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Starting from interpreted undefined predicates governed by true axioms, it switches to an equally economical predicate set with auxiliary arithmetical notations so that old axioms become arithmetical truths. The paper links the routine to implicit definition doctrine and improves a 1940 result by focusing on predicate-level theory, using elementary number theory, and ensuring definitional findability via a strengthened Löwenheim-style theorem.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/the-journal-of-philosophy-vol-lxi-implicit-definition-sustained/321331/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/the-journal-of-philosophy-vol-lxi-implicit-definition-sustained/321331.png","ImageObject",300,407,{"name":92,"@type":93},"Skyler","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the note aim to accomplish?","Question",{"text":112,"@type":113},"It states a purpose to discharge a “somber duty” by defending axioms as implicit definitions with detailed technical literalness.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the mechanical routine work at a high level?",{"text":117,"@type":113},"Given interpreted undefined predicates governed by true axioms, it produces new undefined predicates and definitions plus auxiliary arithmetical notations so the old axioms become true by arithmetic.",{"name":119,"@type":110,"acceptedAnswer":120},"What improvements does the paper claim over the 1940 result?",{"text":121,"@type":113},"It is geared to predicates rather than singular terms, draws specifically on arithmetic (elementary number theory) instead of set theory, and provides a mechanical routine for finding the definitions.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},321331,1791164695,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},2336464648746,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","DETROIT. MICHIGAN  \nTHE  \nEASE DO NOT REMOVe  \nJOURNAL  \nOF  \nPHILOSOPHY  \nVoL.LXI, No.2:JANUARY 16,1964  \nImplicit Definition Sustained:W.V.QUINE ………………………71  \nComments and Criticism  \nAyer on Negation: SIDNE AXIN ………………………………………74  \nBook Reviews  \nERNESTNAGEI,PATRICK SUPPES, and ALFRED TARSKI, eds.: Logic,  \nMethodology,and the Philosophy of Science. Three reviews:  \n…………………………76  \nELLIOTT MENDELSON ………………  \n…………………………79  \nRICHARD C. JEFFREY ……  \n…………………………89  \nERNEST ADAMS ………………………  \n…………………………94  \nNotes and News …………………  \n………………………………95  \nNew Books …………………………  \nPUBLISHED FORTNIGHTLY  \nBY THE  \nJOURNAL OF PHILOSOPHY, INC.  \nTHE JOURNAL OF PHILOSOPHY  \nFoUNDED BY FREDERICK J.E.WoODBRIDGE AND WENDELLT.BUSH  \nEDITORS:John H.Randall,Jr.,Robert D.Cumming,George L.Kline,Sidney Morgenbesser,Arthur Danto,and James j.Walsh.  \nCoNSULTING EDITORS:Herbert w.Schneider,Alexandre Koyré,andJosé Ferrater Mora.  \nMANAGING EDITOR:Leigh S.Cauman.  \nCommunieations to the editors should be addressed to the Managing Edi-tor,720 Philosophy Hall,Columbia University,New York,N.Y,10027.Subseriptions and advertisements should be sent to THE JOURNALOF PHILOSOPHY,720 Philosophy Hall,Columbia University,NewYork,N.Y.,10027.The annual subseription price(24 numbers)is  \n$7.50;to students,$6.00.The price of single numbers is $0.50;double numbers,$1.00;complete volumes(from 1960 on),$12.00.  \nTHE JOURNAL OF PHILOSOPHY is owned by the Journal ofPhilosophy,Ince.,and published bi-weekly(every four weeks in Julyand August)by Lancaster Press,Ine.,Prince and Lemon Sts.,Lan-easter,Pa.,17604.Editorial Offce:720 Philosophy Hall,ColumbiaUniversity,New_York,N.Y.,10027.President,Albert G.Redpath;Vice President,John H.Randall,Jr.;Treasurer,Frederick A.Dewey;Secretary,Corliss Lamont.  \nSecond-class postage paid at Lancaster,Pa.  \nStechert-Hafner,Inc.,New York-Atlas Publ.&Distr.Co.,Ltd.Lon-don-Hermann&Cle,Paris-Nicola Zanichell,Bologna-H.Bouvler u.Co.,Bonn a/Rh.-Librerla Editorlal_Augustinus,Madrid-F.Machado&Cia,Porto-Gerold &Co.,Wien-Librafrle Payot,S.A,Lausanne-TheMaruzen Company,Tokyo.  \n# INTERNATIONAL REVIEW OF SCIENTIFICSYNTHESIS(A REVIEW COVERING ALL SCIENCES)(1964—58th year)Chief-Editor:P.BONETTI\n\nScientifc Committee:G.ABETTI-G.B.BONINO -P.CALDIROLA  \nL.CALIFANO-R.CANESTRARI -G.COLONNETTI-B.DE FI-NETTI-M.GORTANI-G.LEVI DELLA VIDA-G.MONTALENTI  \nE.PADOA-V.SOMENZI-S.TONZIG  \n“SCIENTIA”is the only review of its type which:has a world wide cir-culation·deals with the most recent and fundamental problems of allbranches of science·can boast among its contributors of the most illus-trious men of science in the whole world·publishes the articles in thenative language of ther Authors(English,French,Italian,German,Spanish).Each issue includes a,Supplement containing the complete Frenchtranslation of the articles which in the text are published in language other thanFrench.  \n“SCIENTIA”has therefore a very strong appeal to the scientific-mindedreader all over the world.  \nFuli details and a free back copy will be sent by appiying to“SCIENTIA,,一ASSo(Como,Italy)sending 80.25,or equivalent amount in other currency,preferabiy inalr-mail postage stamps of your country,merely to cover_packing andpostage.For a number of the current year,piease send $1.50,or equiva-lent amount in other currency,which wli be deducted from the sub-scription price.ANNUAL SUBSCRIPTION:$15.50 U.S.A.  \n# THE JOURNAL OF PHILOSOPHY\n\nIMPLICIT DEFINITION SUSTAINED  \nTHE characterization of axioms as implicit definitions can befound as far back as 1818,in Gergonne,¹and it was stillvigorous thirty years ago.What is exasperating about the doc-trine is its facility,or cheapness,as a way of endowing statementswith the security of analytic truths without ever having to showthat they follow from definitions properly so called,definitionswith eliminable dcfinienda.  \nRussell gave the doctrine its due,I felt,though he did notmention it by name,when he wrote in 1919 that'the method of‘postulating'what we want has many a","cbCaihPlLXZ7kVCS","https://ap.wps.com/l/cbCaihPlLXZ7kVCS","pdf",1457178,32,"English","# Implicit Definition Sustained\n## Aims and background\n## Mechanical routine for implicit definitions\n## Relation to the 1940 result\n## Strengthened Löwenheim-style theorem","[{\"question\":\"What does the note aim to accomplish?\",\"answer\":\"It states a purpose to discharge a “somber duty” by defending axioms as implicit definitions with detailed technical literalness.\"},{\"question\":\"How does the mechanical routine work at a high level?\",\"answer\":\"Given interpreted undefined predicates governed by true axioms, it produces new undefined predicates and definitions plus auxiliary arithmetical notations so the old axioms become true by arithmetic.\"},{\"question\":\"What improvements does the paper claim over the 1940 result?\",\"answer\":\"It is geared to predicates rather than singular terms, draws specifically on arithmetic (elementary number theory) instead of set theory, and provides a mechanical routine for finding the definitions.\"}]","THE JOURNAL OF PHILOSOPHY - Vol. LXI - Implicit Definition Sustained | PDF",1789959012,81]