If validity isn’t defined in terms of necessary truth-preservation (whether general or restricted to ‘when it matters’), how is it to be understood? In my view, the best approach is to take it as a primitive notion that governs our inferential or epistemic practices...for instance, when we discover that the inference from A and B to C is valid, then we should ensure that our degree of belief in C is no lower than the sum of our degrees of belief in A and in B, minus 1.) From this viewpoint, we can easily explain the naturalness of thinking that validity coincides with necessary truth-preservation. It is natural because the following argument is natural: The validity of the inference from A1, …, An to B is equivalent to the validity of the inference from True(), …, True() to True(), by the usual truth rules. That in turn is equivalent to the validity of the inference from True() and … and True() to True(), by the usual rules for conjunction. And that in turn is equivalent to the validity of the sentence If True() and … and True(), then True(), by the usual rules for the conditional. But validity of a sentence is necessary truth (by virtue of form), so this last is just the claim that the inference necessarily preserves truth (by virtue of form). This argument looks very persuasive. However, it turns on principles that can’t be jointly accepted! In particular, we can’t subscribe both to the truth rules employed in the first step of the argument and to the rules for the conditional employed in the last step, on pain of triviality: that is the upshot of the Curry paradox. (See, for instance, Field 2008, §19.1.) There are different views on how the Curry paradox is to be resolved, but every one of them undermines one or another step in the argument that validity is to be identified with necessary truth-preservation. As I’ve said, one could still stipulate that ‘valid’ is to mean ‘necessarily preserves truth’. But this doesn’t undermine the main point, which is that that notion of validity isn’t what underwrites our notion of goodness in deductive argument—validity in that sense isn’t even extensionally equivalent to goodness of deductive argument. Our notion of good argument is an essentially normative notion, not capturable even extensionally in terms of truth-preservation. In this sense, logic is essentially normative. -Hartry Field. (2009). What is the Normative Role of Logic? [bit.ly/1sdYggU]
Posted on: Thu, 23 Oct 2014 20:01:01 +0000
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