Philosophy 12A

Logical reasoning is essential in most areas of human inquiry. The discipline of Logic treats logical reasoning itself as an object of study. Logic has been one of the main branches of philosophy since Aristotle; it revolutionized the foundations of mathematics in the 20th century; and it has been called “the calculus of computer science,” with applications in many areas. Logic has also played an important role in the investigation of language and the mind, as the basis for formal semantics in linguistics and automated reasoning in artificial intelligence. Today, Logic is an interdisciplinary subject with many applications.

PHILOS 12A is intended as a first course in logic for students with no previous exposure to the subject. The course treats symbolic logic. Students will learn to formalize reasoning in symbolic languages with precisely defined meanings and precisely defined rules of inference. Symbolic logic is by nature a mathematical subject, but the course does not presuppose any prior coursework in mathematics—only an openness to mathematical reasoning.

The Spring 2025 installment of 12A will concentrate on three systems of symbolic logic: propositional logic (also known as sentential logic); syllogistic logic; and predicate logic (also known as first-order logic). Propositional logic formalizes reasoning involving “propositional connectives” such as ‘and’, ‘or’, ‘not’, ‘if…then’, and ‘if and only if’, as these words are used in mathematics. Syllogistic logic formalizes reasoning involving basic patterns of “quantification” such as ‘all whales are mammals’ or ‘some animals are carnivores’. Finally, predicate logic formalizes reasoning involving a greater variety of patterns of quantification, plus the attribution of properties to objects, both of which are on display in a statement such as ’for every number that is prime, there is a larger number that is prime’.

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