{"id":"https://openalex.org/W2789953504","doi":"https://doi.org/10.1007/s11229-018-1752-5","title":"Two roads to the successor axiom","display_name":"Two roads to the successor axiom","publication_year":2018,"publication_date":"2018-03-13","ids":{"openalex":"https://openalex.org/W2789953504","doi":"https://doi.org/10.1007/s11229-018-1752-5","mag":"2789953504"},"language":"en","primary_location":{"id":"doi:10.1007/s11229-018-1752-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11229-018-1752-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11229-018-1752-5.pdf","source":{"id":"https://openalex.org/S255146","display_name":"Synthese","issn_l":"0039-7857","issn":["0039-7857","1573-0964"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Synthese","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11229-018-1752-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056736933","display_name":"Stefan Buijsman","orcid":"https://orcid.org/0000-0002-0004-0681"},"institutions":[{"id":"https://openalex.org/I161593684","display_name":"Stockholm University","ror":"https://ror.org/05f0yaq80","country_code":"SE","type":"education","lineage":["https://openalex.org/I161593684"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Stefan Buijsman","raw_affiliation_strings":["Filosofiska Institutionen, Stockholm University, Universitetsv\u00e4gen 10D, 106 91, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-0004-0681","affiliations":[{"raw_affiliation_string":"Filosofiska Institutionen, Stockholm University, Universitetsv\u00e4gen 10D, 106 91, Stockholm, Sweden","institution_ids":["https://openalex.org/I161593684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056736933"],"corresponding_institution_ids":["https://openalex.org/I161593684"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.7313,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71842211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"197","issue":"3","first_page":"1241","last_page":"1261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11345","display_name":"Cognitive and developmental aspects of mathematical skills","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9613000154495239,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/successor-cardinal","display_name":"Successor cardinal","score":0.9549298286437988},{"id":"https://openalex.org/keywords/numeral-system","display_name":"Numeral system","score":0.9141967296600342},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.671223521232605},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.6133161783218384},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.506583571434021},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47250640392303467},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4250373840332031},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3905065059661865},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.3793150782585144},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3695370554924011},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3455742299556732},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.3204590082168579},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1811249852180481},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.138208270072937}],"concepts":[{"id":"https://openalex.org/C75306776","wikidata":"https://www.wikidata.org/wiki/Q7632662","display_name":"Successor cardinal","level":2,"score":0.9549298286437988},{"id":"https://openalex.org/C204160518","wikidata":"https://www.wikidata.org/wiki/Q122653","display_name":"Numeral system","level":2,"score":0.9141967296600342},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.671223521232605},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.6133161783218384},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.506583571434021},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47250640392303467},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4250373840332031},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3905065059661865},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3793150782585144},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3695370554924011},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3455742299556732},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.3204590082168579},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1811249852180481},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.138208270072937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11229-018-1752-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11229-018-1752-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11229-018-1752-5.pdf","source":{"id":"https://openalex.org/S255146","display_name":"Synthese","issn_l":"0039-7857","issn":["0039-7857","1573-0964"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Synthese","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11229-018-1752-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11229-018-1752-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11229-018-1752-5.pdf","source":{"id":"https://openalex.org/S255146","display_name":"Synthese","issn_l":"0039-7857","issn":["0039-7857","1573-0964"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Synthese","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.8199999928474426}],"awards":[],"funders":[{"id":"https://openalex.org/F4320325669","display_name":"Stockholms Universitet","ror":"https://ror.org/05f0yaq80"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2789953504.pdf","grobid_xml":"https://content.openalex.org/works/W2789953504.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W207447885","https://openalex.org/W652242727","https://openalex.org/W656709765","https://openalex.org/W1490628945","https://openalex.org/W1537592620","https://openalex.org/W1627030236","https://openalex.org/W1665809640","https://openalex.org/W1738097990","https://openalex.org/W1746920086","https://openalex.org/W1892167953","https://openalex.org/W1964857359","https://openalex.org/W1980510330","https://openalex.org/W1980606684","https://openalex.org/W1995896110","https://openalex.org/W2001569942","https://openalex.org/W2012106277","https://openalex.org/W2013454280","https://openalex.org/W2029234748","https://openalex.org/W2050286428","https://openalex.org/W2051630709","https://openalex.org/W2052513004","https://openalex.org/W2061853836","https://openalex.org/W2066537596","https://openalex.org/W2067998532","https://openalex.org/W2071849949","https://openalex.org/W2071921795","https://openalex.org/W2079283016","https://openalex.org/W2082797154","https://openalex.org/W2092491984","https://openalex.org/W2107892800","https://openalex.org/W2108627731","https://openalex.org/W2108790250","https://openalex.org/W2130776778","https://openalex.org/W2137859097","https://openalex.org/W2144373230","https://openalex.org/W2160820865","https://openalex.org/W2161130277","https://openalex.org/W2323988862","https://openalex.org/W2344416341","https://openalex.org/W2402997934","https://openalex.org/W2526940069","https://openalex.org/W2549527009","https://openalex.org/W2560719313","https://openalex.org/W2564708475","https://openalex.org/W2749185405","https://openalex.org/W4249468442","https://openalex.org/W6742995156","https://openalex.org/W7044164732"],"related_works":["https://openalex.org/W3123320268","https://openalex.org/W2473542051","https://openalex.org/W2994519609","https://openalex.org/W2054269721","https://openalex.org/W4214635639","https://openalex.org/W2390822611","https://openalex.org/W2084522819","https://openalex.org/W1547957076","https://openalex.org/W2112023055","https://openalex.org/W1987374635"],"abstract_inverted_index":{"Most":[0],"accounts":[1],"of":[2,5,17,29,94,104,116,142,153,157,176,196],"our":[3],"knowledge":[4],"the":[6,15,59,64,68,92,102,105,113,117,124,127,130,154,158,166,170,193],"successor":[7,65],"axiom":[8,66],"claim":[9,24],"that":[10,40,46,50,76,85,97,109,136,165,183,187,216],"this":[11,34,41,137],"is":[12,42,78,138],"based":[13],"on":[14,91,192],"procedure":[16],"adding":[18,190],"one.":[19],"While":[20],"they":[21,44,62,72,86,110,163,184],"usually":[22],"don\u2019t":[23],"to":[25,99,123],"provide":[26],"an":[27,79,174],"account":[28],"how":[30,43],"children":[31,213],"actually":[32],"acquire":[33],"knowledge,":[35],"one":[36,128],"may":[37],"well":[38],"think":[39],"get":[45],"knowledge.":[47],"I":[48,83],"argue":[49,84],"when":[51,61],"we":[52],"look":[53],"at":[54],"children\u2019s":[55],"responses":[56],"in":[57,211],"interviews,":[58],"time":[60],"learn":[63,89,135,215],"and":[67,120],"intermediate":[69],"learning":[70],"stages":[71],"find":[73],"themselves":[74],"in,":[75],"there":[77,217],"empirically":[80],"viable":[81],"alternative.":[82],"could":[87],"also":[88,185],"it":[90],"basis":[93],"a":[95,139,151,197,200],"method":[96,141],"has":[98],"do":[100],"with":[101,129],"structure":[103,115,156],"numeral":[106,118,159,198],"system.":[107,160],"Specifically,":[108],"(1)":[111],"use":[112],"syntactic":[114,155],"system":[119],"(2)":[121],"attend":[122],"leftmost":[125,167],"digits,":[126],"highest":[131,171],"place-value.":[132],"Children":[133],"can":[134],"reliable":[140],"forming":[143],"larger":[144,201],"numbers":[145],"by":[146],"combining":[147],"two":[148],"elements.":[149],"First,":[150],"grasp":[152],"That":[161],"way":[162],"know":[164],"digit":[168],"receives":[169],"value.":[172],"Second,":[173],"interpretation":[175],"numerals":[177],"as":[178],"designating":[179],"cardinal":[180],"values,":[181],"so":[182],"realise":[186],"increasing":[188],"or":[189],"digits":[191],"lefthand":[194],"side":[195],"produces":[199],"number.":[202],"There":[203],"are":[204,218],"thus":[205],"two,":[206],"currently":[207],"equally":[208],"well-supported,":[209],"ways":[210],"which":[212],"might":[214],"infinitely":[219],"many":[220],"natural":[221],"numbers.":[222]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
