{"id":"https://openalex.org/W2079963815","doi":"https://doi.org/10.1305/ndjfl/1038336841","title":"Cardinality, Counting, and Equinumerosity","display_name":"Cardinality, Counting, and Equinumerosity","publication_year":2000,"publication_date":"2000-07-01","ids":{"openalex":"https://openalex.org/W2079963815","doi":"https://doi.org/10.1305/ndjfl/1038336841","mag":"2079963815"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1038336841","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1038336841","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-41/issue-3/Cardinality-Counting-and-Equinumerosity/10.1305/ndjfl/1038336841.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-41/issue-3/Cardinality-Counting-and-Equinumerosity/10.1305/ndjfl/1038336841.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003502918","display_name":"Richard G. Heck","orcid":"https://orcid.org/0000-0002-2961-2663"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I87650153","display_name":"Emerson College","ror":"https://ror.org/011xz5b94","country_code":"US","type":"education","lineage":["https://openalex.org/I87650153"]},{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard G. Heck","raw_affiliation_strings":["Harvard University 208 Emerson Hall Cambridge MA 02138","University of Notre Dame Department of Philosophy"],"affiliations":[{"raw_affiliation_string":"Harvard University 208 Emerson Hall Cambridge MA 02138","institution_ids":["https://openalex.org/I87650153","https://openalex.org/I136199984"]},{"raw_affiliation_string":"University of Notre Dame Department of Philosophy","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003502918"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I136199984","https://openalex.org/I87650153"],"apc_list":null,"apc_paid":null,"fwci":6.7884,"has_fulltext":true,"cited_by_count":68,"citation_normalized_percentile":{"value":0.96849539,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"41","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12558","display_name":"Wittgensteinian philosophy and applications","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12558","display_name":"Wittgensteinian philosophy and applications","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9909999966621399,"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/T10297","display_name":"Philosophical Ethics and Theory","score":0.961899995803833,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.8190820217132568},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7976131439208984},{"id":"https://openalex.org/keywords/cardinal-number","display_name":"Cardinal number (linguistics)","score":0.7557625770568848},{"id":"https://openalex.org/keywords/grasp","display_name":"GRASP","score":0.5592923760414124},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5305008888244629},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.46342742443084717},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.3181699812412262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16130977869033813},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.07254797220230103}],"concepts":[{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.8190820217132568},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7976131439208984},{"id":"https://openalex.org/C2778408900","wikidata":"https://www.wikidata.org/wiki/Q1329258","display_name":"Cardinal number (linguistics)","level":2,"score":0.7557625770568848},{"id":"https://openalex.org/C171268870","wikidata":"https://www.wikidata.org/wiki/Q1486676","display_name":"GRASP","level":2,"score":0.5592923760414124},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5305008888244629},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.46342742443084717},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.3181699812412262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16130977869033813},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.07254797220230103},{"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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1038336841","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1038336841","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-41/issue-3/Cardinality-Counting-and-Equinumerosity/10.1305/ndjfl/1038336841.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1038336841","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1038336841","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:10.1.1.92.1001","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.1001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://frege.brown.edu/heck/pdf/published/Copyrighted/CountingEquinumerosityEtc.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1038336841","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1038336841","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-41/issue-3/Cardinality-Counting-and-Equinumerosity/10.1305/ndjfl/1038336841.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310260","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43"},{"id":"https://openalex.org/F4320314033","display_name":"Amherst College","ror":"https://ror.org/028vqfs63"},{"id":"https://openalex.org/F4320320278","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2079963815.pdf","grobid_xml":"https://content.openalex.org/works/W2079963815.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W164418409","https://openalex.org/W436153143","https://openalex.org/W1982564681","https://openalex.org/W2010782644","https://openalex.org/W2020935285","https://openalex.org/W2109323615","https://openalex.org/W2147405006","https://openalex.org/W2230259633","https://openalex.org/W2493971814","https://openalex.org/W2786004892","https://openalex.org/W2799147727","https://openalex.org/W3034638766","https://openalex.org/W3047368878","https://openalex.org/W3153988519","https://openalex.org/W4206815099","https://openalex.org/W4388166880","https://openalex.org/W4388216386"],"related_works":["https://openalex.org/W4327724964","https://openalex.org/W2612896625","https://openalex.org/W2596944507","https://openalex.org/W2168299207","https://openalex.org/W4321499188","https://openalex.org/W2783449121","https://openalex.org/W2331093826","https://openalex.org/W2079963815","https://openalex.org/W1974360440","https://openalex.org/W2157535554"],"abstract_inverted_index":{"Frege,":[0],"famously,":[1],"held":[2],"that":[3,32,39,79,85,98],"there":[4,33],"is":[5,34,91],"a":[6,21,62,95,102],"close":[7,37,82],"connection":[8,22],"between":[9],"our":[10,40,48,86],"concept":[11,63,87],"of":[12,18,44,50,53,61,64,88,99],"cardinal":[13,89],"number":[14,65,90],"and":[15,28],"the":[16,51,73],"notion":[17,96,105],"one-one":[19,100],"correspondence,":[20,101],"enshrined":[23],"in":[24,72],"Hume's":[25],"Principle.":[26],"Husserl,":[27],"later":[29],"Parsons,":[30],"objected":[31],"no":[35],"such":[36],"connection,":[38],"most":[41],"primitive":[42,104],"conception":[43],"cardinality":[45],"arises":[46],"from":[47],"grasp":[49],"practice":[52],"counting.":[54],"Some":[55],"empirical":[56],"work":[57],"on":[58],"children's":[59],"development":[60],"has":[66],"sometimes":[67],"been":[68],"thought":[69],"to":[70,83],"point":[71],"same":[74],"direction.":[75],"I":[76],"argue,":[77],"however,":[78],"Frege":[80],"was":[81],"right,":[84],"closely":[92],"connected":[93],"with":[94],"like":[97],"more":[103],"we":[106],"might":[107],"call":[108],"just":[109],"as":[110],"many.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}