Philosophy | Logical Theory I
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.