{"id":"https://openalex.org/W2057326334","doi":"https://doi.org/10.1305/ndjfl/1093636009","title":"Linear diagrams for syllogisms (with relationals).","display_name":"Linear diagrams for syllogisms (with relationals).","publication_year":1991,"publication_date":"1991-12-01","ids":{"openalex":"https://openalex.org/W2057326334","doi":"https://doi.org/10.1305/ndjfl/1093636009","mag":"2057326334"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093636009","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093636009","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011706774","display_name":"George Englebretsen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"George Englebretsen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5011706774"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.17688856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"33","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9190000295639038,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9190000295639038,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/venn-diagram","display_name":"Venn diagram","score":0.9823135137557983},{"id":"https://openalex.org/keywords/syllogism","display_name":"Syllogism","score":0.9001488089561462},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.6085181832313538},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5682679414749146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5426957011222839},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4551122784614563},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4149113595485687},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38238197565078735},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37879678606987},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.1711561679840088},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11604121327400208},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09045761823654175},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08480918407440186}],"concepts":[{"id":"https://openalex.org/C55508974","wikidata":"https://www.wikidata.org/wiki/Q190763","display_name":"Venn diagram","level":2,"score":0.9823135137557983},{"id":"https://openalex.org/C131598440","wikidata":"https://www.wikidata.org/wiki/Q107342","display_name":"Syllogism","level":2,"score":0.9001488089561462},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.6085181832313538},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5682679414749146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5426957011222839},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4551122784614563},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4149113595485687},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38238197565078735},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37879678606987},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.1711561679840088},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11604121327400208},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09045761823654175},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08480918407440186},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093636009","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093636009","pdf_url":null,"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/1093636009","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093636009","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W188634130","https://openalex.org/W333471691","https://openalex.org/W379742404","https://openalex.org/W938361001","https://openalex.org/W1977026695","https://openalex.org/W1985947713","https://openalex.org/W1997704656","https://openalex.org/W2016887700","https://openalex.org/W2144325908","https://openalex.org/W2319356165","https://openalex.org/W2325116448","https://openalex.org/W2907074674","https://openalex.org/W4230547059","https://openalex.org/W4232980159","https://openalex.org/W4248286167"],"related_works":["https://openalex.org/W2804328824","https://openalex.org/W2610972775","https://openalex.org/W2367118530","https://openalex.org/W1582793335","https://openalex.org/W4294837686","https://openalex.org/W1489371471","https://openalex.org/W2742062470","https://openalex.org/W2567204906","https://openalex.org/W751375708","https://openalex.org/W2004933030"],"abstract_inverted_index":{"A":[0],"system":[1],"for":[2,79,195,218],"diagramming":[3],"syllogisms":[4,177],"is":[5,84,150,186,190],"developed":[6],"here.Unlike":[7],"Venn,":[8],"and":[9,64,71,76,156,170,181,233,251],"other":[10],"planar":[11,168],"diagrams,":[12,141],"these":[13],"diagrams":[14,73,105,165,197,217],"are":[15,74],"linear.This":[16],"allows":[17],"one":[18],"to":[19,41,91,262],"diagram":[20,128,244],"inferences":[21,42],"which":[22,198],"exceed":[23],"the":[24,37,100,132,160,203,211,222,260],"virtual":[25,204],"four":[26,96,205],"term":[27,206],"limit":[28,207],"on":[29,208],"nonlinear":[30],"systems.It":[31],"also":[32],"can":[33,199],"be":[34,49],"extended":[35],"(by":[36],"use":[38,138],"of":[39,46,102,117,127,139,145,224,248,273],"vectors)":[40],"involving":[43],"all":[44],"kinds":[45],"relational":[47],"expressions....":[48],"he":[50,62],"a":[51,115,191,242,267],"Triangle,":[52],"Square,":[53],"Pentagon,":[54],"Hexagon,":[55],"Circle,":[56],"what":[57,253],"you":[58],"willa":[59],"straight":[60],"Line":[61],"looks":[63],"nothing":[65],"else.E.":[66],"A.":[67],"Abbott,":[68],"Flatland":[69],"1Euler":[70],"Venn":[72,228],"simple":[75,176],"effective":[77],"devices":[78],"illustrating":[80],"syllogistic":[81,219,274],"validity.Their":[82],"potential":[83],"limited,":[85],"however,":[86],"since":[87],"they":[88,148,172],"cannot":[89],"apply":[90],"arguments":[92],"with":[93,266],"more":[94],"than":[95,167],"terms.Attempts":[97],"at":[98],"extending":[99],"scope":[101],"plane":[103,209],"figure":[104],"(e.g.,":[106],"by":[107,227],"Lewis":[108],"Carroll)":[109],"have":[110],"been":[111],"only":[112,175],"marginally":[113],"successful.(For":[114],"survey":[116],"such":[118,241],"attempts,":[119],"see":[120],"Gardner":[121],"[2].)Aristotle":[122],"probably":[123],"used":[124,163],"some":[125,247],"sort":[126],"method":[129,194,261],"in":[130,271,275],"teaching":[131],"syllogistic.And":[133],"many":[134],"ancient":[135,161],"commentaries":[136],"made":[137],"linear":[140,164,193,216,243],"though":[142],"our":[143],"understanding":[144],"just":[146],"how":[147],"worked":[149],"sketchy":[151],"(see":[152],"Ross":[153],"[13],":[154],"pp.301-302":[155],"Kneale":[157],"[5],":[158],"pp.71-72).If":[159],"syllogists":[162],"rather":[166],"ones,":[169],"if":[171],"diagrammed":[173],"not":[174],"but":[178],"sorites,":[179],"polysyllogisms,":[180],"compound":[182],"syllogisms,":[183],"then":[184],"it":[185],"likely":[187],"that":[188],"there":[189],"satisfactory":[192],"logical":[196],"readily":[200],"go":[201],"beyond":[202],"diagrams.(In":[210],"eighteenth":[212],"century,":[213],"Lambert":[214],"attempted":[215],"[5]":[220],"(pp.111-150).See":[221],"critiques":[223],"his":[225],"systems":[226],"[15]":[229],"(pp.504-527),":[230],"Peirce":[231],"[7],":[232],"Keynes":[234],"[4]":[235],"(pp.":[236],"243-247).)Here,":[237],"I":[238],"will":[239,264],"describe":[240],"method,":[245],"illustrate":[246],"its":[249],"uses,":[250],"do":[252],"no":[254],"syllogist":[255],"has":[256],"done":[257],"before":[258],"-extend":[259],"relations.I":[263],"conclude":[265],"brief":[268],"polemical":[269],"remark":[270],"favor":[272],"general.":[276]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
