Extrapolating Plato’s Definition of Being
8 August 2009
In the venerable Jowett translation of Plato’s Sophist dialogue, the complete text of which can be found online at Project Gutenberg (and can also be found at Google Books, p. 379), we find the following exchange between Theaetetus and the Eleatic Stranger:
STRANGER: Let us push the question; for if they will admit that any, even the smallest particle of being, is incorporeal, it is enough; they must then say what that nature is which is common to both the corporeal and incorporeal, and which they have in their mind’s eye when they say of both of them that they ‘are.’ Perhaps they may be in a difficulty; and if this is the case, there is a possibility that they may accept a notion of ours respecting the nature of being, having nothing of their own to offer.
THEAETETUS: What is the notion? Tell me, and we shall soon see.
STRANGER: My notion would be, that anything which possesses any sort of power to affect another, or to be affected by another, if only for a single moment, however trifling the cause and however slight the effect, has real existence; and I hold that the definition of being is simply power.
The Greek text of the Eleatic Stranger’s crucial formulation is as follows:
Ξένος: λέγω δὴ τὸ καὶ ὁποιανου̂ν [τινα] κεκτημένον δύναμιν [247e] εἴτ’ εἰς τὸ ποιει̂ν ἕτερον ὁτιου̂ν πεφυκὸς εἴτ’ εἰς τὸ παθει̂ν καὶ σμικρότατον ὑπὸ του̂ φαυλοτάτου, κἂν εἰ μόνον εἰς ἅπαξ, πα̂ν του̂το ὄντως εἰ̂ναι: τίθεμαι γὰρ ὅρον [ὁρίζειν] τὰ ὄντα ὡς ἔστιν οὐκ ἄλλο τι πλὴν δύναμις.
This I shall simply call Plato’s definition of being.
This memorable definition of being in Plato — the power to affect or be affected (Sophist, 247e) — has been construed by Abbagnano in terms of possibility: being is the possibility to affect or be affected. The Greek term that Jowett translated as “power” — “δύναμις” — Abbagnano translated as “possibility.” While this isn’t quite as creative as some Heideggerian “translations” of Greek, it is an unusual translation. Despite this, I count the transformation from power to possibility as justified, since the Platonic account of being does not demand acting or suffering in actuality, but only the possibility of acting or suffering. Abbagnano, to my mind, has retained the essence of Plato’s meaning. And the Platonic definition, such as it is, seems reasonable to me, as we can scarcely credit anything with being if it has no relation whatsoever to us (or to the world). Thus the Platonic definition of being so construed also provides us with a definition of non-being.
This Platonic conception of being immediately suggests a tripartite division among beings:
1) those which both act and suffer,
2) those which act only but do not suffer, and
3) those which suffer only but do not act.
There remains, obviously, a fourth possibility, but I noted above that the schematization of the Platonic definition of being introduces a tripartite division among beings, while the fourth possibility excludes all beings:
4) those which neither suffer nor act.
This fourth possibility — those which neither act nor suffer — represents, by definition, non-being and may be considered the null permutation (analogous to the empty set). There is an implicit paradox here, since we seem to be referring to beings that neither act nor suffer, which of course are impossible. Does non-being consist of impossible beings? And there is, as well, the ontologically interesting question of the possibility of the individuation of non-beings. Nothingness has always been a philosophical puzzle, and the above approach allows us a novel perspective on nothingness. It is difficult if not impossible to imagine the utter oblivion of non-being. Even the sinners trapped in the ice of the frozen Cocytus are able to converse with Dante (or, at least, are merely seen encased in ice), and therefore seem possess being to some degree in virtue of this interaction.
It is difficult to resist observing that the ontological “inertness” which has of late been ascribed to mathematics by Jody Azzouni (and we may generally suppose this to hold for all beings, if such they be, which constitute the formal sciences) would seem to indicate that mathematics is concerned not with beings but with non-being: we do not affect the objects of the formal sciences, and they do not affect us. But this is ultimately much too simplistic: the objects of the formal sciences — numbers, propositions, etc. — affect us in so far as we conceive them, and, depending upon the philosophy of mathematics that one advocates, there remains the possibility that might affect the objects of the formal sciences, for example, by creating and conceiving them (as in a constructivist philosophy of mathematics).
If man is the measure of all things, as according to Protagoras, then mathematics has no measure since mathematics is resolutely anti-anthropocentric. If, as Russell held, mathematics is the study in which we never know what we are talking about nor whether what we are saying is true, this is entirely justified, because we are, as it were, talking about nothing, and what we are saying is neither true nor false. But Russell’s philosophy of mathematics exemplified a classically anti-anthropocentric position, and Russell himself was willing to formulate some of his positions in terms of non-being (as in, for example, his “no classes” theory of classes), so in this particular context Russell’s modern formulation is a re-statement of traditional view, and in his thought no suggestion of a constructivist alternative is ever made. Nevertheless, Azzouni’s account of ontological inertness does closely correspond to the definition of non-being in terms of neither suffering nor acting, and it would be worthwhile to follow up on this correspondence in a systematic way. But another time.
And there is more. Within each ontological division outlined above we may adopt a hierarchy of being, securely based upon quantification of the number of beings which a given being affects or by which it is affected. The measure of ontological power — ontological potency, as it were — is a being’s scope of acting and suffering. Now, we may assume that those beings that both act and suffer possess a greater scope of being than those one-sided beings which act only or suffer only. Whether either one of these two inferior forms of being — viz. acting only or suffering only — ought to be superior to the other is a greater problem, and we will not address it here.
We can go further than this by defining acting and suffering within regional ontologies (to invoke a formulation of Husserl). Regional ontologies themselves admit a scope of possible acting and suffering. They overlap and intersect (to invoke a formulation of Wittgenstein).
A further note: construing the Platonic definition of being in terms of the possibility of affecting or being affected, as Abbagnano does, suggests a distinction between so construing Plato and, in contrast, interpreting the Platonic definition of being in terms of actually affecting or being affected. This latter interpretation would require specifying a scope of time during which a putative existent’s affecting or being affected would be relevant, for not everything affects or is affected by everything else at any one moment. But this too suggests a further division (perhaps the narrowest formulation of being) in terms of which only that which affects or is affected by a given being at a given instant contributes to its reality: call it, if you will, being at an instant. More of this at another time.
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