Although the irony of the Socratic elenchus has long been recognized, little attention has been given to attempting to resolve in detail the aporias in Plato's early dialogues.1 In this paper, I wish to present a few specimen resolutions based on the assumption that the fallacies, omissions, and apparent contradictions producing the aporias are fully intentional on Plato's part.2 The evidence for Plato's deliberateness falls into two main categories: external, or pre-Platonic; and internal, or within Plato's own writings. Into the first category should be placed the fact that before Plato's time deductive techniques and semantic analysis were well developed, intimately related in practice, and repeatedly applied to discussion of philosophical problems. Parmenides' poem presents unprecedented exercise in logical deduction: 3 using geometric reasoning as a model, a metaphysical issue is divided into two cases, and unwanted positions are eliminated by reduction to absurdity. Zeno's paradoxes, which lead to the verge of infinitesimal analysis 4 and reveal an even more thorough mastery of the reductio ad absurdum, suggest also a sophisticated position involving the relativity of movement and the theoretical character of geometric concepts.5 Hippocrates of Chios, who might be called a sophist, though he specialized in the mathematical field, B is probably the inventor of formalized geometric reduction and analysis, both of which as logical techniques are constantly used by Plato's Socrates in the discussion of philosophic issues. Protagoras' dicta and the reports on his work indicate, according to Dupreel's brilliant reconstruction, a pragmatic theory of language, logic, and knowledge.8 Far from denying the principle of contradiction, the great sophist was able to solve the puzzle presented in Parmenides' confusion between a negative predication and a negative existential judgement 9 by an analysis of the relative character