[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-40901-en":3,"doc-seo-40901-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},40901,962075114101,"Seraphina","https://ap-avatar.wpscdn.com/avatar/e000253a75eb197efd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780044092746381165",8,"Research & Report","Philosophy and Geometry: Theoretical and Historical Issues","Philosophy and Geometry: Theoretical and Historical Issues by Lorenzo Magnani examines how geometrical knowledge functions as a laboratory for conceptual experimentation and as a key case for scientific rationality. The text connects geometry to central epistemological problems, including diagrammatic inferences and reasoning. It develops themes of “conceptual space” and “latent geometry,” distinguishes these from Euclidean space, and links explicit rational modeling to Greek symbolization, axioms, and rules of inference, while also addressing ritual origins and Kantian schematism and construction.","PHILOSOPHY AND GEOMETRY  \nTHE WESTERN ONTARIO SERIESIN PHILOSOPHY OF SCIENCE  \nA SERIES OF BOOKS  \nIN PHILOSOPHY OF SCIENCE,METHODOLOGY,EPISTEMOLOGY,LOGIC,HISTORY OF SCIENCE,AND RELATED FIELDS  \nManaging EditorWILLIAM DEMOPOULOSDepartment of Philosophy,University of Western Ontario,Canada  \nManaging Editor 1980-1997ROBERT E.BUTTSLate,Department of Philosophy,University of Western Ontario,Canada  \nEditorial Board  \nJOHNL.BELL,University of Western Ontario  \nJEFFREY BUB,University of Maryland  \nROBERT CLIFTON,University of Pittsburgh  \nROBERT DiSALLE,University of Western Ontario  \nMICHAEL FRIEDMAN,Indiana University  \nWILLIAM HARPER,University of Western Ontario  \nCLIFFORDA.HOOKER,University of Newcastle  \nKEITHHUMPHREY,University of Western Ontario  \nAUSONIO MARRAS,University of Western Ontario  \nJÜRGEN MITTELSTRASS,Universität Konstanz  \nJOHN M.NICHOLAS,University of Western Ontario  \nITAMAR PITOWSKY,Hebrew UniversityGRAHAM SOLOMON,Wilfrid Laurier University  \nVOLUME 66  \nPHILOSOPHYAND GEOMETRY  \nTheoretical and Historical Issues  \nby  \nLORENZO MAGNANI  \nUniversity of Pavia,Pavia,Italy andGeorgia Institute ofTechnology,Atlanta,Georgia,U.S.A.  \nKLUWER ACADEMIC PUBLISHERSDORDRECHT/BOSTON /LONDON  \nLibrary of Congress Cataloging-in-Publication Data  \nMagnani,Lorenzo.  \nQA447.M342001516'.001--dc21  \nISBN-13:978-1-4020-0241-0  \nDOI:10.1007/978-94-010-9622-5  \nPhilosophy and geometry:theoretical and historical issues/by Lorenzo Magnani.p.cm.--(Western Ontario series in philosophy of science;v.66)Includes bibliographical references and index.  \n1.Geometry--Philosophy.I.Title.II.University of Western Ontario series inphilosophy of science  \n2001022473  \ne-ISBN-13:978-94-010-9622-5  \nPublished by Kluwer Academic Publishers,P.O.Box 17,3300 AA Dordrecht,The Netherlands.  \nSold and distributed in North,Central and South Ameicaby Kluwer Academic Publishers,101 Philip Drive,Norwell,MA 02061,U.S.A.  \nIn all other counuies,sold and distributedby Kluwer Academic Publishers,P.O.Box 322,3300 AH Dordrecht,The Netherlands.  \nPrinted on acid-free paper  \nAll Rights Reserved◎2001 Kluwer Academic Publishers  \nSoftcover reprint of the hardcover 1st edition 2001  \nNo part of the material protected by this copyright notice may be reproduced orutilized in any form or by any means,electronic or mechanical,including photocopying,recording or by any information storage andretrieval system,without written permission from the copyright owner  \nTo my wife Anna  \nIntroduction  \nIn A Commentary on the First Book of Euclid's Elements,Proclus saysthat geometry“At the upper and most intellectual height [..]shows us whatfigures are appropriate to the gods,which ones belong to primary beings andwhich ones to the substance of souls”.In a passage of the Critique of PureReason devoted to the philosophical traits of “mathematical knowledge”,Kant shows that geometry and mathematics present “the most splendid ex-ample of the successful extension of pure reason,without the help of experi-ence”.  \nSince ancient times many philosophers have studied geometry.Geomet-rical knowledge has often played the role of a laboratory for the philoso-pher's conceptual experiments dedicated to the ideation of powerful theoriesof knowledge.This book addresses some of the main aspects of geometricalknowledge,connecting it to the central epistemological question of scientificrationality and to the problem of diagrammatic inferences and reasoning,where geometry exhibits its most appealing logical and cognitive virtues.  \nChapter 1 introduces some important aspects of the concept of spacecentral to correctly posing the problem of what I call “conceptual space”and“latent geometry”.In some historical,anthropological,and cognitive studiesdealing with the problem of the “origins”of geometry,many interestingways to design the role of geometry and space are described,which are oftenconsidered in the perspective of pragmatic activities (everyday life,home,body,commerce,moving,routes,maps,rituals).All ","cbCaiaALPCiJBUrC","https://ap.wps.com/l/cbCaiaALPCiJBUrC","pdf",14477889,2,1,264,"English","en",105,"# Introduction\n## Geometry as epistemic laboratory\n## Conceptual space and latent geometry\n## Rational modeling and Greek achievements\n## Ritual origins and historical influences\n## Kantian schematism and construction","[{\"question\":\"How does the book relate geometry to scientific rationality and epistemology?\",\"answer\":\"It connects geometrical knowledge to the epistemological question of scientific rationality and to diagrammatic inferences and reasoning, highlighting geometry’s logical and cognitive strengths.\"},{\"question\":\"What are “conceptual space” and “latent geometry” in the book’s framework?\",\"answer\":\"Chapter 1 introduces “conceptual space” and “latent geometry” as locally generated spatial frameworks that are often implicit rather than explicitly modeled in ordinary natural language.\"},{\"question\":\"How does Kant’s philosophy of mathematics and geometry influence the discussion?\",\"answer\":\"Through analysis of Kantian philosophy, the book treats geometry as a source of models for constructing theories of knowledge, focusing on schematism and construction and how Kant builds a philosophical model from geometrical construction.\"}]",1783316474,665,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"philosophy-and-geometry-theoretical-and-historical-issues","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/philosophy-and-geometry-theoretical-and-historical-issues/40901/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-13","2026-07-06",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"How does the book relate geometry to scientific rationality and epistemology?","Question",{"text":75,"@type":76},"It connects geometrical knowledge to the epistemological question of scientific rationality and to diagrammatic inferences and reasoning, highlighting geometry’s logical and cognitive strengths.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What are “conceptual space” and “latent geometry” in the book’s framework?",{"text":80,"@type":76},"Chapter 1 introduces “conceptual space” and “latent geometry” as locally generated spatial frameworks that are often implicit rather than explicitly modeled in ordinary natural language.",{"name":82,"@type":73,"acceptedAnswer":83},"How does Kant’s philosophy of mathematics and geometry influence the discussion?",{"text":84,"@type":76},"Through analysis of Kantian philosophy, the book treats geometry as a source of models for constructing theories of knowledge, focusing on schematism and construction and how Kant builds a philosophical 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