Quantification and Paradox

Dissertation, University of Massachusetts Amherst (2018)

Authors
Edward Ferrier
Tufts University
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.
Keywords Absolutism  Restrictivism  Russell's Paradox  Cantor's paradox  Burali-Forti's paradox  Iterative conception of set  Logical conception of set
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

New Work for a Theory of Universals.David Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Essence and Modality.Kit Fine - 1994 - Philosophical Perspectives 8:1-16.
Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109-36.
On What Grounds What.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.

View all 121 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

An Order-Theoretic Account of Some Set-Theoretic Paradoxes.Thomas Forster & Thierry Libert - 2011 - Notre Dame Journal of Formal Logic 52 (1):1-19.
Against the Iterative Conception of Set.Edward Ferrier - 2019 - Philosophical Studies 176 (10):2681-2703.
On the Iterative Explanation of the Paradoxes.Christopher Menzel - 1986 - Philosophical Studies 49 (1):37 - 61.
Las Paradojas De La Teoria De Conjuntos: Un Analysis Sistematico.Julián Garrido - 2002 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 17 (1):35-62.
Las Paradojas De La Teoria De Conjuntos.Julián Garrido Garrido - 2002 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 17 (1):35-62.
Rescuing Poincaré From Richard’s Paradox.Laureano Luna - 2017 - History and Philosophy of Logic 38 (1):57-71.
Modal Set Theory.Christopher Menzel - forthcoming - In Otávio Bueno & Scott Shalkowski (eds.), The Routledge Handbook of Modality. London and New York: Routledge.
Another Paradox In Naive Set-Theory.Loïc Colson - 2007 - Studia Logica 85 (1):33-39.

Analytics

Added to PP index
2018-07-19

Total views
152 ( #54,603 of 2,289,505 )

Recent downloads (6 months)
52 ( #16,174 of 2,289,505 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature