Modality, propositional functions, and logical learning: a historical look at the conflict between Kripke and Frege-Russell in the preface to Naming and Necessity

Abstract

We argue that the technical advantages of rigidity are not the most important factor in accepting Kripke's thesis against Frege-Russell (sense-wide-scope). Kripke's philosophical thesis is far removed from Frege-Russell's in that the former evaluates the function of "identity" in a different - metaphysical - way than the latter. In this paper, we argue that the discussion can evolve along a different path: evaluating and assessing the divergence between different conceptions of counterfactual knowledge, and studying the motives and prices that seemed reasonable to Russell-Frege to deal with the modal problem without expanding the extensional universe of classical logic. In particular, we will consider the merits of the Russellian option, understood as a theory of logical knowledge of the various ways in which a proposition can be false, depending on how we analyze the anti-extension of the proposition using propositional functions. Modal predicates can essentially be understood within the structures of fallible truth models by finding an extensional interpretation for counterfactual scenarios and extensionalizing complex identities. This provides a non-metaphysical understanding of what happens when one learns something logically about modality and counterfactuality.