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Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Philosophy

Year Degree Awarded

2018

Month Degree Awarded

February

First Advisor

Kevin Klement

Second Advisor

Phillip Bricker

Third Advisor

Christopher Meacham

Fourth Advisor

Robert Kusner

Subject Categories

Logic and Foundations of Mathematics

Abstract

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible.

It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but on the ``logical'' conception of set which motivates naive set theory. The accepted solution is to replace this with the ``iterative'' conception of set.

I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected.

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