A Note on FDE "All the Way Up"

Abstract

There is a natural ‘combinatorial argument’ for the philosophical view that if the standard (socalled classical) account of logical consequence (henceforth, logic) is right about logic’s fundamental truth values (viz., The True and The False), then FDE, a well-known subclassical logic [1, 2, 6, 8], is a more natural account of the space of ‘logical possibility’. Without officially endorsing that argument, our aim in this note is to defend it from an otherwise powerful objection. Our defense rests on an explicit generalization of a result by Priest [11]. In particular, by way of answering the target objection, we explicitly show that after combining the standard (classical) values in {>,⊥} to get a space of four values, as FDE demands, the given process of combining values ‘all the way up’ to α many values, for any ordinal α, results in the same account of logical consequence (viz., FDE).