Mathematics and fiction II: Analogy

Logique Et Analyse 45:185-228 (2002)
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Abstract

The object of this paper is to study the analogy, drawn both positively and negatively, between mathematics and fiction. The analogy is more subtle and interesting than fictionalism, which was discussed in part I. Because analogy is not common coin among philosophers, this particular analogy has been discussed or mentioned for the most part just in terms of specific similarities that writers have noticed and thought worth mentioning without much attention's being paid to the larger picture. I intend with this analogy (looking at others' comparisons) to shed a little light on what is going on in mathematics, how one can understand it a bit other than experientially. This intention is philosophical and the way that I am attempting to accomplish it is also philosophical. I shall conclude my attempt to explain how it is possible and even natural for mathematics and fiction to have the analogy they have, taking it for granted, as argued in part I, that they are not to be identified. To this end I shall discuss philosophers' comparisons, mainly those of Hodes, Resnik, Tharp, and Wagner, who are the writers that seem to me to have written most thoughtfully and sufficiently extensively about fiction in making the comparison and of Körner, whose comparison is different. Whether either of these comparisons or the more general analogy is of permanent philosophical interest will have to be decided by philosophers now that they have had a fuller examination. I shall mention some other writers' reference to fiction, but not all; indeed, I am sure that I have not even found all the comparisons that there are.

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Citations of this work

Fictionalism, theft, and the story of mathematics.Mark Balaguer - 2009 - Philosophia Mathematica 17 (2):131-162.
Mathematics and bleak house.John P. Burgess - 2004 - Philosophia Mathematica 12 (1):18-36.
Platonism in Metaphysics.Markn D. Balaguer - 2016 - Stanford Encyclopedia of Philosophy 1 (1):1.
Fictionalism in the philosophy of mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.
Platonism in metaphysics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.

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Speech Acts: An Essay in the Philosophy of Language.John Rogers Searle - 1969 - Cambridge, England: Cambridge University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.

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