The Concept Of Motion In Ancient Greek: Thought Foundations In Logic, Method, And Mathematics

440 Pages·2020·3.749 MB·English

by  Barbara M. Sattler

THE CONCEPT OF MOTION
IN ANCIENT GREEK THOUGHT
Thisbookexaminesthebirthofthescientificunderstandingofmotion.It
investigateswhichlogicaltoolsandmethodologicalprincipleshadtobein
place to give a consistent account of motion, and which mathematical
notions were introduced to gain control over conceptual problems of
motion. It shows how the idea of motion raised two fundamental pro-
blemsinthefifthandfourthcenturyBCE:bringingtogetherBeingand
non-Being,andbringingtogethertimeandspace.Thefirstproblemleads
to the exclusion of motion from the realm of rational investigation in
Parmenides,thesecondtoZeno’sparadoxesofmotion.Methodological
and logical developments reacting to these puzzles are shown to be
present implicitly in the atomists, and explicitly in Plato, who also
employs mathematical structures to make motion intelligible. With
Aristotle we finally see the first outline of the fundamental framework
withwhichweconceptualisemotiontoday.
barbaram.sattlerhastaughtattheUniversityofStAndrewsandis
now Professor for Ancient and Medieval Philosophy at the Ruhr-
Universität Bochum. She works mainly on metaphysics and natural
philosophy in the ancient Greek world, with a particular focus on the
Presocratics,Plato,andAristotle.

THE CONCEPT OF MOTION
IN ANCIENT GREEK
THOUGHT
Foundations in Logic, Method, and Mathematics
BARBARA M. SATTLER
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DOI:10.1017/9781108775199
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Names:Sattler,BarbaraM.,1974–author.
Title:TheconceptofmotioninancientGreekthought:foundationsinlogic,method,and
mathematics/BarbaraSattler,UniversityofStAndrews,Scotland.
Description:Cambridge,UnitedKingdon;NewYork,NY,USA:CambridgeUniversity
Press,2020.|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2020009167|ISBN9781108477901(hardback)|ISBN9781108775199
(ebook)
Subjects:LCSH:Motion.|Philosophy,Ancient.
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CONTENTS
Acknowledgements pageix
Introduction 1
OverviewoftheProject 1
Methodology,TreatmentofSources,andRelationships
ofThinkersInvestigated 5
OverviewoftheChapters 11
1 ConceptualFoundations 17
1.1 TheConceptsofKinêsis,Physis,andNaturalPhilosophy 17
1.1.1 TheConceptofMotion(Kinêsis) 17
1.1.2 TheAncientGreekConceptionsofPhysisandNatural
Philosophy 27
1.1.3 TheConceptofBeing 30
1.2 CriteriaofInquiry 31
1.2.1 ThePrincipleofNon-Contradiction 32
1.2.2 ThePrincipleofExcludedMiddle 37
1.2.3 ThePrincipleofSufficientReason 39
1.2.4 RationalAdmissibility 46
1.2.5 SavingthePhenomena 49
1.3 TheRoleofLogic 53
1.3.1 OperatorsandOperands 55
1.3.2 NegationandIdentityasOperators 57
1.4 TheRoleofMathematics:TheConnectionbetweenMathematics
andNaturalPhilosophy 67
1.4.1 TheUseofMathematicsforScienceinGeneral 67
1.4.2 HowtoDoThingswithNumbers:Measurement
andCountability 73
2 Parmenides’AccountoftheObjectofPhilosophy 80
2.1 Introduction 80
2.2 Parmenides’CriteriaforPhilosophyandHisLogicalApparatus 83
2.2.1 CriteriaforPhilosophy 83
2.2.2 LogicalOperators 92
2.3 Parmenides’LogicalApparatusasIntimatelyTiedtoHisOntology 103
2.4 ProblemsfortheVeryPossibilityofNaturalPhilosophy 111
v
vi contents
2.4.1 TheAbsenceofAdequateBasicConceptsforNatural
Philosophy 111
2.4.2 NoDistinctionbetweenOperatorsandOperands 114
2.4.3 TheIndeterminacyofBackgroundConcepts 116
2.4.4 ProblemswithRelations 117
2.5 RelationtotheDoxaPart:TheRoleofCosmology 119
3 Zeno’sParadoxesofMotionandPlurality 124
3.1 Introduction 124
3.2 TheGeneralAimofZeno’sParadoxes 128
3.3 ParmenideanInheritance 130
3.3.1 AdvancingParmenides’Criteria 130
3.3.2 DeepeningoftheChallengeParmenidesPoses 134
3.4 TheFragments,TheirSources,andTheirConnection 134
3.5 TheParadoxesofPlurality 136
3.6 TheParadoxesofMotion 143
3.6.1 TheDichotomy:PassingInfinitelyManySegments
inaFiniteTime 144
3.6.2 Achilles:AVariationoftheDichotomyParadox 155
3.6.3 TheFlyingArrow:MotionasaSequenceofRests 156
3.6.4 TheMovingRows:DoubletheTimeIsHalftheTime 164
3.6.5 TheBasicProblemsofAllParadoxesofMotion 174
4 TheAtomisticFoundationforanAccountofMotion 176
4.1 Introduction 176
4.2 EleaticInheritanceintheAtomists 178
4.2.1 RationalAdmissibility 179
4.2.2 Consistency 182
4.2.3 ThePrincipleofSufficientReason 183
4.3 AtomisticChanges 184
4.3.1 WhatTrulyIsMustExplainthePhenomena 184
4.3.2 APhysicalTheory 185
4.3.3 ChangeofLogicalOperators 187
4.3.4 TheAtomisticAccountofWhatIs 190
4.3.5 NewPhysicalFeaturesandTheirFunctions 191
4.4 ConsequencesoftheAtomisticChangesforNaturalPhilosophy 194
4.4.1 ReplytoEleaticProblems 194
4.4.2 MotionandChangesintheAtomisticFramework 198
4.4.3 ProblemsthatRemain 200
5 ThePossibilityofNaturalPhilosophyAccordingtoPlatoI:
TheLogicalBasis 202
5.1 Introduction:TheInvestigationoftheNaturalWorldasanEikôs
Mythos 202
5.2 TheSophist 210
5.2.1 TheReinterpretationofNegationandtheConnection
Operator 211
contents vii
5.2.2 TheReinterpretationoftheCriteriaforPhilosophy1:
ThePrincipleofNon-ContradictionandthePrinciple
ofExcludedMiddle 225
5.2.3 WideningtheConceptualPossibilities 230
5.2.4 PossibleAnswerstoParmenides’Problems 232
5.3 TheTimaeus:LogicalAdvances 235
5.3.1 TheReinterpretationoftheCriteriaforPhilosophy2:
ThePrincipleofSufficientReasonandRational
Admissibility 236
5.3.2 AnEikôsMythos 240
6 ThePossibilityofNaturalPhilosophyAccordingtoPlatoII:
MathematicalAdvancesandUltimateProblems 245
6.1 Introduction 245
6.2 IntroducingMathematicalStructures 246
6.3 LocomotionandMathematicalStructures 253
6.3.1 TimeandEternity 253
6.3.2 TimeastheMeasureofMotion 256
6.3.3 SpaceasExcludedfromtheMeasurementProcess 266
6.4 ProblemswithaSimpleMeasure 269
6.4.1 RestrictedComparability 274
6.4.2 LackingConsistency:TheTortoiseWinstheRace 274
7 Aristotle’sNotionofContinuity:TheStructureUnderlying
Motion 277
7.1 Introduction 277
7.2 NotionsofMagnitudeInfluencingAristotle’sConcept
ofaContinuum 284
7.2.1 Parmenides’Suneches 285
7.2.2 AtomisticNotionsofMagnitude 289
7.2.3 AMathematicalNotionofSuneches 291
7.3 Aristotle’sTwoAccountsoftheContinuum 295
7.3.1 ThingsWhoseLimitsTouchandAreOne 296
7.3.2 ThingsBeingDivisiblewithoutLimits 299
7.4 ImplicationsofAristotle’sConceptofaContinuum 303
7.4.1 ANewUnderstandingofthePart-WholeRelation 305
7.4.2 ANewTwofoldConceptofaLimit 311
7.4.3 ANewConceptionofInfinity 328
8 TimeandSpace:TheImplicitMeasureofMotioninAristotle’s
Physics 335
8.1 TheGeneralConceptofMeasureinAristotle’sMetaphysics 337
8.1.1 ASimpleMeasure:BeingOne-Dimensionaland
oftheSameKindasWhatIsMeasured 338
8.1.2 ComparisonwithaModernConceptionandtheRelation
betweenCountingandMeasuring 344
viii contents
8.2 TheMeasureofMovementinAristotle’sPhysics 350
8.2.1 TimeasaOne-DimensionalMeasureandNumber
ofMotion 351
8.2.2 TheSearchforaMeasureoftheSameKindasMotion 356
8.2.3 TheRelationofTimeandSpace 374
9 TimeastheSimpleMeasureofMotion 385
9.1 OtherAccountsofSpeed 385
9.2 ReasonsWhyAristotledidnotExplicitlyUseaComplexMeasure 393
9.3 ConstructiveDevelopments:ARésumé 403
Bibliography 404
IndexLocorum 423
GeneralIndex 426