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The mathematics-physics analogy

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The basic goal of this chapter is to delve deeply into Godel’s second great strategy in the philosophy of mathematics: the analogy between deductive and empirical sciences. Moreover, I shall try to explore the holistic, and even conventionalist implications of the analogy, such as it appears in some contemporary philosophers of mathematics who have defended the analogy to some extent. To do this, it has been necessary to present an overview of the most important precedents in the use of the analogy, such as Russell, Hilbert, Carnap, Tarski, Quine. After that, I shall present Godel’s views on the analogy, in both his published and unpublished writings. Surprisingly, most of these authors maintained very different philosophical conceptions, in spite of the fact that they all believed that mathematics and physics are very similar, both in their objectivity and methods.