{"id":"https://openalex.org/W2078107200","doi":"https://doi.org/10.2307/2273129","title":"On carnap and popper probability functions","display_name":"On carnap and popper probability functions","publication_year":1979,"publication_date":"1979-09-01","ids":{"openalex":"https://openalex.org/W2078107200","doi":"https://doi.org/10.2307/2273129","mag":"2078107200"},"language":"en","primary_location":{"id":"doi:10.2307/2273129","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273129","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/A5016040469","display_name":"Hugues Leblanc","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]},{"id":"https://openalex.org/I84392919","display_name":"Temple University","ror":"https://ror.org/00kx1jb78","country_code":"US","type":"education","lineage":["https://openalex.org/I84392919"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Hugues Leblanc","raw_affiliation_strings":["Temple University, Philadelphia, PA 19122","University of Southern California, Los Angeles, CA 90007","University of Toronto, Toronto, CanadaM5S 1A1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Temple University, Philadelphia, PA 19122","institution_ids":["https://openalex.org/I84392919"]},{"raw_affiliation_string":"University of Southern California, Los Angeles, CA 90007","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"University of Toronto, Toronto, CanadaM5S 1A1","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005922054","display_name":"Bas C. van Fraassen","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]},{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]},{"id":"https://openalex.org/I84392919","display_name":"Temple University","ror":"https://ror.org/00kx1jb78","country_code":"US","type":"education","lineage":["https://openalex.org/I84392919"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Bas C. van Fraassen","raw_affiliation_strings":["Temple University, Philadelphia, PA 19122","University of Southern California, Los Angeles, CA 90007","University of Toronto, Toronto, CanadaM5S 1A1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Temple University, Philadelphia, PA 19122","institution_ids":["https://openalex.org/I84392919"]},{"raw_affiliation_string":"University of Southern California, Los Angeles, CA 90007","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"University of Toronto, Toronto, CanadaM5S 1A1","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8199,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.69362586,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"44","issue":"3","first_page":"369","last_page":"373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9269000291824341,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9269000291824341,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.914900004863739,"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":0.9068999886512756,"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/tautology","display_name":"Tautology (logic)","score":0.9086353778839111},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.6224308609962463},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6091863512992859},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5776281952857971},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.5078042149543762},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40935590863227844},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3955458998680115},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.35993412137031555},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3481651544570923},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.2869643568992615},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20965465903282166},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10547783970832825}],"concepts":[{"id":"https://openalex.org/C166374712","wikidata":"https://www.wikidata.org/wiki/Q209555","display_name":"Tautology (logic)","level":5,"score":0.9086353778839111},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.6224308609962463},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6091863512992859},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5776281952857971},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.5078042149543762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40935590863227844},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3955458998680115},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.35993412137031555},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3481651544570923},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.2869643568992615},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20965465903282166},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10547783970832825},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273129","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273129","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/1183740432","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740432","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1565693361","https://openalex.org/W2010556813","https://openalex.org/W2027705302","https://openalex.org/W2077128876","https://openalex.org/W2133690097","https://openalex.org/W2371818109","https://openalex.org/W3028000971"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2418518962","https://openalex.org/W2373681119","https://openalex.org/W3204670144","https://openalex.org/W2963377682","https://openalex.org/W2163101548","https://openalex.org/W4297794244","https://openalex.org/W4286698828"],"abstract_inverted_index":{"With":[0],"PC":[1,19],"understood":[2],"to":[3,20,93],"be":[4],"the":[5,16,21,47,77,85,181],"propositional":[6],"calculus":[7],"of":[8,18,76,183,192,203],"[3],":[9],"call":[10,46],"a":[11,23,43,49,68,90,109,130,136,156,168,199,204,231],"binary":[12],"function":[13,26,48,52,66,132,158,197,206],"Pr":[14,107,128,154,207,213],"from":[15,113],"wffs":[17],"reals":[22],"Carnap":[24,65,200],"(probability)":[25,51],"if":[27,53,217,220],"it":[28,54,208],"meets":[29,55,214],"requirements":[30,56],"A1\u2014A5":[31],"in":[32,38,61,83,121,227],"Table":[33],"I":[34],"(with":[35],"\u2018\u22a2\u2026\u2019":[36],"short":[37],"A3\u2014A4":[39],"for":[40],"\u2018\u2026":[41],"is":[42,67,108,129,135,155,167,178,198,209,230],"tautology\u2019),":[44],"and":[45,72,133,159,218],"Popper":[50,69,110,131,157,196,205],"Bl\u2014B6":[57],"there:":[58],"Leblanc":[59,115,188],"established":[60],"[3]":[62],"that":[63,125,151,194,212],"every":[64,195],"one":[70,201],",":[71,148],"he":[73,173],"tendered":[74],"proof":[75,86],"converse.":[78],"As":[79],"reported":[80],"by":[81],"Stalnaker":[82],"[5],":[84],"unfortunately":[87],"was":[88],"incomplete,":[89],"mishap":[91],"due":[92],"Leblanc's":[94],"abbreviating":[95],"\u2018":[96],"Pr(A,":[97,139,160,221],"\u223c":[98,140,161,222],"A)":[99,141,162,223],"=":[100,142,163,224],"1\u2019":[101],"as":[102,118,180],"\u2018\u22a2":[103],"A":[104,134,166,229],"\u2019":[105],"when":[106],"function.":[111],"Borrowing":[112],"[4],":[114],"did":[116,146],"show,":[117],"Harper":[119],"notes":[120],"[2,":[122],"footnote":[123],"17],":[124],"(1)":[126],"If":[127,153],"tautology,":[137],"then":[138,165],"1":[143,225],".":[144,170],"He":[145],"not":[147],"however,":[149],"show":[150],"(2)":[152,177],"1,":[164],"tautology":[169],"Nor":[171],"could":[172],"have":[174],"done":[175],"so:":[176],"false,":[179],"simplest":[182],"counterexamples":[184],"shows.":[185],"Denied":[186],"(2),":[187],"had":[189],"no":[190],"hope":[191],"proving":[193],":":[202],"easily":[210],"ascertained":[211],"requirement":[215],"A4":[216],"only":[219],"just":[226],"case":[228],"tautology.":[232]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
