Intuitionism Reconsidered

The debate between intuitionists and classical logicians is fought on two fronts. First, there is the battle over subject matter-the disputants disagree regarding which mathematical structures are legitimate domains of inquiry. Second, there is the battle over logic-they disagree over which algebraic structure correctly codifies logical consequence. In this article the emphasis is on the latter issue-it focuses on what the correct (formal) account of correct inference might look like, and, given such an account, how we should understand disagreements regarding the extension of the logical consequence relation. In the next two sections of the article, two typical sorts of arguments for intuitionistic logic are examined. The article then examines exactly what is at stake when one provides a logic as an account of logical consequence.