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The theory that virtue is knowledge is, as we have seen, flawed, in that one of its central propositions, that virtue is always in the agent's interest, is nowhere adequately supported in the Socratic dialogues. It also has a deeper flaw in that it is incoherent. The incoherence emerges when we ask 'What is virtue knowledge of?' The answer indicated by Meno and Protagoras is that virtue is knowledge of the agent's good, in that, given the standing motivation to achieve one's good, knowledge of what that good is will be necessary if one is to pursue it reliably, and sufficient to guarantee that the pursuit is successful. But that requires that the agent's good is something distinct from the knowledge which guarantees that one will achieve that good. 'Virtue is knowledge of the agent's good' is parallel to 'Medicine is knowledge of health'. Given that parallel, the value of virtue, the knowledge which guarantees the achievement of the good, will be purely instrumental, as the value of medicine is, and derivative from the intrinsic value of what it guarantees, that is, success in life (eudaimonia). But Socrates, as we saw, regards virtue as intrinsically, not merely instrumentally, valuable, and explicitly treats it as parallel, not to medicine, but to health itself. Virtue is, then, not a means to some independently specifiable condition of life which we can identify as eudaimonia; rather, it is a constituent of it (indeed, one of the trickiest questions about Socratic ethics is whether Socrates recognizes any other constituents). So, far from its being the case that virtue is worth pursuing because it is a means to a fully worthwhile life (e.g. a life of happiness), the order of explanation is reversed, in that a life is a life worth living either solely or at least primarily in virtue of the fact that it is a life of virtue.
The incoherence of the theory thus consists in the fact that Socrates maintains both that virtue is knowledge of what the agent's good is and that it is that good itself, whereas those two theses are inconsistent With one another. It could, of course, be the case both that virtue is knowledge of what the agent's good is, and that the agent's good is knowledge, but in that case the knowledge which is the agent's good has to be a distinct item or body of knowledge from the knowledge of what the agent's good is. Otherwise we have the situation that the knowledge of what the agent's good is is the knowledge that the agent's good is the knowledge of what the agent's good is, and that that knowledge (i.e. the knowledge of what the agent's good is) is in turn the knowledge that the agent's good is the knowledge of what the agent's good is, and so on ad infinitum. So, if Socrates wishes to stick to the claim that virtue is knowledge, he must either specify that knowledge as knowledge of something other than what the agent's good is, or he must give up the thesis that virtue is the agent's good.
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C.C.W. Taylor (Socrates: A Very Short Introduction (Very Short Introductions))