Associate Professor, Department of Logic and Philosophy of Science, University of California, Irvine. Courtesy appointment in Department of Mathematics, Department of Linguistics.
Associate Director, The Center for the Advancement of Logic, its Philosophy, History, and Applications (C-ALPHA).
Ph.D., Logic and Foundations of Mathematics, University of Notre Dame
Research Interests: Philosophy of mathematics, philosophy of logic, mathematical logic.
Email: walsh108 at uci.edu
Office: SST 703
- Structure and Categoricity: Determinacy of Reference and Truth-Value in the Philosophy of Mathematics. Joint with Tim Button. Forthcoming in Philosophia Mathematica.
- Realizability Semantics for Quantified Modal Logic: Generalizing Flagg’s 1985 Construction. Joint with Benjamin G. Rin. Forthcoming in The Review of Symbolic Logic. http://dx.doi.org/10.1017/S1755020316000095
- The Strength of Abstraction with Predicative Comprehension. The Bulletin of Symbolic Logic, 22(1):105–120, 2016. http://dx.doi.org/10.1017/bsl.2015.39
- Fragments of Frege’s Grundgesetze and Gödel’s Constructible Universe. The Journal of Symbolic Logic, 81(2):605 – 628, 2016. http://dx.doi.org/10.1017/jsl.2015.32
- Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic. The Journal of Philosophical Logic, 45(3):277–326, 2016. http://dx.doi.org/10.1007/s10992-015-9375-5
- Relative Categoricity and Abstraction Principles. Joint with Sean Ebels-Duggan. The Review of Symbolic Logic, 8(3):572–606, 2015. http://dx.doi.org/10.1017/S1755020315000052
- Empiricism, Probability, and Knowledge of Arithmetic: A Preliminary Defense.
Journal of Applied Logic, 12(3):319–348, 2014. Special Issue on Combining Probability and Logic to Solve Philosophical Problems. http://dx.doi.org/10.1016/j.jal.2013.12.002
- Logicism, Interpretability, and Knowledge of Arithmetic. The Review of Symbolic Logic, 7(1):84-119, 2014. http://dx.doi.org/10.1017/S1755020313000397
- Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.
Annals of Pure and Applied Logic, 163:1679-1709, 2012. http://dx.doi.org/10.1016/j.apal.2011.12.016
- Incongruent Counterparts and Causality. Kant-Studien 98(4):418-430, 2007. http://dx.doi.org/10.1515/KANT.2007.026
- Critical Review of Mathematics and Scientific Representation. Joint with Eleanor Knox and Adam Caulton. Philosophy of Science, 81(3):460-469, 2014. http://www.jstor.org/stable/10.1086/676560
Edited Volumes/ Special Issues:
- Notre Dame Journal of Formal Logic, Volume 56, Number 1, 2015. Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments. Co-edited with Salvatore Florio, Øystein Linnebo, and Philip Welch. https://projecteuclid.org/euclid.ndjfl/1427202970
Author Profile Pages on Various Preprint Servers and Paper Indexes:
Co-Organization of Various Seminars, Conferences, & Workshops:
- The Number Concept: Axiomatization, Cognition and Genesis, Nancy, November 3-5, 2010.
- Séminaire de philosophie des mathématiques 2010-2011, Université Paris Diderot – Paris 7.
- Summer School: Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments, London, August 1-6, 2011.
- Various Research Seminars, Birkbeck, University of London 2010-2012.
- FregeFest IV, UC Irvine, April 12-13, 2013.
- So-Cal PhilMath + PhilLogic + FoM Workshops, 2012-2015.
- Logic Seminar Winter 2014, UC Irvine.
- Logic Seminar Winter 2015, UC Irvine.
- Logic Seminar Winter 2016, UC Irvine.
- Probability and Randomness, Winter 2016, UC Irvine.
- Frege Fest V, UC Irvine, April 8 2016
Selected Teaching Materials:
- Introduction to Symbolic Logic (Introductory Undergraduate Course)
- Empiricism, Probability, and Knowledge of Arithmetic. Numbers and Truth. October 21 2012.
- Realizability Semantics for Quantified Modal Logic. Notre Dame Logic Seminar. March 1 2016.
- Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic. FPMW7 November 7 2015 and APA/ASL March 2 2016.
- The Strength of Abstraction with Predicative Comprehension. Operations, Sets, and Types. April 19 2016, Logic and Theory Group, University of Bern.