The Metaphysics of the Socratic Position

Socrates’ metaphysical account of plural predication is explicit. In plural-predication the predicated attribute belongs to all the subjects together; this belonging is not reducible to, nor does it need to be grounded on that very attribute belonging to each of the individual subjects; Plato says: ‘when each of them is inexpressible, both together may be expressible, or possibly inexpressible’ (Hipp. Maj. 303b7-c1). If they are expressible together, this is not grounded on individual expressibility if each of them is inexpressible. Let us further consider two colours; each is attractive, and both together unattractive. Hippias could hold that we are justified in saying that the colours are attractive (in a distributive sense), since each is attractive. But it is also true that juxtaposed together, the colours are unattractive. The attribute of being unattractive belongs to them together, but does not belong to each individually, contra Hippias. This is what is distinctive of the Socratic position: his metaphysics allows that several individuals together can be the subjects of a single instance of an attribute (‘unattractive’), which may not be instantiated in each individual; and an attribute instantiated in each individual (‘attractive’) may not be instantiated jointly in all of them together (although it can be collectively attributed to them in a distributive (Hippian) way). A plural instantiation can coexist, as a different instantiation of an attribute, with instances of the same attribute in each of the subjects, as when each colour is attractive, but also, they are all attractive, too; or, it can coexist with its opposite, as when the colours are unattractive together, despite each of them being attractive; in such a case, each colour possesses an attribute (attractiveness) which they do not possess together, and they possess an attribute together (unattractiveness) which neither of them possesses by itself.

This ontological independence of plural-predication from individual-predication is just what Hippias denied when he said: ‘how could that be, Socrates? That any state of being, whatever, could be attributed to neither, since that attribute, which is attributed to neither, is attributed to both?’ (300b6-8). Socrates does have an answer; he says that ‘it was by the being that adheres to both, if both are [f ]... — it was by that they had to be [f ]..., and not by what falls off one or the other’ (302c4-7, my emphasis). This attribute does not make each of them f if ‘that attribute adheres in both, but not in each... then that’s not what makes each of them [f ]...;it doesn’t adhere in each’ (302e5-10).

How does a colour’s possession of attractiveness, which it possesses together with another colour, differ from the colour’s possession of attractiveness all by itself? The metaphysical innovation of Socrates is that a single instance of an attribute can be shared by a number of subjects; the instance is literally shared between the subjects; they co-possess it; they co-own that instance of the attribute. I do not use the terms ‘part-own’, or ‘part-possess’, as they may mislead by suggesting that there are parts of the attribute, each of which is fully possessed by each of the subjects respectively.1 A plurally shared attribute belongs to each individual subject differently than the way that that attribute would belong to any one of these subjects if fully possessed by that subject alone. Shared ownership involves only all the sharing-subjects together possessing the attribute. It is like a statue being supported by two pillars. The statue is not partitioned so that one part of it stands on one pillar, and the other part on the second; nor does the statue stand on the first pillar, or even on the second; rather, the statue stands as a

Plato does consider partitioning of attributes in the Parmenides (130e-131e) but rejects it.

whole on the two pillars. Without both pillars, the statue would fall; the whole statue would fall, not just part of it. In an alternative setup, the statue could be supported by several pillars and not fall by the removal of one or more of them, but only come to be fully supported by fewer of them. Similarly with the many owners of an instance of an attribute. In the case of their being ‘two people’, the loss of one would be detrimental to the plural-instantiation of that attribute, but if they are so many as to form ‘a crowd’, the loss of one would not undermine the plural-predication of ‘a crowd’.

For Socrates, qualifications can come to belong to particular things in two ways, the way Hippias described, distributively, but also the way Hippias denied, plurally (shared):

If they come to belong to both, they do to each also; and if to each, to both—all the

examples that you [Hippias] gave____But the examples I [Socrates] gave were not that

way. (Hipp. Maj. 303a5-10)

And the Socratic type of plural, non-distributive predication, can occur together with individual-predication:

Then they [the fine things] have some thing that itself makes them be fine, that common thing [i.e. the Form of Fine] that belongs to both of them in common, and to each privately. Because I don’t suppose there’s any other way they would both and each be fine. (Hipp. Maj. 300a9-b2)

(It is interesting here that Plato seems to be introducing a linguistic criterion for the distinction between distributive and plural predication, e.g. not the Hippian ‘they are fine’, but the Socratic ‘they are jointly fine’.) The Socratic type of plural- predication can alternatively occur without individual-predication of the same attribute:

[Socratic hypothesis:] Doesn’t that attribute [the fine] adhere in both, but not in each? ...

Then that’s not what makes each of them fine; it doesn’t adhere in each. So the [Socratic] hypothesis lets us call both of them fine, but it doesn’t let us call each of them fine.

(Hipp. Maj. 302e5-303a1)

In both Socratic cases of plural-predication, the instance of the attribute which qualifies jointly the many as f is different from any individual instances of it in each of the many. Although it is ‘textually underdetermined’ what the ontology of the cases where Socrates agrees with Hippias’ examples is, I have tried to shed light on the ontological difference between the two for Socrates, premised on whether or not the collective attribution involves a shared attribute. (Plato’s position could have been more thoroughly developed in the text with correlations between linguistic forms and distributive versus plural attributions of collective qualification. For instance correlating more explicitly an attribution such as ‘they are tall’ with distributive predication, and an attribution such as ‘they are vivacious’ with plural predication, if they are jointly vivacious.) The complex ontological account presented above is required to explain the intricate semantics of plural-predication in language through the Theory of Forms.

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