Philosophia Mathematica (III), Vol. 13 No. 2 © Oxford University Press, 2005, all rights reserved
Book Review |
Ontological Independence as the Mark of the Real
Jody Azzouni. Deflating Existential Consequence: A Case for Nominalism. New York: Oxford University Press, 2004. Pp. viii + 241. ISBN 0-19-515988-8.
*Philosophy Program, University of Queensland Brisbane, Queensland, Australia. mcolyvan@uq.edu.au
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In recent times there have been a number of proposals for a nominalistic philosophy of mathematics. These proposals divide into two quite distinct camps: those who take mathematical propositions to be true, and those who take them to be untrue.1 Both options face substantial difficulties, but let's focus on the first option. The problem here is in asserting that mathematical propositions such as ‘there exist infinitely many complex roots of the Riemann zeta function’ are true (as this one surely is) and then to go on to deny that there are any complex numbers. To do this just seems inconsistent, or at least ‘intellectually dishonest’ (Putnam [1971]
, p. 347). One way to approach this problem is to reinterpret the mathematical claims in question so that they come out true, but do not refer to mathematical objects. So, for example, Geoffrey Hellman [1989] interprets mathematical claims to be about possible
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1. Overview of Azzouni's Project |
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1.1 Quantifier Commitment versus Ontological Commitment
1.2 Ontological Independence
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2. Critical Discussion |
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3. Conclusion |
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  Y. Raley Deflating Existence Away? A Critique of Azzouni's Nominalism Philosophia Mathematica, February 1, 2009; 17(1): 73 - 83. [Abstract] [Full Text] [PDF]
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