, 78b-80b, 102a-107a; Phaedrus 245c-246a, 246a-257a; Republic 436a-444a, 608c-611a; Timaeus 34b-36d, 41a-44d, 68e-72d; Laws 891d-893a, 893b-896b, 896b-899d. Alcibiades 1 seems to present an exception where it invokes something like the "self itself at 129b1 (auto tauto [[phrase omitted]]) and 130d4 (auto to auto [[phrase omitted]]). But it is difficult to take this reference (especially in its more literal translation as the "itself itself) as conclusive evidence of a Form for the soul, which is not established even in the Phaedo, where the matter remains open to interpretation despite meticulous exploration of the connection between the soul and the Forms. Had Plato thought there were Forms for individual persons, or even if he had simply acknowledged a Form for the soul (one Form for all souls, that is, a generic Form for "soulness" or "soulstuff), the best place to make that clear would have been the Phaedo, where three of the four arguments for the immortality of the soul turn on its relationship with the Forms: the recollection argument (72e-77a for the argument, 77b-84b for objections and replies), the analogic argument (78b-80b for the logical core, 80c-84b for supporting imagery), and the causal argument (96a-107a, or 105b-107a, depending on the focus). See Alican (2012) for an analysis of these three arguments (pp. 413-418, 418-424, 446-450) and of the Phaedo in general (pp. 391-491).

(82.) The centaurs and the Chimera also come up together in the Phaedrus (229d), where their juxtaposition recalls just such a distinction between fictional kinds and fictional individuals (cf. Fine, 1993: 127; Thomas, 2008: 636).

(83.) Fine (1984: 31-87) is not claiming here that artifacts have Forms (nor even that Plato says they do). She is exploring the implications of the assumption that they do (or that Plato says they do). Broadie (2007), in contrast, lays out some of the main reasons for rejecting Forms for artifacts (which then precludes empty Forms for them), together with a critical survey of the early history of that rejection.

(84.) Specifically, we know that "the model was itself an everlasting Living Thing" and that "it was the Living Thing's nature to be eternal" (Timaeus 37d). Thus, the Forms (or whatever answers to the description of that "everlasting Living Thing") were the model for the creation of time, and they were therefore in existence "when" time was not, that is, "before" time was created.

(85.) Even though the textual evidence leaves us with a contradiction between the Timaeus (30c-31a, 37c-39e) and the Republic (597b-d) on this specific point, what we know of Plato's Forms in general provides additional insight: If the Forms are transcendent, they must exist outside spacetime and ipso facto outside time. For if they are transcendent, yet are not outside spacetime, what then do they transcend? This would seem to favor atemporality over durability or longevity.

(86.) See Patterson (1985b) and Whittaker (1968) for various interpretations of the eternality of Forms.

(87.) One can always dismiss inconvenient details or implications in the cosmogony of the Timaeus by invoking the ostensibly fragile credibility of the report as a creation myth. But that is not a self-sufficient appeal. It requires argumentation. The matter of how seriously to take the "likely story" (eikos muthos [[phrase omitted]]), or "likely account" (eikos logos [[phrase omitted]]), of the Timaeus (29b-d ff passim) has yet to be settled. While the tension between metaphorical and literal interpretation is an ancient one, the balance in scholarly dialogue has been shifting from allegory to philosophy (or at least to philosophy through allegory). Taylor (1928: 18-19) and Cornford (1937: 24-32, 34-39), for example, both favor a less literal reading, though Cornford takes issue with Taylor for identifying the likely story as a bricolage of existing theories. Vlastos (1939: 71-73 [= 1965: 380-383]; 1965: 401-419) and Hackforth (1959: 17-22, especially 19), in contrast, move away from deliteralization, finding a greater commitment by Plato to the story offered. Recent contributions include Burnyeat (2005: 143-165), Sedley (2007: 93-132, especially 98-107), and Brisson (2012: 369-391).

(88.) Fine later places greater emphasis (2003: 293) on what she originally presents as an implicit distinction (1984: 79) between the "traces of fire" mentioned and "sensible fire as we know it." The discussion here is compatible with her observation at either level of emphasis.

(89.) What if justice and goodness (or any other Forms) came before the demiurge? Would they not then be empty Forms, not being instantiated by anything at all, including the demiurge? They would be until the demiurge came along, but this is not a good counterexample. One might object that, if both the demiurge and the Forms (of justice, of goodness, and of whatever else) preceded time, and were both eternal in that sense, then neither one could have come before the other, since there would never have been a time when either one did not exist. At least in this sense, the demiurge can arguably be said to have always instantiated whatever it instantiates prior to the creation of time. But this objection is no better than the counterexample it targets. Both tend to come up, but they both rest on the independent problem of whether succession is possible (or conceivable) without time, or perhaps more generally on whether anything at all can happen outside time. Neither the counterexample nor the objection to it does anything to solve that problem.

(90.) As intimated earlier in this section, immediately upon introducing Armstrong's (1978: 64-65) scenario, the example of traveling faster than light points to a structural complexity bringing together too many elements to constitute a single Form. One way around this difficulty, and hence a reason not to dismiss Armstrong's example offhand, is to use "starship" as shorthand for the otherwise busy combination of elements in the original example. Starships routinely come with warp engines enabling superluminal travel. They thus qualify as unitary wholes without conceptual modification because it is not necessary (since redundant) to add that they happen to be able to travel faster than light. Continuing references below to "superluminal" starships are for emphasis and not for substantive qualification of the starships themselves, which are already superluminal. Our acquaintance with starships is restricted largely to science fiction, especially to Star Trek, but this should not be much of a problem where we are already discussing unicorns. What this shows is not necessarily that Armstrong's original example works but that its failure need not come from its complexity, which can thus be ironed out through conceptual consolidation.

(91.) An alternative reading is that there is just the one Form for the state, which, as a Form, happens to be an ideal one, with any degeneration or corruption confined to its phenomenal manifestations. On this reading, the Form of the state is, by default, the Form of the ideal state (which is simply the just state, since we already know that the ideality Plato attributes to the state is justice) because there is no other (less than ideal) kind among the Forms, only among the ones established in practice. This might overturn my objection that the ideal state is not simple enough a notion to be considered a Form in and of itself. But this unified Form of "state = ideal state (just state)" would no longer serve Maula (1967: 35) and Vlastos (1969: 301) as an example of a Form that is not or cannot be instantiated, as it would instead be an example of one that is badly or imperfectly instantiated--rather like every other Form we know. If the Form of "state = ideal state (just state)" must be empty simply because phenomenal manifestations of statehood are always less than ideal (not quite just), then all Forms must be empty for analogous reasons. Yet the Form of the equal (Phaedo 74a-75e), for example, is decidedly not empty despite being notorious for how everything that strives to be like it (like the equal itself) inevitably comes up short in instantiation.

(92.) As noted in section 3 (on Formless things), Forms are what Plato makes them out to be. This lifelong experimentation with abstraction springs from and operates with what Plato himself found valuable, significant, important, or at least interesting. See the role of Plato's valuation tendencies in Alican and Thesleff (2013: 29-33, 44) and in Alican (2014: 51-52). That is why we keep encountering the same Forms throughout the various dialogues invoking the Forms. And that is why we are confronted over and over with justice and beauty and goodness, and not with flights of fancy that tax the imagination.

(93.) Recall that Alican and Thesleff present the classification of Forms as a thought experiment (2013: 14, 17, 43). This does not in any way trivialize the initiative, as Plato's own schemes and projects, including the so-called theory of Forms, are also thought experiments.

(94.) The exact terms are not important. An alternative might be "accidentally" empty Forms versus "essentially" empty Forms. In temporal terms, the first kind would be occasionally empty, the second, permanently empty.

(95.) This is also consistent with the tripartition of Forms, where naturally empty Forms are ruled out because the status of Forms as Forms, especially Ideal Forms but also the other two kinds, reflects the importance Plato attaches to their phenomenal manifestations (Alican and Thesleff, 2013: 29-33, 44; Alican, 2014: 51-52). Forms of any kind are recognized as Forms if and only if their phenomenal manifestations seem important enough to Plato to attract his attention. This does not mean that beautiful things, for example, cannot possibly be destroyed en masse, thus vacating the Form of beauty. It means, rather, that any Form, including that of beauty, is instantiated by default. This is because, given that the process of conceptualization and reification in Plato proceeds with phenomenal value assignments by Plato himself, the things to which the values are assigned will naturally instantiate the corresponding Forms.

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NECIP FIKRI ALICAN necipalican@gmail.com Ph.D., Washington University in St. Louis

How to cite: Alican, Necip Fikri (2017), "Ontological Symmetry in Plato: Formless Things and Empty Forms," Analysis and Metaphysics 16: 7-51.

Received 7 October 2016 * Received in revised form 16 November 2016

Accepted 17 November 2016 * Available online 19 December 2016

doi:10.22381/AM1620171

[Please note: Some non-Latin characters were omitted from this article].
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