{"id":"https://openalex.org/W7225329121","doi":"https://doi.org/10.5281/zenodo.23968031","title":"Chapter 1: The History of Mathematical Ontology - Ontological Mathematics","display_name":"Chapter 1: The History of Mathematical Ontology - Ontological Mathematics","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225329121","doi":"https://doi.org/10.5281/zenodo.23968031"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23968031","doi":"https://doi.org/10.5281/zenodo.23968031","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23968031","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23968031","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133296696","display_name":"Philip Lilien","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lilien, Philip","raw_affiliation_strings":["UCTE FOUNDATION"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCTE FOUNDATION","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133296696"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"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":0.0003000000142492354,"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/T11477","display_name":"Epistemology, Ethics, and Metaphysics","score":0.00019999999494757503,"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/ontology-of-mathematics","display_name":"ontology of mathematics","score":0.9549999833106995},{"id":"https://openalex.org/keywords/nature-of-mathematics","display_name":"nature of mathematics","score":0.8220000267028809},{"id":"https://openalex.org/keywords/history-of-philosophy-of-mathematics","display_name":"history of philosophy of mathematics","score":0.7379999756813049},{"id":"https://openalex.org/keywords/mathematical-realism","display_name":"mathematical realism","score":0.5799999833106995},{"id":"https://openalex.org/keywords/mathematical-fictionalism","display_name":"mathematical fictionalism","score":0.6919999718666077},{"id":"https://openalex.org/keywords/mathematical-platonism","display_name":"mathematical Platonism","score":0.671999990940094},{"id":"https://openalex.org/keywords/mathematics-and-reality","display_name":"mathematics and reality","score":0.5270000100135803},{"id":"https://openalex.org/keywords/emergent-coherence","display_name":"emergent coherence","score":0.7630000114440918},{"id":"https://openalex.org/keywords/metaphysics-of-mathematics","display_name":"metaphysics of mathematics","score":0.7639999985694885}],"concepts":[{"id":"https://openalex.org/C25810664","wikidata":"https://www.wikidata.org/wiki/Q44325","display_name":"Ontology","level":2,"score":0.7254999876022339},{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.6608999967575073},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.5874000191688538},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5715000033378601},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4636000096797943},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4059000015258789},{"id":"https://openalex.org/C40238689","wikidata":"https://www.wikidata.org/wiki/Q180536","display_name":"Philosophy of mathematics","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36629998683929443},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C72074766","wikidata":"https://www.wikidata.org/wiki/Q185264","display_name":"History of mathematics","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C2780573756","wikidata":"https://www.wikidata.org/wiki/Q977433","display_name":"Wonder","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C2780506305","wikidata":"https://www.wikidata.org/wiki/Q3909934","display_name":"Mathematical practice","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28459998965263367},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.26910001039505005},{"id":"https://openalex.org/C521332185","wikidata":"https://www.wikidata.org/wiki/Q185816","display_name":"Analogy","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.2587999999523163},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C42525527","wikidata":"https://www.wikidata.org/wiki/Q1209955","display_name":"Formative assessment","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23968031","doi":"https://doi.org/10.5281/zenodo.23968031","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23968031","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23968032","doi":"https://doi.org/10.5281/zenodo.23968032","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23968032","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23968031","doi":"https://doi.org/10.5281/zenodo.23968031","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23968031","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7140229284","https://openalex.org/W1989896452","https://openalex.org/W4220867169","https://openalex.org/W7156706487","https://openalex.org/W7115172158","https://openalex.org/W7167415924","https://openalex.org/W7160704999","https://openalex.org/W2490838253","https://openalex.org/W7201958600","https://openalex.org/W4383825270"],"abstract_inverted_index":{"Mathematics":[0],"has":[1],"always":[2],"carried":[3],"an":[4],"aura":[5],"of":[6,29,39,60,88,97],"inevitability.":[7],"To":[8],"count,":[9],"to":[10,12],"measure,":[11],"calculate":[13],"\u2014":[14,74,91],"these":[15],"acts":[16],"feel":[17],"natural":[18],"and":[19,53,81,101,127,129],"universal,":[20],"as":[21,143],"if":[22],"they":[23,58,70],"were":[24],"inscribed":[25],"in":[26,132],"the":[27,30,61,86,92,95,108,136,148],"fabric":[28],"world":[31],"itself.":[32],"Yet":[33],"beneath":[34],"this":[35,133],"familiarity":[36],"lies":[37],"one":[38],"philosophy\u2019s":[40],"deepest":[41],"questions:":[42],"what":[43],"is":[44],"mathematics?":[45],"Are":[46,57],"numbers":[47],"eternal":[48],"truths":[49],"existing":[50],"beyond":[51],"space":[52],"time,":[54],"awaiting":[55],"discovery?":[56],"fictions":[59],"human":[62],"mind,":[63],"useful":[64],"but":[65],"ultimately":[66],"artificial?":[67],"Or":[68],"are":[69],"something":[71],"else":[72],"entirely":[73],"a":[75,139],"generative":[76],"principle":[77],"underlying":[78],"both":[79],"mind":[80],"cosmos?":[82],"This":[83],"chapter":[84],"explores":[85],"history":[87,134],"mathematical":[89],"ontology":[90],"search":[93],"for":[94,124,138],"being":[96],"mathematics.":[98],"Across":[99],"cultures":[100],"epochs,":[102],"great":[103],"thinkers":[104],"have":[105],"wrestled":[106],"with":[107],"same":[109],"puzzle:":[110],"does":[111],"mathematics":[112,142],"describe":[113],"reality,":[114],"construct":[115],"it,":[116],"or":[117],"constitute":[118],"it?":[119],"Their":[120],"answers":[121],"laid":[122],"foundations":[123],"science,":[125],"philosophy,":[126],"metaphysics,":[128],"each":[130],"step":[131],"prepares":[135],"ground":[137],"new":[140],"synthesis:":[141],"emergent":[144],"coherence,":[145],"generated":[146],"by":[147],"ontological":[149],"seed":[150],"we":[151],"call":[152],"Zeta":[153],"Naught.":[154]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}