**The** **William Reinhardt Memorial Lecture in the Philosophy of Mathematics** was founded to commemorate the life of William Reinhardt, Professor of Mathematics at the University of Colorado from 1967 until his death in 1998. He did important work in set theory, logic, and the foundations of mathematics. A central focus of his work was the search for new axioms of mathematics. The study of new axioms in mathematics requires the ability to stand back from mathematical practice and ask questions about the general principles that guide and justify it -- questions that engage philosophical as well as mathematical issues. For this reason, Professor Reinhardt was considered a philosopher as well as a mathematician. He made profound contributions to the philosophy and foundations of mathematics.

The Reinhardt Lecture, which is co-sponsored by the Reinhardt Fund and the Department of Philosophy, brings a leading contemporary philosopher of mathematics to Boulder to give a talk on some topic in set theory, logic, or the foundations of mathematics.

## 2019 Fall Reinhardt Lecture

**Steve Awodey**, Carnegie Mellon University

"Intensionality, Invariance, and Univalence"

September 13, 2019, 3:15 PM, HUMN 150

Abstract: What does a mathematical proposition mean? Under one standard account, all true mathematical statements mean the same thing, namely True. A more meaningful account is provided by the Propositions-As-Types conception of type theory, according to which themeaning of a proposition is its collection of proofs. The new system of Homotopy Type Theory provides a further refinement: The meaning of a proposition is the homotopy type of its proofs. A homotopy type may be seen as an infinite-dimensional structure, consisting of objects, isomorphisms, isomorphisms of isomorphisms, etc. Such structures represent systems of objects together with all of their higher symmetries. The language of Martin-Löf type theory is an invariant of all such higher symmetries, a fact which is enshrined in the celebrated Principle of Univalence.

**Past Reinhardt Lectures**

**John Bell, **University of Western Ontario

"Infinitesimals and the Labyrinth of the Continuum"

October 5, 2018, 3:15 PM, HLMS 199

**Professor James Robert Brown**, University of Toronto

“Pure and Applied: Mathematics and Ethics”

October 6 2017, 3:15-5:00pm

**W. D. Hart**, University of Illinois at Chicago

'Orayen’s Paradox’

Friday, December 6, 2013 3:15-5pm, HUMN 150

Abstract: A central application of sets is the standard theory of truth, Tarsi’s. But that view of truth fits set theory only awkwardly; that awkwardness is Orayen's Paradox.

W.D. Hart (A.B. scl, Harvard College 1964; PhD Harvard University 1969) is Professor Emeritus of Philosophy at the University of Illinois at Chicago, where he was chair of the philosophy department from 1994 until 2006 and from which he retired in June 2011. He previously taught at the University of Michigan (1969-74), University College London (1974-91), and the University of New Mexico (1992-93). His primary interests are logic,

philosophy of mathematics, metaphysics, and epistemology. His book The Engines of the Soul (Cambridge 1988, 2009 pbk) is an argument for dualism as a solution to the mind-body problem. The Evolution of Logic (Cambridge 2010) is a critical history of the relations between logic and philosophy over the last 130 years, and it reflects the core of his teaching over his career. Readings in the Philosophy of Mathematics (Oxford 1996), which he edited with an introduction, is a successor to the old Hintikka volume (the two have no overlap, the newer volume being a collection of philosophy papers, not mathematics).

**Otávio Bueno**, University of Miami

"What Does a Mathematical Proof Really Prove?"

Friday, May 3, 2013

3:00 PM, President's Room, Old Main Heritage Center

**Michael Potter**, University of Cambridge

"Does Mathematics Need Replacement (and Is It Even True)?"

Friday, March 16, 2008

3:15 PM, Eaton Humanities 150

**Donald A. Martin**, UCLA

"Is Set Theory about Sets?" (flier)

Friday, March 12, 2004

6:00 PM, Humanities 250

**William Tait**, University of Chicago

"Frege's Three Methodological Principles" (flier)

Monday, March 17, 2003

7:00 PM, UMC 289

**Vann McGee**, MIT

"Private Meanings, Shared Truths" (flier with abstract)

Monday, September 11, 2001

6:30 PM, British Studies Room, Norlin LIbrary