How to be a minimalist about sets

Incurvati, Luca

doi:10.1007/s11098-010-9690-1

Cited by 24 publications

(7 citation statements)

References 9 publications

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“…So I set aside this kind of revisionist option in this paper. For a recent discussion and summary of the arguments against constructivism, see for instance Incurvati (2012). 36 This way of making sense of expandability fits with Tait (2005) and Parsons (1974).…”

Section: Interpreted Modalitymentioning

confidence: 83%

Why is the universe of sets not a set?

Soysal

2017

Synthese

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According to the iterative conception of sets, standardly formalized by ZFC, there is no set of all sets. But why is there no set of all sets? A simple-minded, though unpopular, "minimal" explanation for why there is no set of all sets is that the supposition that there is contradicts some axioms of ZFC. In this paper, I first explain the core complaint against the minimal explanation, and then argue against the two main alternative answers to the guiding question. I conclude the paper by outlining a close alternative to the minimal explanation, the conception-based explanation, that avoids the core complaint against the minimal explanation.

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Section: Interpreted Modalitymentioning

confidence: 83%

Why is the universe of sets not a set?

Soysal

2017

Synthese

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“…Restall (2013) develops this into a quite general challenge to naive set theories of various stripes. 9 Another example: Grisin like a deflationist approach to set membership, although one quite unlike that of Incurvati (2012). Just as in the case of truth, deflationism can motivate naivete, but naivete itself does not seem to require deflationism.…”

Section: The Comprehension Rulementioning

confidence: 99%

Naive Set Theory and Nontransitive Logic

Ripley

2015

The Review of Symbolic Logic

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In a recent series of papers, I and others have advanced new logical approaches to familiar paradoxes. The key to these approaches is to accept full classical logic, and to accept the principles that cause paradox, while preventing trouble by allowing a certain sort of nontransitivity. Earlier papers have treated paradoxes of truth and vagueness. The present paper will begin to extend the approach to deal with the familiar paradoxes arising in naive set theory, pointing out some of the promises and pitfalls of such an approach.

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“…a similar point is made in Linnebo (2008: 72). It's been argued by Incurvati (2012) that this notion of dependence isn't a necessary component of the iterative conception. I won't dispute this-for my purposes it will be enough that some notion of dependence mattered to Gödel's take on the iterative conception.…”

Section: Weylmentioning

confidence: 99%

Structuralism and Its Ontology

Gasser¹

2015

Ergo, an Open Access Journal of Philosophy

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a prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious difficulties with this kind of view: its proponents rely on a distinction between "essential" and "nonessential" features of mathematical objects, and there's no good way to articulate this distinction which is compatible with basic structuralist commitments. But all is not lost. For I further argue that the insights motivating structuralism (or at least those worth preserving) can be preserved without formulating the view in ontologically committal terms.

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How to be a minimalist about sets

Cited by 24 publications

References 9 publications

Why is the universe of sets not a set?

Why is the universe of sets not a set?

Naive Set Theory and Nontransitive Logic

Structuralism and Its Ontology

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