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

The Derivation of Poiseuille’s Law: Heuristic and Explanatory Considerations, Synthese, forthcoming. Abstract. Preprint. Online First.

Reichenbach, Russell, and Scientific Realism, Synthese, forthcoming. Abstract. Preprint.

A Defense of Truth as a Necessary Condition on Scientific Explanation, Erkenntnis, forthcoming. Abstract. Preprint.

Concrete Scale Models, Essential Idealization and Causal Explanation, British Journal for the Philosophy of Science, forthcoming. 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

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, forthcoming. Preprint.

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

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

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.