#### Date of Award

2013

#### Document Type

Thesis

#### Department

Computing, Mathematics and Physics

#### Abstract

What exactly is a number? The ontological status of mathematical entities is a question that has concerned philosophers since the time of the Ancient Greeks. Plato suggests a view of mathematics corresponding to his idea of true Forms, setting the stage for later mathematical Platonists. Aristotle, on the other hand, presents mathematics in a way that is consistent with his philosophy and could be seen as the first mathematical anti-Platonist. Skipping forward more than a thousand years, we will look at Kant’s synthetic a priori idea of mathematics and Mill’s empirical mathematical beliefs. The second half of the literature review is concerned with examining the four main schools of thought in the philosophy of mathematics; logicism, intuitionism, formalism and structuralism. At the end of the paper I present my views of the problems faced in seeking an answer to the question of the ontological status of mathematical entities and argue for the existence of an innate mathematical sense in support of mathematical Platonism.

#### Recommended Citation

Andrews, Stephanie, "A Philosophical Investigation of the Ontological Status of Mathematical Entities [Being a Brief Undertaking of the Philosophy of Mathematics by a Poor Undergraduate Student who had no Idea of What She was Getting Herself Into]" (2013). *Honors Projects and Presentations: Undergraduate*. 147.

https://mosaic.messiah.edu/honors/147