From Arithmetic to Metaphysics: A Path through Philosophical Logic

402 Pages·2018·1.96 MB·English

by  Ciro de Florio

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
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|
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
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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
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