Self-Instantiation and Self-Participation

Abstract: While each Form is what it is to be F, While each Form is what it is to be F, some Forms also instantiate F (or “self-instantiate”). Here I consider whether the explanation for a Form’s instantiating F should be the Form’s participating in itself. First, I motivate the need for an explanation of self-instantiation. Second, I consider the advantages and disadvantages of self-participation alongside an alternative explanation—that the Form’s being what it is to be F is a sufficient explanation of its instantiation of F. The result is not a conclusive case for self-participation, but only some initial considerations in favor of it.


INTRODUCTION
Starting in the Parmenides and continuing into the late dialogues, Plato's metaphysics develops in at least two ways. First, there is a shift from the Forms being predicationally simple to being predicationally many. By "predicationally simple," I mean that the Form has one and only one predicate-the predicate that refers to the nature that the Form is . By "predicationally many," I mean that the Form has many predicates-both in the sense that it is many things and in the sense that it is not many things (Prm. 161e-162b; Sph. 252d-257a).
Second, there is a shift from an Assimilation approach to predication, participation, and paradeigmatism to a Plural Predication approach. Christine Thomas describes the Assimilation approach as one where there is "a single predication relation for cases of self-predication and participation alike. The Form of Beauty and a beautiful sensible have Beauty predicated of them in the same way: both instantiate beauty. … Forms are paradigms by being perfect exemplars of properties (or kinds), and sensibles participate in Forms by deficiently resembling them, by being imperfect copies" (Thomas, 2014, p. 171). Thomas describes the Plural Predication approach as one where "the self-predication relation differs from the participation relation. … a Form is F or is what it is to be F, while the sensible has F. … Forms are paradigms as definable essences, and sensibles are dependent on Forms in at least the following sense: no sensible can instantiate F unless something-a Form-is what it is to be F" (Thomas, 2014, p. 171).
This paper explores whether there should be a third shift in Plato's late metaphysics-whether the explanation for some Form's instantiating F (what I shall sometimes call "self-instantiation") should be that the Form participates in itself. For there are some Forms that both are the what it is to be F and instantiate F. There are some scholars that argue that there is this third shift in Plato's late metaphysics. Yet framing the question in this way-whether the explanation for some Form's instantiating F is that the Form participates in itself-restricts discussion to just three passages: Prm. and Sph. 256a. 1 The former question, however, imposes no such restriction; it allows for consideration of the matter from a broader perspective.
I shall argue that there is some support for the claim that self-participation should be the explanation for self-instantiation. First, I shall motivate the need for an explanation for self-instantiation by reviewing a problem for the theory of Forms from the Parmenides, as well as the section on the Great Kinds from the Sophist. Second, I shall consider the advantages and disadvantages of selfparticipation as the explanation by setting it alongside an alternative explanation -that the Form's being what it is to be F is a sufficient explanation of its instantiation of F. The result shall not be a conclusive case for self-participation, but only some initial considerations in favor of it.

BOTH/AND
While all Forms are the what it is to be F for their respective properties (or kinds), some Forms must also instantiate F. Minimally, this group of Forms includes Being, Oneness, Identity, Difference, Likeness, and Unlikeness-a group that is often called the "structuring Forms." 2 Consider the first section of argument in the second part of the Parmenides (137c-142a). This section starts from the hypothesis "if it is one" and ends with Parmenides arguing that there is no name, account, knowledge, perception, or opinion of the One because the One neither is one nor is (Prm. 141e-142a). Why? The One does not partake of Being (Prm. 141d-e). Yet Aristotle, when prompted by Parmenides, says that these conclusions cannot be true of the One (Prm. 142a). It is no surprise, then, that the second section of argument (Prm. 142b-155e) begins by confirming that if the One is one and is, then the One must partake of Being (142b-d). So, the One has the property of being-it is-because it partakes of Being. Yet the One is not just the what it is to be one; it also has the property of being one-it is one being (Prm. 142d). What is the explanation for this?
The same question is raised by the investigation of some of the Great Kinds (Sph. 254b-257b). Once the Eleatic Visitor and Theaetetus mark off Being, Change, Stability, Identity, and Difference, the Eleatic Visitor proposes that they draw some conclusions. Some of these conclusions are: Change has the property of being because it partakes of Being; Change has the property of being self-identical because it partakes of Identity; Change has the property of difference in relation to Identity, and so is not Identity, because of its association with Difference; Change also has the property of difference in relation to Stability, Difference, and Being for the same reason-it associates with Difference. Yet Being, Identity, and Difference-in addition to being the what it is to be, the what it is to be self-identical, and the what it is to be different, respectively-must themselves instantiate the properties of being, self-identity, and difference (in relation to something), respectively. If the explanation for Change instantiating these properties is that it partakes of the Kinds that are the what it is to be for these properties, what is the explanation for those Kinds themselves instantiating the properties of which they are the natures?
What about Forms that are not structuring Forms? The Beautiful is arguably described in the Symposium as not just the what it is to be beautiful, but also as instantiating beauty-and in a maximal or perfect way (211aff.). And perhaps the Good-what goodness is, the cause of knowledge and truth, an inconceivably beautiful thing-has the property of being good (R. 507a-509c). I suspend judgment about these Forms here, save only to note that if they too have the properties of which they are the natures, then the need for an explanation for selfinstantiation is all the more pressing. There is a diverse and foundational group of Forms that both are the nature of some property and instantiate that property.
Do all Forms self-instantiate, though? Arguably, no. While Largeness, say, is the what it is to be large, it is difficult to make sense of the Form being a large thing, and why it would need to instantiate largeness. The same is the case for Smallness too. Yet even if it could be shown that Largeness and Smallness need to self-instantiate and explained what it means for them to be a large thing and a small thing, respectively, there is one Form that cannot self-instantiate-Change. The Forms are stable, unchanging entities; the Forms do not move from here to there, they do not turn around in the same place, and they are unalterable. Therefore, no Form is a changing thing-including Change. This observation is important, as it suggests that self-instantiation is limited. Only some Forms are both the what it is to be F and instantiate F. This too requires an explanation.

ADVANTAGES AND DISADVANTAGES
The case for some Forms both being the what it is to be F and instantiating F was made in the previous section. It is time to explore possible explanations for the latter. There are two candidates. First, it is the Form's being the what it is to be F that explains the Form's instantiating F. For example, Identity's being the what it is to be self-identical explains why it also has the property of being self-identical. I call this the "Nature Explanation" (NE). Second, it is the Form's participating in itself that explains the Form's instantiating F, just as things other than the Form must participate in the Form to instantiate F. For example, it is because Identity participates in itself that it has the property of being self-identical, just as things other than Identity are self-identical because they participate in it. I call this the "Self-Participation Explanation" (SPE). The initial difference between these two candidates is that by NE, the Form's being the what it is to be F is sufficient to explain its instantiating F; by SPE, the Form's being the what it is to be F is not sufficient to explain its instantiating F-the Form must also participate in itself.
NE as currently formulated is unacceptable. The case was made above that not all Forms instantiate the property of which they are the nature. So, NE must be revised-it cannot be the case that the Form's being the what it is to be F is sufficient to explain its instantiating F. There must be something more, something in addition to the Form's being the what it is to be F that explains its instantiating F. While it might seem that this is a point in favor of SPE, SPE is subject to a similar requirement. Since SPE too must limit which Forms selfinstantiate, which it can accomplish by limiting which Forms participate in themselves, there must be some reason why, say, Difference participates in itself, while Change does not participate in itself. And though some may say that Change's instantiating the property of change conflicts with the immutability of the Forms, this reason cannot explain why Largeness and Smallness do not instantiate largeness and smallness, respectively. Perhaps there are different reasons for different Forms. Yet a single reason seems preferable, if there is such a reason.
What might such a reason be? Above I wrote that there is a special group of Forms, the structuring Forms. The name highlights the structuring role that these Forms fulfill in the intelligible and sensible realms. By "structuring role," I mean that these Forms provide the (minimally) necessary properties that anything that is-whether completely or deficiently-must have if it is to be. It is necessary for anything that is that it possess the following properties: it must be, be one, be self-identical, be different (from everything other than itself), and be like and unlike other things in various ways. It is not possible for something to be, yet lack one or more of these properties. By contrast, it is not necessary for something that is that it be a changing thingthe Forms are, but are not changing things. Similarly, it is not necessary for something that is that it be beautiful-Socrates is, yet he is not beautiful. If this is correct, then recognition of the structuring role that some Forms fulfill, while others do not, can serve as the reason that both NE and SPE need to meet the previous difficulty. On NE, if some Form is a structuring Form, then this, in addition to its being the what it is to be F, explains its instantiating F. Similarly, on SPE if some Form is a structuring Form, then this explains why that Form participates in itself and therefore instantiates F. Finally, on both explanations, Forms that are not structuring Forms do not instantiate the properties of which they are the natures. Why? These Forms do not fulfill the requisite role for self-instantiation.
It seems that attending to the structuring role that some Forms fulfill in the intelligible and sensible realms puts NE and SPE on equal footing. If this is the case, then why prefer SPE to NE? SPE is preferable because it provides what I call a "uniform explanation for instantiation." Consider NE. It is a consequence of NE that there are two explanations for something's instantiating F: either something is the what it is to be F-and it is a structuring Form-or something participates in the what it is to be F. On SPE, however, there is only one explanation for something's instantiating F: something instantiates F just in case it participates in the what it is to be F. For example, everything other than Difference is different (from everything else) because of their participation in Difference; for Difference itself, the explanation for its being different (from everything else) is its participation in itself. The explanation is the same for both groups of objects, save that for the former they participate in something other than themselves, while for the latter it participates in itself. This is what I mean by a "uniform explanation for instantiation." Why prefer a single explanation to two explanations? There is nothing inherently objectionable about the latter. Yet it would be an unnecessary revision to the theory of Forms. Consider the two ways in which Plato's metaphysics develops that I outlined in the Introduction. The first, that the Forms shift from being predicationally simple to being predicationally many, is a necessary revision to the theory of Forms. As I explained at the outset of Both/And, the first and second sections of the second part of the Parmenides show that if the One has only one predicatethe one that refers to the nature that it is-then it is not one (Prm. 141e-142a). If the One to be one, it must partake of Being (Prm. 142bd). Moreover, if my above claim about the importance of the structuring Forms for all things in the intelligible and sensible realms is correct, then the One must (minimally) also partake of Identity, Difference, Likeness, and Unlikeness. The previous, predicationally simple understanding of the Forms led to unacceptable conclusions (Prm. 142a). If these unacceptable conclusions are to be avoided, then the Forms must be predicationally many.
The second development, from the Assimilation approach to the Plural Predication approach, is also a necessary revision to the theory of Forms. There are several reasons for this, though I shall mention just two of them. First, as I argued at the end of Both/And, it is not the case, as the Assimilation approach would have it, that all Forms self-instantiate. There must be some distinction between being and having, where the former is not sufficient for the latter. Second, while understanding the sense in which the Forms are paradigms as the perfect exemplars of properties is plausible for aesthetic and moral Forms, it leads to absurd results if we consider the structuring Forms. For example, there are no degrees of self-identity. And while it might be the case for Plato that there are "degrees of being," all Forms completely are, even if Being itself is the what it is to be. Therefore, the Forms cannot be paradigms in the perfect exemplar sense. Rather, the Forms must be paradigms in the sense of being the natures of properties or, as Thomas would put it, "definable essences" (2014, p. 171).
It is not, however, necessary to introduce a second explanation for instantiation, as NE does. The participation relation is sufficient to explain both how things other than the structuring Form instantiate some property and how the structuring Form itself instantiates that property. And this is because by the late dialogues the Forms are paradigms in the sense of being the natures of properties. Consider this: suppose "participation" refers to the paradigm-copy account of participation proposed by Socrates in the Parmenides (132d). On this account, something participates in something else-the paradigm-by resembling it, by being modeled on it. So, "selfparticipation" on this account means that the structuring Form is modeled on itself. Yet on the perfect exemplar sense of paradeigmatism, this requires that the structuring Form already instantiates F, so that it is the model of F. The resulting explanation is circular-if paradeigmatism understood as perfect exemplification of properties, then self-participation offers no explanation for self-instantiation. There is no such circularity, however, if the Forms are the natures of properties, where this is not sufficient for instantiating properties. This is not to say that Plato does not introduce a second explanation for instantiation in the late dialogues. He may do so. I am arguing only that he need not introduce a second explanation for instantiation. Participation can be the single explanation for instantiation. This tips the scale, if only slightly, in favor of a uniform of explanation for instantiation and, therefore, of SPE.

CONCLUSION
There are some Forms that are both the what it is to be F and instantiate F. How it is that these Forms instantiate the properties of which they are the natures requires some explanation. This paper explored the possibili-ties available to Plato in the light of certain ways in which the theory of Forms develops in the Parmenides and the late dialogues. It does not argue that Plato does adopt either of the explanations considered here. Rather, the paper considers only the advantages and disadvantages of these explanations to assess their preferability. The conclusion reached is that there is a slight preference for SPE, for self-participation's being the explanation for self-instantiation, because this results in the theory of Forms' having a uniform explanation for instantiation. The explanation for instantiation is always participation, whether the object participated in is something else or the thing itself. What remains is consideration of what explanation, if any, Plato did offer for self-instantiation.

APPENDIX: TEXTUAL EVIDENCE
T1: This is how being would most of all be and not-being would not be: being partaking of being with respect to being a being, and not-being with respect to not being a notbeing, and not-being partaking of not-being with respect to not being a being, and being with respect to being a not-being, if not-being is completely not to be. -Most true. (Prm. 162a5-b8) 3 T2: We must then say that the nature of the Different is fifth among the Forms we chose. -Yes. -And shall we say that it goes through all of them; for each one is different from the rest not on account of its own nature, but on account of participating in the Form of the Different. (Sph. 255d9-e6) 4 T3: First, let us say that Change is completely different from Stability. Shall we say