Of Numbers and Electrons

Proceedings of the Aristotelian Society 110 (2pt2):133-181 (2010)
Abstract
According to a tradition stemming from Quine and Putnam, we have the same broadly inductive reason for believing in numbers as we have for believing in electrons: certain theories that entail that there are numbers are better, qua explanations of our evidence, than any theories that do not. This paper investigates how modal theories of the form ‘Possibly, the concrete world is just as it in fact is and T’ and ‘Necessarily, if standard mathematics is true and the concrete world is just as it in fact is, then T’ bear on this claim. It concludes that, while analogies with theories that attempt to eliminate unobservable concrete entities provide good reason to regard theories of the former sort as explanatorily bad, this reason does not apply to theories of the latter sort
Keywords Nominalism  Explanation  Indispensability  Numbers
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    References found in this work BETA
    Hartry Field (1984). Can We Dispense with Space-Time? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:33 - 90.

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