Unpicking Priest's Bootstraps

Toby Meadows

doi:10.1002/tht3.172

Unpicking Priest's Bootstraps

Toby Meadows

Philosophy

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

8 Downloads (Pure)

Abstract

Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument [Priest, 2006]. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on [Priest, 2006] and attempts some fixes and alternative construals to get around some elementary problems. Despite these efforts the argument remains unconvincing.

Original language	English
Pages (from-to)	181-188
Number of pages	8
Journal	Thought: A Journal of Philosophy
Volume	4
Issue number	3
Early online date	27 Aug 2015
DOIs	https://doi.org/10.1002/tht3.172
Publication status	Published - Sep 2015

Keywords

philosophy of mathematics
philosophical logic
set theory
foundations of mathematics
nonclassical logic

Access to Document

10.1002/tht3.172Licence: Unspecified

Unpicking Priests Bootstraps
This is the peer reviewed version of the following article: Meadows, T. (2015), Unpicking Priest's Bootstraps. Thought: A Journal of Philosophy, 4: 181–188. , which has been published in final form at 10.1002/tht3.172. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."
Accepted author manuscript, 142 KB

Cite this

@article{ce3b5c608b39459c9eae4e452ba12a9f,

title = "Unpicking Priest's Bootstraps",

abstract = "Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument [Priest, 2006]. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on [Priest, 2006] and attempts some fixes and alternative construals to get around some elementary problems. Despite these efforts the argument remains unconvincing.",

keywords = "philosophy of mathematics, philosophical logic, set theory, foundations of mathematics, nonclassical logic",

author = "Toby Meadows",

note = "Date of Acceptance: 13/07/2015",

year = "2015",

month = sep,

doi = "10.1002/tht3.172",

language = "English",

volume = "4",

pages = "181--188",

journal = "Thought: A Journal of Philosophy",

issn = "2161-2234",

publisher = "John Wiley and Sons Ltd",

number = "3",

}

TY - JOUR

T1 - Unpicking Priest's Bootstraps

AU - Meadows, Toby

N1 - Date of Acceptance: 13/07/2015

PY - 2015/9

Y1 - 2015/9

N2 - Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument [Priest, 2006]. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on [Priest, 2006] and attempts some fixes and alternative construals to get around some elementary problems. Despite these efforts the argument remains unconvincing.

AB - Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument [Priest, 2006]. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on [Priest, 2006] and attempts some fixes and alternative construals to get around some elementary problems. Despite these efforts the argument remains unconvincing.

KW - philosophy of mathematics

KW - philosophical logic

KW - set theory

KW - foundations of mathematics

KW - nonclassical logic

U2 - 10.1002/tht3.172

DO - 10.1002/tht3.172

M3 - Article

VL - 4

SP - 181

EP - 188

JO - Thought: A Journal of Philosophy

JF - Thought: A Journal of Philosophy

SN - 2161-2234

IS - 3

ER -

Unpicking Priest's Bootstraps

Abstract

Keywords

Access to Document

Fingerprint

Cite this