Against Categoricity

Matteo de Ceglie

Abstract

According to the universism position in set theory, there is only aSingle Universe for set theory and all the models we build throughforcing have instrumental value: they are useful only until we findthe “true” one. The belief that this universe actually exists and theconsequent dismissal of a pluralist conception is based on two mainarguments: first, already inVwe can simulate different universes, sothere is no need to assume the existence of other universes: second, settheory is actually categorical, i.e. all the different models stemmingfrom it are in fact isomorphic. I argue that both arguments are offtarget

Originalsprache	Englisch
Seitenumfang	6
Publikationsstatus	Veröffentlicht - 10 Juli 2020
Veranstaltung	Joint Session of the Mind Association and Aristotelean Society: Open sessions - University of Kent, Canterbury, Großbritannien/Vereinigtes Königreich Dauer: 10 Juli 2020 → 12 Juli 2020 Konferenznummer: 94 https://research.kent.ac.uk/js2020/

Konferenz

Konferenz	Joint Session of the Mind Association and Aristotelean Society
Kurztitel	Joint Session
Land/Gebiet	Großbritannien/Vereinigtes Königreich
Ort	Canterbury
Zeitraum	10/07/20 → 12/07/20
Internetadresse	https://research.kent.ac.uk/js2020/

Systematik der Wissenschaftszweige 2012

603 Philosophie, Ethik, Religion
101 Mathematik

Zugriff auf Dokument

https://www.matteodeceglie.com/against_categoricity.pdf

A Naturalist Account of the Generic Multiverse with a Core
de Ceglie, M. (Projektleitung)
1/07/19 → 30/06/21
Projekt: Forschung

Against Categoricity
de Ceglie, M. (Redner/in)
10 Juli 2020
Aktivität: Gastvortrag oder Vortrag › Vortrag › science to science / art to art

Datei

Dieses zitieren

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title = "Against Categoricity",

abstract = "According to the universism position in set theory, there is only aSingle Universe for set theory and all the models we build throughforcing have instrumental value: they are useful only until we findthe “true” one. The belief that this universe actually exists and theconsequent dismissal of a pluralist conception is based on two mainarguments: first, already inVwe can simulate different universes, sothere is no need to assume the existence of other universes: second, settheory is actually categorical, i.e. all the different models stemmingfrom it are in fact isomorphic. I argue that both arguments are offtarget",

keywords = "Philosophy of Mathematics, Set theoretic multiverse, Forcing, Categoricity, Foundations of Mathematics",

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TY - CONF

T1 - Against Categoricity

AU - de Ceglie, Matteo

N1 - Conference code: 94

PY - 2020/7/10

Y1 - 2020/7/10

N2 - According to the universism position in set theory, there is only aSingle Universe for set theory and all the models we build throughforcing have instrumental value: they are useful only until we findthe “true” one. The belief that this universe actually exists and theconsequent dismissal of a pluralist conception is based on two mainarguments: first, already inVwe can simulate different universes, sothere is no need to assume the existence of other universes: second, settheory is actually categorical, i.e. all the different models stemmingfrom it are in fact isomorphic. I argue that both arguments are offtarget

AB - According to the universism position in set theory, there is only aSingle Universe for set theory and all the models we build throughforcing have instrumental value: they are useful only until we findthe “true” one. The belief that this universe actually exists and theconsequent dismissal of a pluralist conception is based on two mainarguments: first, already inVwe can simulate different universes, sothere is no need to assume the existence of other universes: second, settheory is actually categorical, i.e. all the different models stemmingfrom it are in fact isomorphic. I argue that both arguments are offtarget

KW - Philosophy of Mathematics

KW - Set theoretic multiverse

KW - Forcing

KW - Categoricity

KW - Foundations of Mathematics

M3 - Abstract

T2 - Joint Session of the Mind Association and Aristotelean Society

Y2 - 10 July 2020 through 12 July 2020

ER -

Against Categoricity

Abstract

Konferenz

Systematik der Wissenschaftszweige 2012

Zugriff auf Dokument

Projekte

A Naturalist Account of the Generic Multiverse with a Core

Aktivitäten

Against Categoricity

Dieses zitieren