P505 | 12459 | Ebbs

This course presents the central concepts and methods of first-order logic, with an emphasis on the schematic conception of logical truth, according to which a logical truth is a true sentence that stays true when its so-called ‘logical’ words, such s ‘and’, ‘or’, ‘not’, ‘all’, and ‘some’, are held fixed and we uniformly replace any of the other words and phrases in the sentence with different ones. The lectures cover truth-functional logic, first-order monadic and polyadic quantificational logic, identity, and descriptions, as well as some of the central results in the metatheory of first-order logic, including the soundness, completeness, and undecidability of first- order polyadic quantificational logic and the Löwenheim-Skolem theorem. The problem sets for the course are designed to familiarize students with a wide range of proof techniques and to help students learn how to paraphrase sentences of English into regimented sentences to which the proof techniques of formal logic directly apply. Prerequisites: graduate standing and P250 or an equivalent background in formal logic. Book order: W. V. Quine, Methods of Logic, 4th edition.