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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
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.
DOI
https://doi.org/10.7275/11246028.0
Recommended Citation
Ferrier, Edward, "Quantification and Paradox" (2018). Doctoral Dissertations. 1165.
https://doi.org/10.7275/11246028.0
https://scholarworks.umass.edu/dissertations_2/1165