From Arithmetic to Metaphysics Philosophische Analyse/ Philosophical Analysis Herausgegeben von/Edited by Rafael Hüntelmann, Christian Kanzian, Uwe Meixner, Richard Schantz, Erwin Tegtmeier Band/Volume 73 From Arithmetic to Metaphysics A Path through Philosophical Logic Edited by Ciro de Florio and Alessandro Giordani ISBN 978-3-11-052882-4 e-ISBN (PDF) 978-3-11-052949-4 e-ISBN (EPUB) 978-3-11-052901-2 ISSN 2198-2066 Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2018 Walter de Gruyter GmbH, Berlin/Boston Printing: CPI books GmbH, Leck ♾ Printed on acid-free paper Printed in Germany www.degruyter.com | toSergioGalvan Contents Preface|IX MicheleAbrusci Hilbert’sτandϵinProofTheory:aproof-theoreticalrepresentationofuniversal andexistentialstatements|1 TatianaArrigoni TruthsinContemporarySetTheory|23 MarcoBuzzoni Gödel,Searle,andtheComputationalTheoryofthe(Other)Mind|41 MassimilanoCarrara NaïveProofandCurry’sParadox|61 RobertoFestaandGustavoCevolani Exploringandextendingthelandscapeofconjunctiveapproachesto verisimilitude|69 AntonellaCorradini MentalCausationandNonreductivePhysicalism,anUnhappyMarriage?|89 CiroDeFlorio OnGroundingArithmetic|103 LorenzoFossati RiskvsLogic.KarlBarthandHeinrichScholzonFaithandReason|119 AldoFrigerio OntheOntologyofBiologicalSpecies|135 MariaCarlaGalavotti WhoisAfraidofSubjectiveProbability?|151 GeorgGasser Agent-causationandItsPlaceinNature|159 VIII | Contents AlessandroGiordani QuantifiedModalJustificationLogicwithExistencePredicate|179 FranzvonKutschera TheCaseforConceptualism|195 WolfgangLenzen Twodaysinthelifeofagenius|207 WinfriedLöffler MultipleReligiousBelonging:ALogico-PhilosophicalApproach|241 PaoloMancosu DefinitionsbyAbstractioninthePeanoSchool|261 UweMeixner IntelligibleWorlds|289 CarloNicolai NecessaryTruthsandSupervaluations|309 EdmundRunggaldier TheWittgensteinianandtheontological(3-dimensional)reactiontothe naturalisticchallenge|331 GerhardSchurzandErnestAdams(1926–2009) Measure-EntailmentandSupportintheLogicofApproximate Generalizations|341 Bibliography|373 Preface Thedistinctionbetweenappearanceandreality,introducedbyParmenidesand Heraclitus,issaidtobeoneofthepillarsofWesternthought.Andthisisprecisely whatthisvolumeis,i.e.arealtributetoitsaddressee,eventhoughitdoesnot appear as the typical collection of papers in honor of someone. It is indeed an homage to a professor and to his influence in the research areas which the collectedessaysarearepresentationof. SergioGalvangraduatedin1969underEvandroAgazzi’stuitionwithadisser- tationonAlfredTarski’ssemanticconceptionoftruth.AtthattimeAlfredTarski wasstillaliveandhiswell-knownessayTruthandProof appearedonScientific American. Galvan spent a period as visiting researcher in Germany; then, he taughtatsecondaryandhighschool,bravelyexplainingto–likelyastounded– studentsthetheoryofsyllogism.Finally,heworkedattheuniversitiesinMilan andVerona,becomingfullprofessorofLogicatTrentoUniversityin1994.Three yearslater,hereturnedtotheCatholicUniversityofMilanwherehepreviously hadstudied.AtCatholicUniversityhewaschairofLogic,PhilosophyofScience andAnalyticOntology. In the Sixties, the Italian philosophical scenario, in which Galvan intellec- tually grew up, was dominated by discussions concerning political philosophy (in particular, the debate between Catholics and Communists), philosophy of existence,aesthetics,andmoralphilosophy.Logicandphilosophyhavebeenjust introduced,eachoftheminhisownwayandpeculiarattitude,bysuchscholars asLudovicoGeymonat,EttoreCasari,AlbertoPasquinelli,andGalvan’steacher EvandroAgazzi,.Metaphysicsliedidle,ratherforgotten.However,CatholicUni- versitystillpaidgreatattentiontothescienceofbeing,thankstosomeimportant teachers:AmatoMasnovo,GustavoBontadiniandSofiaVanniRovighi.Indeed, GustavoBontadiniwastheformerteacherofEvandroAgazziandGalvanhimself attendedhislectures.Throughouttheyearsofstudy,Sergionurturedthepassion fortheclassicmetaphysicalthemes–fromtheproblemofbecomingtotheground ofreality,fromtheconstitutionofentitiestotheproblemofuniversals–andthe interestforthemhasbeenaconstantinhisthought. Sergio Galvan is a logician and all his scientific work embodies Hilbert’s motto: clear thought is axiomatic thought. His main areas of research can be summarizedasfollows:mathematicallogic,modallogic,logicofexplanationand metaphysics.HisfirstfieldofresearchconcernstheanalysisofTarskiantheoryof truthanditsconnectionwiththeclassicalcorrespondentistconceptionoftruth. ThepassagefromthestudyofTarski’stheoryoftruthtothegenerallimitationsof axiomaticsystemswasquickandleadedGalvantofacetheproblemofformalizing DOI:10.1515/9783110529494-001 Brought to you by | UCL - University College London Authenticated Download Date | 2/12/18 11:51 AM X | Preface arithmetics.Theoutcomeoftheseyearsofwork,Formaltheoryofnaturalnumbers (inItalian:Teoriaformaledeinumerinaturali),isaformidablebookonfirstand second order, and continues to be an unsurpassed landmark for the complete presentationofproposedresults.IntroductiontotheIncompletenessTheorems(in Italian:Introduzioneaiteoremidiincompletezza;in2006thebookwastranslated in German as: Einführung in die Unvollständigkeitstheoreme) is the synthesis of manycoursesonGödel’stheoremandonitsphilosophicalmeaningwhichGalvan hasbeentaughtforthreedecades.InthelastyearsGalvaninvestigatedtheanal- ysisofweaksystemsofarithmetic,fromQtoPA,correlatingdifferentversionsof inductionaxiomswiththeirepistemiccommitmenttowardsformsofmoreorless finitaryconstruction,takingpartinthedebateonfinitismthatwasraised,among others,byWilliamTaitandCharlesParsons.AccordingtoGalvan,thereflectionon axiomatictheorieshasbothanintrinsicvalue–relatedtothedynamicoflogical characterization–andafundamentalphilosophicalrelevance,whichisanaspect hehasbeenalwaysinterestedin:limitationtheorems(Gödel,Tarski,Löwenheim Skolem,Church)canbewidelyappliedtothehumanknowledge,therealism,the natureofeideticintuition,andevenintheconceptionofthemechanicthought. Galvan’ssecondvastareaofresearchisconstitutedbythemodallogic,asub- jecthehelpedtointroducetoItaly,withhistextbookIntensionalLogics.Systemsof modal,denotic,andepistemicpropositionallogic(inItalian:Logicheintensionali, Sistemi proposizionali di logica modale, deontica, epistemica). In particular, his essays on epistemic and deontic laws, with reference to the formalization of Hume’slawandKantiandeonticprinciples,areworthofconsideration.Moreover, Galvanhasalwaystightlyconnectedtheinvestigationsaboutmodallogicwiththe metaphysicalreflection;aspecificinterpretationofthesemanticsofmodallogic broughthimtoaconstrualofthenegation,analyzedinthebookNoncontradiction andExcludedMiddle(inItalian:Noncontraddizioneeterzoescluso).Moreover,he formulatedamodalsystemforthelogicofessence,PIES5,thataimstoadequately grasp the classical conception of modalities and the essential constitution of individuals in order to come up with an original solution to the trans-world identityandpersistenceproblems. Galvan’s view of metaphysics, reflects, in a way his classical philosophical background(inaword,theAristotelianandThomisticthinking)butitisenriched by some fundamental issues of the philosophy of science: metaphysics has, at the end of the day, the ultimate explanatory function of the experience. Accordingly, the issue of explanation has been always relevant in Galvan’s thought,particularlyasfarasthefinalisticexplanationsoccurringinthehuman sciencesareconcerned. FromArithmetictoMetaphysicsisinnowayjustthestartingpointorthefinal destinationofajourney;thiscollectionofessaysratherrepresentsthepolesof Brought to you by | UCL - University College London Authenticated Download Date | 2/12/18 11:51 AM