Laws and Explanations; Theories and Modal Possibilities

186 Pages·2019·2.832 MB·English

by  Arnold Koslow

Synthese Library 410
Studies in Epistemology, Logic, Methodology,
and Philosophy of Science
Arnold Koslow
Laws and
Explanations;
Theories
and Modal
Possibilities
Synthese Library
Studies in Epistemology, Logic, Methodology,
and Philosophy of Science
Volume 410
Editor-in-Chief
OtávioBueno,DepartmentofPhilosophy,UniversityofMiami,USA
Editors
BeritBrogaard,UniversityofMiami,USA
AnjanChakravartty,UniversityofNotreDame,USA
StevenFrench,UniversityofLeeds,UK
CatarinaDutilhNovaes,VUAmsterdam,TheNetherlands
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Arnold Koslow
Laws and Explanations;
Theories and Modal
Possibilities
ArnoldKoslow
DepartmentofPhilosophy,TheGraduateCenter
CityUniversityofNewYork
NewYork,NY,USA
SyntheseLibrary
ISBN978-3-030-18845-0 ISBN978-3-030-18846-7 (eBook)
https://doi.org/10.1007/978-3-030-18846-7
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Contents
PartI BurnishingtheLegacy
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Hempel’sDeductive-NomologicalModel:IntheBeginning.... . . . 15
3 LawsandCorrespondingCounterfactuals,–AnUntenable
Connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 F.Dretske’sTotalRejectionoftheHempel-Model. . . . . . . . . . . . . 31
4.1 TheChallenge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 LawsasRelations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.1 LawsasSingularStatements. . . . . . . . . . . . . . . . . . . . 35
4.3 LawsasSingularStatementsthatRelateIntensionalTerms. . . . 36
4.3.1 AreThereManyRelationsThatAreUsedin
VariousLaws?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.2 WhatAboutNon-equationalLaws?. . . . . . . . . . . . . . . 40
5 PreludetoArmstrong:AMathematicalRevolutionThat
InspiredF.Ramsey,andLeftRussellandArmstrong
Unmoved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.1 ExtensionalandIntensionalRelations. . . . . . . . . . . . . . . . . . . . 45
5.1.1 NonextensionalityandScientificLaws. . . . . . . . . . . . . 55
6 D.Armstrong’sAccountofLaws:IdentityLost,Regained,
andLostAgain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.1 AdvantagesandDisadvantagesofArmstrong’sAlmost
ExclusiveDependenceonUniversalsinHisAccount
ofLaws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.2 Universals,Predicates,andPropositionalFunctions. . . . . . . . . . 67
6.3 ExamplesofSecond-OrderLawsandTheirFirst-Order
Instantiations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.4 SomeFormalPropertiesoftheRelationofNecessitationN(F,G). . . 71
vii
viii Contents
7 LawsandAccidentalGeneralities. . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.1 TheLotzeUniformityCondition. . . . . . . . . . . . . . . . . . . . . . . 75
7.2 ObservationsandConsequencesfor(LAG). . . . . . . . . . . . . . . . 79
7.3 LawsasBoundwithExplanation. . . . . . . . . . . . . . . . . . . . . . . 83
7.4 GoldSpheres,RustyScrews,andRockswithIron. . . . . . . . . . 85
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
PartII TheoreticalScenarios,SchematicTheoriesandPhysical
andNomicModals
8 TheExplanationofLaws:TwoNeglectedandRadically
DifferentTheories.OneInspiredbyD.Hilbert;theOther
InspiredbyF.Ramsey. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.1 TheCampbellianBackground. . . . . . . . . . . . . . . . . . . . . . . . . 91
8.2 DeductiveSystemsandTheirLaws. . . . . . . . . . . . . . . . . . . . . 92
8.3 DeductiveSystemsandTheories. . . . . . . . . . . . . . . . . . . . . . . 94
8.4 TheMill-Ramsey-BraithwaiteAccountofLaws(MRB). .. . . .. 96
8.5 DeductiveSystemsandtheExplanationofLaws. . . . . . . . . . . . 98
8.6 ErnestNagel’sTheory;CampbellianOrigins. . . . . .. . . . . . . .. 99
8.7 ExplanationandTheoriesWithoutTruth-Values. . . . . . . . . . . . 100
8.8 Explanation:AxiomatizationandtheHilbertConnection. . . . . . 101
8.9 Explanation:TheSchematicAccount. . . . . . . . . . . . . . . . . . . . 104
8.10 Explanation:WhitherCampbell’sDictionary?. . . . . . . . . . . . . . 105
8.11 Explanation,SchematicSubsumption,andFactivity. . . . . . . . . 106
8.12 ExplanationandGenerality. . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8.13 TheModel-TheoreticViewofTheories–ADisclaimer. . . . . . . 110
9 DavidHilbert’sArchitectureofTheoriesandSchematic
Structuralism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.1 TheArchitectureofTheories. . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.2 HilbertianConcepts. . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 121
9.3 SchematicPhysicalTheories. . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.4 SchematicTheories,SchematicSubsumtion,Subsumptive
ExplanationandSuccesses. . . . . . . . . . . . . . . . . . . . . . . . . . . 126
10 Theories,TheoreticalScenarios,TheirMagnitudeVector
SpacesandtheModalPhysicalPossibilitiestheyProvide. . . . . . . . 131
10.1 TheoreticalScenariosandLaws. . . . . . . . . . . . . . . . . . . . . . . 131
10.2 TheVarietyofStatesofTheories. . . . . . . . . . . . . . . . . . . . . . 134
10.3 TheMagnitudeVectorSpaceofaTheory(MVS). . . . . . . . . . 136
10.4 AShift:TheFocusonLawswithBackgroundTheories
(orTheoreticalScenarios). . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.5 TheMagnitudeVectorSpacesAssociatedwithTheories. . . . . 139
Contents ix
11 ThePossibilitiesThatTheoriesProvide(PhysicalModals)
andthePossibilitiesofLaws(NomicModals). . . . . . . . . . . . . . . . . 143
11.1 Theoretical(Physical)Possibilities. . . . . . . . . . . . . . . . . . . . . 143
11.2 GentzenImplicationStructures,andTheirModals. . . . . . . . . . 145
11.3 NecessityandPossibilityOperatorsontheVector
MagnitudeSpaceofTheories. . . . . . . . . . . . . . . . . . . . . . . . . 146
11.3.1 ProbabilitySpacesandModality. . . . . . . . . . . . . . . . 146
11.4 MagnitudeVectorSpaces,andTheirTheoretical(Physical)
Possibilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
11.5 LawsandLaw-DesignatedPossibilities:TheNomic
Possibilities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
11.5.1 Ohm’sLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
11.5.2 Galileo’sLawofFallingBodies. . . . . . . . . . . . . . . . 155
11.5.3 AMach-StyleGeneralizationof(D). . . . . . . . . . . . . 155
11.5.4 ALogicalRelation(GentzenImplicationRelation)
BetweenNomicPossibilities. . . . . . . . . . . . . . . . . . . 156
12 SchematicTheories,SubsumtionofLaws,andNon-accidental
Generalizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
12.1 TheIncorporationofLawsintoSchematicTheories. . . . . . . . 159
12.1.1 TheNewtonianTheoryofMechanics. . . . . . . . . . . . 160
12.1.2 TheLagrangianTheoryofMechanics. . . . . . . . . . . . 165
12.1.3 TheHamiltonianTheory. . . . . . . . . . . . . . . . . . . . . . 167
12.1.4 Kolmogorov’sSchematicAxiomatization
ofProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
12.1.5 TheKolmogorovAxiomatizationof
ProbabilityasaSchematicModalTheory. . . . . . . . .. 169
12.1.6 Probabilistic-TruthandtheLogicalOperators. . . . . . . 171
12.1.7 TheModalCharacterofKolmogorov’sTheory
ofProbability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
12.2 SubsumtiveExplanation(cid:1),Truth,andNon-accidentality. . . . . . 174
12.3 AConnectionBetweenExplanationandExplanation(cid:1). . . . . . . 174
12.4 GeneralityRedux.TheGeneralityofTheoriesCompared
totheLawsThatTheyExplain. . . . . . . . . . . . . . . . . . . . . . . 175
Bibliography. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . 179
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Part I
Burnishing the Legacy