Existence and definability of states of the world

Autores
Tohmé, Fernando Abel
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present here a notion of state of the world general enough to embrace most circular phenomena in economics and game theory. We prove that it obtains by unfolding beliefs only if the process of belief generation has a fixed point. Otherwise, we are led to an unending transfinite hierarchy. This result indicates that Zermelo-Frenkel's set theory cannot provide the modeling tools for the representation of states of the world. We apply, instead, a theory of non-well-founded sets. In that framework, states of the world are legitimate objects which can be seen as fixed points of the belief-generation operator. Not every possible state of the world can be unfolded in a hierarchy of beliefs. It will be shown by means of a simple argument, based in Tarski's indefinability theorem, that there exist states of the world that are not expressible in that way. Moreover, this result implies that there is no way to represent those states of the world in a consistent language. However, if we assume agents do not have negative self-referential beliefs, the unfolding of beliefs suffices.
Fil: Tohmé, Fernando Abel. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina
Materia
CIRCULARITY
DEFINABILITY
NON-WELL-FOUNDED SETS
STATES OF THE WORLD
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98624
Acceder
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spelling Existence and definability of states of the worldTohmé, Fernando AbelCIRCULARITYDEFINABILITYNON-WELL-FOUNDED SETSSTATES OF THE WORLDhttps://purl.org/becyt/ford/5.2https://purl.org/becyt/ford/5We present here a notion of state of the world general enough to embrace most circular phenomena in economics and game theory. We prove that it obtains by unfolding beliefs only if the process of belief generation has a fixed point. Otherwise, we are led to an unending transfinite hierarchy. This result indicates that Zermelo-Frenkel's set theory cannot provide the modeling tools for the representation of states of the world. We apply, instead, a theory of non-well-founded sets. In that framework, states of the world are legitimate objects which can be seen as fixed points of the belief-generation operator. Not every possible state of the world can be unfolded in a hierarchy of beliefs. It will be shown by means of a simple argument, based in Tarski's indefinability theorem, that there exist states of the world that are not expressible in that way. Moreover, this result implies that there is no way to represent those states of the world in a consistent language. However, if we assume agents do not have negative self-referential beliefs, the unfolding of beliefs suffices.Fil: Tohmé, Fernando Abel. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; ArgentinaElsevier Science2005-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98624Tohmé, Fernando Abel; Existence and definability of states of the world; Elsevier Science; Mathematical Social Sciences; 49; 1; 1-2005; 81-1000165-4896CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.mathsocsci.2004.03.008info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S016548960400054Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:44Zoai:ri.conicet.gov.ar:11336/98624instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:54:44.577CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Existence and definability of states of the world
title Existence and definability of states of the world
spellingShingle Existence and definability of states of the world
Tohmé, Fernando Abel
CIRCULARITY
DEFINABILITY
NON-WELL-FOUNDED SETS
STATES OF THE WORLD
title_short Existence and definability of states of the world
title_full Existence and definability of states of the world
title_fullStr Existence and definability of states of the world
title_full_unstemmed Existence and definability of states of the world
title_sort Existence and definability of states of the world
dc.creator.none.fl_str_mv Tohmé, Fernando Abel
author Tohmé, Fernando Abel
author_facet Tohmé, Fernando Abel
author_role author
dc.subject.none.fl_str_mv CIRCULARITY
DEFINABILITY
NON-WELL-FOUNDED SETS
STATES OF THE WORLD
topic CIRCULARITY
DEFINABILITY
NON-WELL-FOUNDED SETS
STATES OF THE WORLD
purl_subject.fl_str_mv https://purl.org/becyt/ford/5.2
https://purl.org/becyt/ford/5
dc.description.none.fl_txt_mv We present here a notion of state of the world general enough to embrace most circular phenomena in economics and game theory. We prove that it obtains by unfolding beliefs only if the process of belief generation has a fixed point. Otherwise, we are led to an unending transfinite hierarchy. This result indicates that Zermelo-Frenkel's set theory cannot provide the modeling tools for the representation of states of the world. We apply, instead, a theory of non-well-founded sets. In that framework, states of the world are legitimate objects which can be seen as fixed points of the belief-generation operator. Not every possible state of the world can be unfolded in a hierarchy of beliefs. It will be shown by means of a simple argument, based in Tarski's indefinability theorem, that there exist states of the world that are not expressible in that way. Moreover, this result implies that there is no way to represent those states of the world in a consistent language. However, if we assume agents do not have negative self-referential beliefs, the unfolding of beliefs suffices.
Fil: Tohmé, Fernando Abel. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina
description We present here a notion of state of the world general enough to embrace most circular phenomena in economics and game theory. We prove that it obtains by unfolding beliefs only if the process of belief generation has a fixed point. Otherwise, we are led to an unending transfinite hierarchy. This result indicates that Zermelo-Frenkel's set theory cannot provide the modeling tools for the representation of states of the world. We apply, instead, a theory of non-well-founded sets. In that framework, states of the world are legitimate objects which can be seen as fixed points of the belief-generation operator. Not every possible state of the world can be unfolded in a hierarchy of beliefs. It will be shown by means of a simple argument, based in Tarski's indefinability theorem, that there exist states of the world that are not expressible in that way. Moreover, this result implies that there is no way to represent those states of the world in a consistent language. However, if we assume agents do not have negative self-referential beliefs, the unfolding of beliefs suffices.
publishDate 2005
dc.date.none.fl_str_mv 2005-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/98624
Tohmé, Fernando Abel; Existence and definability of states of the world; Elsevier Science; Mathematical Social Sciences; 49; 1; 1-2005; 81-100
0165-4896
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98624
identifier_str_mv Tohmé, Fernando Abel; Existence and definability of states of the world; Elsevier Science; Mathematical Social Sciences; 49; 1; 1-2005; 81-100
0165-4896
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mathsocsci.2004.03.008
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S016548960400054X
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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