The Justification of the Basic Laws of Logic

Abstract

Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form φ.1 Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to answer the question of how beliefs in such attributions are justified, on both its descriptive and normative interpretations; I aim to say when we generally take ourselves to be justified in forming such beliefs, and to make it plausible that beliefs formed this way really are justified. We can ask such questions about many domains (e.g. unobserved matters of fact Hume [9]) but there are special difficulties for answering them in logic. Some of the difficulties stem from the fact that logic is thought to be necessary and a priori; it is difficult to account for both a priori justification, and justification for thinking that something couldn’t have been otherwise. Moreover, it is often thought that logic is epistemically basic; we normally think that it is permissible to presuppose logic in the justification of our beliefs in other domains—engineering and arithmetic, for example, and even in justifying everyday common sense beliefs— yet we are not supposed to presuppose claims from these other domains when justifying our beliefs about logic. Logical beliefs come first, epistemologically speaking.