Quantifying Aristotle The Impact, Spread and Decline of the Calculatores Tradition

492 Pages·2022·9.608 MB·English

by  Daniel A. Di Liscia, Edith D. Sylla

QuantifyingAristotle
Medieval and Early Modern
Philosophy and Science
Editors
C.H.Lüthy(RadboudUniversity)
P.J.J.M.Bakker(RadboudUniversity)
EditorialConsultants
JoëlBiard(UniversityofTours)
SimoKnuuttila(UniversityofHelsinki)
JürgenRenn(Max-Planck-InstitutefortheHistoryofScience)
TheoVerbeek(UniversityofUtrecht)
volume 34
Thetitlespublishedinthisseriesarelistedatbrill.com/memps
Quantifying Aristotle
TheImpact,SpreadandDeclineof the
CalculatoresTradition
Editedby
DanielA.DiLiscia
EdithD.Sylla
Withthecollaborationof
PaulJ.J.MBakker
leiden | boston
Coverillustration:PortraitofNicoleOresme.Ms.Paris,BibliothèquenationaledeFrance,fr.565,1r(detail).
LibraryofCongressCataloging-in-PublicationData
Names:DiLiscia,DanielA.,editor.|Sylla,EdithDudley,editor.|Bakker,PaulJ.J.M.
Title:QuantifyingAristotle:theimpact,spread,anddeclineoftheCalculatores
Tradition/editedbyDanielA.DiLiscia,EdithD.Sylla;withthecollaboration
ofPaulJ.J.MBakker.
Description:Leiden;Boston:Brill,2022.|Series:Medievalandearlymodern
quantifyingAristotlephilosophyandscience,2468-6808;volume34|Includes
bibliographicalreferencesandindex.
Identifiers:lccn2022011340(print)|lccn2022011341(ebook)|
isbn9789004499829(hardback)|isbn9789004512054(ebook)
Subjects:lcsh:Aristotle.|Philosophy,Medieval.|Science,Medieval.|
Science–Philosophy.
Classification:lcc b725.q362022(print)|lcc b725(ebook)|
ddc185–dc23/eng/20220503
lcrecordavailableathttps://lccn.loc.gov/2022011340
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isbn978-90-04-51205-4(e-book)
Copyright2022byDanielA.DiLisciaandEdithD.Sylla.PublishedbyKoninklijkeBrillnv,Leiden,
TheNetherlands.
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Contents
Acknowledgements vii
ListofFigures viii
NotesonContributors ix
Introduction 1
DanielA.DiLiscia
1 ThomasWyltonontheCeasingofanInstantofTime 20
CeciliaTrifogli
2 TheNewInterpretationofAristotle:RichardKilvington,Thomas
Bradwardine,andtheNewRuleofMotion 37
ElżbietaJung
3 TheOpusculademotuAscribedtoRichardSwineshead:TheTestimony
oftheOngoingDevelopmentoftheOxfordCalculators’Scienceof
Motion 80
RobertPodkoński
4 CalculationsinThomasBradwardine’sDecausadei,Booki 106
EditAnnaLukács
5 TheCalculatorsontheInsolubles:Bradwardine,Kilvington,Heytesbury,
Swyneshed,andDumbleton 126
StephenRead
6 TheInfluenceoftheOxfordCalculatoresontheUnderstandingofLocal
Motion:TheExampleoftheTractatusdesexinconvenientibus 153
SabineRommevaux-Tani
7 Wyclif,theBlackSheepoftheOxfordCalculators 186
MarkThakkar
8 OntheReceptionofEnglishLogicatUniversitiesofCentralEurope:
HelmoldusdeZoltwedel(Prague,Leipzig)ontheLiar-Paradox 215
HaraldBerger
vi contents
9 BlasiusofParmaontheCalculationoftheVariationofQualitiesand
AristotelianPhysics 232
JoëlBiard
10 TheCalculators’TraditioninOresme’sDevisionestellarum 255
AníbalSzapiro
11 PerfectionsandLatitudes:TheDevelopmentoftheCalculators’
TraditionandtheGeometrisationofMetaphysicsandTheology 278
DanielA.DiLiscia
12 DeclineoftheCalculatorsinParisc.1500:HumanismandPrint 328
RichardJ.Oosterhoff
13 SomeAspectsofthe‘Rules’ofmotusdifformisinAngeloda
Fossambruno’sCommentaryonHeytesbury’sDetribus
praedicamentis 352
FabioSeller
14 LeibnizandtheCalculators 381
EdithD.Sylla
Manuscripts 427
Bibliography 430
IndexNominum 470
Acknowledgements
It is my pleasant duty to thank a series of institutions and persons who, in
one way or another, made possible the 2018 Munich conference, as well as
the present publication. First of all, I would like to mention my ‘home insti-
tute’,the MunichCenterforMathematicalPhilosophy(mcmp)of theLudwig-
Maximilians-UniversitätMünchen,whichprovideduswithallthenecessary
assistanceinorganisationalmatters.Besides,itwasapleasuretocollaborate
on this occasion with the Lehrstuhl fürWissenschafstgeschichte of the same
university. Special thanks should be addressed to the Fritz Thyssen Stiftung
foritsgenerousfinancialsupportof themeeting.Iwouldalsoliketoexpress
mygratitudetoLindaGrohmannforhervaluablehelpwiththeproductionof
thecomplexbibliographyandafirstformalverificationofthechapters.Ivery
much appreciate that Paul Bakker and Christoph Lüthy have welcomed this
booktotheprestigiousseries MedievalandEarlyModernPhilosophyandSci-
ence.SpecialthanksgotoPaulBakkerforhisaccurateworkascollaboratorof
thisvolumeandforhisengagementwiththevariousaspectsconnectedwith
therealisationofthisproject.
Mywarmestgratitudegoestomyco-editor,EdithD.Sylla,forherdedicated
andpreciousworkonthisvolume.ItisnosecretthatEdithSyllamorethan
anyone else is the person we all identify with this research topic, the Calcu-
latores,atopictowhichshecontributedformanydecadesatthehighestlevel
ofquality.Hence,notonlyisitagreathonourformethatsheacceptedtoparti-
cipateintheconferenceandpublication,settingthecrownonthisvolumewith
aground-breakingpaperonLeibnizandhiscalculatorybackground.Itwasalso
agreatreliefformethatshewashappytoassumethetaskofbeingco-editor
ofthepresentvolume.Shehasreadallthepaperswithherusualaccuracyand
providedmanyimprovementstomanyofthem.Iamgratefulforherkindcor-
rections,suggestions,andvariousimprovements.
DanielA.DiLiscia
Munich/Copenhagen,October2021.
Figures
10.1 AtmosphericrefractionaccordingtoPtolemy 259
10.2 Arayoflightpassingthroughtwomediawithdifferentdensities 261
10.3 FirstexperiencesupportingatmosphericrefractionaccordingtoOresme 263
10.4 Secondexperiencesupportingatmosphericrefractionaccordingto
Oresme 264
10.5 ThirdexperiencesupportingatmosphericrefractionaccordingtoOresme 265
10.6 Oresme’sdiagramtoproverefractioninauniformdifformmedium 268
10.7 Refractionsinthepartitionsofthehour,accordingtoOresme’s
speculation 271
10.8 ImplicationsofconsideringrepresentationoftimeinOresme’sdiagram 274
10.9 Oresme’sspeculationrepresentedinperspective 275
11.1 AreconstructionofarepresentationsystemmentionedbyJacques
Legrand 304
11.2 ThebeginningofthetextuntilnowcalledTractatusbonusinmanuscript
København,KongeligeBibliothek,Ms.Nykgl.saml.1904° 308
11.3 RepresentationsusedintheMetaphysicscommentarybyNicholasof
Amsterdam 313
11.4 OneoftherepresentationsystemsmentionedbyPaulofVeniceinhisSumma
philosophiaenaturalis 318
11.5 ReconstructionofthediagramNifohastakenfromthequestionsonDe
latitudinibusformarumbyBlasiusofParma 320
11.6 Thediagramasfoundinthe1486editionofBlasiusofParma’squestionsonDe
latitudinibusformarum 322
13.1 Originaldiagram(andreconstruction)ofavelocityincreasinguniformly
difformlyinAngelodaFossambruno’scommentaryonHeytesbury’sRegule
solvendisophismata 367
Notes on Contributors
HaraldBerger
is an Associate Professor at the University of Graz (Austria), Department of
Philosophy.Heteachesclassic,medieval,andearlymodernphilosophy.Hespe-
cializesinlatemedievalphilosophy,includingmanuscriptstudiesandhistory
of universities.Amonghispublicationsarethevolumes:AlbertvonSachsen,
Logik.Lateinisch—Deutsch(Hamburg,2010)andHeinrichTottingvonOyta,
SchriftenzurArsvetus(Munich2015)andacontributionon‘Albertof Saxony
onPartsandWholes,’inF.Amerini,I.Binini,M.Mugnai(eds.), Mereologyin
MedievalLogicandMetaphysics(Pisa2019).
JoëlBiard
is Professor Emeritus at the University of Tours (France), Centre d’Études
SupérieuresdelaRenaissance.Hisresearchfieldsarethelatemedievalphilo-
sophyof language,theoriesof mindandknowledge,andnaturalphilosophy.
FocussingonJohnBuridanandBlasiusofParmahehaspublished,amongsev-
eralspapers,Scienceetnature.Lathéorieburidaniennedusavoir,(Paris2012),
LesQuestionssurl’âmedeJeanBuridan(Paris2019)and,withAurélienRobert,
thecollectivevolumeLaphilosophiedeBlaisedeParme.Physique,psychologie,
éthique(Florence2019).HeiscurrentlypreparingamonographaboutBlasius
ofParma’stheoryofmatter.
DanielA.DiLiscia
isLecturerattheLudwig-Maximilians-UniversitätMünchen(Germany),atthe
MunichCenterforMathematicalPhilosophy.Hecarriedoutseveralresearch
projectsontheCalculators’tradition,especiallyonthegeometrisationofnat-
ural philosophy and metaphysics. His most recent publications are ‘Biagio
PelacanidaParma’sGeometrisationofLatitudesandtheProblemsoftheMean
DegreeTheorem’(in:J.BiardandA.Robert[eds.],LaphilosophiedeBlaisede
Parme.Physique,psychologie,éthique[Florence2019])andEineWienerExposi-
tiozumTractatusdelatitudinibusformarum.EditionmitEinführungundKom-
mentar(Vienna,2022).HeiscurrentlyeditingJacquesLegrand’sCompendium
utriusquephilosophie.
ElżbietaJung
is a historian of science, medieval philosophy and theology focusing on the
mathematicalphysicsoftheOxfordCalculators.Additionally,sheworksonthe
historyoflatemedievaluniversitiesandthehistoryoffeminism.SheisChairof