Book Review "Ptolemy's Philosophy: Mathematics as a Way of Life"

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Book Review ”Ptolemy’s Philosophy: Mathematics as a

Way of Life”

Gianluca Longa

To cite this version:

Gianluca Longa. Book Review ”Ptolemy’s Philosophy: Mathematics as a Way of Life”. 2021,

Available online atwww.sciencedirect.com

ScienceDirect

Historia Mathematica 54 (2021) 117–122

www.elsevier.com/locate/yhmat

Book

Reviews

Ptolemy’s Philosophy: Mathematics as a Way of Life

ByJacquelineFeke.PrincetonUniversityPress.ISBN 978-0-691-17958-2.256pp.

With Ptolemy’sPhilosophy: MathematicsasaWayofLife,Jacqueline Fekeaimstopursueandbroaden

LidiaTaub’sresearchonPtolemy’sphilosophy1andtopropose“thefirsteverreconstructionandintellectual

history of Ptolemy’s general philosophical system” (p. 2). The book substantially reworks her doctoral

thesis2andcompletesitwithherlatestresearch.3

AstheIntroduction(chapter1,pp.1–9)announces,themajorclaimdefendedinthebookisthatPtolemy

“wasverymuchamanofhistime”(p.3)andhisphilosophy“ismostsimilartomiddlePlatonism”(p.3)

withitssyncreticandeclectictendencieswhoseambitionistoreunifyclassicalandHellenisticphilosophy

ina unitaryall-embracing mathematicalweltanschauung.This statementisanythingbutsimpletoprove

consideringthatPtolemy’s“philosophicalclaimsliescatteredacrosshiscorpusandintermixedwith

tech-nical studies in the exact sciences” (p. 1). Further,Ptolemy says nothing inhis works “concerning any

philosophicalallegiance[and]hedoesnotalignhimselfwithaphilosophicalschool”(p.2).Therefore“in

order todiscern where his philosophical ideascame from,one must minehis corpus, extract the

philo-sophical content, and,with philological attention,relate his ideastoconcepts presentedin textsthatare

contemporarywithhisown”(p.3).

Thebookisstructuredintwopartsdistributedoverninechapters.Thefirstpart(chapters2–4),which

constitutes the mainbody of the book, describes Ptolemy’s philosophical system whilethe second part

(chapters 5–8) closely examines the philosophical ideas containedin some specific works ofthe extant

Ptolemaiccorpus.Theconclusion(chapter9)thensketchestheinfluenceofPtolemy’sphilosophicalideas,

especiallytheclaimoftheindisputabilityofmathematicaldemonstration,onmedievalandmodernthought.

After the Introduction, the secondchapter (“Defining the Sciences”, pp.10–25) undertakesa careful

examinationofAlmagest I,5.7–6.11andassertsthatthedistinctionbetweenthe mathematical,the physical

andthe theologicalproposedbyPtolemy,althoughAristotelian,isnotAristotle’s(p.19).Inparticular,itis

notare-proposalofMetaphysics E1asclaimedbyBollmorethanacenturyago.4 WhiletheAristotelian

distinction isinfact basedon theontologicalpropertiesoftheobjectstudied (separability/inseparability,

movability/immovability),thePtolemaicdistinctionisbasedonacriterionofperceptibilitythatcombines

epistemologicalandontologicalconsiderations.Iwouldputintoquestionthislaststatement.Perceptibility

seemstobeonlyoneofthetwocriteriaproposedbyPtolemy,theotherbeingthe‘elevationoftheobject’.

1 _{Taub,L.,1993.Ptolemy’sUniverse:TheNaturalPhilosophicalandEthicalFoundationsofPtolemy’sAstronomy.Chicago:} OpenCourt.

2 _{Feke,J.,2009.PtolemyinPhilosophicalContext:AStudyoftheRelationshipsbetweenPhysics,Mathematics,andTheology.} Ph.D.diss.,UniversityofToronto.

3 _{Feke,J.,2012.“MathematizingtheSoul: TheDevelopmentofPtolemy’sPsychological TheoryfromOntheKriterionand}

Hegemonikon totheHarmonics.”StudiesinHistoryand PhilosophyofScience 43,pp.585–94;Feke,J.,2014.“Metamathematical Rhetoric:HeroandPtolemyagainstthePhilosophers.”HistoriaMathematica 41,pp.261–76;Feke,J.,2012.“Ptolemy’sDefense ofTheoreticalPhilosophy.”Apeiron 45,pp.61–90.

4 _{Boll,F.,1894.“StudienüberClaudiusPtolemäus:EinBeitragzurGeschichtedergriechischenPhilosophieundAstrologie.”}

JahrbücherfürclassischePhilologie,supplement21,p.71.

Book Reviews Historia Mathematica 54 (2021) 117–122

Almagest I,5.7–6.11reallydisplaystwoinverselyproportionalcriteria:whileperceptibilitydecreasesfrom

physicstotheology,theelevationoftheobject,quiteobviously,decreasesfromtheology(“somewhereup

inthehighestreachesofthecosmos”)tophysics(“belowthelunarsphere”).Thisreasoningseemstohave

acertainsimilaritywiththedescriptionoftheworld’sbodyinTimaeus 31b-c5wherePlatoproposestwo

inversely proportional criteriafor the elements composing the world: visibility (ὁρατόν) and tangibility

(ἁπτόν).

Thethirdchapter(“KnowledgeandConjecture”,pp.26–51)takesintoaccountthemostmarkedly

epis-temologicalpassageoftheProem totheAlmagest (I6.11-21).ItisherethatoneunderstandshowPtolemy’s

positionissomewhat‘subversive’comparedtohispredecessors.Therelevantclaimconcernsthe

epistemo-logicalstatusofmathematicswithrespecttophysicsandtheology:whilethelatterdonothaveascientific

characterandproduceonlyconjecture(εἰκασίαν),mathematics,ontheotherhand,iscertainand

unshake-able (βεβαίαν καὶ ἀμετάπιστον) and proceeds through the indisputable demonstrations ofgeometry and

arithmetic(ἀποδείξεωςδι’ἀναμφισβητήτωνὁδῶνγιγνομένης,ἀριθμητικῆςτεκαὶγεωμετρίας).Compared

tothePlatonicandtotheAristotelianepistemologythisrepresentsadecisivebreakthrough:mathematicsis

nolongerancillarytophilosophybutrathertheonlyknowledgethatcanprovidecertaintybymeansofboth

arithmetical andgeometricaldemonstrations. Amongthemany pointsofinterestinthischapter(thelink

betweenAlcinousandPtolemy,theisagogiccharacterofthepreface,etc.),itisworthmentioningthe

anal-ysis(pp.40–44)oftheaffirmationoftheindisputabilityofmathematicscontainedinthePtolemaictext.By

comparingthewordingofthispassageintheGreekcorpus,FekeshowshowPtolemy’saccount(already

statedby HerointheprefacetoMetrica III)doesnotcomedirectlyfromtheclassicaltraditionbutisthe

resultofpost-Hellenistic reflections on thestatus ofwell-foundedknowledge, andinparticular theshift

fromtheindisputabilityofpremisestotheindisputabilityofdemonstrations. WhatFekedoesnotexplain,

inthisinterestingreconstruction,isthatHero’sandPtolemy’saccountsarenotidentical: whilethelatter

infact says thatbotharithmetical andgeometrical(ἀριθμητικῆςτε καὶγεωμετρίας)demonstrations

pro-vide certainty, Hero’saccountattributesthispropertyonlytothe geometricalones(μόνηςπροσδεήσεται

γεωμετρίας) and explicitly statesthat no other techniques or sciences can provide it (ὅπερ τῶν ἄλλων

τεχνῶνἢἐπιστημῶνοὐδεμίαὑπισχνεῖται).Thisdifferentapproachtothe‘canonofrigour’hasimportant

consequencesinthedemonstrativeproceduresadoptedbytheauthors,asforexampleinthepractise ofthe

so-calledmethodofanalysisandsynthesis.

ThefourthchapterdealsrespectivelywithAlmagest I4.6-5.7andAlmagest I6.21-8.16.Thesedifficult

passageslinktheaffirmationoftheepistemologicalsupremacyofmathematicsoverphysicsandtheology

withpracticalphilosophy,extendingtheargumenttoethicalconsiderations:theresultistheaffirmationthat

thegoodlifeisintrinsicallylinkedtothepractise ofmathematics.Thisreasoningisdifficulttofathomand

presentsbothtextual andphilosophical problems.However,theanalyticalreading andthe

conceptualisa-tionproposedbyFekeprovideaclearunderstandingofthemeaningofPtolemy’sstatements.Particularly

effective is the argument that shows the weakness of the translation proposed by Toomerof Almagest,

I 4.18-5.2:Fekepointsoutthatαὐτῶνinthesentenceτὰςμὲνπράξειςἐνταῖςαὐτῶντῶν φαντασιῶν

ἐπι-βολαῖςῥυθμίζεινshouldrefernotto“affairs”butto“theories”intheprecedingsentence.Infact,asFeke

rightlysays,“impressionsofactionsdonotorderactions;impressionsofhigherorderphenomena,suchas

theories,orderactions”.

ThefinalfourchaptersexplorePtolemy’scorpus inthelightofthephilosophicalsystemexposedinthe

firstpart:theauthorshowshowthemetaphysical,epistemologicalandethicalideasproposedintheProem

totheAlmagest supplyakeytoanadequatereadingofhisstudiesonharmonics,astronomy,psychology,

astrology, andcosmology. Theresulting pictureisofa substantial systematicity:in Ptolemy’sworkswe

findanimpulsetowardsthesearchforharmony,orderandsymmetry;thisresearchisbasedonthe

system-5 _{AsfarasIknow,theonlyscholarwhoseesthispossibleliaisonisVitrac,B.,2008.“Lespréfacesdestextesmathématiques} grecsanciens.”InLiberamicorumJeanDhombres,editedbyP.RadeletdeGrave,Turnhout:Brepols,p.528n.

Book Reviews Historia Mathematica 54 (2021) 117–122

aticapplicationofmathematicalmethodswhichareconfiguredastheprivilegedmeansforthesearchfor

knowledge.However,thisisnottheresultofamerelyblindinstrumentalapplication,butofa meditated

philosophicalreflectionandaneclecticrethinkingofclassicalandHellenisticphilosophy.

On the whole, Ptolemy’s Philosophy: Mathematics as a Way of Life is clear and well argued. Feke

rarelypresentsinterpretationswithoutfirstintroducing,contextualisingandanalysingthematboth

philo-logical and philosophical levels. Thephilosophical theories ofancient authors are well articulated. The

relationshipsandfracturespresent intheintricatedevelopmentofphilosophyintheimperialagearewell

analysed anddeeplyrooted,especiallythankstoa systematicuseoftheconcordances foundintheTLG.

However,somecriticalaspectsshouldbestressed.Apartfromsomelacunae inthecriticalapparatus,6 the

leastconvincing aspectistheauthor’sattitudetowardscertainworksofthePtolemaiccorpus,theOptics

inparticular.Ptolemy’sworks,takenasawhole,caninfactbeconceivedasapathwaytoacomprehensive

knowledgeoftheworld.TheAlmagest andtheHarmonics designthestructureofreality;theapplicationof

thisstructuretoetherealspheresiscarriedoutinPlanetaryHypotheses,andtheanalysisofitsinfluences

inthesublunaryworldintheTetrabiblios.Theseresearchesarethensupportedbyspecificextensionsthat

strengthen andcomplete the already richpicturedepicted: amongthese,Geography and Optics areofa

particularinterest.Now,concerningthephilosophicalanalysisoftheGeography wearereferredbythe

au-thor(p.7n)toher“Ptolemy’sPhilosophyofGeography”,7 whichshouldthereforebeconsideredasasort

ofappendixtothetext under examination(butwhynotinclude itdirectlyinthebook?).Concerningthe

Optics,Feke’spositionisfarfromclear:thereareseveralreferencestoOptics (p.7,16n,22n,125n,131n)

insupportofsomenotionsproposedinthetext(primemover,discussionofthecommonsensibilities,etc.)

as well asa number ofreferences to Siebert’sDieptolemäische “Optik”8 thatquestionthe authenticity

ofthe text (or bettersaid, theextant textof theOptics). Inthis respect,theauthor doesnot take aclear

position.IfinfactFekeinclinestowards itsnon-authenticity,onecannotseethe reasonwhy itshouldbe

includedasareference(aswellasitwouldbeuselesstorefertothePseudo-PtolemyKarpos).Ifinstead

itisPtolemy’swork,itwoulddeserveacarefulanalysisaswellastheHarmonics ortheTetrabiblios.In

addition,ananalysisoftheOptics wouldbeanexcellentconfirmationofFeke’sthesis.

Gianluca Longa

Availableonline 22October2020

https://doi.org/10.1016/j.hm.2020.08.004

6 _{Forexample,Heiberg’seditionofPtolemy’sworks(fromwhichFeketakestheGreektext)isnotevenmentionedinthefinal} bibliography;thesameistrueforallreferenceeditionsofancientauthors.Instead,aquickreferencetotheEnglishtranslation (whenexisting)ispreferred.Moreover,sincethe bookconstantly mentionstheProem tothe Almagest (135referencesin234 pages)andthevariouspartsoftheproemaretranslatedandanalysedindetailinthesinglechapters,itwouldperhapshavebeen usefultoincludetheGreektextofPtolemy’sProem asanincipit oranexplicit tothebookwithapossibletranslation.Thiswould havemadeiteasiertocomprehendandexhibitanoverallviewofPtolemy’sargument,indeedagoodexampleofGreekprosethat woulddeservetobereadinitsentiretytoappreciateitsquality.Beingabout80lines,itwouldcertainlynothaveweighedthetext down.Besides,itwouldhavemadethereferencetoitmoreagileandavoidedsometiresomerepetitions.

7 _{Feke,J.,2018.“Ptolemy’sPhilosophyofGeography”,InClaudioPtolomeo,Geografia (Capitulosteoricos),editedbyRene} Cecena,281–326.Mexico:UniversidadNacionalAutonomadeMexico.

8 _{Siebert,H.,2014.Dieptolemäische“Optik”inSpätantikeundbyzantinischeZeit:HistoriographischeDekonstruktion,textliche}

Neuerschliessung,Rekontextualisierung.Stuttgart:FranzSteiner.