For a while now I've been working in three areas, connected by my interest in investigating the nature of mathematics and its role in science, especially in physics.
In addition to occasionally writing on general topics in philosophy of science (e.g., explanation, understanding, underdetermination, etc.), I have tackled certain issues in philosophy of physics. In particular, I am intrigued by several conceptual difficulties arising within the (so-called) 'non-fundamental' physics, more precisely in the domain of condensed matter theory (including phenomena such as phase transitions, superconductivity, as well as the notions of symmetry and symmetry-breaking, etc.) I try to understand the 'more-is-different' idea (and its variations) and, in relation to this, the merits and shortcomings of reductionism, the role of idealizations, the possibility of emergence, what is to be 'fundamental', the challenges of complexity, etc. A common theme here is the role of the mathematical formalism in expressing, or even shaping, the actual physical content of these theories. The philosophical relevance of these issues consists in clarifying physicists' accounts of familiar phenomena such as water boiling and freezing, or of less mundane ones, e.g., the fact that (some) elementary particles have mass.
In the philosophy of mathematics, I continue to work mainly on issues related to the applicability of mathematics. This includes indispensability arguments, the 'unreasonable effectiveness' issue, also topics having to do with the role of mathematics in formulating explanations of physical phenomena, the credibility of various metaphysics of mathematics (realism/platonism, nominalism, fictionalism), the justifications of (new) axioms in set-theory, etc. A new angle on the connection between mathematics and the world is an attempt to evaluate how the experimental evidence gathered by cognitive psychologists and neuroscientists is relevant for the philosophical debates on the nature of mathematical (and logical) knowledge. I recently edited a volume collecting work in this area by philosophers, psychologists and cognitive scientists. In terms of philosophical significance, it all boils down to addressing two deceivingly simple questions: what is to say that 1+1=2 is true, and how we can know that.
My interests in the history of analytical philosophy concentrate on the views of Quine and especially later Wittgenstein (whom I also regard as a kind of 'naturalist'). My focus is on their take on modality, in particular in relation to mathematics and logic. The basic question here is what these two thinkers, and those following in their footsteps, make of the claim that certain facts can't be otherwise than they are.
Topics in theoretical philosophy.
Naturalizing Logico-Mathematical Knowledge: Approaches from Philosophy, Psychology and Cognitive Science. (Routledge, 2018) Edited collection of essays, 306p.
The Applicability of Mathematics in Science: Indispensability and Ontology. (Palgrave-Macmillan, 2012) Monograph, 252p.
SELECTED ARTICLES (full list and copies are available on my personal website)
'Discontinuities and Singularities, Data and Phenomena: For Referentialism'. Synthese. Special issue on Infinite Idealizations in Science. Eds. L. Ruetsche, P. Palacios, S. Fletcher, E. Shech. Forthcoming.
'Phase Transitions'. The Routledge Companion to the Philosophy of Physics. Eds. E. Knox and A. Wilson. Routledge. Forthcoming.
'Later Wittgenstein and the Genealogy of Mathematical Necessity'. In Wittgenstein and Naturalism. Eds. K. Cahill and T. Raleigh. Routledge, 2018. Pp. 151-73
'Indispensability, Causation and Explanation'. Theoria. Special issue 'Updating Indispensabilities: Hillary Putnam In Memoriam'. Ed. Mary Leng. 33(2): 219-32
'The "Miracle" of Applicability? The Curious Case of the Simple Harmonic Oscillator' (Co-author Robert Moir) Foundations of Physics. 48(5): 507-525 (2018) Special issue on Philosophical Aspects in the Foundations of Physics. Eds. Miklos Redei, Harvey Brown, Klaas Landsman
'Scientific Explanation and Understanding: Unificationism Reconsidered'. European Journal for Philosophy of Science. 7(1): 103-126 (2017)
'On 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences''. In Models and Inferences in Science. Eds. T. Nickles, E. Ippoliti, F. Sterpetti. Pp. 11-29. Springer (2016)
'Later Wittgenstein on the Logicist Definition of Number'. In Early Analytic Philosophy. New Perspectives on the Tradition. Ed. S. Costreie. Western Ontario Series in Philosophy of Science Series. Pp. 233-257. Springer (2016)
'Numerical Methods, Complexity and Epistemic Hierarchies'. Co-author N. Fillion. Philosophy of Science 82.5: 941-955 (2015)
'Why does Water Boil? Fictions in Scientific Explanation'. In Recent Developments in the Philosophy of Science. Ed. U. Mäki et al. Pp. 319-330. Springer (2015)
'Neither Weak, Nor Strong? Emergence and Functional Reduction'. In Why More is Different. Philosophical Issues in Condensed Matter Physics and Complex Systems. Eds. M. Morrison and B. Falkenburg. Springer (2015)
'Indispensability and Explanation' British Journal for the Philosophy of Science 64(2): 255-277 (2013)
'Symmetry' In The Oxford Handbook of Philosophy of Physics. Ed. R. W. Batterman. Oxford Univ. Press (2013), pp. 287-317.
'Ludwig Wittgenstein: Later Philosophy of Mathematics' Entry for Internet Encyclopedia of Philosophy (2012)
‘Bridge Laws in Inter-theoretic Relations’. Philosophy of Science 78.5: 1108-1119 (2011)
‘Probability Assignments and the Principle of Indifference. An Examination of Two Eliminative Strategies’. In Probabilities, Causes and Propensities in Physics. Ed. M. Suarez. Synthese Library. Springer (2011), pp. 61-76.
'On Bertrand's Paradox' Analysis 70: 30-35 (2010)
'Understanding Thermodynamic Singularities. Phase transitions, Data and Phenomena' Philosophy of Science 76.4: 488-505 (2009)
'Inference to the Best Explanation and Mathematical Realism' Synthese. 160: 13-20 (2008)
FRIPRO-FRIHUMSAM research grant co-held with K. Cahill (Univ. of Bergen) awarded by the Norwegian Research Council, 2019-2023: Mathematics with a Human Face. Set Theory within a Naturalized Wittgensteinean Framework