Education
Ph.D. (Philosophy), Stanford University
B.A. (Philosophy), University of California, San Diego
Employment
August 1993 – Present: University of Notre Dame, Dept. of Philosophy
- June 2020 – Present: McMahon-Hank Chair of Philosophy
- June 2017 – June 2020 Present: Glynn Family Honors Collegiate Chair, Professor of Philosophy
- May 2012 – Present: Professor
- Director of Graduate Studies 2004-2007, 2008-2011
- May 2000 – May 2012: Associate Professor
- August 1993 – May 2000: Assistant Professor
July 1990 – July 1993: Yale University. Assistant Professor, Dept. of Philosophy.
Publications:
Book
- Frege’s Conception of Logic, Oxford University Press 2012
Reviewed in:
- Philosophia Mathematica 22, 1 (2014) pp 108-120.
- Journal of the History of Philosophy 52 (2014) pp 176-177.
- Bulletin of Symbolic Logic 19, 2 (2013) pp 219-222.
- Notre Dame Philosophical Reviews (2013) online.
Articles
- “Second Philosophy and Realism” in Penelope Maddy on the Philosophy of Mathematics, J. Kennedy and S. Arbeiter (eds), Springer Outstanding Contributions to Logic series, forthcoming.
- “Frege on Caesar and Hume’s Principle” in Origins and Varieties of Logicism: A Foundational Journey in the Philosophy of Mathematics, A. Sereni and F. Boccuni (eds), Routledge, Studies in the Philosophy of Mathematics and Physics series, 2021, 27-54.
- “Axioms in Frege,” Essays on Frege’s Basic Laws of Arithmetic, edited by Marcus Rossberg and Philip Ebert, Oxford University Press, 31-56.
- “Models in Geometry and Logic: 1870-1920,” Logic, Methodology and Philosophy of Science – Proceedings of the 15th International Congress, edited by Niiniluoto, Seppälä, & Sober, College Publications 2017, 41-61.
- “Philosophy of Logic,” Philosophy of Logic: 5 Questions, Automatic Press 2016, 25-35.
- “Models and Independence circa 1900,” Logica Yearbook 2015, London: College Publications 2016, 17-38. Much of the material in this paper appears also in the expanded “Models in Geometry and Logic: 1870-1920,”
- “Frege on Mathematical Progress,” Early Analytic Philosophy: New Perspectives on the Tradition edited by Sorin Costreie; Springer Verlag 2016, 3-19.
- “The Breadth of the Paradox,” Philosophia Mathematica Vol 24 No. 1 (2015), 30-49.
- “Reply to Cook, Rossberg, and Wehmeier,” Journal of the History of Analytic Philosophy, Vol 3 No. 7 (2015).
- “Frege” in Oxford Handbook of German Philosophy in the Nineteenth Century, M. Forster and K. Gjesdal (eds), Oxford University Press 2015, 207-227.
- “Frege’s Critique of ‘Modern’ Axioms” in Frege: Freund(e) und Feind(e), Proceedings of the International Conference, Dieter Schott (ed), Berlin: Logos Verlag 2015, 105-120.
- “Frege on Formality and the 1906 Independence Test,” Formalism and Beyond: On the Nature of Mathematical Discourse, Godehard Link (ed), Boston/Berlin: de Gruyter 2014, pp 97-118.
- “From Logicism to Metatheory,” The Palgrave Centenary Companion to Principia Mathematica, B. Linsky and N. Griffin (eds), Palgrave Macmillan 2013, pp 59-78.
- “Frege on Shared Belief and Total Functions,” Journal of Philosophy CIX 1/2 (Jan/Feb 2012) pp 9-39.
- “Frege on Consistency and Conceptual Analysis,” Philosophia Mathematica 15, 3 (2007) pp 321-346.
- “Mathematical Objects and Identity,” Situating Semantics: Essays on the Philosophy of John Perry, M. O’Rourke and C. Washington (eds) MIT Press 2007, pp 73-92.
- “The Frege-Hilbert Controversy” in the Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/frege-hilbert/ (first posted 2007; substantial update 2018)
- “Logical Consequence,” Blackwell Guide to Philosophical Logic (Blackwell: Malden MA and Oxford 2001), 115-135.
- “Realism and Paradox,” Notre Dame Journal of Formal Logic 41, 3 (2000) 227-241.
- “Models and Modality,” Synthese Vol 124, No.1/2 (July 2000), 45-72.
- “Relative Identity and Cardinality,” Canadian Journal of Philosophy 29, No. 2 (June 1999), 205-224.
- “Frege and Hilbert on Consistency,” Journal of Philosophy XCIII (July 1996), 317-336.
- Reprinted in The Philosopher’s Annual Vol XIX (1998), 33-51.
- Reprinted in Gottlob Frege: Critical Assessments of Leading Philosophers Vol II (Reck, E. and M. Beaney, eds), Routledge 2005 pp 29-49.
- “Frege’s Reduction,” History and Philosophy of Logic 15 (1994), 85-103.
- “Fregean Thoughts and Indexicals,” CSLI Report CSLI-88-134, Center for the Study of Language and Information, Stanford University, Nov. 1988.
Book Reviews
- Review of Alexander George and Daniel Velleman: Philosophies of Mathematics in Philosophia Mathematica (Series III) Vol 11 Number 3 (2003) pp 358-362.
- Review of Colin McGinn’s Logical Properties. Notre Dame Philosophical Reviews, 2002.
Encyclopedia Entries
- “Logical Consequence” in Encyclopedia of Language and Linguistics, 2nd Edition, Elsevier Press (2005)
- “Realism in the Philosophy of Mathematics,” Routledge Encyclopedia of Philosophy (1998).
PodCast
- Podcast on Frege’s Logicism for Elucidations, University of Chicago
Invited Lectures
“Rigor and Formalism in Logic” at the Rigor and the Growth of Knowledge conference, Université Paris Cité and CNRS, Paris, February 2024
“Conceptual analysis in Logic and Mathematics”:
- Univeristy of Calgary, Calgary, Alberta, Canada December 2023
- Oxford University: Jowett Society Lecture, Oxford, England, June 2023
- St. Andrews University: “Analysis: History and Metaphilosophy” conference, St. Andrews, Scotland, May 2023
- Princeton University: “Philosophies of Mathematics in Dialogue” conference, Princeton New Jersey, May 2023
- Canadian Society for the History and Philosophy of Mathematics (online) May 2023
“Formalism in Logic” – the Online Logic Lecture series, Sept 2022
“Formalism in Logic” – the 2022 Gödel Lecture at the Association for Symbolic Logic, Reykjavik, Iceland: June 2022
“Inferentialism, Content, and Frege” at the Institute Vienna Circle, University of Vienna (via Zoom), June 2021
“Geometry, Logic and Philosophy: the Case of the Parallels Postulate,” The Calgary Mathematics and Philosophy Lecture, University of Calgary, Calgary, Alberta (via Zoom), March 2021
“Frege on Caesar and Hume’s Principle” at the Oxford Philosophy of Maths Seminar, Oxford University (via Zoom), October 2020
“Logicisms and Epistemology: Frege and Dedekind,” Society for the Study of the History of Analytic Philosophy at the APA Central meeting, Chicago, February 2020
“Mathematical Realisms,” French Philosophy of Mathematics Workshop, Paris, November 2019
“Logic and Geometry: Why Logical Claims Aren’t Always What They Seem to Be” at Macalester College, October 2019
“Frege and what Philosophy of Mathematics Can(not) Do” at the Madison meeting of the American Mathematical Society, September 2019
“Models from Geometry to Logic,” Association of Symbolic Logic, Denver, February 2019
“Caesar and Objects Again” at the University of Connecticut History of Analytic Philosophy Workshop, November 2018
– “Axioms: From Geometry to Logic” at the Modern Axiomatics and Early Metatheory Workshop, Vienna, February 2018
– “What Does a Model Show?” University of Illinois at Chicago, November 2017
– “What Does a Model Show?” SWIP-Analytic at NYU, October 2017
– “Geometry and Logic,” plenary address at the Cambridge Graduate Conference on Philosophy of Mathematics and Logic, University of Cambridge (England), January 2017
– “Models from Geometry to Logic,” The 50th Chapel Hill Colloquium, UNC-Chapel Hill, October 2016
– “Models in Geometry and Logic,” department colloquium at the University of Ottawa (Canada), September 2016
– “Arbitrariness and Conceptual Analysis in Frege,” Society for the Study of the History of Analytic Philosophy, Central APA, Chicago March 2016.
– “Models in Geometry and Logic: 1870-1920,” Plenary address at the International Congress on Logic, Methodology and Philosophy of Science, Helsinki. August 2015.
– “Models and Independence circa 1900,” Invited lecture at the Logica conference, Hejnice, Czech Republic. June 2015.
– “Logic and Conceptual Analysis in Frege,” University of Pavia (Italy), May 2015.
– “Frege on Abstraction”:
- Università Vita-Salute San Raffaele, Milan; May 2015
- Logica seminar, University of Barcelona, May 2015
– “Models in Geometry and Logic,” Oberlin College Philosophy Department Colloquium, April 2015
– “The Birth of Semantic Entailment” :
- Plenary address at the Logic Colloquium 2014 in Vienna (“Vienna Summer of Logic”), July 2014;
- Southern Wisconsin Logic Colloquium, October 2014
– “Frege on Mathematical Progress,” Invited address at the Philosophy of Mathematics session of the Logic Colloquium, Vienna, July 2014
-“What Does a Model Show?”
- Plenary address at the Society for the Study of the History of Analytical Philosophy, Montreal, May 2014;
– “Sense and Ignorance,” invited address at the “Content, Context and Inference in Frege; Frege@Stirling II” workshop, Stirling, Scotland, May 2014
– “Getting to Hilbert-Ackermann Completeness: Early Steps,” invited address at the Association of Symbolic Logic Spring Meeting, San Diego, April 2014
– “Author Meets Critics” book symposium on my Frege’s Conception of Logic at the American Philosophical Association Pacific Division Meeting, San Diego, April 2014
– Contribution to the Book Symposium on Richard Heck’s Frege’s Theorem, American Philosophical Association Eastern Division Meeting, Baltimore, December 2013
– “Applications and Content: Frege and Gödel on Mathematics as Syntax,” Munich Center for Mathematical Philosophy, Munich, July 2013
– “Axioms in Frege”:
- Third International Frege Conference, Wismar, Germany, May 2013
- FregeFest IV, University of California, Irvine, April 2013
- Grundgesetze conference, New York University, May 2012
– “Frege’s Conception of Logic,” Wittgenstein Workshop at the University of Chicago, February 2013
– “The Breadth of the Paradox,” Munich Center for Mathematical Philosophy, Munich, January 2013
– “Models and Independence in Geometry and Logic,” The Ohio State University Philosophy Department, October 2012
– “Logic and Conceptual Analysis in Frege,” CUNY Logic Workshop, September 2012
– “(Frege On) Axioms as Foundations” at the “What are Foundations and What are they For?” conference at Cambridge University, July 2012
– “Axioms and Conceptual Analysis in Frege” at the Bucharest Conference in Analytic Philosophy, University of Bucharest, Romania, June 2012
– “Independence and Entailment” at the Moral Sciences Club, Cambridge University, May 2012
– “Axioms and Structure in Frege” at the “The Classical Model of Science II – the Axiomatic Method,” conference, Vrije Universiteit Amsterdam, August 2011
– “Conceptual Analysis, the Peano Axioms, and Logicism in Frege” at the “Logicism Today” workshop, Besse-en-Chandesse, France, June 2011
– “Frege on Conceptual Analysis and Logical Entailment”:
- University of Chicago Workshop on Formal Philosophy, April 2011;
- Plenary address at the North American annual meeting of the Association for Symbolic Logic, Notre Dame, IN, May 2009;
- Formal Epistemology Workshop, Pittsburgh PA, June 2009
– “Frege’s Metatheory” at the 2010 Paris PhilMath Workshop at the École Normale Superieur, Paris, France, November 2010
– “From Logicism to Metatheory” at the “PM@100: Logic from 1910 to 1927” conference at McMaster University, Hamilton Ontario, May 2010
– “Domain Extensions and Total Functions in Frege” at the Institut für Logik und Wissenschaftstheorie, Ludwig-Maximilians-Universität, Munich, June 2008
– “A Fregean Conception of Logic” at the American Philosophical Society, Philadelphia PA, May 2008
– “Analysis and the Logical Relations in Frege” at:
- Dept. of Philosophy, University of Wisconsin at Madison, November 2005;
- Dept. of Philosophy, University of Wisconsin at Milwaukee, October 2004;
- Dept. of Philosophy, Ohio State University, July 2004
“Partial Mathematical Objects” at the Metaphysical Mayhem conference, Syracuse NY, August 2002
– “Universalism: A Fregean Perspective” at the Association of Symbolic Logic meeting, Urbana-Champaign, IL, June 2000
– “Frege’s Metatheory” at the Dept. of Logic and Philosophy of Science, University of California/Irvine (February 2000).
– “Frege’s Metatheory and the 1906 Independence Test”:
- Northwestern University, Program for the History and Philosophy of Science, January 1999;
- Purdue University Philosophy Dept, November 1998
– “Platonism and Reduction” at the Inland Northwest Philosophy Conference, Moscow, Idaho, April 1998
– “Models and Modality” at Indiana University – Bloomington Logic Group, November 1997
– “Frege, Hilbert, and Ordinary Consistency” at the University of California, Riverside Philosophy Dept.,January 1995
– “Frege’s Reduction” at the University of Calgary Philosophy Department, October 1993
– “Frege’s Logicism”:
- Brandeis University Philosophy Department, March 1993;
- University of Wisconsin, Madison Philosophy Dept., November 1992;
- Manhattanville College Philosophy Department, April 1992
– “Frege’s Logicism: A Response to Benacerraf”:
- CUNY Graduate Center, Philosophy Colloquium (October 1990);
- Stanford University; University of California/Berkeley; University of California/Riverside; University of Texas/Austin; University of Rochester; University of Washington/Seattle (Fall-Winter 1989-90).
Invited Conference Replies
– “Reply to Landini” (topic: Frege’s Logicism), American Philosophical Association, Central Division (April 2006)
– “Reply to Newhard” (topic: Kripke’s theory of truth), Inland Northwest Philosophy Conference (March 2000).
– “Reply to Rumfitt” (Topic: Frege’s Logicism), American Philosophical Association, Central Division, New Orleans (May 1999).
– “Reply to Tait” (Topic: Cantor’s Grundlagen), American Philosophical Association, Central Division, Chicago (May 1998).
– “Davidson on Quotation: a Reply to Stainton,” Canadian Philosophical Association, Western Division, Winnipeg, Manitoba (October 1997).
– “Reply to Macbeth” (Topic: Frege’s theory of number), American Philosophical Association, Central Division, Chicago (April 1996).
– “Reply to Ray” (Topic: Logical Consequence), American Philosophical Association, Pacific Division, San Francisco (March 1995).
– “Reply to Perry” (Topic: Indexicals in ordinary language), Berkeley Conference on Philosophy of Language, Berkeley, California (April 1993).
– “Reply to Sher” (Topic: Logical Consequence), American Philosophical Association, Eastern Division, New York (December 1991).
Presentations at Notre Dame:
– October 2015: “Models in Geometry and Logic,” Philosophy Department Colloquium.
– October 2014: “The Birth of Semantic Entailment,” Logic Colloquium.
– April 2012: “Disquotationalism: It’s Worse Than You Thought,” mini-conference in honor of Marian David.
– November 2006: “Analysis and the Logical Relations in Frege,” Philosophy Department colloquium.
– March 2001: “Realism and Paradox” at the Logicism and the Paradoxes conference.
– April 1999: “Frege’s Views on Metatheory,” Notre Dame Logic Group.
– March 1999: “Frege’s Metatheory and the 1906 Independence Test,” Philosophy Department Colloquium.
– December 1998: Reply to David VanderLaan’s “Impossible Worlds and Counterfactual Semantics,” Philosophy Department Colloquium.
– August 1998: Reply to Mike Rea’s “Theism and epistemic truth-equivalences,” Midwestern Metaphysics meeting.
– February 1998: “Models and Modality,” Philosophy Department Colloquium and Notre Dame Logic Group.
– August 1997: “Relative Identity and Cardinality,” Midwestern Metaphysics meeting.
– November 1996: “Reply to Halbach” (Topic: Axiomatic Truth-Theories), Philosophy Department Colloquium.
– November 1994: “Frege, Hilbert, and Ordinary Consistency,” Philosophy Department Colloquium.
– September 1994: “Reply to Detlefsen” (Topic: Constructivism and Mathematical Knowledge), Philosophy Department Colloquium.
– December 1993: “Frege’s Reduction,” Philosophy Department Colloquium.
Courses Taught at Notre Dame
Introductory:
- Introduction to Philosophy
- Introductory Philosophy of Mind
- Introductory Logic
- Critical Thinking
Intermediate/Advanced:
- Philosophy, Science and Mathematics
- Foundations of Analytic Philosophy
- Philosophy of Language
- Philosophy of Mathematics
- History and Philosophy of Logic
- Logic
Graduate Seminars:
- Frege, Carnap, and Quine
- Topics in Philosophical Logic
- Philosophy of Logic (Logical Pluralism)
- Philosophy of Logic (The Emergence of First-Order Logic, 1879-1930)
- Philosophy of Logic (Consequence)
- The Philosophy of Gottlob Frege
- Frege’s Philosophy of Logic and Mathematics
- Frege’s Philosophy of Language
- Logic in Metaphysics and Metaphysics in Logic
- Contemporary Philosophy of Mathematics
Directed Readings (Graduate Students)
- Logical Consequence
- Foundations of Analytic Philosophy
- Frege
- Wittgenstein
Dissertations Directed:
Joongol Kim, 2004 (co-directed with Michael Detlefsen)
Dissertation Committees
Bokai Yao (PhD 2924) – Philosophy of Logic
Matteo Bianchetti (PhD 2021) – Philosophy of Math
Ellen Lehet (PhD 2020) – Philosophy of Math
Ben Middleton (PhD 2020) – Philosophy of Logic
Paul Anh Tran Hoang (PhD 2019) – Philosophy of Math
Justin Christy (PhD 2017) – Metaphysics
Graham Leach-Krouse (PhD 2013) – Logic / Philosophy of Math
Lorraine Keller (PhD 2012) – Philosophy of Language
Iulian Toader (PhD 2011) – History and Philosophy of Science
Sean Walsh (PhD 2010) – Logic / Philosophy of Math
John Keller (PhD 2010) – Philosophy of Language
Josh Rasmussen (PhD 2010) – Metaphysics
Christian Johnson (PhD 2008) – History of Philosophy
Andy Arana (PhD 2003) – Logic / Philosophy of Math
Alicia Finch (PhD 2002) – Metaphysics
Michael Thrush (PhD 2001) – Metaphysics
Alisa Bokulich (PhD 2001) – Philosophy of Science
External Reviewer
- DPhil, University of Oxford, 2023. History and Philosophy of Logic
- PhD thesis, University of Amsterdam, 2022. History and Philosophy of Mathematics
- PhD thesis, Cambridge University, 2016-17. History and Philosophy of Logic
- PhD thesis, University of Ottawa, 2014. History and Philosophy of Mathematics
Service history:
Department:
- Program Committee for Midwest PhilMath Workshop (every year)
- Committee on Appointments and Promotions: 2001-2, 2003-4, 2005-7, 2009-11, 2013 – 2015, 2017-18
- Member, Interview and Hiring Committee 2013-14, 2016-17, 2017-18
- Chair, Departmental Climate Committee 2012–2015, 2016-17, 2019-22; Member of the Committee: 2017-18
- Member, Graduate Committee 2013 – 2015, 2016-17, 2017-18
- Full Professors’ Committee 2013 – 2015
- Director of Graduate Studies: 2004-2007, 2008-2011
- Member, External Review Committee: 1999-2001, 2010-11
- Member, Core Curriculum Review Committee: 2005 – 07
- Member, Graduate Admissions Committee: 1999 – 2000, 2003 – 04
- Organizer, Departmental Colloquium Series: 2001 – 2003
- Director, Graduate Student Placement: 1995-97, 2000 – 01
- Member, Graduate Student Placement Committee: 1998-99
- Affirmative Action Officer for Hiring: 1999 – 2000
College and University
- NDIAS Selection Committee: 2016-17, 2017-18
- University Committee on Appeals: 2017-19, 2020-22
- Select Fellowships Selection Committee 2014
- Summer Language Awards Selection Committee 2014
- Chair, College of Arts & Letters Honesty Committee 2012-13
- Co-chair, College of Arts & Letters Honesty Committee 2010-12
- Rhodes/Marshall/Mitchell scholarship committee 2006-07
- Executive Committee, Gender Studies Program 2004 – 07
- Academic Council 2000-03
- Judge, PLS Essay Contest: 1999-2000, 2001-02
- ISLA Course Development Grant review panel 2001-02
- Distinguished Women’s Lecturer evaluation committee 2000 – 01
Service to the Profession
Associations:
Association of Symbolic Logic:
- Chair of the Program Committee, North American Annual Meeting 2016
- Chair and co-organizer (with Pen Maddy) of the special session on Philosophy of Mathematics for the 2015 European Summer Meeting in Helsinki
- ASL Membership Committee, 2009 – 2015
- ASL Council, 2014 – 2017
American Philosophical Association:
- Chair, Program Committee for 2020 Eastern meeting;
- Member, Program Committee for 2019 Eastern meeting;
- Referee for the Eastern 2017 meeting;
- Advisory Committee to the Eastern 2016 meeting;
- Nominating Committee, Central Division 2010
International Association for the Philosophy of Mathematics (PMA):
- Board member 2010 – present; Vice President 2015 – present
- Chair of nominating committee 2014
Journals:
Editorial Board, Philosophia Mathematica 2014 – present
Subject Editor, Bulletin of Symbolic Logic 2013 – 2019
Editorial Board, Notre Dame Journal of Formal Logic – present
Editorial Board, HOPOS
Conferences in addition to APA and ASL (above):
Program Committee, 7th Indian Conference on Logic and Application (2017);
Program Committee, Graduate Conference of the Italian Network for the Philosophy of Mathematics, Trento (2017)
Program Committee, Logica 2018, 2017, 2016, and 2015, Hejnice, Czech Republic;
Program Committee, Scandinavian Summer School in Logic (2014-15);
Program Committee, Scandinavian Logic Symposium 2014;
Program Committee, Midwest PhilMath Workshop, each year 1999-2017
Reviewing and Refereeing:
Reviewer for: National Science Foundation, American Philosophical Society, Social Sciences and Humanities Research Council (Canada), FNRS (Belgium), Deutsche Forschungsgemeinschaft (Germany), Cambridge University (U.K.)
Referee for: American Catholic Philosophical Quarterly, American Philosophical Quarterly, Analysis, Australasian Journal of Philosophy, Broadview Press, The Bulletin of Symbolic Logic, Canadian Journal of Philosophy, Dialectica, Dialogue, Ergo, Erkenntnis, Grazer Philosophische Studien, History and Philosophy of Logic, History of Philosophy Quarterly, The Journal for the History of Analytic Philosophy, The Journal of the History of Philosophy, The Journal of Philosophical Logic, The Journal of Philosophical Research, The Journal of Symbolic Logic, Linguistics and Philosophy, Mind, The Notre Dame Journal of Formal Logic, Nous, Oxford University Press, Philosophers’ Imprint, Philosophia Mathematica, Philosophical Quarterly, Philosophical Studies, Philosophy and Phenomenological Research, The Review of Symbolic Logic, Studia Aristotelica, Synthese, Wadsworth Press; various conferences.
External Evaluator:
- Oberlin College Philosophy Department, 2016-17
- University of Wisconsin, Milwaukee, Philosophy Department, February 2020