•  337
    Set-theoretic justification and the theoretical virtues
    Synthese 199 (1-2): 1245-1267. 2020.
    Recent discussions of how axioms are extrinsically justified have appealed to abductive considerations: on such accounts, axioms are adopted on the basis that they constitute the best explanation of some mathematical data, or phenomena. In the first part of this paper, I set out a potential problem caused by the appeal made to the notion of mathematical explanation and suggest that it can be remedied once it is noted that all the justificatory work is done by appeal to the theoretical virtues. I…Read more
  •  350
    Representational indispensability and ontological commitment
    Thought: A Journal of Philosophy 9 (2): 105-114. 2020.
    Recent debates about mathematical ontology are guided by the view that Platonism's prospects depend on mathematics' explanatory role in science. If mathematics plays an explanatory role, and in the right kind of way, this carries ontological commitment to mathematical objects. Conversely, the assumption goes, if mathematics merely plays a representational role then our world-oriented uses of mathematics fail to commit us to mathematical objects. I argue that it is a mistake to think that mathema…Read more
  •  54
    On Constraints, Context, and Spatiotemporal Explanation
    Philosophy and Phenomenological Research 99 (3): 732-738. 2019.
    Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 732-738, November 2019.