Logic

An introduction to the techniques of modern logic. These include the representation of arguments in symbolic notation, and the systematic manipulation of these representations in order to show the validity of arguments. Regular homework assignments, in class test, and final examination. Course not for field credit.

In this course, we will prove the soundness and completeness of deductive systems for both sentential and first-order logic. We will also establish related results in elementary model theory, such as the compactness theorem for first-order logic, the Lowenheim-Skolem theorem and Lindstrom’s theorem. (B) (II)

Course not for field credit. 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.

In this class, we will look at various forms of non-deductive reasoning and will try to understand the relationships between them and the problems that surround them. Of particular interest will be the nature of inductive reasoning, the nature of abductive reasoning (inference to the best explanation), and the relationship between them. Some have argued that both of these forms of inference should be viewed as autonomous and independent forms of non-deductive inference, while others have argued that one should be subsumed under the other. We will also look at criticisms of both induction and abduction. We will begin by looking at the writings of Pierce, and will use this as a springboard to the modern literature. (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)

The course will take up a number of themes that are central to Wittgenstein’s Tractatus as they arise in the history of philosophical thought about logic— themes that arise out of questions such as the following: What is the status of the basic law(s) of logic?; Is it possible to draw a limit to logical thought?, What is the status of the reflecting subject of logical inquiry?; What is the relation between the logical and the psychological?; What, if anything ,is the relation between the following two inquiries into forms of unity: “What is the unity of the judgment (or the proposition)?" and “What is the unity of the judging subject?”; What (if any) sort of distinction between form and matter is relevant to logic?; How should one understand the formality of logic?; How, and how deeply, does language matter to logic? Topics will include various aspects of Aristotle's logical theory and metaphysics, Descartes’s Doctrine of the Creation of Eternal Truth, Kant on Pure General and Transcendental Logic, Frege on the nature of a proper Begriffsschrift and what it takes to understand what that it is, and early Wittgenstein’s inheritance and treatment of all of the above. Secondary readings will be from Jan Lukasiewicz, John MacFarlane, Clinton Tolley, Sebastian Roedl, Matt Boyle, John McDowell, Elizabeth Anscombe, Cora Diamond, Peter Geach, Matthias Haase, Thomas Ricketts, and Peter Sullivan. (III or V)

Course not for field credit. An introduction to the techniques of modern logic. These include the representation of arguments in symbolic notation, and the systematic manipulation of these representations in order to show the validity of arguments. Regular homework assignments, in class test, and final examination.

This class will look at old and new attempts to develop formal theories of the concept of truth. After a presentation of the paradoxes of disquotation, we will do a fairly close reading of Tarski's 'The Concept of Truth in Formalized Languages'. We will follow this with a close examination of Kripke's formal theory of truth, and will then look at Hartry Field's recent work on truth and the liar paradox. If time permits, we will briefly survey some other modern approaches, including those that revolve around the idea of so-called 'indefinite extensibility' (Glanzberg et al.) (II)

The study of logic in the second half of the 19th century was dominated by an algebraic approach to the subject. This tradition, as exemplified in George Boole’s Laws of Thought, aimed to develop a calculus of deductive reasoning based on the standard algebraic techniques employed in mathematics. In this course, we will trace the historical development of the algebraic tradition in logic, beginning with the early attempts of Leibniz to formulate a calculus ratiocinator. We will consider the various systems of algebraic logic developed in the 19th century in the works of De Morgan, Boole, Jevons, Peirce, and Schroder, and conclude by examining Frege’s critique of Boole’s system in relation to Frege’s own Begriffsschrift. (B) (II) (V)

Topic: What is a “Science of Logic” for Hegel? (instructor: T. Evnen)
This course is designed to introduce students to the philosophical aims and method of Hegel’s Science of Logic. Hegel often referred to the Logic as his most important work; by providing Hegel’s account of certain fundamental concepts—his concept of the concept, his account of self-consciousness and pure knowledge, and his idea of “absolute method”—the Logic serves both as a statement of what, for Hegel, philosophy is and, at least in a certain sense, as the ground upon which his philosophical system rests. Unfortunately, however, the Logic also has a strong claim to being Hegel’s most difficult work. We will attempt to ameliorate this difficulty a bit by beginning with an oblique approach to the text that situates it in its philosophical context. Specifically, we will seek to understand the Logic as a response to a determinate set of philosophical concerns that Hegel took himself to find in Kant—an approach to the text that is  made possible by the fact that Hegel himself evidently understood the Logic not only as the culminating text of his own philosophical system, but also as the culmination of a philosophical project inaugurated by Kant.In particular, we will develop the relationship between Hegel’s “speculative logic” and Kant’s “transcendental logic” by examining three lines of thought in Kant: 1) Kant’s account of spontaneity (and of the relationship between understanding and sensibility) in the B-Deduction of the First Critique; 2) Kant’s transcendental idealism as it is presented and motivated in certain passages of the Transcendental Aesthetic and the Transcendental Dialectic; and, 3) Kant’s treatment of the idea of an “intuitive understanding” in §77 of the Critique of the Power of Judgment. Any one of these topics could rightly be the subject of its own course, but of necessity our concern here will be to focus narrowly on the difficulties and insights that Hegel himself finds in them. (Our narrow focus also means that prior familiarity with Kant’s philosophy will not be presupposed).In the latter half of the course, we will approach the Logic directly. We will orient ourselves by beginning with selections from the introductory materials (as well as a few of the concluding passages) of both the Encyclopedia Logic and the Science of Logic. These are the places in the text that contain Hegel’s most explicit reflections on his philosophical aims and methodology. From there, we will dive into the thick of the text and examine (as “case studies”) Hegel’s treatment of the progression from teleology to life to cognition.

Topic: Logic and Thought (instructor: G. Nir)

How does logic relate to thought? A course in Elementary Logic teaches us formal methods of evaluating arguments, but does it purport to tell us anything about how we actually reason?  Through a discussion of central issues in the philosophy of logic, this course will explore ways in which this question may receive a positive answer. We will concern ourselves particularly with the kind of philosophy of mind that logicians like Frege and Wittgenstein took themselves to offer.   The course has four parts. We will start by looking at the conception of logic advocated by Frege and Wittgenstein, according to which logic is primarily concerned with thought, its structure, form, uses and laws.  In the second part of the course, we will ask whether puzzles which beset formal logic must also plague thought, inasmuch as the later is understood as endowed with logical form. We will then try to capture what is unique in the concern of logic with thought by contrasting it with the kinds of concern that science, in particular psychology, has. Finally, we will look at two other approaches to the relation of logic and thought which differ markedly from the one we developed so far, and contrast their virtues with what we will call the constitutive conception of logic.