an abstract on the elenchos

by metalogike

Contemporary accounts of Socratic method embark from a problem famously posed by Gregory Vlastos in “The Socratic Elenchus: Method Is All”. To reach the conclusion of an elenctic argument, Plato’s Socrates appears to slide from agreement that a set of his interlocutor’s theses are jointly contradictory to singling out a particular thesis, the target of refutation, as false. As presented, the inference from inconsistency as a property of a set of propositions to falsity as a property of a single proposition appears invalid, resting on Socrates’ unjustified selection of a culpable thesis (for instance the interlocutor’s proposed definition of a virtue) from out of the set of incompatible theses, on the basis of some unarticulated certainty. The problem of the elenchos, according to Vlastos, would therefore consist in giving an account of what considerations, if any, justify this selection.

The problem is a good one. It implicates fundamental issues in the interpretation of the dialogues – whether the elenchos is “positive” or “negative”, its relations with Socratic ignorance and the unity of the latter’s exceptions, whether Socratic method is continuous or discontinuous with Platonic dialectic. Beyond this, it quickly opens issues of fundamental importance for philosophy – what the correct application of reductio arguments is from a formal standpoint, and whether formal reflection, especially the experience of contradiction, can actually compel us to reevaulate concepts as thickly woven into the web of belief as ethical ones. At the heart of Vlastos’ difficulty is the elusive relation of foreground to background in thinking. How should we think about the context of a thought? Can the background of a thesis ever be foregrounded if it is thought as something different in kind – for instance, if lived experience is opposed to the proposition? How precisely? At what cost? On the other hand, if we reapportion the difficulty by agreeing to think of the background of a thesis as consisting of other theses, then how pointedly can this multiplicity of theses be referred to in any thesis? Is there a true grasp of the manifold of thinking as such available to philosophical reflection, or does the truth of any concept of difference unfold always in a different concept?

Rebuttals of Vlastos’ analysis have largely failed, I claim, to address this grounding problem directly, and have contented themselves either with contesting the details and tenor of his assessment (redefining failure as success), or else with hoping to sweep it away in a turn to the dramatic aspects of the dialogues, attempting to redeem the failure of the logoi by redescribing the elenchos as some or another edifying “practice”. But if any defense of the elenchos that cedes the logical terrain to Vlastos issues in Pyrrhic victory, while neglect of the logoi is singularly un-Socratic, a third option is desirable to the friends of dialectic. It can be obtained by contesting two central formal features of Vlastos’ model of the elenchos, which jointly have gone (as far as I know) strangely unchallenged by both of these parties. In Vlastos’ elenchos, 1) theses are unanalyzed P’s with no more structure than is required by propositional logic, while 2) at the metalogical level there is in play only one strong norm, that of consistency, and a weak norm of truth as correctness. Weak? Indeed, the very “problem of the elenchos” – which despite obvious differences of idiom belongs to the same philosophical moment as the Quine-Duhem thesis and even Heidegger’s critique of Platonism as forgetting of what cannot be kept in presence – consists in showing the weakness of this second norm, that it is too powerless in the face of the multiplicity of theses to provide a dialectical counterweight to the norm of consistency; in the absence of such a constraint, either arbitrary choice, or (what is logically the same) the disappointing insertion of dogmatic moral knowledge, has to take up the slack. (The latter is in fact, Vlastos’ own resolution of the problem: Socrates just knows that certain moral beliefs are true.) In this paper, by contrast, I offer a model of the Socratic elenchos that meets Vlastos’ objection on its formal grounds. The revision I propose can be pictured as follows: correctness is the ball in the air, but the players are consistency and completeness. Starting from a reconstruction of the elenchos of the Charmides, I argue against the second point that we must recognize two strong metalogical desiderata in dialectical tension with each other in the elenchos – consistency and completeness, in senses surprisingly familiar not from propositional logic or even first-order logic, but from metalogic – and against the first, that it is characteristic of the concepts in play in the elenchos, such as “virtue” and “rule”, to engage both of these desiderata, not merely to fall under them. That is, the elenchos is fully metalogical – its operands move between aspects of use and mention of the two poles of a metalogical duality – they are, and are about, the desire to bring together these conflicting norms, while what the elenchos finally discloses is the original negation that links them, inseparably and without synthesis. Among the fruits of a reinterpretation of the truth of the elenchos as disclosure of the disjunctive synthesis of consistency and completeness are clearer pictures of each of the following: 1) the continuity of Socratic questioning with its roots in pre-Socratic philosophy, 2) the latent potentiality in the Socratic elenchos for the Platonic mathematical turn. 3) Finally, it makes it possible to improve on recent suggestions of Kahn and Rowe with respect to the other great impasse of Platonic scholarship – a really interesting formal treatment of the Idea of the Good. In light of the metalogical rethinking of the elenchos, Socrates’ words at Republic 505 become legible not only as reminiscent of the elenchos of the Charmides, Euthydemus, and related dialogues, but as Plato’s own succinct map of the elenchos, presented in maximally concise form at the moment that the Idea of the Good is introduced, and as the gateway to its interpretation. Grasping the metalogical duality at play in the elenchos, therefore, opens the possibility of identifying the form of the Good in terms of the reflective apprehension of this duality.