The Cumulative Case for Platonism about Universals Attribute-Identification in Mathematics

Date of Award

2005

Document Type

Thesis

Degree Name

Bachelors

Department

Humanities

Second Department

Natural Sciences

First Advisor

Edidin, Aron

Keywords

Philosophy of Mathematics, Universals, Metaphysics, Logic, Platonism, Collections, Sets, Set-Theory

Area of Concentration

Philosophy

Abstract

In this thesis I develop and defend a Platonistic, attribute-theoretic, account of natural number arithmetic as part of a cumulative case for Platonism about universals. In Chapter 1, I argue that three incontrovertible facts about natural number arithmetic commit us to arithmetic Realism, or the view that numbers exist as abstract objects. In Chapter 2, I introduce three more such facts and argue that the best explanation of the six taken together is that numbers are attributes whose most salient instances are collections. I then defend this conclusion against Paul Benacerraf's influential argument from multiple reductions, arguing that the conditions which he claims are adequate for an account of the numbers are far too lenient. In Chapter 3, I sketch a semantical account of number-talk as a special case of attribute-talk. And in Chapter 4, I consider the ontological status of collections, arguing that they are things with parts, not in their most evident manifestations, at least, sets. I conclude with the suggestion that, contrary to popular belief, sets may not figure into our best ontological account of reality at all.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

This document is currently not available here.

Share

COinS