Semantic inferentialists hold that understanding an expression amounts to having a practical mastery over the ‘material’ infererences it is involved in. (‘Material’ is intended to invoke the old Aristotelian distinction between form and matter: logically valid inferences are hold in virtue of their form, materially valid inferences hold in virtue of their content.) Grasping ‘That’s red’, to use a well-trodden example, involves treating the commitment as incompatible with ‘That’s green’ and as entailing commitment to ‘That’s coloured’. Logical locutions (paradigmatically negation and the conditional), are used to make explicit the inferential relations one endorses in practice. The inference from ‘That’s red’ to ‘That’s coloured’, although materially valid, is logically invalid. The enthymematic gap can be plugged with ‘For all x, if x is red then x is coloured’.
That’s a (very) brief synopsis of one central tenet of semantic inferentialism, but what bearing does this have on the Meno paradox? Plato’s Socrates states the paradox this way:
Do you realize what a controversy you’re conjuring up? The claim is that it’s impossible for a man to search either for what he knows or for what he doesn’t know: he wouldn’t be searching for what he knows, since he knows it and that makes the search unnecessary, and he can’t search for what he doesn’t know either, since he doesn’t even know what it is he’s going to search for. [Meno, 80e]
Socrates was inquiring into the nature of virtue, but any project of analysis—the analysis of knowledge, for instance—is subject to the paradox. If we already understand what knowledge is, then the analysis of knowledge appears superfluous; but, if we do not understand what knowledge is then we will have no grip on what analysis is the correct one. It looks like the semantic inferentialist can avoid this dilemma by appealing to the difference between practical mastery and making explicit. We began with an implicit understanding of ‘knowledge’; a practical mastery of the inferences it licenses, its circumstances and consequences of application. By making explicit the inferences that a concept licenses, what is gained from the project of analysis is an explicit understanding of the concept of knowledge; so on the one hand analysis is not superfluous. On the other hand, our implicit understanding of knowledge allows us to check it against various analyses: are there occasions where it is appropriate to ascribe knowledge but where it is not appropriate to ascribe the analysans, or vice versa? So, there is no puzzle surrounding how we can know which analysis is the correct one. Our implicit inferential mastery of concepts makes the project of analysis possible.
