Corine Besson (Birkbeck, University of London)
Interpreting What Achilles Said to the Tortoise
An important question in the epistemology of logic concerns the relation of logical knowledge to deductive reasoning. It is widely accepted that Lewis Carroll’s regress argument in “What Achilles Said to the Tortoise” sets up a constraint on what logical knowledge has to be like, if it is to account for deductive reasoning. The constraint is that it cannot be wholly propositional. In this talk, I will discuss three fundamental ways in which the relation between logical knowledge and deductive reasoning can be spelled out, which any account of logical knowledge has to do justice to. I will argue, against the orthodoxy, that Lewis Carroll’s argument, or successive interpretations of it, poses no threat to a propositional account of logical knowledge; and I will show how such an account can do justice to the relation between logical knowledge and deductive reasoning in any of the three fundamental ways of understanding it.