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The paper concerns the relationship between mathematical logic and its suposed subject matter: correct reasoning. I suggest that a formal logic iS a mathematical model of reasoning, un much the same sense, as a system of point masses is a model of moving objects. There are gaps between the model and what it is a model of. The papar explores the possibility of using a logic, so understood, to motivate revisions in reasoning. The main case studies are classical logic, ralevance logic, and intuitionism. The paper is an extended commentary on John Corcoran's classic paper "Gaps between logical theory and mathematical practice" (The methodological unity of science edited by M. Bunge, Dordrecht, Holland, D. Reidel, 23-50).
Key words: logic, modal, reasoning.
