In an interesting forthcoming paper, my colleague Philip Ebert discusses an argument, due to Paul Boghossian, to the effect that we can have a priori knowledge of logical principles through implicit definition, on the basis of the following kind of 'template' argument (slightly revised by Philip from its original form):
1. If ‘and’ is to mean what it does, then ‘P and Q --> P’ has to be valid (by the nature of implicit definition)
2. ‘and’ means what it does
3. ‘P and Q --> P’ is valid
4. P and Q --> P
Philip objects that the essential ‘disquotational step’ from 3 to 4 cannot be made unless one already understands ‘and’. (This claim is supported by a trivial principle about disquotation). This understanding of ‘and’ in turn requires (by a Context Principle) that one understands sentences like 4. But by Boghossian’s lights, 4 is epistemically analytic, so that understanding it suffices for being warranted in believing it. Hence anyone who can use the disquotational step already has a warrant for believing the conclusion of the argument. This, Philip says, means that the argument fails to transmit a warrant for its conclusion.
I think one should reply on Boghossian's behalf that the epistemic analyticity of 4 only means that a warrant for believing 4 is available to anyone who understands 4, not that understanding implies possession of a warrant. But no worry about transmission of warrant failure arises unless understanding 4 implies possession of a warrant.
Philip comments on this response in his paper, though he does not put my mind at rest. I won't post my comments on his comments here however (though I will happily share them with parties interested enough to email me for them). Rather, I want to suggest that there is a different (though not entirely dissimilar) problem with the template argument as an account of our knowledge of P and Q --> P, namely that it doesn't tell us very much until we are told how premise 2 is known.
One reason to think knowledge of 2 is no trivial matter is that it implies that 'and' has a meaning . But if 'and' is implicitly defined as whatever makes ‘P and Q --> P’ (and some other rules) valid, knowing 2 requires knowing that something makes ‘P and Q --> P’ (and the relevant other rules) valid. How is this fact known? Plausibly, the way we know it is by knowing that P and Q --> P, but that can't be Boghossian's answer.
Boghossian (in the appendix to his 1997 paper 'Analyticity', included in this anthology) addresses this sort of worry by saying that 'we are a priori entitled to believe that our basic logical constants are meaningful because we cannot coherently doubt that they are'. There are many things to say about this claim. One of them is that, in the presence of Boghossian's views on implicit definition, it seems to imply that one of the things we rely on to secure a priori knowledge that P and Q --> P is the fact that we cannot doubt that there is some meaning for 'and', even when it is defined as that which makes ‘P and Q --> P’ (and other relevant rules) valid. One wonders exactly how far this is from simply saying that we cannot doubt, of the rule expressed by 'P and Q --> P' on its intended interpretation, that it is a valid rule. But to say that would hardly be to provide a satisfying acccount of our a priori knowledge of P and Q --> P.