Philosophy 12A

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.