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Maximality and Ontology: How axiom content varies across philosophical frameworks

Barton, Neil and Friedman, Sy-David (2017) Maximality and Ontology: How axiom content varies across philosophical frameworks. [Preprint]

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Abstract

Discussion of new axioms for set theory has often focussed on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barton, Neilbartonna@gmail.com0000-0002-3637-1730
Friedman, Sy-David
Keywords: set theory, multiverse, axiom, foundations of mathematics
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Depositing User: Dr. Neil Barton
Date Deposited: 06 May 2018 15:33
Last Modified: 06 May 2018 15:33
Item ID: 14637
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Date: 2017
URI: http://philsci-archive.pitt.edu/id/eprint/14637

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