# Philosophy 12A

## Spring 2023

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

12A | Introduction to Logic | Mancosu | MWF 9-10 | Physics 1 |

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 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 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.

**Previously taught:**
FL22, SU22D, SU22C, SU22A, SP22, FL21, SU21D, SU21C, SU21A, SP21, FL20, SU20D, SU20C, SU20A, SP20, FL19, SU19D, SU19C, SU19A, SP19, FL18, SU18D, SU18C, SP18, FL17, SU17D, SU17A, SP17, FL16, SU16D, SU16A, SP16, FL15, SU15D, SU15A, SP15, FL14, SU14D, SU14A, SP14, FL13, SU13D, SU13A, SP13, FL12, SU12D, SU12A, SP12, FL11, SU11D, SU11A, SP11, FL10, SU10D, SU10A, SP10, FL09, SU09D, SU09A, SP09, FL08, SU08D, SU08A, SP08, FL07, SU07A, SP07, FL06, SU06A, SP06, FL05, SU05D, SP05, FL04, SU04D, SU04A, SP04, FL03.