{"id":"https://openalex.org/W2065559740","doi":"https://doi.org/10.2307/2267171","title":"The identity of individuals in a strict functional calculus of second order","display_name":"The identity of individuals in a strict functional calculus of second order","publication_year":1947,"publication_date":"1947-03-01","ids":{"openalex":"https://openalex.org/W2065559740","doi":"https://doi.org/10.2307/2267171","mag":"2065559740"},"language":"en","primary_location":{"id":"doi:10.2307/2267171","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267171","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/A5005756614","display_name":"Ruth C. Barcan","orcid":null},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ruth C. Barcan","raw_affiliation_strings":["Yale University","Yale University  ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University","institution_ids":["https://openalex.org/I32971472"]},{"raw_affiliation_string":"Yale University  ;","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005756614"],"corresponding_institution_ids":["https://openalex.org/I32971472"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":272,"citation_normalized_percentile":{"value":0.24102564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"12","issue":"1","first_page":"12","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9611999988555908,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9611999988555908,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9520999789237976,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9437000155448914,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.6735920906066895},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.6589972376823425},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6584234833717346},{"id":"https://openalex.org/keywords/blank","display_name":"Blank","score":0.6239720582962036},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5513857007026672},{"id":"https://openalex.org/keywords/functional-calculus","display_name":"Functional calculus","score":0.5502748489379883},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5467014908790588},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5196287035942078},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4998178482055664},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49138012528419495},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45859068632125854},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3754669427871704},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30618375539779663},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.21087834239006042},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.11064568161964417},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.09393978118896484},{"id":"https://openalex.org/keywords/aesthetics","display_name":"Aesthetics","score":0.07446262240409851}],"concepts":[{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6735920906066895},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.6589972376823425},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6584234833717346},{"id":"https://openalex.org/C2778089247","wikidata":"https://www.wikidata.org/wiki/Q368951","display_name":"Blank","level":2,"score":0.6239720582962036},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5513857007026672},{"id":"https://openalex.org/C205107259","wikidata":"https://www.wikidata.org/wiki/Q1474584","display_name":"Functional calculus","level":2,"score":0.5502748489379883},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5467014908790588},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5196287035942078},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4998178482055664},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49138012528419495},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45859068632125854},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3754669427871704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30618375539779663},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.21087834239006042},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.11064568161964417},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.09393978118896484},{"id":"https://openalex.org/C107038049","wikidata":"https://www.wikidata.org/wiki/Q35986","display_name":"Aesthetics","level":1,"score":0.07446262240409851},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2267171","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267171","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/1183395204","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183395204","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":[{"display_name":"Reduced inequalities","score":0.6200000047683716,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1968233326"],"related_works":["https://openalex.org/W2361638505","https://openalex.org/W1993662208","https://openalex.org/W2370352440","https://openalex.org/W2009954581","https://openalex.org/W4296141694","https://openalex.org/W2379220204","https://openalex.org/W3160305016","https://openalex.org/W2363541254","https://openalex.org/W1554018104","https://openalex.org/W10565164"],"abstract_inverted_index":{"In":[0,21],"previous":[1],"papers":[2],"we":[3,16],"developed":[4],"two":[5],"functional":[6,33],"calculi":[7],"of":[8,35,41,45,47],"first":[9],"order":[10,37],"based":[11],"on":[12],"strict":[13],"implication":[14],"which":[15],"called":[17],"S2":[18],"and":[19],"S4.":[20],"the":[22,39,43,55],"present":[23],"paper,":[24],"these":[25],"systems":[26],"will":[27],"be":[28,59],"extended":[29],"to":[30,58],"include":[31],"a":[32],"calculus":[34],"second":[36],"with":[38],"purpose":[40],"introducing":[42],"relation":[44],"identity":[46],"individuals.":[48],"Primitive":[49],"symbols.":[50],"\u0302":[51],"{the":[52],"abstraction":[53],"operator,":[54],"blank":[56],"space":[57],"replaced":[60],"by":[61],"an":[62],"appropriate":[63],"variable}.":[64]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":27},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":23},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}