I've been reading "Socrates' Moral Intellectualism", to which the author, Sam Rickless, was kind enough to refer me in a comment. Published in the Pacific Philosophical Quarterly 78 (1998) 355-367, one can obtain it through the Blackwell Enquiry service if one's library is a subscriber.
According to Rickless, Socrates in the Protagoras maintains that courage, temperance, justice, and piety are all forms of knowledge (or 'wisdom'). These virtues are related as are various coordinate species of the same genus. Each is the same as wisdom, in the sense that each is a species of wisdom. So too each is the same as any other, in the sense that each is the same sort of thing as any other. As for wisdom, it consists of these species of knowledge all taken together.
This interpretation, Rickless maintains, is different from the two common interpretations which hold the field. Penner takes Socrates to be maintaining that 'courage', 'temperance', 'justice', and 'piety' are four different names for the same sort of knowledge, which is simply equivalent to virtue. Vlastos takes claims such as 'piety is justice' to be asserting biconditionals involving instances of the virtues: 'An act is pious just in case it is just'.
I may raise some difficulties in Rickless' view in a subsequent post. For now, I want to draw attention to a consequence of this view, which then leads to an interesting question.
The consequence is that Socrates does not end up endorsing any alternative he presents at the start of the dialogue. As you recall, Socrates gives Protagoras three ways of resolving the difficulty that 'virtue is a single thing' and yet we have different words for various virtues:
1. The different words all name the same thing.Socrates clearly takes himself to be refuting 2(b). But on Rickless' interpretation, Socrates ends up endorsing neither 1. nor 2(a). The relationship of species to genus is not quite like any of these forms of composition (which are indeed more appropriate to corporeal things).
2. Each word indicates a part of virtue, and the parts of virtue are either:
(a) similar to one another, as the parts of gold, or
(b) different from one another in their function and power, as the parts of the face.
This might look like a disability of the interpretation. And yet, one thinks that the relationship of species of knowledge to genus would precisely be the sort of thing that would perplex Plato.
Hence the question. After reading Rickless' paper, I found myself wondering whether that curious passage in the Categories (11a20ff) is a record of a dispute in the Academy concerned precisely with these sorts of problems of classification. Read 'justice' and 'piety' for 'grammar' and 'music', and then wouldn't one have the Protagoras problem?
...the genera are spoken of in relation to something, but none of the particular cases is. For knowledge, a genus, is called just what it is, of something else (it is called knowledge of something); but none of the particular cases is called just what it is, of something else. For example, grammar is not called grammar of something nor music music of something. If at all it is in virtue of the genus that these too are spoken of in relation to something: grammar is called knowledge of something (not grammar of something) and music knowledge of something (not music of something). Thus the particular cases are not relatives. But it is with the particular cases that we are said to be qualified, for it is these which we possess (it is because we have some particular knowledge that we are called knowledgeable).And take that last line to be Aristotle's insistence, against Plato, that the way the words are used with respect to particulars should be decisive for ethics, where particulars count.