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Defending the View That Mathematics Is Like Father Christmas

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Defending the view that Mathematics is like Father Christmas

An explanation of why one should not be persuaded by the Quine-Putnam indispensability thesis that mathematical objects exist.

This essay will argue that the Quine-Putnam indispensability thesis is not particularly persuasive. It will be shown that there are good reasons to reject the idea that mathematics is indispensable to science and that, instead of accepting the existence of objects that are indispensable to scientific theories, one ought to reject the truth of the theory itself until all the indispensable objects are confirmed to exist by observation.

The Quine-Putnam indispensability thesis challenges the idea that mathematical objects do not exist and are merely fictional entities. It is simple in form and is presented in the following way by Mark Colyvan[1]:

Premise 1: If one must unavoidably cite certain objects in a scientific explanation then one must accept the existence of those objects.
Premise 2: One must unavoidably cite mathematical objects in scientific explanations
Conclusion: One must accept the existence of mathematical objects.

The second premise of the Quine-Putnam indispensability thesis seems fairly intuitive at first glance, if one thinks of the majority of scientific explanations or problems that have been solved one will find some form of mathematics. Hartry Field approaches the indispensability thesis by questioning this common view that one has to cite mathematical objects in scientific explanations[2]. He does this by making claims about physical objects and phenomena without referencing any mathematical objects such as numbers. Such explanations and theories are referred to as nominalistic. Field provides an account of how Newtonian gravitation can be explained without mathematics, in order to advance this notion and cast doubt on the claim that

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