Kevin Davey received his PhD from the University of Pittsburgh in 2003, and also has Masters degrees in both physics and mathematics. His main areas of interest are the philosophy of science, the philosophy of mathematics, logic, epistemology and the philosophy of physics. In the general philosophy of science and epistemology he is particularly interested in understanding the character of non-deductive inference, both within and outside the context of science. In the philosophy of mathematics, he is currently engaged in a close study of the origin of proof in both the western and non-western mathematical traditions, and the light that sheds on contemporary debates about the nature of mathematics. In logic, he is currently looking at the way we reason about truth, focusing both on philosophical questions about the nature of the truth predicate and technical questions about formal theories of truth.

## Selected Publications

"A Note on the Unprovability of Consistency in Formal Theories of Truth" (in progress)

"Inference to the Best Explanation and Norton’s Material Theory of Induction" (forthcoming)

"On Euclid and the Genealogy of Proof "(forthcoming)

"Can Good Science Be Logically Inconsistent?" (PDF)

Review of Halvorson’s "The Logic in Philosophy of Science" (https://ndpr.nd.edu/news/the-logic-in-philosophy-of-science/)

"Aristotle, Zeno and the Stadium Paradox" (PDF)

Is Mathematical Rigour Necessary in Physics?

*The British Journal for the Philosophy of Science* 2003 54(3):439-463 (Link)

Obligation and the Conditional in Stit Theory

*Studia Logica* Volume 72, Number 3 / December, 2002 (Link)

## Recent Courses

## PHIL 23106/33106 Topics in the Philosophy of Mathematics

In this course, we examine the modern incarnation of the idea that the foundations of mathematics should be understood from the point of view of type theory rather than set theory. We will carefully work through the central ideas of the Curry-Howard correspondence and Martin-L of type theory with a view to understanding some of the central issues involved therein. (B) (II)

## PHIL 53506 Non-Deductive Inference

This course will examine modern non-Bayesian ways of understanding non-deductive inference. Topics include the problem of induction, Pierce’s theory of abduction, inference to the best explanation, and the general connection between explanation and non-deductive inference. (III)

## PHIL 23951 Introduction to Eastern Philosophy

This course will be an overview of Eastern philosophy, focusing on the historical development of Buddhist and Confucian ideas from their early Indian origins to the present day. (A)

## PHIL 20405/30405 Further Topics in Logic

This course will closely examine the concept of quantification in logic, with special attention being given to alternatives to first-order quantification - e.g., second order quantification, higher order quantification, and substitutional quantification. Is there something fundamental about first order quantification as presented by Frege? Quine answers this question affirmatively, while others have answered negatively. We examine this debate. If time permits, we will also look at the conception of quantification implicit in modern category theory and the theory of types. (B) (II)

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.

## PHIL 49702 Revision Workshop

This is a workshop for 2nd year philosophy graduate students, in which students revise a piece of work to satisfy the PhD program requirements.

All and only philosophy graduate students in the relevant years.

## PHIL 22401/32401 Modern Logic and the Structure of Knowledge

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)

## PHIL 49701 Topical Workshop

This is a workshop for 3rd year philosophy graduate students, in which students prepare and workshop materials for their Topical Exam.

A two-quarter (Autumn, Winter) workshop for all and only philosophy graduate students in the relevant years.

## PHIL 49701 Topical Workshop

This is a workshop for 3rd year philosophy graduate students, in which students prepare and workshop materials for their Topical Exam.

A two-quarter (Autumn, Winter) workshop for all and only philosophy graduate students in the relevant years.

## PHIL 49700 Preliminary Essay Workshop

The workshop involves discussion of general issues in writing the essay and student presentations of their work. Although students do not register for the Summer quarter, they are expected to make significant progress on their preliminary essay over the summer.

All and only philosophy graduate students in the relevant years. A two-quarter (Spring, Autumn) workshop on the preliminary essay required for all doctoral students in the Spring of their second year and the Autumn of their third year.

## PHIL 50616 Merleau-Ponty and the Scientific Image

This course will be a reading of Merleau-Ponty's 'Structure of Behavior'. In this book, Merleau-Ponty critiques many of the scientific paradigms of the time concerning the nature of perception and behavior, proposing his own anti-Cartesian paradigm. Where appropriate, we will read some of the scientific texts to which Merleau-Ponty was responding, such as the work of the Gestalt Psychologists, Goldstein, Pavlov, and Peiron, as well as older texts such as Descartes' Optics. At stake in Merleau-Ponty's book is the question of the extent to which our conception of ourselves as mere biological creatures responding to environmental stimuli in accordance with the laws of physiology, and our conception of ourselves as thinking, feeling creatures experiencing the world are at odds with one another, and this question will loom large in our reading. The course will touch on important issues in general philosophy of science, philosophy of biology, and phenomenology. (II)

## PHIL 31414 MAPH Core Course: Contemporary Analytic Philosophy

The goal of this course is to have MAPH students explore the historical origins of analytic philosophy. Beginning with Frege, we will look at the development of analytic philosophy through the work of figures such as Russell, Wittgenstein, looking also at the rise and fall of positivism and the philosophical traditions that emerged afterwards with figures such as Quine, Kripke, Putnam and beyond. At the end of the course, MAPH students should have a more solid understanding of the central issues that have shaped modern American-European analytic philosophy, and some of the important ways in which this tradition diverges from contemporary continental philosophy.

This course is open only to MAPH students. MAPH students who wish to apply to Ph.D. programs in philosophy are strongly urged to take this course.

## PHIL 49700 Preliminary Essay Workshop

The workshop involves discussion of general issues in writing the essay and student presentations of their work. Although students do not register for the Summer quarter, they are expected to make significant progress on their preliminary essay over the summer.

All and only philosophy graduate students in the relevant years. A two-quarter (Spring, Autumn) workshop on the preliminary essay required for all doctoral students in the Spring of their second year and the Autumn of their third year.

## PHIL 53709 Conceptual Change and the A-Priori

In light of continual upheavals in the sciences, Kant's view that the sciences should be built on a foundation of synthetic a-priori knowledge has fallen out of favor. Should we then completely abandon the idea that the a-priori plays a significant role in science, or does some variant of the synthetic a-priori still in fact turn out to be necessary for science? To address this question, we will look at the writing of thinkers like Schlick, Reichenbach, Carnap, Quine, Kuhn, Friedman and others. (II) (III)

## PHIL 20616 Merleau-Ponty and the scientific view of the human

A major theme in modern philosophy is to try and understand the relationship between our view of ourselves as thinking, feeling creatures experiencing the world with our more scientific view of ourselves as mere biological creatures responding to environmental stimuli in accordance with the laws of physiology, physics and chemistry. Are these two views of human life at odds with each other? If not, why not? We will explore the views of the 20th century French philosopher Maurice Merleau-Ponty on these and related questions, focusing on his seminal work, 'The Structure of Behavior.'

Open to students who have been admitted to the Paris Humanities Program. This course will be taught at the Paris Humanities Program.

## PHIL 53106 Topics in the Philosophy of Mathematics

This course will broadly be about the concept of mathematical proof, focusing on the case of geometry, and more specifically, focusing on the works of Euclid. While many mathematicians think of Euclid as the pioneer of the modern axiomatic method, this way of thinking seems somewhat anachronistic. How then should we think of Euclidean proofs? What does a Euclidean proof accomplish, how does it accomplish it, and what does this tell us about the nature of mathematical proof more generally? This course will look both at ancient sources and modern sources as a way of tackling these questions. (II)

## PHIL 29405/39405 Advanced Logic

Since Russell's discovery of the inconsistency of Frege's foundation for mathematics, much of logic has resolved around the question of to what extent we can or cannot prove the consistency of the basic principles with which we reason. This course will explore two main efforts in this direction. We will first look at proof-theoretic efforts towards demonstrating the consistency of various foundational systems, discussing the virtues and limitations of this approach. We will then closely examine Godel's theorems, which are famous for demonstrating limits on the extent to which we can formulate consistency proofs. Much has been written on the implications of Godel's theorems, and we will spend some time trying to carefully separate what they really entail from what they do not entail. Assessment will be by regular homework sets. (B) (II)

Intermediate logic or prior equivalent required, or with consent of instructor.

For full list of Kevin Davey's courses back to the 2012-13 academic year, see our searchable course database.