{"id":"https://openalex.org/W2060700159","doi":"https://doi.org/10.2307/421032","title":"Incompleteness, Mechanism, and Optimism","display_name":"Incompleteness, Mechanism, and Optimism","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W2060700159","doi":"https://doi.org/10.2307/421032","mag":"2060700159"},"language":"en","primary_location":{"id":"doi:10.2307/421032","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421032","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin 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/A5030334025","display_name":"Stewart Shapiro","orcid":"https://orcid.org/0000-0002-4895-0772"},"institutions":[{"id":"https://openalex.org/I4210107394","display_name":"The Ohio State University Newark","ror":"https://ror.org/01r8m0a35","country_code":"US","type":"education","lineage":["https://openalex.org/I4210107394","https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stewart Shapiro","raw_affiliation_strings":["Department of Philosophy, Ohio State University at Newark, Newark, Ohio 43055, USAE-mail:","Department of Philosophy, Ohio State University at Newark, Newark, Ohio 43055, USA E-mail/i: shapiro@osu.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy, Ohio State University at Newark, Newark, Ohio 43055, USAE-mail:","institution_ids":["https://openalex.org/I4210107394"]},{"raw_affiliation_string":"Department of Philosophy, Ohio State University at Newark, Newark, Ohio 43055, USA E-mail/i: shapiro@osu.edu","institution_ids":["https://openalex.org/I4210107394"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030334025"],"corresponding_institution_ids":["https://openalex.org/I4210107394"],"apc_list":null,"apc_paid":null,"fwci":1.0199,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.76851449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","issue":"3","first_page":"273","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9990000128746033,"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":0.9735000133514404,"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"}},{"id":"https://openalex.org/T11883","display_name":"Embodied and Extended Cognition","score":0.945900022983551,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.6181192398071289},{"id":"https://openalex.org/keywords/mechanism","display_name":"Mechanism (biology)","score":0.6131711602210999},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.5017077922821045},{"id":"https://openalex.org/keywords/description-number","display_name":"Description number","score":0.4822738468647003},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.4813402593135834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47432583570480347},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.45950907468795776},{"id":"https://openalex.org/keywords/g\u00f6dels-incompleteness-theorems","display_name":"G\u00f6del's incompleteness theorems","score":0.4588592052459717},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.45361781120300293},{"id":"https://openalex.org/keywords/g\u00f6del","display_name":"G\u00f6del","score":0.4386652112007141},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4273962378501892},{"id":"https://openalex.org/keywords/cognitive-science","display_name":"Cognitive science","score":0.3403109014034271},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3377295732498169},{"id":"https://openalex.org/keywords/universal-turing-machine","display_name":"Universal Turing machine","score":0.2680169343948364},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.22335141897201538},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.1570296585559845}],"concepts":[{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.6181192398071289},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.6131711602210999},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.5017077922821045},{"id":"https://openalex.org/C179061269","wikidata":"https://www.wikidata.org/wiki/Q5263786","display_name":"Description number","level":5,"score":0.4822738468647003},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.4813402593135834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47432583570480347},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.45950907468795776},{"id":"https://openalex.org/C180937797","wikidata":"https://www.wikidata.org/wiki/Q200787","display_name":"G\u00f6del's incompleteness theorems","level":3,"score":0.4588592052459717},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.45361781120300293},{"id":"https://openalex.org/C2781302003","wikidata":"https://www.wikidata.org/wiki/Q3294091","display_name":"G\u00f6del","level":2,"score":0.4386652112007141},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4273962378501892},{"id":"https://openalex.org/C188147891","wikidata":"https://www.wikidata.org/wiki/Q147638","display_name":"Cognitive science","level":1,"score":0.3403109014034271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3377295732498169},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.2680169343948364},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.22335141897201538},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.1570296585559845},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/421032","is_oa":false,"landing_page_url":"https://doi.org/10.2307/421032","pdf_url":null,"source":{"id":"https://openalex.org/S130801046","display_name":"Bulletin of Symbolic Logic","issn_l":"1079-8986","issn":["1079-8986","1943-5894"],"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":"Bulletin of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.bsl/1182353578","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.bsl/1182353578","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.27.1366","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.1366","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/~asl/bsl/0403/0403-002.ps","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":41,"referenced_works":["https://openalex.org/W129840577","https://openalex.org/W992186155","https://openalex.org/W1525820284","https://openalex.org/W1540074734","https://openalex.org/W1550872402","https://openalex.org/W1571003765","https://openalex.org/W1596092532","https://openalex.org/W1963521012","https://openalex.org/W1970654545","https://openalex.org/W1990401544","https://openalex.org/W1990474964","https://openalex.org/W2001771035","https://openalex.org/W2005337919","https://openalex.org/W2009171410","https://openalex.org/W2011021254","https://openalex.org/W2016108150","https://openalex.org/W2020829707","https://openalex.org/W2049953015","https://openalex.org/W2077128566","https://openalex.org/W2089128760","https://openalex.org/W2117832390","https://openalex.org/W2127352247","https://openalex.org/W2145482038","https://openalex.org/W2188058249","https://openalex.org/W2320853213","https://openalex.org/W2325530839","https://openalex.org/W2326972230","https://openalex.org/W2330014749","https://openalex.org/W2335484545","https://openalex.org/W2530006810","https://openalex.org/W2798840070","https://openalex.org/W2932189326","https://openalex.org/W2998385477","https://openalex.org/W3190240787","https://openalex.org/W4239779666","https://openalex.org/W4245927665","https://openalex.org/W4247819482","https://openalex.org/W4255721438","https://openalex.org/W4291166496","https://openalex.org/W4301024087","https://openalex.org/W6687157058"],"related_works":["https://openalex.org/W2273345230","https://openalex.org/W2119244842","https://openalex.org/W4312201671","https://openalex.org/W4324016496","https://openalex.org/W2090113742","https://openalex.org/W1559604976","https://openalex.org/W4231495498","https://openalex.org/W4285436350","https://openalex.org/W298497181","https://openalex.org/W2379575195"],"abstract_inverted_index":{"\u00a71.":[0],"Overview":[1],".":[2],"Philosophers":[3],"and":[4,15,23,59,64,90,121,176,186],"mathematicians":[5],"have":[6,77],"drawn":[7],"lots":[8],"of":[9,81,87,101,181,184,199,213],"conclusions":[10],"from":[11,18],"G\u00f6del's":[12,30,127],"incompleteness":[13],"theorems,":[14],"related":[16],"results":[17],"mathematical":[19],"logic.":[20],"Languages,":[21],"minds,":[22],"machines":[24],"figure":[25],"prominently":[26],"in":[27],"the":[28,65,72,78,97,115,130,134,156,179,188,197,211],"discussion.":[29],"theorems":[31],"surely":[32],"tell":[33],"us":[34],"something":[35],"about":[36],"these":[37],"important":[38],"matters.":[39],"But":[40],"what?":[41],"A":[42],"descriptive":[43],"title":[44],"for":[45,171],"this":[46,88],"paper":[47],"would":[48,67],"be":[49,69,140],"\u201cG\u00f6del,":[50],"Lucas,":[51],"Penrose,":[52],"Turing,":[53],"Feferman,":[54],"Dummett,":[55],"mechanism,":[56],"optimism,":[57],"reflection,":[58],"indefinite":[60],"extensibility\u201d.":[61],"Adding":[62],"\u201cGod":[63],"Devil\u201d":[66],"probably":[68],"redundant.":[70],"Despite":[71],"breath-taking,":[73],"whirlwind":[74],"tour,":[75],"I":[76,107],"modest":[79,99],"aim":[80,100],"forging":[82],"connections":[83],"between":[84],"different":[85],"parts":[86],"literature":[89,116],"clearing":[91],"up":[92],"some":[93],"confusions,":[94],"together":[95],"with":[96],"less":[98],"not":[102],"introducing":[103],"any":[104],"more":[105],"confusions.":[106],"propose":[108],"to":[109],"focus":[110],"on":[111,117],"three":[112],"spheres":[113],"within":[114],"incompleteness.":[118],"The":[119,151],"first,":[120],"primary,":[122],"one":[123],"concerns":[124],"arguments":[125],"that":[126,133,166,178,191,210],"theorem":[128],"refutes":[129],"mechanistic":[131],"thesis":[132],"human":[135,193,200],"mind":[136],"is,":[137],"or":[138,147,196,204],"can":[139,205],"accurately":[141],"modeled":[142],"as,":[143],"a":[144,148,167,172,192],"digital":[145],"computer":[146],"Turing":[149],"machine.":[150],"most":[152],"famous":[153],"instance":[154],"is":[155,215],"much":[157],"reprinted":[158],"J.":[159],"R.":[160],"Lucas":[161],"[18].":[162],"To":[163],"summarize,":[164],"suppose":[165],"mechanist":[168],"provides":[169],"plans":[170],"machine,":[173],"M":[174,182,214],",":[175],"claims":[177],"output":[180,212],"consists":[183],"all":[185],"only":[187],"arithmetic":[189],"truths":[190],"(like":[194],"Lucas),":[195],"totality":[198],"mathematicians,":[201],"will":[202],"ever":[203,206],"know.":[207],"We":[208],"assume":[209],"consistent.":[216]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}