Logic

This course will undertake a critical review of the some of the seminal logical and metaphysical writings of the American pragmatist philosopher Charles Sanders Peirce. Peirce made numerous original contributions to the field of mathematical logic, particularly to the fields of relational and quantificational logic, and, in the first part of the course, we will carefully examine some of Peirce's most important writings on the subject. In the second half of the course, we will examine some of Peirce's most characteristic metaphysical doctrines. These include: triadism - the view that all experience may be classified within a tripartite scheme consisting of the categories of "firstness," "secondness," and "thirdness;" tychism - the view that objective chance is an operative feature of the cosmos; haecceitism - the view that individual substances have an essence de re and not merely de dicta; and synechism - the view that the cosmos is fundamentally a continuum, no part of which is fully separate or determinate. (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 provides a first introduction to mathematical logic for students of philosophy. In this course we will prove the soundness and completeness of deductive systems for both propositional and first-order predicate logic. (B) (II)

One of the most curious ideas in the foundations of logic to emerge over the last several decades is the idea that logic is in some sense reducible to the theory of types and computer programs. This course will introduce students to the technical material needed to understand such claims and tackle the question of whether this new way of thinking of the foundations of logic is plausible. The course will cover such topics as the lambda calculus, intuitionistic logic, the Curry Howard correspondence, and Martin-Lof type theory. Students will be assumed to have a grasp of the basic theory of first order logic. Some exposure to undergraduate level mathematics will also be helpful. (B) (II)

For each second of John’s life, consider the claim that he is young at that second. Many of these claims will be clearly true: he is young at all of the seconds that make up the first year of his life. Many of these claims will be clearly false: he is not young at all of the seconds that make up his 89th year. If all of these statements are either true or false, it follows that there was a last second at which it is true to say that he is young, and a first second at which it is true to say that he is not young. But that seems wild! One second can’t make the difference between a young person and an old person.

This is one of the central problems raised by the phenomenon of vagueness. This course will examine a variety of philosophical issues raised by the phenomenon of vagueness in the philosophy of language, philosophical logic, epistemology, and metaphysics. Among other things, we will discuss: the philosophical significance of vagueness, the relationship between vagueness and ignorance, decision-making under indeterminacy, and the question of whether vagueness is an essentially linguistic phenomenon. (B)

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)

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 first introduction to mathematical logic. In this course we will prove the soundness and completeness of deductive systems for both propositional and first-order predicate logic. (B) (II)