Burgess's ‘scientific’ arguments for the existence of mathematical objects

Philosophia Mathematica 14 (3):318-337 (2006)
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Abstract

This paper addresses John Burgess's answer to the ‘Benacerraf Problem’: How could we come justifiably to believe anything implying that there are numbers, given that it does not make sense to ascribe location or causal powers to numbers? Burgess responds that we should look at how mathematicians come to accept: There are prime numbers greater than 1010 That, according to Burgess, is how one can come justifiably to believe something implying that there are numbers. This paper investigates what lies behind Burgess's answer and ends up as a rebuttal to Burgess's reasoning.

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References found in this work

The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.
The Scientific Image.Michael Friedman - 1982 - Journal of Philosophy 79 (5):274-283.
Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, MA, USA: Reading, Mass., Addison-Wesley Pub. Co..
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.

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