Book: Mathematics and Scientific Representation (2012)

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book I tackle this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. 

OUP Amazon Google Books Oxford Scholarship

Reviews & discussions: J. Saatsi, NDPR 2012.10.06, M. Balaguer, E. Landry & S. Bangu, Metascience 22 (2013): 247-273, S. Baron, Mind 122 (2013): 1167-1171, A. Kennedy, Int. Stud. Phil. Sci. 27 (2013): 95-98, M. Liston, Phil. Math. 21 (2013): 371-385, S. Walsh, E. Knox & A. Caulton, Phil. Sci. 81 (2014): 460-469, A. Baker, Brit. J. Phil. Sci. 66 (2015): 695-699.





Journal Articles

A Defense of Truth as a Necessary Condition on Scientific Explanation, Erkenntnis 88 (2023): 621-640. Abstract. Preprint. Online.

The Derivation of Poiseuille’s Law: Heuristic and Explanatory Considerations, Synthese 199 (2021): 11667-87. Abstract. Preprint. Online .

Reichenbach, Russell, and Scientific Realism, Synthese 199 (2021): 8485-8506. Abstract. Preprint. Online.

Concrete Scale Models, Essential Idealization and Causal Explanation, British Journal for the Philosophy of Science 73 (2022): 299-323. Preprint. Advance Access.

Explanatory Relevance and Contrastive Explanation, Philosophy of Science (Symposium Proceedings) 85 (2018): 806-818.

Abstract Explanations in Science, British Journal for the Philosophy of Science 66 (2015): 857-882.

The Unsolvability of the Quintic: A Case Study in Abstract Mathematical Explanation, Philosophers’ Imprint 15 (2015): 1-19. 

How to Avoid Inconsistent Idealizations, Synthese 191 (2014): 2957-2972.

Mathematical Models of Biological Patterns: Lessons from Hamilton’s Selfish Herd, Biology and Philosophy 27 (2012): 481-496.

Mathematical Explanations of the Rainbow, Studies in History and Philosophy of Modern Physics 42 (2011): 13-22.

Modeling Reality, Synthese 180 (2011): 19-32.

Mathematics, Science and Confirmation Theory, Philosophy of Science (Symposium Proceedings) 77 (2010): 959-970.

From Sunspots to the Southern Oscillation: Confirming Models of Large-Scale Phenomena in Meteorology, Studies in the History and Philosophy of Science 40 (2009): 45-56.

Russell’s Last (and Best) Multiple-Relation Theory of Judgment, Mind 117 (2008): 107-139.

Mathematical Idealization, Philosophy of Science (Proceedings) 74 (2007): 957-967.

A Role for Mathematics in the Physical Sciences, Nous 41 (2007): 253-275.

Richard Semon and Russell’s Analysis of Mind, Russell 26 (2006): 101-125.

Overextending Partial Structures: Idealization and Abstraction, Philosophy of Science (Proceedings) 72 (2005): 1248-1259.

A Reserved Reading of Carnap’s Aufbau, Pacific Philosophical Quarterly 86 (2005): 518-543.

A New Perspective on the Problem of Applying Mathematics, Philosophia Mathematica 12 (2004): 135-161.

A Revealing Flaw in Colyvan’s Indispensability Argument, Philosophy of Science 71 (2004): 61-79.

Russell’s Influence on Carnap’s Aufbau, Synthese 131 (2002): 1-37.

Invited Articles

(with P. Mancosu and F. Poggiolesi) “Mathematical Explanation”, Stanford Encyclopedia of Philosophy (Fall 2023),

Understanding the Success of Science & Reply to Potochnik, in K. Khalifa, I. Lawler & E. Shech (eds.), Scientific Understanding and Representation: Modeling in the Physical Sciences, Routledge, 2023, 135-150, 167-171. Preprint.

Logical Empiricism in the Anglophone World, in T. Uebel (ed.), Handbook of Logical Empiricism, Routledge, 2022, 325-333.

Mathematical Explanation Requires Mathematical Truth, in S. Dasgupta, R. Dotan & B. Weslake (eds.), Current Controversies in Philosophy of Science, Routledge, 2021, 39-50.

Neutral Monism, in R. Wahl (ed.), Bloomsbury Companion to Russell, Bloomsbury Press, 2019, 312-333.

Accommodating Explanatory Pluralism, in A. Reutlinger and J. Saatsi (eds.), Explanation Beyond Causation, Oxford University Press, 2018, 39-56.

Introduction, with S. Lapointe, in S. Lapointe & C. Pincock (eds.), Innovations in the History of Analytical Philosophy, Palgrave Macmillan, 2017, 1-23.

Ernest Nagel’s Naturalism: A Microhistory of the American Reception of Logical Empiricism, in A. Preston (ed.), Analytic Philosophy: An Interpretive History, Routledge, 2017, 160-174.

Logical Empiricism, in J. Hawthorne, H. Cappelen and T. Szabo Gendler (eds.), Oxford Handbook of Philosophical Methodology, Oxford University Press, 2016, 93-111.

Philosophy of Mathematics, J. Saatsi & S. French (eds.), Companion to the Philosophy of Science, Continuum, 2011, 314-333.

The Applicability of Mathematics, Internet Encyclopedia of Philosophy,

Carnap’s Logical Structure of the World, Philosophy Compass4/6 (2009): 951-961.

Towards a Philosophy of Applied Mathematics, in O. Bueno & Ø. Linnebo (eds.), New Waves in Philosophy of Mathematics, Palgrave Macmillan, 2009, 173-194.

Mathematical Structural Realism, in A. Bokulich & P. Bokulich (eds.), Scientific Structuralism, Boston Studies in the Philosophy of Science, volume 281, Springer, 2011, 67-79.

Carnap, Russell and the External World, in M. Friedman & R. Creath (eds.), Cambridge Companion to Carnap, Cambridge University Press, 2008, 106-128.

The Limits of the Relative A Priori, Soochow Journal of Philosophical Studies(Taiwan) 16 (2007): 51-68.

Accounting for the Unity of Experience in Dilthey, Rickert, Bradley and Ward, in U. Feest (ed.), Historical Perspectives on Erklären and Verstehen, Archimedes, Vol. 21, Springer, 2010, 187-206. (Also available in Max Planck Institute for the History of Science, Preprint Series, Vol. 324, 2007, 175-192.)

Conditions on the Use of the One-dimensional Heat Equation, in G. Sica (ed.), Essays on the Foundations of Mathematics and Logic, Vol. 2, Polimetrica, 2005, 67-79.

Carnap and the Unity of Science: 1921-1928, in T. Bonk (ed.), Language, Truth and Knowledge: Contributions to the Philosophy of Rudolf Carnap, Vienna Circle Institute Library, Volume 2, Kluwer, 2003, 87-96.






Selected Critical Notices, Discussion Notes and Reviews

Book Forum: “C. Rice’s Leveraging Distortions: Explanation, Idealization, and Universality in Science”, Studies in the History and Philosophy of Science 95 (2022): 230-232.

Book Symposium: “S. French’s There are No Such Things as Theories”, Metascience 30 (2021): 3-8.

Review: B. Skow, Reasons Why, Notre Dame Philosophical Reviews, 2017.05.14.

Book Symposium: “A. Casullo’s Essays on A Priori Knowledge and Justification”, Philosophical Studies 173 (2016): 1687-1694.

Review: I. Hacking, Why is There Philosophy of Mathematics At All?, British Journal for the Philosophy of Science 67 (2016): 907-912.

Review: W. Demopoulos, Logicism and its Philosophical Legacy, Russell 35 (2015): 82-87.

Critical Notice: S. Bangu, The Applicability of Mathematics in Science: Indispensability and Ontology, Philosophia Mathematica 22 (2014): 401-412.

Review: J. R. Brown, Platonism, Naturalism, and Mathematical Knowledge, Mind 123 (2014): 1174-1177.

Book Symposium: H. J. Glock, What is Analytic Philosophy?, Journal for the History of Analytical Philosophy 2/2 (2013): 6-10.

Review: B. Linsky, The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition, Bulletin of Symbolic Logic 19 (2013): 106-108.

Book Symposium: Reply to Balaguer, Landry and Bangu, Metascience 22 (2013): 266-273.

Literature Review: (with P. Mancosu) Mathematical Explanation, Oxford Bibliographies in Philosophy, D. Pritchard (ed.), 2012. doi: 10.1093/OBO/9780195396577-0029.

Book Symposium: M. Leng, Mathematics and Reality, Metascience 21 (2012): 269-275.

Review: B. van Fraassen, Scientific Representation: Paradoxes of Perspective, British Journal for the Philosophy of Science 62 (2011): 677-682.

Discussion Note: On Batterman’s ‘On the Explanatory Role of Mathematics in Empirical Science’, British Journal for the Philosophy of Science 62 (2011): 211-217.

Critical Notice: Mark Wilson, Wandering Significance: An Essay on Conceptual BehaviorPhilosophia Mathematica 18 (2010): 106-121.


Additional reviews are listed on my CV.