Recent, Current & Upcoming Teaching

Between Mathematics & Philosophy (Phil 43912, Fall 2012)

An introduction to some of the many important interactions between mathematics and philosophy throughout history. After a look at some ancient and medieval cases, we’ll turn our attention to the modern era and, following that, the nineteenth and twentieth centuries. Particular attention will be given to the use of so-called "imaginary" or "ideal" elements and methods in mathematics (e.g. infinitesimals and imaginary and complex numbers in algebra and analysis, points at infinity, etc. in geometry) and their justification.

PhilMath Intersem 2013

The focal topic of this year's seminar will be "Indirect Proof". For more information check here: PhilMath Intersem 2013

Seminar Fall 2013

Major Foundational Schools of the 19th and 20th Centuries


The focal topics will be the three main schools of 19th and 20th century foundations of mathematics, Logicism, Intuitionism and Formalism. Special attention will be paid to the supposed features of mathematics that each regarded as critically important to account for. Attention will also be given to their assessment and to what extent they may still be regarded as significant and plausible.

Readings will include selections from Brouwer, Dedekind, Frege, Heyting, Hilbert, Weyl and others.

Recent & Current PhD Advisees

• Emmylou Haffner (U of Paris 7) (expected Aug 2014)

Thesis: Arithmetization in Richard Dedekind's works, between foundational and mathematical investigations

• Anthony Strimple (expected 2014)

Thesis: Logic and Deductive Inference: A Study of the Role of Formality in the Psychology of Deductive Reasoning

• Graham Leach-Krouse (expected August 2013)

Thesis: Conceptions of Absolute Provability

• Christopher Porter (2012)

Thesis: Mathematical and Philosophical Perspectives on Algorithmic

• Iulian Toader (2011)

Thesis: Objectivity sans Intelligibility: Hermann Weyl's Symbolic Constructivism

•Sean Walsh (2010)

Thesis: Arithmetical Knowledge and Arithmetical Defi nability: Four Studies

• Andrew Arana (2004)

Thesis: Arithmetical Investigations: A Study of Models of Arithmetic and
Purity of Methods

• Joongol Kim (2004)

Thesis: A Philosophical Inquiry into the Concept of Number

Recent Post-Docs

• Andrew Arana (U of Notre Dame, PhD),  Ideals of Proof (IP)

• Paola Cantu (U of Milan, PhD), Ideals of Proof (IP)

• Renaud Chorlay (U of Paris 1, PhD), Ideals of Proof (IP)

• Walter Dean (Rutgers U, Philosophy, PhD;  CUNY Graduate School, Computer Science, PhD), Ideals of Proof (IP)

• Sebastien Maronne (U of Paris 7, PhD), Ideals of Proof (IP)

• Paul McCallion (U of Stirling, PhD), Ideals of Proof (IP)

• John Mumma (Carnegie-Mellon U, PhD), Ideals of Proof (IP)

• Andrei Rodin (Moscow State U, PhD), Ideals of Proof (IP)

• Fabien Schang (U of Nancy, PhD), Ideals of Proof (IP)

Other theses with which I've recently been involved ...

• Rebecca Morris (Carnegie Mellon)(201?)

Thesis: Shades of "Character": From Gauss to Landau

• Roman Ikonicoff (U of Paris 7) (2011)

Thesis: Penser l'E ffectivité: Naissance de la notion chez Émile Borel

• Soazig Le Bihan (U of Nancy 2)(2008)

Thesis: Understanding Quantum Phenomena

• Fredérick Tremblay (U of Nancy 2)(2008)

Thesis: La Rationalité d'un point de vue logique: entre
dialogique et inferentialisme. Etude comparative de Lorenzen et Brandom