The Philosophy of Mathematics: A Study of Indispensability and Inconsistency

Abstract

This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe in the existence of mathematical entities present within our best scientific theories. The second half of this discussion surveys Newtonian Cosmology and other inconsistent theories as they pose issues that have received insignificant attention within the philosophy of mathematics. The application of these inconsistent theories raises questions about the effectiveness of mathematics to model physical systems.

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References found in this work

On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
What is Mathematics, Really?Reuben Hersh - 1997 - New York: Oxford University Press.

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