Phil 12A

Introduction to Logic


Spring 2017

Professor Paolo Mancosu

Office: 230 Moses Hall


Class meets: M, W, F 10-11, Hearst Field Annex A1

Office hours: M 11-12, F 12-1

Course Description

The course will introduce the students to the syntax and semantics of propositional and first-order logic. Both systems of logic will be motivated by the attempt to explicate the informal notion of a valid argument. Intuitively, an argument is valid when the conclusion ‘follows’ from the premises. In order to give an account of this notion we wil introduce a deductive system (a natural deduction system), which explicate the intuitive notion of 'follow’ in terms of derivational rules in a calculus. This will be done in stages, first for propositional reasoning (only connectives such as 'and’, 'or’, 'if… then…’ and later for the full first-order calculus (including expressions such as 'for all…’ and 'there exists…’. In addition, we will also develop techniques to show when a claim does not follow from the premisses of an argument. This is done by developing the semantics for the propositional and the predicate calculus. We will introduce truth-tables for the propositional connectives and 'interpretations’ for sentences of first-order logic. At the end of the course, if time allows, we will also cover some metatheoretical issues, such as soundness and completeness of the propositional calculus.

Prerequisites: None


We shall cover roughly part I and II of the textbook at the rate of one chapter per week, possibly condensing the first eight chapters into seven weeks (as to finish part I by mid-term).


J. Barwise and J. Etchemendy, Language Proof and Logic, CSLI (University of Chicago Press), second edition. IMPORTANT: This is a text/software package. DO NOT buy it used. (The included software contains a registration ID that can only be used once. If you buy it used, you will not be able to complete the homework assignments.) The text is available at the Cal Student Store. Alternatively you can order it through

Updated on 2017-01-09 17:18:47 -0800 by Paolo Mancosu