{"id":"https://openalex.org/W2062097337","doi":"https://doi.org/10.2178/jsl/1096901765","title":"Patterns of paradox","display_name":"Patterns of paradox","publication_year":2004,"publication_date":"2004-09-01","ids":{"openalex":"https://openalex.org/W2062097337","doi":"https://doi.org/10.2178/jsl/1096901765","mag":"2062097337"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1096901765","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1096901765","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053081905","display_name":"Roy T. Cook","orcid":"https://orcid.org/0000-0001-7584-9197"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Roy T. Cook","raw_affiliation_strings":["Arch\u00e9: The AHRB Centre for the Philosophy of Logic, Language, Mathematics, and Mind School of Philosophical and Anthropological Studies, University of St. Andrews, UK, E-mail:","University of St Andrews"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Arch\u00e9: The AHRB Centre for the Philosophy of Logic, Language, Mathematics, and Mind School of Philosophical and Anthropological Studies, University of St. Andrews, UK, E-mail:","institution_ids":["https://openalex.org/I16835326"]},{"raw_affiliation_string":"University of St Andrews","institution_ids":["https://openalex.org/I16835326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053081905"],"corresponding_institution_ids":["https://openalex.org/I16835326"],"apc_list":null,"apc_paid":null,"fwci":1.832,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.87571572,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"69","issue":"3","first_page":"767","last_page":"774"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/denotation","display_name":"Denotation (semiotics)","score":0.8870595693588257},{"id":"https://openalex.org/keywords/conjunction","display_name":"Conjunction (astronomy)","score":0.7910948991775513},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.770615816116333},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.765531063079834},{"id":"https://openalex.org/keywords/falsity","display_name":"Falsity","score":0.7237758636474609},{"id":"https://openalex.org/keywords/atomic-sentence","display_name":"Atomic sentence","score":0.6731423735618591},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4975338280200958},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.49476903676986694},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4860263466835022},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.44575217366218567},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4355280101299286},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.4244399666786194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.313620924949646},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.2882866859436035},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25962013006210327},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10723087191581726}],"concepts":[{"id":"https://openalex.org/C149106765","wikidata":"https://www.wikidata.org/wiki/Q1982453","display_name":"Denotation (semiotics)","level":3,"score":0.8870595693588257},{"id":"https://openalex.org/C59656382","wikidata":"https://www.wikidata.org/wiki/Q191536","display_name":"Conjunction (astronomy)","level":2,"score":0.7910948991775513},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.770615816116333},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.765531063079834},{"id":"https://openalex.org/C2777685122","wikidata":"https://www.wikidata.org/wiki/Q170028","display_name":"Falsity","level":2,"score":0.7237758636474609},{"id":"https://openalex.org/C34849589","wikidata":"https://www.wikidata.org/wiki/Q4345785","display_name":"Atomic sentence","level":3,"score":0.6731423735618591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4975338280200958},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.49476903676986694},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4860263466835022},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.44575217366218567},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4355280101299286},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.4244399666786194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.313620924949646},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.2882866859436035},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25962013006210327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10723087191581726},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C139997677","wikidata":"https://www.wikidata.org/wiki/Q60195","display_name":"Semiotics","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1096901765","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1096901765","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1096901765","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1096901765","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1538303046","https://openalex.org/W2083316690","https://openalex.org/W2530194309","https://openalex.org/W4229652763","https://openalex.org/W4388284697"],"related_works":["https://openalex.org/W2358878837","https://openalex.org/W2348729074","https://openalex.org/W2096992842","https://openalex.org/W2056830452","https://openalex.org/W2897866277","https://openalex.org/W2062097337","https://openalex.org/W2362026785","https://openalex.org/W2889599075","https://openalex.org/W2353234699","https://openalex.org/W2110138067"],"abstract_inverted_index":{"We":[0,28,209],"begin":[1],"with":[2,112],"a":[3,11,23,49,88,113,141],"prepositional":[4],"language":[5],"L":[6,94,175],"p":[7],"containing":[8],"conjunction":[9,185],"(\u039b),":[10],"class":[12,38],"of":[13,39,60,157,160,188],"sentence":[14,40,96,193],"names":[15,41,78,194],"{":[16,42,105,162,196],"S":[17,43,100,108,121,126,163,197],"\u03b1":[18],"}":[19,45,165,199],"\u03b1\u03f5A":[20],",":[21,47],"and":[22,202],"falsity":[24],"predicate":[25],"F":[26,98,106,124],".":[27,138],"(only)":[29],"allow":[30],"unrestricted":[31],"infinite":[32,184],"conjunctions,":[33],"i.e.,":[34],"given":[35,207],"any":[36],"non-empty":[37],"\u03b2":[44],"\u03b2\u03f5B":[46],"is":[48,68,85,87,206],"well-formed":[50,61],"formula":[51],"(we":[52],"will":[53],"use":[54],"WFF":[55],"to":[56,81],"denote":[57],"the":[58,93,130,192,203],"set":[59],"formulae).":[62],"The":[63],"language,":[64],"as":[65],"it":[66],"stands,":[67],"unproblematic.":[69],"Whether":[70],"various":[71],"paradoxes":[72],"are":[73,79,195],"produced":[74],"depends":[75],"on":[76],"which":[77,82],"assigned":[80],"sentences.":[83],"What":[84],"needed":[86],"denotation":[89,114,204],"function:":[90],"For":[91],"example,":[92,144],"P":[95,176],"\u201c":[97],"(":[99,107,120,125],"1":[101,109,122,127],")\u201d":[102],"(i.e.,":[103],"\u039b":[104],")}),":[110],"combined":[111],"function":[115,205],"\u03b4":[116,119],"such":[117],"that":[118],")\u201c":[123],")\u201d,":[128],"provides":[129],"(or,":[131],"in":[132,186,213],"this":[133,152,212],"context,":[134],"a)":[135],"Liar":[136],"Paradox":[137,146,155],"To":[139],"give":[140],"more":[142,214],"interesting":[143],"Yablo's":[145,154],"[4]":[147],"can":[148,180,210],"be":[149,181],"reconstructed":[150],"within":[151],"framework.":[153],"consists":[156],"an":[158,177],"\u03c9-sequence":[159],"sentences":[161],"k":[164],"k\u03f5\u03c9":[166],"where,":[167],"for":[168],"each":[169],"n":[170],"\u03f5":[171],"\u03c9":[172],":":[173],"Within":[174],"equivalent":[178],"construction":[179],"obtained":[182],"using":[183],"place":[187],"universal":[189],"quantification":[190],"-":[191],"i":[198,200],"\u03f5\u03c9":[201],"by:":[208],"express":[211],"familiar":[215],"terms":[216],"as:":[217],"etc.":[218]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}