Indispensability and Holism

Author: Busch, Jacob

Source: Journal for General Philosophy of Science, Volume 42, Number 1, May 2011 , pp. 47-59(13)

Publisher: Springer

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Abstract:

It is claimed that the indispensability argument for the existence of mathematical entities (IA) works in a way that allows a proponent of mathematical realism to remain agnostic with regard to how we establish that mathematical entities exist. This is supposed to be possible by virtue of the appeal to confirmational holism that enters into the formulation of IA. Holism about confirmation is supposed to be motivated in analogy with holism about falsification. I present an account of how holism about falsification is supposed to be motivated. I argue that the argument for holism about falsification is in tension with how we think about confirmation and with two principles suggested by Quine for construing a plausible variety of holism. Finally, I show that one of Quine's principles does not allow a proponent of mathematical realism to remain agnostic with regard to how we establish that mathematical entities exist.

Keywords: Indispensability; Holism; Mathematical realism; Confirmation; Quine

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10838-011-9142-4

Affiliations: 1: Aarhus Universitet, 8000, Aarhus, Denmark, Email: filjab@hum.au.dk

Publication date: 2011-05-01