Logic

In this seminar, we will examine the logical and metaphysical writings of Gottfried Wilhelm Leibniz. We will begin by exploring the metaphysical underpinnings of Leibniz’s calculus of analytic containment, as developed in such essays as General Inquiries into the Analysis of Concepts and Truths (1686) and A Mathematics of Reason (1690). We then consider how Leibniz’s logic informs some of the metaphysical ideas developed in some of Leibniz’s less technical philosophical writings, including Discourse on Metaphysics (1686) and On the Ultimate Origination of Things (1697). These distinctive logico-metaphysical conceptions, which give a singular shape to Leibniz’s philosophy, reach their full maturity in his best known essay on metaphysics, the Monadology (1714), with which the seminar will conclude. (IV)

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. (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.

Issues attending the concepts of negation, limit, and intentionality (construed as thought’s capacity to be answerable to reality) are typically approached in isolation one from another. The course will pursue the contrary hypothesis: namely, that the puzzles arising in connection with these three concepts form a nexus, so that none of them can be comprehended apart from the relations that it entertains with the two others. In order to motivate and substantiate this hypothesis, we will exhume and revive a philosophical tradition that runs from Plato to Wittgenstein through Kant and Sartre and whose defining feature lies in the upholding of this approach. We will examine how the three notions come into play in what Wittgenstein calls “the mystery of negation”: “This is not how things are, and yet we can say how things are not.” Bringing out their nexus requires accounting for the unity and univocity of the concept of negation across two ways of using negation that seem to pull in opposite directions: in the one case, “not-p” makes use of “not” in order to reject p as false (as in “The shirt is not red”), which requires that p lies within the limits of the realm of the intelligible; in the other case, “not-p” makes use of “not” to reject p as nonsensical (as in “The sweet is not a colour”), as if excluding p from the realm of the intelligible. (B)

Readings will include texts by Plato, Maïmonides, Duns Scotus, Spinoza, Kant, Hegel, Brentano, Husserl, Heidegger, Sartre, Frege, and Wittgenstein.

This course introduces non-classical extensions and alternatives to classical logic, and the philosophical debates surrounding them. Topics include modal logic (the logic of possibility and necessity), intuitionistic and many-valued logics (in which sentences may be neither true nor false, or both true and false), and relevant logic (which tries to refine the classical concept of entailment to capture the idea that the premises of arguments should be relevant to their conclusions). 

Students will learn tableau-style proof theories and Kripke frame semantics for a variety of non-classical logics, and will discuss adjacent philosophical issues, including the nature of necessity and possibility, the metaphysics of ordinary objects and fictional characters, the nature of truth, and the relationship between the world and the logical theories we use to describe it. (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.

Logic is, and always has been, a branch of philosophy. Why? What is logic? In this course we will explore the nature of logic, and how it relates to thought; to reasoning; to ordinary language; to mathematics; and to philosophy. We will read texts on the subject of logic by Aristotle, Kant, Hegel, Frege, Russell, Wittgenstein, Quine, Black, Prior, Gödel, Kripke, Dummett, Boolos, Putnam, Benacerraf, Harman, Williamson, Priest, and others. The course will be completely non-technical: we will be trying to make philosophical sense of logic. (B)

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. (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.

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.