Logical consequence and rationality

Abstract

What is the mathematical formulation of logical consequence answerable to? The prevalent stance among contemporary logicians is that mathematically formulated notion of logical consequence aims to capture the corresponding pre-theoretic notion. However, the notion of pre-theoretic logical consequence is far from being sufficiently clearly formulated in literature. In order to remedy this deficiency, and clear the ground, the paper distinguishes at least two possible readings of it. The first is “pre-theoretical” in the sense of pre-mathematical; such formulations can be and often are quite very sophisticated and in this sense non-ordinary; the second is “pre-theoretical” in the spirit of Tarski, who in this context points to “the common usage of the language of everyday life”; such an ordinary notion even a naïve thinker might turn out to possess. It is argued that both notions should be taken into consideration, and a sketch of framework is proposed, albeit quite programmatically: the formal logician is in the position of the translator from the ordinary into sophisticated and mathematical, in analogy with Quine’s translation schema. I conclude with a short indication of an even more general, moderately naturalistic research program in which logical consequence is understood as a (natural) kind, in the spirit of Putnam’s theory concerning its more concrete relatives.