Set-theoretic justification and the theoretical virtues

Synthese 199 (1-2):1245-1267 (2020)
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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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Author's Profile

John H. Heron
King's College London (PhD)

References found in this work

The Structure of Scientific Revolutions.Thomas Samuel Kuhn - 1962 - Chicago: University of Chicago Press. Edited by Otto Neurath.
The Structure of Scientific Revolutions.Thomas S. Kuhn - 1962 - Chicago, IL: University of Chicago Press. Edited by Ian Hacking.
Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.

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