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date: 21 February 2020

Abstract and Keywords

The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that. It develops the syntax of second-order languages and present typical deductive systems and model-theoretic semantics for them. This will help to explain the role of higher-order logic in the philosophy of mathematics. It is assumed that the reader has at least a passing familiarity with the theory and metatheory of first-order logic.

Keywords: higher-order logic, second-order logic, first-order logic, second-order languages, deductive systems, model-theoretic semantics

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