Validity as Truth-Conduciveness

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving, and taking it instead to be “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view, I argue that validity should instead be defined as truth-conduciveness, a matter of a vast majority (or “almost all”) of the instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness relative to finite sets of instances. I further argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is “the” central notion in logic involves a false presupposition, since there are then arguably at least two central notions. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. In this sense, then, there is no solution to the Liar paradox. If this conjecture is true, further, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. I go on to argue that the central normative notion in logic, which defines the single turnstile, is, in a sense I make precise, “defeasible rationality”, and I further argue that this notion coincides, for basic inferences, with truth-conduciveness, which I take to be that expressed by the double turnstile.