Anubav Vasudevan

In this course, we will examine the various ways in which the concepts and techniques of modern mathematical logic can be utilized to investigate the structure of knowledge. Many of the most well-known results of mathematical logic, such as the incompleteness theorems of Gödel and the Löwenheim-Skolem theorem, illustrate the fundamental limitations of formal systems of logic to fully capture the structure of the semantic models in which truth and validity are assessed. Some philosophers have argued that these results have profound epistemological implications, for instance, that they can be used to ground skeptical claims to the effect that there must be truths that logic and mathematics are powerless to prove. One of the aims of this course is to assess the legitimacy of these epistemological claims. In addition, we will explore the extent to which the central results of mathematical logic can be extended so as to apply to systems of inductive logic, and examine what forms of inductive skepticism may emerge as a result. We will, for example, discuss the epistemological implications of Putnam's diagonalization argument, which shows that, for any Bayesian theory of confirmation based on a definable prior, there must exist hypotheses which, if true, can never be confirmed. (B) (II)

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)

This course is a first introduction to American Pragmatism. We will examine some of the seminal philosophical works of the three most prominent figures in this tradition: Charles Sanders Peirce, William James, and John Dewey. Our main aim will be to extract from these writings the central ideas and principles which give shape to pragmatism as a coherent alternative to the two main schools of modern philosophical thought, empiricism and rationalism. (B) (III)

(II)

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

This course will survey some of the seminal writings of the early American Pragmatist tradition. We will focus primarily on works by the three most prominent figures in this tradition: C.S. Peirce, William James, and John Dewey. Our aim in the course will be to extract from these writings the central ideas and principles which give shape to pragmatism as a coherent philosophical perspective, distinct from both empiricism and rationalism. (B) (II)

This course will begin by examining the central writings of the early American Pragmatists, C.S. Peirce, William James, and John Dewey. We will compare the early formulations of pragmatism that appear in these works, both against one another other, as well against more recent formulations of pragmatism, as put forward by such philosophers as Putnam, Davidson, and Rorty. (II) (III)

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)

This course will provide an introduction to Bayesian Epistemology. We will begin by discussing the principal arguments offered in support of the two main precepts of the Bayesian view: (1) Probabilism: A rational agent's degrees of belief ought to conform to the axioms of probability; and (2) Conditionalization: Bayes's Rule describes how a rational agent's degrees of belief ought to be updated in response to new information. We will then examine the capacity of Bayesianism to satisfactorily address the most well-known paradoxes of induction and confirmation theory. The course will conclude with a discussion of the most common objections to the Bayesian view. (B) (II)