Logic

This course provides an introduction to logic for students of philosophy. It is aimed at students who possess more mathematical training than can be expected of typical philosophy majors, but who wish to study logic not just as a branch of mathematics but as a method for philosophical analysis. (II)

An introduction to the concepts and principles of symbolic logic. We learn the syntax and semantics of truth-functional and first-order quantificational logic, and apply the resultant conceptual framework to the analysis of valid and invalid arguments, the structure of formal languages, and logical relations among sentences of ordinary discourse. Occasionally we will venture into topics in philosophy of language and philosophical logic, but our primary focus is on acquiring a facility with symbolic logic as such.

An introduction to the concepts and principles of symbolic logic. We learn the syntax and semantics of truth-functional and first-order quantificational logic, and apply the resultant conceptual framework to the analysis of valid and invalid arguments, the structure of formal languages, and logical relations among sentences of ordinary discourse. Occasionally we will venture into topics in philosophy of language and philosophical logic, but our primary focus is on acquiring a facility with symbolic logic as such.

This course will be an introductory survey of the philosophical and mathematical foundations of intuitionistic logic, perhaps the most serious rival to classical logic. We will pay attention to its philosophical motivations, especially by examining some of the more philosophical works of Brouwer. The course will also involve a mathematically rigorous presentation of the metatheory of intuitionistic logic, using forcing and Kripke frames. (B) (II)

This course provides a first introduction to formal logic. In this course, we will introduce proof systems for both propositional and first-order predicate logic and prove their soundness and completeness. (B) (II)

An introduction to the concepts and principles of symbolic logic. We learn the syntax and semantics of truth-functional and first-order quantificational logic, and apply the resultant conceptual framework to the analysis of valid and invalid arguments, the structure of formal languages, and logical relations among sentences of ordinary discourse. Occasionally we will venture into topics in philosophy of language and philosophical logic, but our primary focus is on acquiring a facility with symbolic logic as such.

This course provides a historical survey of the philosophy of time. We begin with the problems of change, being and becoming as formulated in Ancient Greece by Parmenides and Zeno, and Aristotle’s attempted resolution in the Physics by providing the first formal theory of time. The course then follows theories of time through developments in physics and philosophy up to the present day. Along the way we will take in Descartes’ theory of continuous creation, Newton’s Absolute Time, Leibniz’s and Mach’s relational theories, Russell’s relational theory, Broad’s growing block, Whitehead’s epochal theory, McTaggart’s A, B and C theories, Prior’s tense logic, Belnap’s branching time, Einstein’s relativity theory and theories of quantum gravity. (B) (II)

Key contemporary debates in the philosophical literature often rely on formal tools and techniques that go beyond the material taught in an introductory logic class. A robust understanding of these debates---and, accordingly, the ability to meaningfully engage with a good deal of contemporary philosophy---requires a basic grasp of extensions of standard logic such as modal logic, multi-valued logic, and supervaluations, as well as an appreciation of the key philosophical virtues and vices of these extensions. The goal of this course is to provide students with the required logic literacy. While some basic metalogical results will come into view as the quarter proceeds, the course will primarily focus on the scope (and, perhaps, the limits) of logic as an important tool for philosophical theorizing. (B)

This class will explore dependent type theory, with a focus on the identity relation. Different ways of thinking of the identity relation will be examined, culminating in a presentation of the Univalence axiom and a discussion of its role as a potential foundation for mathematics. (B) (II)

An introduction to the concepts and principles of symbolic logic. We learn the syntax and semantics of truth-functional and first-order quantificational logic, and apply the resultant conceptual framework to the analysis of valid and invalid arguments, the structure of formal languages, and logical relations among sentences of ordinary discourse. Occasionally we will venture into topics in philosophy of language and philosophical logic, but our primary focus is on acquiring a facility with symbolic logic as such.