Synthese 199 (1-2):1245-1267 (2020)

John H. Heron
King's College London (PhD)
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. In the second part of the paper, I appeal to the theoretical virtues account of axiom justification to provide an argument that judgements of theoretical virtuousness, and therefore of extrinsic justification, are subjective in a substantive sense. This tells against a recent claim by Penelope Maddy that such justification is “wholly objective”.
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DOI 10.1007/s11229-020-02784-z
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References found in this work BETA

The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - University of Chicago Press.
The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press.
Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.

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