# Philosophy 12A

## Fall 2009

Number | Title | Instructor | Days/time | Room |
---|---|---|---|---|

12A | Introduction to Logic | Mancosu | MWF 9-10 | 105 Northgate |

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 will introduce a deductive system (a natural deduction system), which explicates 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 for showing when a claim does not follow from the premises 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. Textbook: J. Barwise, J. Etchemendy, “Language, Proof and Logic”, latest edition. (The book comes with a CD. Do not buy the book used! If you do, you will not be able to submit your exercises on line, which you will be required to.)

**Previously taught:**
SU09D (Beattie), SU09A (Rieppel), SP09 (Warren), FL08 (Fitelson), SU08D (Klempner), SU08A (Fitelson), SP08 (Mancosu), FL07 (Fitelson), SU07A (Fitelson), SP07 (Mancosu), FL06 (Fitelson), SU06A (Rao), SP06 (Warren), FL05 (Mancosu), SU05D (Khatchirian), SP05 (Shapiro), FL04 (Fitelson), SU04D (Khatchirian), SU04A (Warren), SP04 (Warren), FL03 (Mancosu).