Philosophy 12A

Logical argument and reasoning is fundamental to human inquiry. But how should we argue and reason correctly? The discipline of Logic inquires into correct logical argument and reasoning themselves.

Logic is an interdisciplinary subject with applications in many disciplines. It has been one of the main branches of philosophy since Aristotle, it revolutionized the foundations of mathematics in the 20th century, it has been called “the calculus of computer science”, and it is the foundation of the study of meaning in contemporary linguistics.

PHILOS 12A is a first course in symbolic logic, presupposing no prior knowledge of the subject. Students will learn how to formalize arguments and deductive reasoning in precise symbolic languages. We focus on two systems of logic. First, propositional logic, the logic of expressions like “or”, “and”, “not”, and “if”, as in the argument: “either the butler did it, or the gardener did. The gardener didn’t do it. So the butler did.” Second, predicate or first-order logic, the logic of expressions like “every”, “no” and “some” and of attributions of properties and relations, as in the argument: “if there are finitely many primes, some prime is greater than every other prime. No prime is greater than every other prime. So there are infinitely many primes.”

Students from philosophy, mathematics, computer science, and linguistics will find important connections between the symbolic logic covered in 12A and their other coursework.