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It distinguishes virtual classes from real classes: virtual classes are “classes also as if” and are not values for variables in any formalism. The discussion links this notational framework to elementary first-order logic and highlights renewed attention through Quine’s Set Theory and Its Logic, including references to lectures, thesis work, and later semantic publications.",{"@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":15,"@type":76,"position":81},"https://docshare.wps.com/document/literature/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/the-journal-of-philosophy-issue-13-june-25-1964-the-philosophic-import-of-virtual-classes/321638/",{"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-issue-13-june-25-1964-the-philosophic-import-of-virtual-classes/321638.png","ImageObject",300,407,{"name":92,"@type":93},"Finn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the article claim about virtual classes and their status as entities?","Question",{"text":112,"@type":113},"Virtual classes are described as fictional “as if” classes rather than real entities. Attempts to make them real are said to alter their fundamental character.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the article distinguish virtual classes from real classes?",{"text":117,"@type":113},"Real classes are treated as values for variables in a class-theoretic formalism (and as sets where relevant). Virtual classes, by contrast, are never values for variables in any formalism whatsoever.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the author connect the theory of virtual classes to first-order logic?",{"text":121,"@type":113},"The article argues that discourse about virtual classes and relations can be made exact under logical laws, and suggests that first-order logic can be viewed as the theory of virtual classes and relations in a notational disguise.","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},321638,1791387644,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":14,"category_name":15,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"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},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","# JOURNALOFPHILOSOPHY\n\nVOL LXI,No.13:JUNE 25,1964  \n# The Philosophic Import of Virtual Classes:RICHARD M.\n\n...............377  \nMARTIN ..............  \n.................387  \n‘True'and‘False':T.F.LINDLEY....  \n# Book Reviews\n\nADOLF GRÜNBAUM:Philosophical Problems of Space and Time:  \nJ.J.C.SMART ..........…     …..395MARX W.WARTOFSKY,ed.:Proceedings of the Boston Colloquumfor the Philosophy of Science:HuGUES LEBLANC…   …  402  \nPUBLISHED FORTNIGHTLY  \nBY THE  \nJOURNAL OF PHILOSOPHY,INC.  \nTHE JOURNAL OF PHILOSOPHY  \nFoUNDED BY FBEDERICK 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.Subscriptions 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,Inc.,and published bi-weekly(every four weeks in Julyand August)by Lancaster Press,Ine.,Prince and Lemon Sts.,Lan-caster,Pa.,17604.Editorial Office: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.,and at additional mailing offices.  \n\n| The JoURNAL OF PHILOSOPHY announces the availability of back issues  \u003Cbr>that have been out of print for some time.Complete volumes and all  \u003Cbr>separate issues(some original,some reprinted)are now available back  \u003Cbr>to January 6,1921(vol.XVIII).  \u003Cbr>In order to meet numerous requests for early issues,the Journal has  \u003Cbr>scheduled a program of reprinting all out-of-print issues so as to make  \u003Cbr>complete sets(back to vol.I,1904)available by December,1965.Vol-  \u003Cbr>umes will be available as follows:  \u003Cbr>XVII(1920).………………...August,1964  \u003Cbr>XVI(1919).…      ……...September,1964  \u003Cbr>XV(1918)...  …     ……..October,1964  \u003Cbr>XIV(1917).…  …………...November,1964  \u003Cbr>XIII(1916).…….…    ...December,1964  \u003Cbr>and thereafter,one volume each month in 1965.  \u003Cbr>Present prices will be maintained,as follows:  \u003Cbr>Before 1940(vols.I-XXXVI):  \u003Cbr>Single issues,$1.00;double,$2.00.Volumes,$24.00 each.  \u003Cbr>1940-1959(vols.XXXVII-LVI):  \u003Cbr>Single issues,754;double,$1.50.Volumes,$18.00 each.  \u003Cbr>1960 and later(vols.LVII-LX):  \u003Cbr>Single issues,50c;double,$1.00.Volumes,$12.00 each.   |\n| --- |\n\nJUNE 25,1964  \n# THE JOURNAL OF PHILOSOPHY\n\nTHE PHILOSOPHIC IMPORT OF VIRTUAL CLASSES  \nOUR language is not designed to speak of virtual classes,forstrictly there are no such entities.A virtual class in fact is amere fiction;like Hamlet's father's ghost,'tis here,'tis there,'tisgone—mostly gone.Curiously,however,discourse concerning suchentities,although a mere maniere de parler,can be made as exact asone wishes and is subject to precise logical laws.And even morecuriously,such discourse is not only highly useful but conceptuallyof such interest that it may be viewed as constituting the very nerveof elementary or first-order logic.One can almost go so far asto say in fact that first-order logic is the theory of virtual classes andrelations in a kind of notational disguise.  \nVirtual classes are not values for variables in any way,shape,orform;whereas real classes are.Here in sum is the difference.Butan enormous difference it is and one not sufficiently recognized eitherby logicians or by analytic philosophers.Real classes are values forvariables in some suitable class-theoretic formalism—and likewisefor sets,if one wishes to distinguish in some way between sets andclasses.Bu","cbCaiaGWGoRLCTQL","https://ap.wps.com/l/cbCaiaGWGoRLCTQL","pdf",1370790,32,"English","# THE JOURNAL OF PHILOSOPHY\n## The Philosophic Import of Virtual Classes\n## Book Reviews","[{\"question\":\"What does the article claim about virtual classes and their status as entities?\",\"answer\":\"Virtual classes are described as fictional “as if” classes rather than real entities. Attempts to make them real are said to alter their fundamental character.\"},{\"question\":\"How does the article distinguish virtual classes from real classes?\",\"answer\":\"Real classes are treated as values for variables in a class-theoretic formalism (and as sets where relevant). Virtual classes, by contrast, are never values for variables in any formalism whatsoever.\"},{\"question\":\"Why does the author connect the theory of virtual classes to first-order logic?\",\"answer\":\"The article argues that discourse about virtual classes and relations can be made exact under logical laws, and suggests that first-order logic can be viewed as the theory of virtual classes and relations in a notational disguise.\"}]","THE JOURNAL OF PHILOSOPHY - Issue 13 - June 25, 1964 - The Philosophic Import of Virtual Classes | PDF",1789959866,49]