Which came first: logical truth or consequence?
This term, I am teaching a philosophy of logic class. We've twice run across the following sentiment:
(CPT) Logical consequence is prior to logical truth.
This sentiment is also expressed as 'The real subject matter of logic is the notion of consequence, not a special body of truths.' (References: We've seen this in Stephen Read's Thinking about Logic Ch.2, and in John Etchemendy's work (1988, p.74) too.)
Seeing (CPT) surprised me, since logical truth is (in most cases -- see below) definable in terms of logical consequence, and vice versa: If C is a consequence of P1 ... Pn, then 'If P1 and ... and Pn, then C' is a logical truth. And if T is a logical truth, then T is a consequence of the null set of premises. This is well-known: Beall and Restall, in their recent Logical Pluralism, make exactly this point.
So, in light of the interdefinability of logical truth and consequence, what would prompt someone to say consequence is somehow prior to logical truth? Stephen Read appeals to valid arguments that ineliminably use infinitely many premisses: A(0), A(1), ... Therefore, ∀x Ax. We can't turn this into a logical truth ('If A(0) and A(1) and ..., then ∀x Ax') in standard languages, because standard languages don't allow for infinitely long sentences. This seems like a fair point in favor of (CPT), but it does assume that (i) you accept arguments with infinitely many premises, and (ii) reject languages with infinitely long expressions. [Edit: as Shawn correctly notes in the comments, these two assumptions are fairly widely held. But I have always been a bit suspicious (perhaps for no good reason) about the idea of an argument with infinitely many premises.]
Here's another argument for (CPT), from extremely weak languages. Imagine we have a propositional language with sentence letters p, q, ..., and only two sentential connectives: 'and' and 'or' specified in the usual way. In this language, there are no logical truths (because we don't have 'If... then...' or anything equivalent), but there are still logical consequences: A is still a logical consequence of 'A and B', and 'A or B' is a logical consequence of A. So here is a case where we have logical consequence without logical truth.
But both of these arguments (Read's and mine) rely on somewhat unusual cases. Are there other reasons to accept (CPT) that do not appeal to unusual circumstances? Is there a big literature out there that I don't know about? And does anything really hinge upon whether we think logical truth is prior to consequence, vice versa, or neither?