William Nava

This paper argues that inference rule adoption is a diachronic process during which agents are inferentially guided by a statement of the rule they are adopting, but during which they do not use that rule. Rather, the ability to use the rule is the outcome at the end of the process. This account avoids a regress objection to inferentially guided adoption recently posed by Boghossian and Wright. Adoption, on this model, involves the use of six privileged inference rules, including universal instantiation, modus ponens, and the naive truth rules. However, though these rules play a special role in adoption, they are not indispensable to the process in their full generality: so long as one has reasonably robust restrictions of them, the adoption process is unimpeded. Furthermore, there are no general forms that constitute the minimal restrictions of these rules required for adoption. It follows that these rules, in their fully generality, are themselves adoptable, so long as one begins with reasonable restrictions of them. It is argued that this is enough to overcome the ‘adoption problem’ as a challenge to anti-exceptionalism about logic and to the normative significance of proposals for alternative logics.

Non-classical solutions to semantic paradox can be associated with conceptions of paradoxicality understood in terms of entailment facts. In a K3-based theory of truth, for example, it is prima facie natural to say that a sentence φ is paradoxical iff φ ∨ ¬φ entails an absurdity. In a recent paper, Julien Murzi and Lorenzo Rossi exploit this idea to introduce revenge paradoxes for a number of non-classical approaches, including K3. In this paper, I show that on no understanding of ‘is paradoxical’ (for K3) should both rules needed for their paradox be expected to hold unrestrictedly. Just which rule fails, however, depends on various factors, including whether the derivability relation of a target system of reasoning is arithmetically definable.