spinoza on extension - university of michigan

volume15,no.14 april2015

Spinoza on Extension

Alison PetermanUniversity of Rochester

© 2015 AlisonPetermanThis work is licensed under a Creative Commons

Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/015014/>

§1 Introduction1

SpinozaindicatesintheEthicsthatthereisatleastone“extendedthing(res extensa)”,whichisGod,ornature(e. g.,EIIp2),andthattherearebodies,whichare“modesofExtension(modi Extensionis)” (e. g.,EIIp7).Thisisverynaturallytakentomeanthattherearethings—substances,modes,orboth—thatareextendedinthreedimensions,orthattakeupspace.Inthispaper,however,IarguethatthisisnotwhatSpinozameans.WhenSpinozadiscussestheattributeofextension,hedoesnotmeandimensionality,andby“anextendedthing”hedoesnotmeantodescribesomethingthattakesupspace.Notonlyistheessenceofthephysicalnotmereextensioninspace,forSpinoza,butitisnotpartoftheessenceofsomethingphysicaltobeextendedinspaceatall.

Theargumentproceedsintwoparts.First,in§2,IarguethatwhenSpinozawritesthatGod,corporealsubstance,ornatureis“anExtendedthing”, he does not mean that this substance is extended in length,breadth and depth. In other words, substance is neither space norsomethingthattakesupspace.IargueforthisbyshowingthatSpinozaallowsthatsubstancecanbecharacterizedbyacertainconceptionofquantity,contraststhatwithanotherconceptionofquantitythatcannotbeattributedtosubstance,andassociatesthree-dimensionalextensionwiththesecondkindofquantity,andnotthefirst.

I go on in §3 to make the more controversial case that finitebodies,ormodesof the“extended”substance,arealsonotproperly

1. Iuse the followingabbreviations forSpinoza:E=Ethics,wherep=propo-sition,d=demonstration,def=definitions,c=corollary,a=axiom,app=appendix,l=lemma;KV=Short Treatise on God, Man, and His Well-Being;TIE=Treatise on the Emendation of the Intellect;TTP=Theologico-Political Treatise;PPC=Principles of Cartesian Philosophy;CM=Metaphysical Thoughts.Allref-erencestotranslationsofSpinoza’sworksexceptthelettersaretoCurley’stranslation(C).InreferencestothelettersIhaveusedShirley’stranslation(S).LatinreferencesaregiventoGebhardt’sedition(G).ReferencestoDescartes’Principles of Philosophy are to Cottingham, Stoothoff and Murdoch (CSMorCSMK). I amverygrateful toGeoffGorham,NicholasGresens,YitzhakMelamed,BaronReed,EricSchliesser,andDanielSchneiderfortheirinvalu-able comments, and to the engaged audiences at the 2013meetingof thePacificDivisionoftheAmericanPhilosophicalAssociation,the2013meetingof theFoundationsofPhysicsconferenceatLMUMunichandthe2014At-tributesWorkshopatBarnardCollege.

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it is conceived “abstractly” and “superficially” by the imagination, itdoesnotapplytosubstance,anditisdivisible.Theother,letuscallitquantity2,hasfourrelevantcharacteristics:itisconceivedthroughtheintellect, it isconceived“insofaras it isasubstance”, it is indivisible,and it is conceived correctly “seldom and with great difficulty”. ByconsideringSpinoza’s“LetterontheInfinite”andtwodifferentsectionsoftheCogitata Metaphysica,IshowthatSpinozaassociatesextensionin spacewith quantity1 and not quantity2. The features of quantity1 cannotbeattributedtosubstance.Therefore,Spinoza isarguing(b),andsubstanceisnotextendedinspace.

Spinoza argues in the Ethics that there is one substance. ThatsubstanceisGod,whereGodisdefinedasasubstancewithinfiniteattributes(EId6,GII45/C409).SpinozaalsoreferstoGodas“Nature”,soI’lluse‘God’,‘substance’,and‘nature’moreorlessinterchangeably.2 Spinoza defines ‘attribute’ as “what the intellect perceives of asubstance,asconstitutingitsessence”(EId4,GII45/C408).OfGod’sinfiniteattributes,weareacquaintedwithexactlytwo:ExtensionandThought(EIIa5,GII86/C448).ThephysicalworldisGod,substance,ornatureunderstoodundertheattributeofExtension,andthementalworldisGod,substance,ornatureunderstoodundertheattributeofThought.Finitethings,whichDescartesthoughtofassubstances,areforSpinozamodesofGod,ornature,andnotthemselvessubstances.Intheseterms,afinitebodyisamodeofsubstanceunderstoodundertheattributeofExtension.

InthesecondpartoftheEthics,Spinozaclaimsthat“ExtensionisanattributeofGod,orGodisanextendedthing[res extensa]”(EIIp2,GII86/C448).As‘extendere’isusedfromAristotle’sGreekequivalent

2. Aninterestingquestioniswhethertheargumentsinthispaperwouldapplyequallytoa(hypothetical)non-infinitesubstance,thatis,asubstancethatdidnothaveinfiniteattributes,sincemanyofthefollowingargumentsrelyontheinfinitenatureoftheoneactualsubstance.Isuspectthattheywouldnot.ButalthoughSpinozaentertains thepossibilityofanon-infinite substanceinPartIoftheEthics,heultimatelytakestheideatobenotonlyimpossible(EIIp8,GII49/C412)butincoherent(EIIp8s2,GII50/C413).Substance,thatis,isessentiallyinfinite,sotherecanbenofurtherquestionsaboutthefea-turesofanon-infinitesubstance.

understood as possessing dimensionality, offering three kindsof evidence. First, Spinoza explains that our perception of finitephysical things as volumes is a function of the imagination, andhenceinadequate,andtheimaginationdoesnotinformusaboutthepropertiesofnaturalthings“astheyareinthemselves”.Second,giventherelationshipthatSpinozapositsbetweenExtendedsubstanceanditsmodes,ifExtendedsubstanceisnotitselfextendedinspace,neitherare its modes. Finally, innovations that Spinoza makes in his ownnaturalphilosophyandphilosophyofscienceandinhistreatmentofDescartes’physicseliminatementionofthree-dimensionalextension,alongwith Descartes’ epistemologicalmotivation formaking it theprimaryattributeofbody.

Tomakethingsclearer,fromhereonout,whenIrefertotheattributeofExtension,Iwillwrite‘Extension’.WhenIrefertothree-dimensionalextensioninspace,Iwillwrite ‘extension’.Intheseterms,thethesisofthispaperisthatforSpinoza,‘Extension’doesnotmeanthesamething as ‘extension’.When I intend to remain temporarily agnosticaboutthemeaning,I’llwrite‘Extension’.QuotesfromSpinozareflecthisowndecisiontocapitalizethewordornot.Heusuallycapitalizes‘Extension (Extensio)’, the attribute, and not ‘extended (extensa)’ theadjective.Spinozaisnotevenconsistentinthis(see,e. g.,both“modus extensionis”and“modi Extensionis” inEIIp7s),soIdon’tthinkthereisanysignificancetoit.

§2 Extended substance, or, the physical world

Hereisabriefoutlineoftheargumentofthissection,whichaimstoshow thatExtendedsubstance isnotextended in threedimensions.First, Ethics Ip15s and related propositions show that substance isExtended but not divisible. This means either (a) that substanceis extended in space, but that extension in space does not entaildivisibility;or,(b)thatExtendedsubstanceisnotextendedinspace,and extension in space may entail divisibility. Spinoza makes adistinction inEIp15sbetweentwowaysofconceivingquantity.One,let us call it quantity1, is identifiedby three relevant characteristics:



figure.NothingmoreabsurdthanthiscanbesaidofGod,namely,ofabeingabsolutelyinfinite.

Now, Spinozadefines ‘body (corpus)’ in away that entails that it isfinite: it is “amode that inacertainanddeterminatewayexpressesGod’sessenceinsofarasheisconsideredasanextendedthing”,wheresomething“determinate”islimitedorfinite(EId1,GII45/C408).6SoitispossiblethatSpinozaonlymeanstosayherethatunlikeabody,Godisnotlimitedorfinite.ThisdoesnotseemtoexhaustSpinoza’smeaning, however, since he mentions two more features of bodyfromwhichhisopponentsmightprove that it isabsurd toattributecorporealitytoGod:thatbodyis“anyquantity”andthatitpossesses“length,breadth,anddepth”.ButbecausehedoesnotspecifywhetherallofthesefeaturesorjustsomeofthemareinapplicabletoGod,thistextalone,thoughsuggestive,isnotdecisive.

In the rest of that scholium, Spinoza directly addresses theconcern that claiming that God is a res extensa entails that God isdivisible,becauseanythingthat isextendedcanbedividedandcanbe acted upon.7 Spinoza responds that he has shown already, atEIp12, that “[n]oattributeof substance canbe truly conceived fromwhichitfollowsthatsubstancecanbedivided”,andatEIp13cthat“nosubstance,andconsequentlynocorporealsubstance,insofarasitisasubstance,isdivisible”.Hehasn’tshownyetthatacorporealsubstanceexists—thathappensatEIIp2,whenheproves thatExtension isan

6. Spinoza’suseof‘corporeal’canbeconfusing.HedeniesthatGodhasabody(corpus)butattributescorporealitytoGodquaExtendedsubstance.SinceabodyisamodethatexpressesGod’sattributeofExtension,Itakehimtobeusing‘corporeal’inthesamewayas‘Extended’inthecontextswhereheat-tributesittoGod.Theidea,ashegoesontoshow,isthatwhateveritisthatmakesbodiesbodiesandnototherkindsoffinitemodesissomethingthathastobecontainedinGodasanattribute;here,hecallsitcorporeality,whileelsewhere,hecallsitExtension.

7. DescartesclaimsthisatPrinciplesI26–27,andAristotleinthePhysicsIII;Leib-nizwouldusethesamereasoninglater(e. g.,intheMonadology).Buttheindi-visibilityofGodwasaverycommonreasonforrejectingthepossibilitythatGodisextended.SeeGrant245–247.

‘επεκτείνεται’ up through Spinoza, for something to be extendedsimply means for it to be spread out or to have dimensions.3 So,consideringthisclaiminisolationfromtherestofSpinoza’swork,itisnaturaltothinkthatSpinozatakescorporealsubstance,orGod,tobesomethingwithdimensionality.Thatmightmeanthatitissomethingwith mere dimensionality, as in Jonathan Bennett’s influentialinterpretation,onwhichsubstance,understoodundertheattributeofExtension, is identicalwith space, andmodesofphysical substancearespatiotemporalregionsofqualitativevariation.4Oritmightmeanthat substance is an extended something, be that somethingmatter,impenetrability,force,power,orwhatever.Ineithercase,itsuggeststhat substance has dimensionality. A common worry about such aclaim,inSpinoza’stime,wasthatitseemedtoattributetoGodaslewofimperfectionsassociatedwithmatter,chiefamongthemdivisibility,inertia,andpassivity.5

SpinozaaddressesthisconcerninthescholiumtoIp15oftheEthics, which is a refutation of those who “entirely remove corporeal, or extended,substanceitselffromthedivinenature”.However,Spinozaalsowrites,signalinghisagreement,that

everyonewhohastoanyextentcontemplatedthedivinenaturedeniesthatGodiscorporeal.Theyprovethisbestfrom the fact thatbybodyweunderstandanyquantity,withlength,breadth,anddepth,limitedbysomecertain

3. Inmostancient,medieval,andearlymoderncontexts,somethingisextendedifithasanynumberofspatialdimensionsandcanalsobesaidtobeextendedtemporally.(Descartessometimesidentifiestheessenceofbodiesasjust“ex-tension”,butlikelymeansextensioninlength,breadth,anddepth.)

4. Bennett128.

5. See,e. g.,Grant164:“Toidentifyimaginary,infinitespacewithGod’simmen-sityandalsotoassigndimensionalitytothatspacewouldhaveimpliedthatGodHimselfwasanactuallyextended,corporealbeing.AlthoughBenedictSpinoza, Isaac Newton, and others would do precisely this, such a movewould have been completely unacceptable inmedieval and earlymodernscholasticism.”Ofcourse, Iamarguinghere thatSpinozadoesnotbelongwithNewtononthislist.



spatiallyextendedbutnotdivisible,Spinozaisdenyingthatsubstanceisspatiallyextended.ExtensionisanattributeofGod,butthatdoesnot mean that the substance which has that attribute, when “trulyconceived”,isitselfspatiallyextended.

ToseethisrequirescarefullyconsideringSpinoza’saccountofthevarietiesofquantity(quantitas).Justafterhiscommentinthescholiumthat it is absurd to attribute certain (actual or apparent) features ofcorporeality to God, Spinoza goes on to distinguish between twokindsofquantity.Hewrites:

we conceive quantity in two ways: abstractly, orsuperficially, as we [NS: commonly] imagine it, or asa substance, which is done by the intellect alone [NS:withoutthehelpoftheimagination].Soifweattendtoquantity as it is in the imagination,whichwedooftenandmore easily, it will be found to be finite, divisible,andcomposedofparts;but ifweattend to itas it is inthe intellect,andconceive it insofaras it isasubstance,which happens [NS: seldom and with great difficulty],then (as we have already sufficiently demonstrated) itwillbefoundtobeinfinite,uniqueandindivisible.

Here, Spinoza clearly aligns quantity conceived as divisible with,first, the imagination,and, second,abstraction fromsubstance.11Letuscall thiskindofquantity“quantity1”.

12 Ibelievethatbothof theseentail that when we conceive quantity this way, we conceive itinadequately.Iwillshowthisin§3,anditwillserveasapremiseinthat section’s argument thatmodes are not adequately conceived asspatiallyextended.Butinthissection,regardlessofwhetherquantity1

11. ForfurtherdiscussionofSpinozisticabstraction,seeSchliesser2011.

12. I’lltalkinthispaperabout“kinds”ofquantityinplaceof“waysofconceiving”ofquantity.ButasIhopewillbecomeclear,theargumentsapplyequallywellifwethinkofquantity1andquantity2asdifferentwaysofconceivingthesamething,ratherthandifferentkindsofthings.IamgratefultoJohnCarrieroforsuggestinggreaterclarityonthispoint.

attributeofGod—soallIp15sshowsisthatifsubstanceisExtended,it isn’tdivisible.8Buteven if theproof isabitoutoforder,Spinozademonstrates in theEthics that there is anExtended substance thatcanbeneitherdividednoractedupon—whenthatattributeis“trulyconceived”(EIIp12,GII55/C419).Sotheclaimthat theattributeofExtensionentailsdivisibilitymustbemistaken.SubstanceisExtended,butnotdivisible.9

Thereare,broadly,twopossiblewaystounderstandtheclaimthatsubstanceisExtendedbutnotdivisible.OneistotakeSpinozatobeusing‘Extension’tomeanextension,andtoacceptthatsubstanceisspatiallyextendedbutnotdivisible.SoBennett,forexample,reasons:“…Spinozistic space is aunity: it cannotbedivided in the senseofhaving really distinct parts. … No part of space can exist, or beunderstood,without relation to thespaceasawhole,andhence itspartscannotbereallydistinctfromeachother”.10Bennettgoesontoarguethatweareatlibertytoimagineregionsinspace,butthatthoseregionsarenotproperlyunderstoodaspartsofspace.WhetheryouagreewithBennettthatExtendedsubstanceisspace,orthinkthatitisaspatiallyextendedsomething,onthisview,itbothhasdimensionalityandisindivisible.

Thesecondpossibleapproach,forwhichIwouldliketoargue,takesSpinoza to deny that something can have both dimensionality andindivisibility.Soratherthanclaiminginthispassagethatsubstanceis

8. Spinozatakeshimselftohaveproventhat“anextendedthingandathinkingthingareeitherattributesofGod,or (byA1)affectionsofGod’sattributes”(EIp14c2,GII56/C420).ButIcan’tseethathehasshownanythingmorethanthatifthereisanextendedthing,it’sanattributeofGodoranaffectionofGod’sattributes,becausehedoesn’tshowthatthereareanyextendedthingsuntilEIIa4(GII46/C410).

9. Attheendofthescholium,Spinozamakesthecurioushedgethatanyway,evenifsubstancewerecomposedofparts,hedoes“notknowwhy[divisibili-ty]wouldbeunworthyofthedivinenature”,sincethereisnoothersubstancebywhichGodcouldbeactedupon.Butthisdoesn’tshowthatSpinozathinksthatitispossiblethatsubstanceisdivisible.HehasalreadyshownatEIp12andEIp13(GII55/C420)withitscorollarythatit isnot,forreasonsotherthanthatdivisibilityentailsthepossibilityofbeingactedupon.

10. Bennett129.



represented in sense experience,which comes as part of theEthics’analysisoferror.Spinozawritesthatwe“imagine”thesun“asabout200 feet away from us” (EIIp35s, G II 117/C 473) and continue toimagineitthatwayevenwhenwelatercometoknowitstruedistance.This suggests that at least somedimensionalproperties aredirectlyrepresentedinvisualexperience,forSpinoza.

Second, we might regard this as the default position: there arethosewho have at least come close to denying that any extension-relatedpropertiesarerepresentedinsenseexperience,buttheyhavedonesoonthebasisofcarefulandwell-worked-outtheoriesofsenseperception.14Afulldiscussionofthisissuewouldtakeustoofarafield

theserepresented insenseexperience(andaboutwhether this representa-tionisdirectorindirect)whichwedon’thavethespacetodiscusshere.

14. Iamgratefultoananonymousreviewerforencouragingmoreattentiontothisinterestingandcomplexpoint,andsuggestingHumeandBerkeleyasofferingargumentsthatextensionisnot(directly)representedinsenseex-perience.Neitherstraightforwardlydeny, I think, thatanyproperties relat-edtoextensionaresorepresented.Berkeleysometimessaysthattheonlydirect objects of sight are color and light (“Essay Towards aNewTheoryofVision” 43, 103), but other times he treats visible figure and extensionasdirectobjectsof sightwithoutwhichwecannotconceivecolor (“EssayTowards a New Theory of Vision” 43 and 49, PHK 10). Also, his view ofgeometrical extension seems todependuponextension’sbeing anobjectofsenseperception(e. g.theclaimthatextensionisnotinfinitelydivisiblebecausethereareminima visibile)(“EssayTowardsaNewTheoryofVision”54).Humesuggests thatour ideaof extension is a compound idea,madeupofideasofindivisiblecoloredpoints,“disposedinacertainmanner”(A Treatise of Human Nature 1.2.3).ButevenonHume’sview, thesedotshave“dispositions”whichappear tobe irreducibly spatial.Reid’sposition is yetmore complex—althoughReidmight look like someonewhodenies thatwe candirectly represent spatial properties in sense experience, sincehemakesastrictdistinctionbetweensensation,throughwhichweexperiencecolorsandsmells,forexample,andperception,whichincludesperceptionof sizeand shape,he counts this latterperceptionasdirectperceptionofthoseproperties.TheseconsiderationsillustratetosomeextentthatitwouldbequiteradicalforSpinozatoholdthatnosuchpropertiesarerepresentedinsenseexperience—not tomention thatHume’sandBerkeley’s theoriesofperceptionaremotivatedbyandgroundedincommitmentsthatSpinozadoesnotshare.PerhapsmostimportantamongtheseisthatbothBerkeleyandHumeallowthatevenifspatialpropertiesarenotrepresenteddirectlyin sense experience, they canbe inferred from that experience. Spinoza’sverystrictdistinctionbetweenimaginationandintellectandbetweentheir

canbeconceivedadequatelyornot,IwishonlytoshowthatSpinozaassociatesdivisiblequantitywithabstractionfromsubstanceandwithconception through the imagination. It is thereby to be contrastedwithindivisiblequantity,whichisconceivedthroughtheintellectand“insofaras it isa substance”.Letuscall this secondkindofquantity“quantity2”.Thequestion,then,is:DoesSpinozaassociateoneofthesekindsofquantitywithextension?Andmorespecifically,isitpossiblethat for something to be characterized by quantity2—the infinite,uniqueand indivisibleone thatSpinozaattributes to substance—isforittobespatiallyextended?

EIp15ssuggests,althoughitdoesnotprove,thattheanswerisno.Inthepartofthescholiumquotedonpage6,Spinozawritesthatwecannotapprehendquantity2throughtheimaginationat all.Themindimagineswhen it has ideas of images,which images are affectionsof thehumanbody causedby external objects; such ideas “presentexternalbodiesaspresent tous” (EIIp17s,G II 106/C465). Inotherwords,forSpinoza,imagination(or“imaginativecognition”)includesour sense experience of bodies. EIp15s indicates that quantity2 isaccessedonlybytheintellectandnotbytheimagination,andthatthatconceivingofquantityinthewaythatappliestosubstancecanbedoneonly“seldomandwithgreatdifficulty”.So,ifsomethingcharacterizedbyquantity2weresomethingspatiallyextended,thenwecouldhavenosensoryexperienceofthespatialextensionofthatthing,andanyconceptionwedohaveofitwouldbewith“greatdifficulty”.IsthisaviewthatSpinozaholds?

Finding a sure answer to this questionwould require a detailedSpinozistictheoryofsenseperceptionandofthepropertiesthatarerepresented therein, and Spinoza does not (at least explicitly) offersuchatheory.However,IdonotthinkthisisapositionthatSpinozais likely tohold, for tworeasons.First, there isa littleevidencethatSpinozadoestakeextensionandrelatedproperties13likeshapetobe

13. “Extensionandrelatedproperties”includesalargevarietyofproperties—size,shape,distance,theextensionitself,theabstractideaofextension,andsoon.Therearelotsofinterestingquestionstobeaskedabouttheextenttowhich



delimitQuantity in suchwiseasenablesus to imaginethemeasily,as faraspossible.Again, fromthefact thatweseparatetheaffectionsofSubstancefromSubstanceitself,andarrangetheminclassessothatwecaneasilyimagine them as far as possible, there arises Number,wherebywedelimit them.Hence it canclearlybeseenthatMeasure,TimeandNumberarenothingotherthanmodes of thinking, or rather,modes of imagining. It isthereforenot surprising thatallwhohaveattempted tounderstandtheworkingsofNaturebysuchconcepts,andfurthermorewithoutreallyunderstandingtheseconcepts,havetiedthemselvesintosuchextraordinaryknotsthatintheendtheyhavebeenunabletoextricatethemselvesexceptbybreakingthrougheverythingandperpetratingthegrossestabsurdities.

Spinozaisstandardlyinterpretedasclaiming,inthispassage,thattime,measure,andnumberaregeneratedbytheimagination,butnotthethingsthataretimed,measured,ornumbered.15Forexample,acubehasadefinitevolume,butitisimaginationthatdecideswhetherwedescribethatvolumeasonecubicfootor28liters;astoplightglowsred foradefiniteamountof time,but it is imagination thatdecideswhetherwedescribethattimeas30secondsor30,000milliseconds.Time,measure,andnumberarearbitrarymetricsthatorganizethingsfor our imagination, which does not entail that substance cannotendureorbeextended,orthatDurationandQuantity(andclassesofthings)arethemselvesimaginary.

But this passage ismore radical than that. Spinozadoesnot saythattimeandmeasurearegeneratedbytheimagination;hecallsthem

15. See,forexample,Bennett196–197,Manning.Surprisingly,whilethecritiqueoftheapplicabilityofmathematicalconceptstonaturehasbeenrecognizedhere,Spinozaisstillwidelytakentoendorsemathematicalphysics.Schliess-er(2014)arguesthatSpinozacritiquesmathematicalphysics,butdoesnottakehiscommentsheretoentail thatspaceandtimethemselves, indepen-dentlyofanymetricsapplied,arethemselvesimaginary.

here, but let us takeDescartes’ discussion of the issue in the Sixth Repliesasamodel.There,Descartesarguesthatnothingmorethantheperceptionofcolorandlight“shouldbereferredtothesensoryfaculty,ifwewishtodistinguishitcarefullyfromtheintellect”,andthatthejudgmentthatastickhasacertainsize,shape,anddistanceistheresultofa“rationalcalculation”that“dependssolelyontheintellect”(SixthReplies,AT438/CSM295).Butinthesamepassage,headmitsthatthebasisofthiscalculationistheexperienceof“theextensionofthecolouranditsboundaries”.Descartes’suggestionthatthesenseshaveatleastsomekindofaccesstotheextensionofbodies,andhisviewthatthisisaverynaturalpositiontoadopt,isconfirmedinanumberofotherplaces; to take just one example, Rule 14 claims that “by ‘extendedbeing’everyonestandardlymeanssomethingimaginable…thereisnothingmoreeasilyperceivedbyourimagination”thanextension(AT441/CSM58).ThereisnoindicationthatSpinozadepartsfromthis.

However, these considerations are not decisive. For clearerevidence that Spinoza associates quantity1 and not quantity2 withspatial extension,wemay look at some related butmore detailedcomments in Spinoza’s “Letter on the Infinite” to LodewijkMeyer.ThepassagequotedabovefromEIp15sisalmostexactlyreproducedin the letter, in the interest of explaining “why we have such astrong natural tendency to divide extended Substance”. But thistime,Spinozagoeson toofferparallelanalysesof therelationshipbetweendurationandtime,continuousquantityandmeasure,anddiscretequantityandnumber:

Further,fromthefactthatweareabletodelimitDurationand Quantity as we please, conceiving Quantity inabstraction from Substance and separating the effluxof Duration from things eternal, there arise Time andMeasure: Time to delimit Duration and Measure to

objects,thetwokindsofquantity,suggeststhatthisisnotpossible.Theseconsiderationsraisemorequestionsthananswers,butIhopeonlytomakethepointhere that theview that senseperceptionhasnoaccess to thesepropertiesisradical,rare,andusuallytakentorequirecarefuldefense.



be conceived as composed of parts, yet those parts (improperly socalled)…[are]notpartablewithoutanexpresscontradictioninterms”.So “space consequently is in itself essentially one, and absolutelyindivisible”(Clarke[1717]Reply4,Section11).Leibnizresponds:

I objected that space cannot be in God because it hasparts.HereupontheAuthorseeksanothersubterfuge,bydepartingfromthereceivedsenseofwords,maintainingthatspacehasnoparts,becauseitspartsarenotseparable,andcannotberemovedfromoneanotherbydiscerption.But’tissufficientthatspacehasparts,whetherthosepartsbeseparableornot(Leibniz[1989]Reply5,Section51).17

LeibniztakesthistoshowthatGod’simmensityisnottheimmensityofextension.ItakeSpinozatobeforeshadowingLeibniz,againstClarke,intheclaimthatspacehaspartsinvirtueofitsbeingextended,evenifthosepartscannotbeactuallyremovedfromoneanother.Clarkeisnotthefirstpersontoarguethatspaceisindivisible,buttheviewisuncommonpriortoHenryMore.18

Indeed,itisacommonviewfromAristotlethroughtoSpinozathatforsomethingtobeextendedisidenticalwith,essentiallyinvolves,orentailsitshavingpartem extra partem:part(s)outsideofpart(s),orpartsnext to parts, or spatially contiguous parts. For example, DescarteswritestoMorethat“Icallextendedonlywhatisimaginableashavingpartes extra partes, each of determinate magnitude and figure” (5February1649,AT270).19 InChapter35of theGuide for the Perplexed,

17. DescartesmakesasimilarpointtoMersenne:“…anindivisiblethingcannothaveanylengthorbreadthordepth.Ifithad,wecoulddivideitatleastinourimagination,whichwouldsufficetoguaranteethatitwasnotindivisible:forifwecoulddivideitinimagination,anangelcoulddivideitinreality.”(AT213/CSMK155)

18. SeeGrant,234:“Patrizi,Bruno,Campanella,Gassendi,More,Spinoza,Raph-son,Newton,andotherswereasoneintheassumptionthatspaceisindivis-ible.”(IamchallengingheretheinclusionofSpinozainthatlist.)

19. The‘imaginable’heremightseemtosuggestthatthereisasenseinwhichextension,whenconceivedthroughtheintellect,isnotdivisible.Butitdoes

“aidsoftheimagination”.Thisimpliesthatwhatisbeingmeasured(ortimed,orcounted)isitselfimaginary.Butwhatisbeingmeasuredortimedisquantityandduration:timeenablesustodelimitdurationinordertoimagineiteasily,andmeasureenablesustodelimitquantityin order to imagine it easily. Likewise, to arrange things into kindsinvolves abstracting affections of substance from substance, and tohelpusorganizethoseclasses,weapplynumber.Itisnotmerelytime,measure,andnumberthatareimaginary,butthethingsthattheyarelabelingororganizing:duration,quantity,andmembersofakind.16

Thequantityherethatisbeingdiscussedisquantityconsidered“inabstractionfromsubstance”,whichmustbequantity1.Thesuspicionthat this refers to length,breadth,anddepth isconfirmedwhenweconsider that Spinoza explicitly identifies measure as what labelsor organizes “continuous quantity (quantitati continueæ)” in theMetaphysical Thoughts (I.I, G I 234/C 300). “Continuous quantity”refers unambiguously to geometrical extension. So, the “Letter onthe Infinite” confirms that Spinoza denies that continuous quantity,insofarasitissubjectedtomeasure,ispredicableofGod.

Adefender of the view thatGod is nonetheless extendedmightrespondbyarguingthatSpinozaunderstandsbothkindsofquantitytohavedimensionality.The“continuousquantity”thatisdiscussedinthesepassagesisquantitywhenitisregardedasdivisible,measurable,and manipulable by the imagination. But—the thought goes—wecanalso regard it in anotherway,onewhich is appropriate toGod.Itstillhasdimensionalitywhenregardedinthatway,butitisnotsomeasurable,divisible,ormanipulable.

TheviewexpressedherehassomethingincommonwiththeonethatSamuelClarkeexpressesinhisfamiliardebatewithLeibnizoverthenatureofspace.Clarkearguesthatspace“mayinourimagination

16. ThisrelatestoSpinoza’s(not-always-consistent)denialofuniversalessences.Timeandextension,as faras theyaresituated inSpinoza’s system,wouldseemtohavelittleincommon:Extensionisanattribute,whiletimeisnot;thatistosaythatExtensionisawayofconceivingofthingswhiletime-relat-edconceptslikedurationarise,Spinozasays,fromthemotionofbodies.De-spitethis,Spinozaoftentreatsspaceconceptsandtimeconceptsintandem.



seriously the analogy between time and duration on the one handandmeasureandquantityontheother,itwouldimplythatmerelybyattributingquantitytoGod,weadmitthepossibilityofdividingGodintospatialparts,whichisimpossible.

I have made the point using duration, because, just like in the“LetterontheInfinite”, thelanguageisclearerandthepoint ismoreexplicitinthatcase.Butafewparagraphslater,in“OfGod’sImmensity(Immensitas)”,SpinozahintsatasimilarargumentagainstattributingspatialpropertiestoGod:

Nevertheless, usually when authors deal with God’sImmensity, they seem to ascribe quantity to him. ForfromthisattributetheywishtoconcludethatGodmustnecessarilybepresenteverywhere,asiftheythoughtthatifthereweresomeplacewhichGodwasnotin,thenhisquantitywouldbelimited.ThisisevenclearerfromtheotherargumenttheybringforwardtoshowthatGodisinfinite, or immense (for they confuse these two), andalsothatheiseverywhere.IfGod,theysay,ispureact,asindeedheis,hemustbeeverywhereandinfinite.Forifhewerenoteverywhere,eitherhewouldnotbeabletobewhereverhewishestobe,orhewouldnecessarily—notethis—havetomove.FromthisitisclearthattheyascribeImmensity toGod insofaras theyregardhimashavinga certain quantity; for they seek to argue for God’sImmensity from the properties of extension, which ismostabsurd(CMIIIII,GI254/C319).

What is “God’s Immensity”? Spinoza does not discuss it anywhereoutside of this Appendix. But Spinoza does not, by God’s infinity, understand unlimited size: here,God’s infinity is defined asGod’ssupreme perfection, while later, in the Ethics, God’s infinity isidentified as God’s having infinite attributes. If Spinoza intendsa parallel analysis of immensity here, his meaning is clear: it is a

Maimonideswrites:“…as[acorporealthing]hasextensionitisalsodivisible”,andPasnauwritesthat“thereseemstohavebeengeneralagreement, throughout our four centuries [1274–1761] over whatextensionis:itistohavepartem extra partem”(54).ThatSpinozasideswithDescartesandMaimonides,andwouldhavesidedwithLeibnizagainstClarke, inunderstandingspatialextensiontoentailthekindofdivisibilitythatimperilsGod’sperfection,isconfirmedinanotherparallel treatmentofdurationandextension, found inPart IIof theCogitata Metaphysica. This section deals with, among other things,God’s attributes, among which are numbered eternity and infinity.Althoughthisisanearlytext,andSpinozawillcometorejectaspectsofitsaccountofthedivineattributesinlaterwork,inconjunctionwiththe“LetterontheInfinite”IthinkwecantaketherelevantpassagesasrepresentativeofsomeofSpinoza’senduringcommitments.

In“OfGod’sEternity”,Spinozaarguesthat

sincedurationisconceivedasbeinggreaterorlesser,orascomposedofparts,itfollowsclearlythatnodurationcanbeascribedtoGod:forsincehisbeingiseternal,i. e.,inittherecanbenothingwhichisbeforeorafter,wecanneverascribedurationtohim,withoutatthesametimedestroying the trueconceptwhichwehaveofGod. I. e.,byattributingdurationtohim,wedivideintopartswhatisinfinitebyitsownnatureandcanneverbeconceivedexceptasinfinite[B:Wedividehisexistenceintoparts,orconceiveitasdivisible,whenweattempttoexplainitbyduration](CMIII,GI250/C316).

What iscrucial is thatSpinozadoesnotsayhere thatbyattributingtime toGod,wedividehim intoparts; rather,merelyby attributingdurationtoGod,weareadmittingthepossibilityofdividingGodintotemporalparts,whichisenoughtoimperilGod’seternity.Ifwetake

not:seeDescartes’commenttoMersenne,citedinnote17.Whatitdoessug-gestisthatextensionisessentiallyimaginable,forDescartes.



this interpretation is thatSpinozastatesquiteclearly thatExtensionis the essence of corporeal substance, presupposing nothing else,whilemotionpresupposesExtension.20Somotion (ormotive force)isnotco-fundamentalwithExtension.Butletusconsiderwhethertheargumentsaboveleaveopentheviewthat“Extension”forSpinozaisspatialextension,plussomethingelse—someotherkindofforceorpower,orsomethinglikesolidity,orinertia.Perhapsitistheadditionofthissomethingelsethatmakescorporealsubstance,orsubstanceconceivedundertheattributeofExtension,indivisible.

Afullrebuttalofthisobjectionwouldbeverydifficulthere,becauseitwouldhavetoaddressallthewaysthatthis“somethingelse”mightbeproposed,inamorepreciseway,toberelatedtospatialextension.IcannotmakemuchsenseoftheideathattheattributeofExtension(anessenceofGod)isjustspatialextensionplussomethingelse,asifthesetwofeaturesofit,unrelatedtooneanother,servedasakindofconjunctiveessence.SothebestsenseIcanmakeofthiskindofviewisthatExtensionwouldbeaspatiallyextendedsomething—aspread-outsolidityorinertiaorforceofsomekind.Butwhat,exactly,doesitmeanforpowerorsolidityorinertiatobeextended—orforanythingthat isnotmereextensiontobeextended, forthatmatter?This isadeepprobleminthehistoryofphilosophythatresonatesinquestionsabouthowthemindisrelatedtothebodyandhowGodisrelatedtospaceandmatter.Eitherthethingisspreadout(itispartofitsnaturetobespreadout),oritisrepeated,orisitpresentineverypartofspace.Butonthefirst twoviews, thething(power, inertia,etc.) ispriortoitsbeingspreadoutor repeated—inotherwords,prior to itsbeingextended.21Thethirdviewishardtomakesenseof,giventhatSpinoza

20.ThisargumentisalsomadebyTolandagainstSpinoza;seeLetters to Serena, LetterIV,§11.TherelevanceofTolandtothisissuewaskindlyindicatedtomebyareviewer.

21. Leibniz,readingSpinoza’sExtensionasspatialextension,criticizesSpinozaonpreciselythesegrounds.AccordingtoLeibniz,“…theremustbeasubjectthat isextended—that is tosay,asubstancethatcanproperlyberepeatedor continued. For extension signifies nothing but a repetition or continu-ousmultiplicityoftheparts,andconsequentlyitdoesnotsufficetoexplain

mistake to attribute literal omnipresence toGod, because to do soisto implythatGodhasacertainquantity,orhasthepropertiesofextension,which is “most absurd”. Spinozagoeson in this chapterto claim that to understand howGod is actually in every place is“beyondman’sgrasp”.ButitiscertainlynotinvirtueofGod’shavingthepropertiesofextension.Aswesawabove,Spinozawillultimatelychange his view from the one stated here, to allow that there is acertainkindofquantity—intelligible,infinite,indivisible,andrarelyunderstood—thatdoescharacterizesubstance.Buthere,Spinozaisdiscussingonlywhatwehavecalledquantity1.

Toconcludethissection,I’dliketoaddressthreeobjections.First,theargumentsaboveprecludethattheessenceofsubstance,

understood under the attribute of Extension, is extension. Thatmeans thatSpinozarejectsacentralprincipleofCartesianphysics,anditalsomeansthatBennett’sinterpretationofExtendedsubstanceasspacecannotbecorrect.ButtheyalsoprecludethattheessenceofExtendedsubstanceisnotmereextension,butisstillanextendedsomething, or extension plus something else. This latter is a verycommonviewofSpinoza’smodificationofCartesianphysics.Whatisproposedasthis“somethingelse”usuallyrelatestomotion:perhapsSpinozathinksthattheessenceofExtendedsubstanceisextensionplusmotion,orextensionplussomemotivepowerorforce.ThisistakentobeplausibleinlightofanepistolarycommentthatSpinozamakes to Tschirnhaus late in his life that “… from Extension, asconceivedbyDescartes,towit,aninertmass,itisnotonlydifficult,as you say, but quite impossible to demonstrate the existence ofbodies”(Ep.81,GIV255/S352).Insteadofdefiningmatterthroughextension,asDescartesdoes,hearguesthatmatter“mustnecessarilybe explicated through an attribute which expresses eternal andinfiniteessence”(Ep.83,GIV258/S355).

AmoresustainedargumentagainsttheviewthatSpinozameanstoincludesomethinglikemotionormotiveforceinparticularwhenhe refers to “Extension”,making it part of the essence ofmatter, isgiven in Peterman (2012). The most compelling argument against



without specification, in EIp15s, Spinoza writes that the fact thatquantity2isinfinite,unique,andindivisiblewillbe

sufficiently plain to everyone who knows howto distinguish between the intellect and theimagination—particularly if it is alsonoted thatmatteriseverywherethesame,andthatpartsaredistinguishedinitonlyinsofarasweconceivemattertobeaffectedindifferent ways, so that its parts are distinguished onlymodally,butnotreally(GII60/C424).

However, the argumentof this sectiondependedonlyonSpinoza’sassociation between (whatever kind of) divisibility and quantity1, showingthatheconcludesonthebasisofGod’ssimplicity(ofwhateverkind) thatGodcannotbecharacterizedbyquantity1.Thisargumentdoesnotdependonthekindofdivisibilityinquestion;itleavesopenthepossibilitythatGodismodallydivisible,butnotthepossibilitythatGod isextended.ThequestionofwhetherGod ismodallydivisibleis interesting to theextent that itbearson thequestionofwhethermodesareextended,aquestionthatwillbeaddressedatlengthinthenextsection.

This response supposes that Spinoza takes the question ofsubstance’smodaldivisibilitytobereducibletoquestionsaboutthedivisibility ofmodes from one another. I think this is a reasonablesupposition.InCMChapterV(GI258/C323),“OfGod’sSimplicity”,Spinozaarguesthattherearethreekindsofdistinctionsamongthings:real,modal,andofreason.Hecontinues:

From these three all composition arises. The first sortof composition is thatwhich comes from two ormoresubstanceswhichhavethesameattribute…Thesecondcomesfromtheunionofdifferentmodes.Thethird,finally,doesnotoccur,butisonlyconceivedbythereasonasifitoccurred…Whateverisnotcomposedinthesefirsttwowaysshouldbecalledsimple.

doesnotseemtoacceptthatthereisspaceindependentofmatter.Ifthethingispriortoitsbeingextended,thenitsoundslikethatthingistheessenceofmatter,andnotextension.

Perhapsthereisanotheroption—thatwhatevertheextrathingis,it ispartof its essence tobeextended in space.As far as I can tell,in the scholastic and Cartesian precedent examples of whichwerequotedthroughoutthissection,andinSpinoza’sadaptationofit,forwhichI’vetriedtoofferampleevidence,itisnotjustsomethingwhoseessence is spatial extension alone that is divisible, but anything inwhosenature it is to be extended in space. So if it is in thenatureofmotivepower(forexample)tobeextendedinspace,thatmotivepoweristherebydivisibleandinappropriatetosubstance.

Soweseemtobefacedwithtwofamiliesofthistypeofinterpretation.Eitherextensionissomehowessentialtotheextrathing,sothatthepowerorforceorsolidityisessentiallyspreadout,oritisnot.If it is,thenitfallstoallthecritiquesoutlinedinthissection.Ifitisnot,thenthethingitselfismorefundamental,andthereforethatthingiswhatSpinozameansbyExtension—notspatialextension.

A second objection is that I have ignored Spinoza’s distinctionamong distinctions, and in doing so, ignored the possibility thatSpinoza’smain concern in the passages above is just to argue thatsubstanceisnotreallydivisible,thatis,divisibleintotwosubstances.Although throughoutmostofEIp15sand the “Letteron the Infinite”,Spinoza appears to be concernedwith divisibility and indivisibility

theverynatureof the substance that is spreadoutor repeated,whoseno-tionispriortothatofitsrepetition”(Leibniz179).ApplyingthistoSpinoza,he argues that “what Spinoza imagines tohimself, that fromany attributewhatsoevercomesaninfinitething,fromextensionacertainthinginfiniteinextension,fromthoughtacertaininfiniteintellect,arisesfromtheunsteadyimaginationofcertainheterogeneousdivineattributes,likethoughtandex-tension,and innumerableothers,perhaps.For, since it isonlya repetitionofperceivings,extensionisnot,inandofitself,reallyanattribute”(Leibniz276).IbelievethatSpinozahimselfhassomethinglikethisviewofdurationinmindwhenhewritesthat“durationisanaffectionofexistence,andnotoftheessenceofthings.ButsinceGod’sexistenceisofhisessence,wecanattributenodurationtohim”(CMI,GI25/C315).



comparabletothewrongnessofthinkingthatsurfacesarecomposedoflines,perhapsitisreasonabletothinkthatcorporealsubstance,likesurfacesandlines,hasspatialdimensions.

This passage may seem to suggest that corporeal substance isto bodies as a surface is to lines: both are really extended in theirrespectivedimensions,andwemayimagineparts inthem,buttheyarenotreallydivisibleintothosepartsorcomposedofthoseparts.Butifweextendtheanalogy,thentheviewthatisdeemedabsurdhereisthatcorporealsubstance,beingmadeupofthree-dimensionalbodies,is four-dimensional! (Thatmay soundall right toour ears, but thatissurelynotwhatSpinozaintends.)ThisisobscuredbythefactthatSpinoza is concerned in this scholiumwith several different issues.Oneisthedivisibilityofsubstance,bodies,andlinesingeneral,earlierinthepassage.ButhereSpinozaisstressingtheparticularabsurdityof claiming that linesare composedofpoints, etc.Theabsurdityofasserting that lines aremade up of points arises from the fact thatpointsarezero-dimensionalandlinesareone-dimensional,soifalineiscomposedofpoints,itiscomposedofnothings.Whatisabsurdhereisnot the idea thatwecandivideextensionsofvariousdimensionsintoparts,butrathertheattempttocomposeawholeoutofthewrongkindofthingentirely.

Toconclude:thequantitythatSpinozadeniescanbeattributedtosubstanceisthree-dimensionalextension.EitherspatialextensionisrelatedtoGodinawaythatdoesnotentailthatGod,nature(natura naturans),orsubstanceisitselfspatiallyextended,orSpinozameanssomething other than spatial extension by ‘Extension’, or both. Allthis explains a comment Spinoza makes late in his life to HenryOldenburg, the then-secretary of the Royal Society, responding toOldenburg’s concern that “reasonable and intelligent Christians”who read Spinoza’s Tractatus Theologico-Politicus might be misledintothinkingthatSpinozahas“confused”Godwithnature.Spinozarepliesthatanyonewhobelievesthat theTreatise’sconclusions“restontheidentificationofGodwithNature(bythelatterofwhichtheyunderstandakindofmassorcorporealmatter)”are“quitemistaken”

SpinozagoesontoshowthatGodis“amostsimplebeing”,which,atthispointinthedevelopmentofSpinoza’sthought,meansthatGodisnotevenmodallydivisible.Moreover,somethingwhichismodallydivisibleissomethingthat“comesfromtheunionofdifferentmodes”.NowinthisearlyworkSpinozaalsobelievesthatthereare“nomodesinGod”—apositionwhichobviouslychangesbeforehewritesEIp15s.But there is no reason to think that Spinoza’s conception ofmodaldistinction and divisibility changes between here and the Ethics.Substancecannotbedivided into twoormoremodes,because it isnotcomposedoftwoormoremodes.Italsocannotbedividedintoamodeandasubstance.Complexmodesaremodallydivisible,butwecannotmakesenseoftheideathatsubstanceismodallydivisible.

Third,I’dliketoaddresswhatIthinkisthemostdifficultpassagefortheargumentIammakinghere.AspartoftheanalysisofquantityinEIp15s,Spinozacomparesthosewhothinkthatcorporealsubstanceisdivisibletoothers,who

…aftertheyfeignthatalineiscomposedofpoints,knowhowtoinventmanyarguments,bywhichtheyshowthatalinecannotbedividedtoinfinity.Andindeeditisnolessabsurdtoassertthatcorporealsubstanceiscomposedofbodies,orparts,thanthatabodyiscomposedofsurfaces,thesurfacesoflines,andthelines,finally,ofpoints(GII59/C423).

Here, Spinoza equates the absurdity of thinking that lines arecomposed of points with the absurdity of thinking that corporeal(or Extended) substance is composed of bodies. This suggests thatSpinozaseescorporealsubstance,bodies,surfaces,lines,andpoints,andtherelationshipsamongthem,asofthesameclassinsomerespect.ItdoesnotsoundlikeSpinozaisdistinguishingbetweengeometricalobjects like points and lines (which are entia rationis), on the onehand, andExtended substance (which is an ens reale), on the other.Ifthewrongnessofthinkingthatsubstanceiscomposedofbodiesis



preciselywhattherelationshipbetweensubstanceanditsmodesis.Iwould just like toshowthatwhatever that relationship is, therearereasonstothinkthatmodesarenotfundamentallyextendedinspace.

Here, I’ll discuss threedifferent influential classesof attempts toexplainthissubstance-moderelationshipwhilestillmaintainingthatmodesareextendedinspace.First,Curley(1969)arguesthatincallingbodies modes of extended substance, Spinoza is only committinghimself to the claim that bodies are causally dependent on God.Second,Schmaltz(1999),whoarguesthatcorporealsubstanceisnotextendedinspace,suggeststhatcorporealsubstancecontainsspatialextension eminently, explaining why the finite modes that followtherefrom are themselves extended, while substance is not. Finally,drawingonrecentworkbyYitzhakMelamed,IconsiderthepossibilitythatSpinoza’s infinitemodescanbridge thegapbetweenExtendedsubstanceanditsmodessuchthatmodesareextendedinspaceeventhoughsubstanceisnot.

InhisinfluentialinterpretationofSpinoza’smetaphysicsinCurley(1969), Curley argues that readers of Spinoza from Bayle to todaysystematically misread Spinoza when they understand modes aspropertiesof substanceoras inherent in substance. Instead,modesarejustdependentonGodbecausetheyareefficientlycausedbyGod,and talk ofmodes being “in”God just indicates that Spinoza takesmodestocausallydependonsubstance;otherwise,bodieswouldbethe “wrong logical type” in Spinoza’s system.Curley’s account doesnotexplainexactlyhowextendedmodesfollowfromnon-extendedsubstanceotherthanaseffectsofanefficientcause,butifwereduceSpinoza’s account of the substance-mode relationship to this, thequestionof thegapappears lesspressing.At least, itdoesnotariseanymorethanitwouldariseforsomeonewhoclaimsthatGodisamindwhocreatesbodies:thereisnoobviousreasonwhythecauseandtheeffectshouldbeunderstoodasbeingmodifiedbytheattributeofExtensioninthesameway,oreventhattheyshouldbemodifiedbythesameattributeatall.

(Ep.73toOldenburg,GIV306/S332).AlthoughGodisanExtendedthing,Godisnot“akindofmassorcorporealmatter”.

§3 Extended modes, or, finite bodies

The previous section argued that Extended substance is not itselfextendedinspace,butleftopenthepossibilitythatbodies,orfinitemodesofExtendedsubstance,are.Thissectionarguesthatwedonotconceiveofbodiesadequatelywhenweconceiveofthemasextendedin space. First, in section §3a, I’ll discuss themetaphysical gap thatrequiresbridgingifweacceptthatExtendedsubstanceisnotextended,butcontinuetomaintainthatmodesofExtensionare.I’llarguethatnoneoftheproposedwaysofbridgingthatgaparesatisfactory,takingthreesuchattemptsasrepresentative.Then, insection§3b, I’lloffersometextualevidencethatsuggeststhatSpinozadidnottakemodestobeadequatelyunderstoodasextendedinspace.Finally,insection§3c,I’llarguethatgivenSpinoza’sepistemologyofscience,wehaveno justification for believing that bodies are volumes. On the onehand,weappreciatetheirspatialpropertiesthroughtheimagination,which isunreliable.Ontheother,Descartes’primarymotivationforreducingbodies to geometrical extension—that physics is tractableformathematics—is,Spinozathinks,misguided.

§3aPerhaps,accordingtoSpinoza,substanceisnotextendedbutmodesare, sinceallof theconsiderations in§2preclude theapplicationofspatial extension to substance specifically. If this is true, we’d liketo know how these spatially-extended modes follow from God’sessenceasdescribedinEIp16,howtheirrelationshiptotheattributeof Extension relates to substance’s relation to that attribute, and,ultimately,howthisrelationshipissupposedtoilluminatethenature,behavior,andinteractionsofbodiesinthephysicalworld.TherehavebeenaboutasmanyaccountsoftherelationshipbetweensubstanceanditsmodesastherehavebeenreadersofSpinoza,andIcannotdojusticetoallofthemhere.Ialsodonotwanttotakemyownstandon



whostarts to look,on thisaccount, likeonewhotranscendsnature.Bennett, onwhose view corporeal substance, or God, is just space,takesroute(1).Besidesthetextualevidenceagainstthisinterpretationthat has already been outlined, this view has Spinoza making thedeeplyradicalidentificationofGodwithnature,butdrawsfromthatalmostnoimplicationsforwhatthephysicalworldisactuallylike.

Next,I’llconsideranotherinterpretationthatfollowsroute(3).23In“Spinozaon theVacuum”, Schmaltzdrawsonmanyof thepassagescited in §2 to show that Bennett’s “field-metaphysical” account ofcorporealsubstanceisnottenable.Assuming“Spinoza’sendorsementofDescartes’claimthat thepartsofmatteraredivisible into furtherparts without end” (175), Schmaltz writes that “what we still needfromSpinozainlightofhisremarksinthe“LetterontheInfinite”isan accountof themanner inwhich the conceptionof quantity anddurationas infinitelydivisibledependsona conceptionof themasmodesofaneternalsubstance”(196).Althoughwecannotattributethepropertiesofbodiesthatentailtheirdivisibility(includingextension)tocorporealsubstance,wecansaythatbodieshavethosepropertiesinvirtueofthefactthat“thereissomeattributeinGodwhichcontainsall the perceptions ofmatter in amore excellentway and can taketheplaceofmatter”.24Corporealsubstancemusthavetheattributeofextensioninordertoexplaintheextensionofbodies,butitdoesnothavetorelatetoextensionasasubjecttoapredicate—or,itdoesnothavetobeitselfextended.Rather,wecanseecorporealsubstanceasanindivisibleessence,notanindivisiblesubjectthatinstantiatesthatessence(188).25Inotherwords,“theextensionofindividualbodiesiscontainedinGodeminentlyratherthanformally”(188).

Thereisastrongtextualreasontobesuspiciousofthisinterpretationof the relationshipbetweenGodandExtension. Schmaltz relies on

23. ForamoreextendeddiscussionofSpinozaandnaturalism,seeDouglas.

24.CMI2,GI56/C304.

25. SeealsoGueroult(1997)andHallett(1957)forsimilarviews.SchmaltzalsorelateshisviewtoanaccountoftheinfinitemodesinSchmaltz(1999).

This interpretation has been resisted by compelling argumentsfromanumberofscholars,andsoIwillnotaddressitatlengthhere.22 Remainingasuncommittedaspossibletoexactlywhattherelationshipbetween substance andmodes is for Spinoza, it nonetheless seemsclearthatSpinoza’sclaimisthatmodesinhereinsubstanceaseffectsofanimmanentcause.ThemainreasonthatCurleygivesforreadingmodes this way—that they are of the wrong logical type—is notcompelling. Given Spinoza’s Jewish and Neoplatonic influences, itis not at all surprising that he takes creatures to inhere inGod.Asforwhethermodescanbe“predicated”ofGod,evenNewtonwould,severaldecadeslater,arguethattherelationshipbetweencreaturesandGodismoreliketherelationshipbetweenanaccidentandacreatedsubstancethanlikearelationshipbetweentwosubstances(Newton89).There is quite a lot of evidence in theEthics that Spinoza tookmodestoinhereinsubstance,includingcommentsthatthey“moveinGod”andthat“everythingisinGod”.ForamorethoroughrefutationoftheviewthatforSpinoza,modesdonotinhereinsubstance,see,forexample,Melamed(2009).

ThereasonforconsideringCurley’sview,howeverbriefly, isthatit is a representativeof an approach to addressing the challengeofrespecting Spinoza’s identification of Godwith naturewhile at thesametimemakingsenseofwhathetakestheworldoffinitephysicalthings.Itcanseemthatwearefacedwithatrilemma:shouldwe(1)emphasizetheidentificationofGodandnature,and“naturalize”God;(2)emphasizetheidentificationofGodandnature,and“deify”nature;(3) de-emphasize the identification of God and nature, retainingintuitivelyappealingconceptionsofbothbutlosing,inadifferentwaythan(2),someofSpinoza’snaturalisticresonances?Curley,intakingthethirdpath,providesanappealingaccountofSpinoza’sphysicsandphilosophyof science,yieldingadeductive-nomological,materialist,“sensible”Spinoza.ButitisatthecostofdoingsomeviolencetothemorefundamentalmetaphysicsaswellastoSpinoza’snaturalisticGod,

22. See,forexample,Bennett93andMelamed(2009)117.



isnot.26WhenSpinozaprovesatEIIp2thatExtensionisanattributeof God, he does not leave it at that; instead, he writes pointedly:“ExtensionisanattributeofGod,or[sive]Godisanextendedthing”(GII86/C449).What’smore,Spinozausesthephrase‘res extensa’onlytorefertoGodorsubstance,nevercallingabodya“res extensa”,thoughhedoesnothesitatetocallthem“res”inothercontexts.Similarly,he’lltalkabout“substantia extensa”butnevera“modus extensus”—wefindonly “modi Extensionis”. On Schmaltz’s view, where God possessesthe eternal and indivisible essence of extension while bodies arethemselvesextended,withalltheimperfectionsthatimplies,wewouldnotexpectSpinozatocallGodares extensaandneverdescribebodiesasextended.27WhatthissuggestsisthatSpinozaintendstopreserveastheprimaryandfundamentalsenseof‘Extended’theadjectivalone,applyingthattoGod.Thisisconfirmedbythefact,discussedearlierinthissection,thatSpinozaidentifiesadjectiveslike“learned”and“big”asattributesofamanintheHebrewGrammar(S600).

Finally, one of Spinoza’smotivations for admitting, in theEthics, thatGodisExtendedistosolvetheproblemofhowaGodwhohas

26. Inarecentarticle,FraenkelarguesforareadingofSpinozisticExtendedsub-stancethatdrawsonAristotleandCrescas.Onthisaccount,forSpinoza,“thephysicalrealmistransformedintoGod’sinfiniteextensionthat‘produces,in-dividuates,anddetermines’extendedmodeswithinitself.…Infiniteexten-siontakesovertheroleoftheform,i. e.,theroleofproducing,determining,andindividuatingtheobjectsofthephysicalworld”(92).Whiletherearecer-tainlylinksbetweenSpinozaandCrescas,thetextualevidenceofferedstrikesmeastoothintosupportthisparticularCrescas-inspiredreadingofExtendedsubstance. I am unsurewhether Fraenkelwould agree that Extended sub-stancehasactualdimensionality,orwhetheritisjusttheactivitythatinformsinfiniteextension.Iftheformer,thenitisvulnerabletotextualevidencefrom§2.Ifthelatter,thenitisvulnerabletoargumentsthatresemblethosegivenagainstSchmaltz’s“eminentcontainment”interpretationhere.

27. Comparethistextualevidencealso,forexample,toWoolhouse’sviewthatsubstance“underwritesthepossibilityofactualinstantiationsofextension,ofactualextendedthings”(p.47,myitalics);orFraenkel’sviewthatSpino-za“integrate[s]theattributeofextensionintothe‘activeessence’ofGod’sinfinitebeing…God is… ‘extending’ activity,whichproducesextendedobjectswithin itself” (87).Contrary to the implicationsof these readings,SpinozaseemstobeatpainstostressthatGodistheExtendedthing,prop-erlyspeaking.

a passage from the Cogitata Metaphysica II (G I 237/C 303), whereSpinozaclaims

thatGod contains eminentlywhat is found formally increated things, i. e., thatGodhasattributes inwhichallcreated things are contained in amore eminentway…E. g.,weconceiveextensionclearlywithoutanyexistence,andtherefore,sinceithas,ofitself,nopowertoexist,wehavedemonstratedthatitwascreatedbyGod(Ip21).Andsincetheremustbeatleastasmuchperfectioninthecauseasthereisintheeffect,itfollowsthatalltheperfectionsofextensionare inGod.Butbecausewesawafterwardthat an extended thing, by its very nature, is divisible,i. e., contains an imperfection, we could not attributeextensiontoGod(Ip16).SowewereconstrainedtoallowthatthereissomeattributeinGodwhichcontainsalltheperfectionsofmatterinamoreexcellentway(Ip9s)andcantaketheplaceofmatter.

However, it is clear that Spinoza’s views about the relationshipbetween God and God’s attributes changes dramatically from theCogitata Metaphysica—anearlyandveryCartesiantext,appendedtoSpinoza’s commentary on Descartes’ Principles. This isn’t reason toignore it, but in this case, Spinoza explicitly denies that substancecontainsextensioneminentlyintheShort Treatise:“thiseffectofbodythrough which we perceive it can come from nothing other thanextensionitself,andnotfromanythingelsethat(assomemaintain)hasthatextensioneminently.ForaswehavealreadyshowninthefirstChapter,thisdoesnotexist”(KVXIX,GI90/C130).AndthereisnofurthermentionofeminentcontainmentoftheExtensionofbodiesinGodintheremainderofSpinoza’swritings.

There are further considerations against this account thatweighagainstawiderclassofinterpretations:namely,anyinterpretationonwhich“Extended”hasitsusualmeaning,bodiesareextended,andGod



farastrayfromknowledgeofthefirstcauseandoriginofallthings”.28 Insofaraswecandophysics,corporealsubstancemustbeconsideredas part of the subjectmatter. Spinoza, in callingGod “an Extendedthing”,isafteracertainexplanatoryandontologicalparsimony.Bennett,forexample,retainsthisparsimony,butonlybyignoringthedivinepropertiesofcorporealsubstance.WhileSchmaltz’saccountrespectsthoseproperties,itjeopardizesthisparsimonyandstripsSpinozaofsomeimportantnaturalisticresonances.29

AthirdinterpretationofSpinozahasitthattheinfinitemodescanexplainhowwegetfromcorporealsubstance,whichisnotextendedin space, to modes that are extended in space. It has been widelyaccepted thatSpinoza intends the infinitemodes to transition fromanindivisibleandeternalnatura naturanstodivisibleandsempiternalnatura naturata,although,ofcourse,thedetailsofthewaythisworksvary from interpreter to interpreter. As a most careful and well-arguedexampleofthiskindofview,I’llconsiderYitzhakMelamed’srecentaccountoftheinfinitemodesinMelamed(2013).TheinfinitemodesareintroducedinEIp21–23asmodeswhich“existnecessarilyand are infinite” and “(a) follow either from the absolute natureof someattributeofGod,or (b) fromsomeattribute,modifiedbyamodificationwhichexistsnecessarilyandis infinite”(EIp21–23,GII64/C429–430).(a)areusuallyreferredtoasthe“immediateinfinitemodes”,and(b)asthe“mediateinfinitemodes”.MelamedarguesthatacarefulreadingofLetter12showsthatmodesaredivisiblebytheir

28.Ep.2toOldenburg,seealsoEp.31(GIV168/S61).

29.Baylearticulatesthisthoughtnicely inhisDictionnaireentryonSpinoza:“Iamnotignorant,thatanapologistofSpinozamaintainsthatthisPhilosopherdoesnotascribeamaterialextensiontoGod,butonlyanintelligibleexten-sion,andsuchasfallsnotunderourimagination.Butiftheextensionofthebodiesweseeandimagine,isnottheextensionofGod,whencecomesit?Howhas itbeenmade?If ithasbeenproducedoutofnothing,Spinozaisanorthodoxman,hisnewsystemsignifiesnothing.IfithasbeenproducedoutoftheintelligibleextensionofGod,itisstillatruecreation;fortheintel-ligibleextensionbeingbutan idea,andnothavingreally the threedimen-sions,cannotformthematteroftheextension,whichformallyexistsoutoftheunderstanding.”

nothing of Extension can engender Extended creatures. SpinozarejectstheconceptionofGodascreatorex nihilo,insteadarguingthatmodes shouldbeunderstood asGod’spropria,whichflow fromhisessenceandexpressit(EIp16,GII60/C425).InthescholiumtoIp15,SpinozawritesapprovinglyofthosewhodenythatGodisabodylikefinitebodies,butarguesthattheygotoofarwhen

…theyentirelyremovecorporeal,orextended,substanceitself from thedivinenature.And theymaintain that ithasbeencreatedbyGod.Butbywhatdivinepowercoulditbecreated?Theyarecompletelyignorantofthat.

Afterall,accordingtoSpinoza,“ifthingshavenothingincommonwithoneanother,oneofthemcannotbethecauseoftheother(EIp3,GII47/C410)”.Thispassage raises twohardquestions. First,whatkindofrelationshipdoesSpinozaenvisionwhichavoids,ontheonehand,“entirelyremov[ing]”thecorporealfromGod’snatureand,ontheotherhand, attributing toGod the imperfections ofmodes of Extension?Spinoza’s opponents, for example, would admit that God has anideaofExtension—whydoesthatfailtoexplainhowGodcancreatematter,whileeminentcontainmentsucceeds?Second,whydoesn’taversionofthisargumentapplyto,say,ferrets:whyisn’tferret-nessanattributeofGod,sincethereareferrets,andafterall,howcouldGodhavecreatedthemwithoutsuchanattribute?Inotherwords,whatisspecialaboutExtension,andwhyisSpinozaparticularlyconcernedtoshowthatExtensionhasthekindoffundamentalitythatrequiresthatitbecontainedinGodasanattribute?

Idon’thavedetailedanswerstoallofthesequestions,whichwoulddepend in any caseonupon theparticular versionof the family ofinterpretationsthatIamaddressinghere.ButIseeSpinoza’scommentsinthescholiumasmotivatedbyaconsiderationsimilartotheonethatmotivatesSpinozatorespond,whenaskedwhathebelievesarethesourcesoftheerrorsofDescartesandBacon,thattheyhave“gonetoo



Section2showedthatspatialextensionshouldbeidentifiedwithquantity1,whichSpinozaalsoassociateswithdivisibility,duration,andconceptionthroughtheimagination.Itshowed,further,thatSpinozadeniesthatthiskindofquantity(orthiswayofconceivingquantity)canbeattributed tosubstance,primarilyon thebasis that thiskindofquantityentailsdivisibility(althoughthere is isalso independenttextual evidence that Spinoza dissociates quantity1 from substance).Sometimes it sounds like Spinoza thinks that modes are divisiblewheresubstanceisnot.Forexample,inthispassagefromthe“LetterontheInfinite”:

Whenwehaveregardonlytotheessenceofmodesandnot toNature’sorder,as ismostoften thecase,wecanarbitrarily delimit the existence andduration ofmodeswithouthurtingourconceptionofthem,andconceiveitasgreaterorless,ordivisibleintoparts.

Suchpassagesseemtoassociatemodeswithdurationanddivisibility,contrastingthemwithwithsubstance,whichisonlyrightlyconceivedas eternal and indivisible.Melamed (2013), for example, claims onthe basis of such passages that “division pertains tomodes, not tosubstance”andthat“modesandonlymodesaredivisible”(143).

Itmightseemnaturaltoconcludethatifmodes,unlikesubstance,are divisible, they are also extended in space. After all, wasn’t thewholeproblemwithattributingquantity1orspatialextensiontoGodthatextensionisdivisibleandGodisn’t?Ifweestablishthatmodesaredivisible,whatreasonhavewelefttodenythattheyareextendedin space? If that’s right, thenmodesmaybeproperly conceived ashaving quantity1 even while substance is properly conceived onlythroughquantity2.

In the remainder of this section, Iwill show thatmodes arenotproperlyconceivedashavingquantity2.Beforethat,however,Iwouldlike to note that even if modes are divisible, they need not havethatdivisibility invirtueof theirbeingextended inspace—inother

nature and substance is not, and that the infinitemodes effect thetransitionfromindivisibilitytodivisibility.Iftheinfinitemodeseffectthistransition,cantheyalsoeffectthetransitionfromtheattributeofExtensionasitiscontainedinormodifiesGod,andthesempiternalworldofextendedbodies?

This view can really be adequately addressed only after theargumentsoftherestof§3showindependentlytheconclusionthatmodesarenotadequatelyconceivedasextended,butIwouldliketonoteoneimportantproblemwiththisaccountinparticular.Spinozaidentifiestheimmediate infinitemodeofExtension: it is“motioninmatter”orsometimes,“motionandrest”.30Whatever“motion”signifiesforSpinoza,itseemstobewhathethinksisresponsibleforvariety.31 ButSpinozamakesveryclearthatmotionpresupposesExtension;or,inthewordsoftheShort Treatise,thatExtensionisconceivedthroughitselfbutmotionisconceivedonlythroughExtension.32Theinfinitemodeofmotionand rest, then,alreadyassumesanExtended thing,and that thing is Extended substance. In fact Spinoza does not saymerely thateveryExtended thing is inmotion,but that theentiretyofphysicalnatureistheonlypropersubjectofthemode,motion,andrest.33Inshort,thatthereismotionpresupposesthatExtendednatureexists,whateveritis—itdoesnothelpconstituteit.

§3bIn this section, I’ll argue that a more appealing interpretation ofSpinoza involves simplyadmitting thatSpinozadoesnot think thatmodes are extended in space. I will argue that Spinoza does notthinkthatmodesareadequatelyconceivedwhentheyareconceivedabstractly,superficially,andthroughtheimagination,andthatifthisistrue,theyarenotadequatelyconceivedasextendedinspace.

30.SeeEIp21andIp22(GII64/C426)andEp.64toSchuller(GIV278/S298).

31. See,forexample,KVII14,GI120/C155.

32.Again,TolandmakesthispointinLetters To Serena,LetterIV,§11.

33. KVII,GI45/C48.



fact,Spinozaneverdefinesmotion,ashiscontemporariesandnear-contemporaries35noted.Weknowonlythatmotionisanimmediateinfiniteofextension, that it isapropertyshared incommonbyallbodiesand that (and this issomewhatmorecontentious) it is thatpropertyinvirtueofwhichbodiesinteractwithoneanother,orarethecausesofeffects(EIIp43).

Theuseof ‘motion’ to refer to the causesofmotion inmatter isnotparticularly idiosyncratic.Descartes identifiesmotion“accordingtothecommonlyacceptedsense”as“theactionbywhichsomebodyis transferred fromoneplace toanother”,distinguishing it from thetransfer (Pr II 24–25). Inhis confutationofSpinoza,which includesa criticismonprecisely this point (Letter IV to Serena, §11), Tolandstresses theconfusionengenderedby thiswidespreadequivocation.Spinoza (or an editor, likely acting with his approval) even flagshis ownuse of the term ‘motion’ in thisway in a note to theShort Treatise: “What issaidhereofMotion inmatter isnotsaidseriously.For theAuthor still intends to discover its cause, as hehas alreadydone,tosomeextent,aposteriori.Butitcanstandasitishere,becausenothingisbuiltonit,ordependsonit”(KVIIX,GI48/C91).Inshort,SpinozamakesclearthatmotionpresupposesExtension,butnotthatitpresupposesextension,sincethereisnoindicationthathemeanstranslationinspaceby‘motion’.

Soeveniftheinfinitemodesareintendedtointroducedivisibilityinto Extended substance, there is no reason to think that Spinozaintendsthatdivisibilitytobethesortofdivisibilityentailedbyspatialextension.Thereis,furthermore,evidencethatSpinozadoesnottakemodes to be spatially extended. More precisely: there is evidencethat Spinoza thinks thatwhenwe conceivemodes of Extension asspatiallyextended,weconceivetheminadequately,andnot“astheyareinthemselves”.Wesawin§2thatSpinozaassociatesquantity1withtheintellectandquantity2withtheimagination,andwithconceptionin “abstract” and “superficial” terms.To see the implicationof these

35. See,forexample,Tschirnhaus’sLetter84toSpinoza.ForanaccountofsomelatercritiquesofSpinozaonthispoint,seeSchliesser2014.

words,althoughallextendedthingsaredivisibleforSpinoza,itisnotobviously the case that all divisible things are extended.AccordingtoSpinoza,acompositebody(orcompositethingofanykind)isonewhosepartsmaintain certain causal relationshipswithone another(EIIp13def,GII99/C460)or,onewhosepartsareotherindividualsthat “soconcur inoneaction that together theyareall thecauseofoneeffect”(EIId7,GII85/C447).34Thereisnomentionhereofspatialextension. This should not be surprising, since Spinoza thinks thatwecanspeakofcompositeideas,aswell,andthattheirprinciplesofcompositionshouldmirrorthoseofbodies.

Spinozadoes say that the relationship thatmust bemaintainedamongthepartsofacompositemodeofExtension,orabody, isarelationship of “motion and rest” (ratio motus et quietis), and he isclearthatmodesofExtensionareallinmotionoratrest.Wemightthink that this presupposes their being extended in space. First,however:itispossiblethatthesemodesareinspaceinsomesense,butarenotextended. It isan interestingquestion,andone that isof course very closely related to the one being asked here, whattherelationship isbetweenmodesofExtensiontospaceorspatialproperties, be those properties real ormere appearances. But it isbeyondthescopeofthispaper.Second,thereisnoreasontothinkthatSpinozameans,by‘motion’,localmotion.Inhisreconstructionof Cartesian physics, Spinoza offers Descartes’ definition of ‘truemotion’ asDefinition 8 of Part II of the PPC (G I 181/C 263), butlabelsitinsteadas‘localmotion’—anattempt,seemingly,toremainagnosticastothedefinitionoftruemotionormotionsimpliciter.In

34. Spinoza characterizes the former asone “individual” and the latter asone“singularthing,”raisinganumberofmorefine-grainedquestionsabouthisaccountofindividuationandidentity.DoesSpinozameanthesamethingbytheseterms?Ifnot,howdotheydiffer?Ifso,isoneamorefundamentalchar-acterizationofanindividualthananother?Idon’tthinkthatthesequestionsbearontheargumentshere;inanycase,afullaccountofSpinozaonphysicalcompositionistoocomplextofullyexplorehere.Forrecenttreatmentsrel-evanttothisissue,seePeterman(2012),Shein(2012),andSchliesser(2014).



adequateknowledgeofnature,weshouldatleastbeextremelywaryofinterpretingitsreportsasknowledgeof“Nature,asitisinitself”.

Thediscussionofabstractionheremustbeanabridgedone,butin short, Spinoza consistently holds up abstractions as villains ofepistemology.All thatexists,Spinozawrites, areparticulars, and soall true knowledge is knowledge of particulars; abstracta aremereentia rationis(orworse—entia imaginationis)thattellusnothingaboutthenatureofthingsconsideredinthemselves(EIVp,GII208/C545).Theiruseintryingtounderstandrealbeingsleadsusinto“absurdities”and“interfereswiththetrueprogressof the intellect(TIE75,93,99,GI28,34,36/C33,39,41).Now,thereissomedebateaboutwhetherSpinoza thinks that there are any adequate abstract ideas,39 and ifany abstract ideas were adequate, our idea of Extension would beoneofthem,asacommonnotion(EIIp43,GII127/C481).Butinthecontexts involving spatial extension that we are considering, it isclearthatSpinozaunderstandsabstractiontoinvolveinadequacyandconfusion.Moreover,abstraction,accordingtoSpinoza,isafunctionoftheimagination,wherebyitidentifiesapropertyofthingswhichitthenusestotrytounderstandmultiplethingsatonce,whichmaybeinotherrespectsquiteunlikeoneanother.Thismaysimplifynaturesothatitisgraspableinsomerespectsbyourfiniteminds,butbysmearingoutthedetailsoftheessencesofparticularthings.Thegeometrizationof bodieswould seem tobe theultimate abstraction, since it treatsphysicalobjectsintermsofoneuniversalproperty:theirextension.SoitisnotsurprisingthatSpinozaconsidersthekindofquantityinvolvedinthatgeometrizationaconceptionoftheimagination.

In the “Letteron the Infinite”, Spinozadoesnot suggest that theconfusion, inadequacy or “superficiality” that imagination andabstraction involved in conceiving things in terms of quantity2 ismitigated when modes are conceived in these terms. Recall thatSpinozaarguesthatwecandeterminemeasureandtimeonlywhenwe

39.ForadefenseofsomekindsofabstractiononSpinoza’sbehalf,seeHübnerforthcoming. For another recent discussionof Spinozaon abstract objects,seeNewlands.

commentsforthequestionofwhethermodesareextendedinspace,we have to discuss, as briefly as possible, Spinoza’s view of theimaginationandofabstraction.

TheonlyoneofSpinoza’sthreekindsofcognitionthatadmitsofinadequacyisthefirstkind—whatSpinozacallsimagination,orthekindof cognition that “present[s] externalbodiesaspresent tous”byrepresentingtheaffectionsofthebody(EIIp45,GII106/C465).Spinozaassociatestheimaginationwithinadequateconceptionfortworeasons.First,accordingtoSpinoza,knowledgeofnature“asitisinitself”andnot“asitisrelatedtohumansenseperception”(Ep.6, G IV 28, C 181) should be grounded in knowledge of essencesandoftherealpropertiesandeffectsofthingsthatfollowfromtheiressences (e. g., TIE 91). Imagination cannot give us knowledge ofessences,butonlyabouttheeffectsofthingsonourbodies(e. g.,TIE9, 13).Mistaking theone for theother isaprimarysourceoferror,according to Spinoza. Second, evenwerewe correctly to interpretthedataoftheimaginationasinformationabouttheeffectsofthingsonourbodies,wecouldnotdeducetheirrealpropertiestherefromwithout having complete knowledge of thewhole of nature. Thatis becausewhile the properties and behaviors of a thing taken inisolation flow from its essence, when it is instantiated in natureand infinitely subject to external causes, its actual properties andbehaviorswouldtellusaboutitsessenceonlyif—per impossibile—weknewhowitinteractedwiththerestofnature.36

Now, Spinoza never says that imagination only furnishesinadequateideas,onlythatitisthe“onlycauseoffalsity”.37Buttheseconsiderations of the nature of the imagination suggest that it isimpossibleforittogiveusadequateknowledgeofphysicalthings—oftheiressencesandtherealpropertiesthatfollowtherefrom.38Butevenifweallowthattheimaginationcansometimesyield(moreor less)

36.SeeEp.6(GIV34–36/S76)forSpinoza’scritiqueofBoyle’sexperimentsonthisbasis,andEp.32(GIV170–172/S192)onthewormintheblood.

37. EIIp41,GII122/C478.

38.Forfurtherargumentstothiseffect,seePeterman2014.



Whenwehaveregardonlytotheessenceofmodesandnot toNature’sorder,as ismostoften thecase,wecanarbitrarily delimit the existence andduration ofmodeswithouthurtingourconceptionofthem,andconceiveitasgreaterorless,ordivisibleintoparts.

Thereisawayofreadingthispassagethatdoesnotentailthatmodesareproperlyunderstoodasdivisible.Spinozahasjustfinishedexplainingthatthemostimportantdifferencebetweensubstanceandmodesisthattheessenceofasubstancecannotbeconceivedwithoutexistence,whiletheessenceandtheexistenceofmodesarecompletelydistinctfrom one another. Sowe can read this quote tomean thatwe canthinkoftheexistencesofmodesanywaywewantwithout“hurtingour conception”of their essences.We can thinkof the existenceofmodesthatwaynotbecauseit’stherightwaytothinkaboutthem,butbecause it simplydoesnotmatter, for theiressences,whatspaceortimetheytakeup.Incontrast,ifwethinkoftheexistenceofsubstancethisway,wemissanimportantelementofitsessence.Again,itisnotthattherightwayofconceivingofmodesisasenduringanddivisible,butonly that,unlike in the caseof substance,wedonodamage toourconceptionoftheiressencesbydoingso,sincetheiressencesandexistencesarecompletelyindependentofoneanother.

The arguments above do not show that bodies are not “really”extendedinspace.IthinkthatthereisaninterpretationofSpinozaonwhichmodes,oncetheyareinstantiated,areextendedanddivisible in some sense.Allthattheargumentshereestablishisthatwhentheyareunderstoodthroughtheiressences,“inthemselves”,or(tospeakanachronistically)intermsoftheirmostfundamentalproperties,theyareextendedanddivisible.Thisdoesnotnecessarily reducespatialextension toa “mereappearance”. Spinoza sometimesdistinguishestwowaysofthinkingaboutmodes:astheyflowfromsubstanceandastheyaresituatedinthe“orderandconnectionofthings”.Forexample,speakingabouttheexistenceofsingularbodies,Spinozawrites:

“conceiveQuantityabstractedfromSubstanceandseparateDurationfromthewayitflowsfrometernalthings”,andonlywhen“weseparatetheAffections of Substance from Substance itself and reduce themto classes so that as far as possiblewe imagine them easily, arisesNumber, by which we determine [these affections of substance]”.Thus, concludesSpinoza, “Measure,Time, andNumberarenothingbutModesof thinking,or rather,of imagining”.Hegoeson tonotethat“itisnowonderthatallthosewhohavestriventounderstandthecourseofNaturebysuchNotions—whichinadditionhavebeenbadlyunderstood—havesomarvelouslyentangledthemselves that in theendtheyhavenotbeenabletountanglethemselveswithoutbreakingthrougheverythingandadmittingeventhemostabsurdabsurdities”.Spinozagoesontosaythatthemodesofsubstancethemselvesshouldnot be confused with these aids to the imagination—that is, asportions of quantity or duration determined bymeasure, time, andnumber.Hewrites:

AndiftheModesofSubstancethemselvesareconfusedwith Beings of reason of this kind, or aids of theimagination, they too can never be rightly understood.Forwhenwedothis,weseparatethemfromSubstance,andfromthewaytheyflowfrometernity,withoutwhich,however,theycannotberightlyunderstood(Letter12toMeyer,GIV54/S101).

ThisisnottheonlyplacethatSpinozastressesthatfailingtoconsiderhowfinitethingsrelatetosubstanceleadstoerror—seethequote,citedearlier,thatseesthe“absurdities”ofDescartesphysicsasoriginatingin this failure. It suggests—and this is consistent with the rest ofthe language of the letter—that the inadequacy that accompaniesconceivingthingsintermsofquantity2isnotrestrictedtosubstance.

40 Letusreturntothequote,citedearlier, thatmakesitsoundasif

Spinozaassociatesmeasurable,divisiblequantity1withmodes:

40.ForanalternativereadingofLetter12,seeSchliesser2014.



while the absence of a characterization of Extensionmight suggestthatSpinozaissimplyadoptingtheDescartes’understandingofit,wemight justaswellwonderwhySpinozaomits itwhenhepointedlyincludes it, onDescartes’ behalf, in his reconstruction of Cartesianphysics.There,SpinozaincludesastheveryfirstdefinitionofPartIIthat“Extensioniswhatconsistsofthreedimensions;butbyextensionwedonotunderstandtheactofextending,oranythingdistinctfromquantity”.ThislastclauseisSpinoza’sownclarification,suggestingthatSpinozawishestostressthatDescartesSimilarly,heclearlyarticulatesDescartes’identificationofmatterandspace:Definition6goesontoestablish that “wemakeonlyadistinctionof reasonbetweenspaceandextension”,andProposition2that“ThenatureofBody,orMatter,consistsinextensionalone…Spaceandbodydonotreallydiffer”.Andthevery lastpropositionofPart I is: “Substanceextended in length,breadth,anddepthreallyexists;andweareunitedtoonepartof it”(PPCIp21,GI179/C261).Incontrast,nodefinitionofExtension,noranyidentificationofspaceandbody,norindeedanymentionof“space”or“dimension”atallcanbefoundinSpinoza’sindependentwork.

Further, one of Descartes’ primary motivations in identifyingspatial extension as the primary attribute of bodies is surely hisproject to make physics tractable for mathematics. For Descartes,the bestway to do this is to render the object of physics the pureobjectofgeometry.Ifwearetohaveknowledgeofthepropertiesandknowledgeofbodiesapriori,theymustbegeometricalbeings–thatis,reallyextendedandnothingelse.Descartesdoesnotmerelythinkthatmathematicsisthelanguageofthephysicalworld;hebelievesthat physics is nothing but geometry. In a letter to Clerselier, hewritesthat“mathematicalextensionistheprincipleofphysics”,andinPrincipiaII,64:“Idonotadmitordesireanyotherprinciplesinphysicsthaningeometryorabstractmathematics,sinceallthephenomenaofnatureareexplainedthereby.”

As§3bbegantosuggest,SpinozadoesnotfollowDescartesinthis.WhileDescartesoffersverysimilarcritiquesofabstraction,heultimatelyexceptsthegeometricalpropertiesofbodiesfromthatcritiqueonthe

By existence here I do not understand duration, i. e.,existence insofar as it is conceived abstractly, and as acertainspeciesofquantity.ForIamspeakingoftheverynatureofexistence,whichisattributedtosingularthingsbecause infinite many things follow from the eternalnecessityofGod’snaturein infinitelymanymodes(seeIp16).Iamspeaking,Isay,oftheveryexistenceofsingularthingsinsofarastheyareinGod(EIp45,GII148/C423).

There isno indicationhere thatduration “insofar as it is conceivedabstractly, and as a certain species of quantity” is not real, andelsewhereSpinozawrites thatenduring in timeandspace isakindof actuality (EVp29s, G I 298/C 609). But it is clearly suggestedthat it is derivative, and thatwe donot understand things throughtheiressenceswhenweunderstand them in these terms.WemightconceiveofspatialextensiononthemodelofdurationthatSpinozaprovideshere.ThereisplentyinSpinozathatsuggeststhatbodiesandtheirbehaviorsasweexperiencethemaretheresultofaninfinityofinstantiatedmodalessences,andthattheresultofthisiswhatSpinozathinksofastheseries,ororder,ofnature.Buthetreatsthisorder,andtheknowledgeofit,asderivativefromthemorefundamentalmodalessences as they flow fromGod, understoodunder the attribute ofExtension.Thereismuchmoretobesaidaboutthis,butthereisnotthespacetoaddressithere.Whatisimportantisthatspatialextensionis not the fundamental attribute underwhichbodies and corporealsubstanceareconceived—itisnot,thatis,Extension.

§3cOnmyreadingofit,Spinozaisusingtheword“extension”inaverynonstandard way. Following Descartes, and even having written areconstruction of Cartesian physics, why use this word in such amisleadingway,withoutmakingitclearthatheisredefiningit?41But

41. IamgratefultoMartinLinforpressingthisobjectiontome.



highestgenus,whichhasnogenusaboveit”.Hegoesontoconcludethattheattributesinparticularare“knownthroughthemselves”andthat“weseethatotherthingsareonlymodesofthoseattribute,andwithoutthemcanneitherexistnorbeunderstood”.43Wecantakethistomeanthatknowledgeof thenatureofextensionandmotionwillnot, forSpinoza,beacharacterizationof themlikeDescartes’claimthatExtensionisthree-dimensionality,orthatmotionisdisplacementfromaneighborhood.ButasSpinozaclaimsintheShort Treatise,thisdoesnotmeanthatwecannotknowthematall.Wecanknowtheminsteadbythethirdandhighestkindofknowledge,which,accordingto the Short Treatise (II xxii), is an “immediate manifestation of anobjecttotheintellect”or“anawarenessandenjoymentofthethingitself”whichdoesnotcomefrombeingconvincedbyreasons.44

Passageslikethis indicatethataccordingtoSpinoza,anattributecannot be characterized in terms ofmore basic concepts. Consider43. InalettertoPrincessElizabeth(21May1643),Descartesalsoidentifiesexten-

sionastheprimitivenotionthatpertainstobody,justasthoughtisaprimi-tivenotion.Hewrites that “wegowrong ifwe try toexplainoneof thesenotionsbyanother,forsincetheyareprimitivenotions,eachofthemcanbeunderstoodonlythroughitself(AT665–666,CSMKIII218).

44. Thereisfurtherevidenceforthisreadingofourknowledgeoftheattributes,basedontheanalysisofthecommonnotions.Butthereisnotthespacetodiscussitindetailhere.

Descartesalsoidentifiesthe(primary)attributesofExtensionandThoughtashighestgenera,andwarnsagainstaskingfortheproximategenus,puttingthefollowingwordsinthemouthofhisspokesman,Eudoxus:“…wemustknowwhatdoubt is,what thought is,what existence is,beforebeing con-vincedofthetruthofthisinference,‘Iamdoubting,thereforeIexist’,orwhatamountstothesamething,‘Iamthinking,thereforeIexist.’Butdonotimag-inethatinordertoknowwhattheseare,wehavetorackourbrainstryingtofindthe‘proximategenus’andthe‘essentialdifferentia’whichgotomakeuptheirtruedefinition.Wecanleavethattosomeonewhowantstobeaprofes-sorortodebateintheSchools.…[T]hereare,inmyview,somethingswhicharemademoreobscurebyourattemptstodefinethem:sincetheyareverysimpleandclear,theyareperceivedandknownjustontheirown,andthereis nobetterwayof knowing andperceiving them” (CSM417,ATVII 523).Descartesisrespondingheretoobjections,raisedbytheauthorsoftheSixthSetofObjections,thatthecogitoargumentisunsoundonthegroundsthatwecannotknowwhetheranymindexistswithoutfirstknowingwhatthinkingis(CSM278/ATVII412).IamgratefultoAnatSchechtmanforpointingmetothispassage.

basisthatwehaveaclearanddistinctperceptionofextensionastheessenceofbodies(see,e. g.,LettertoGibieuf,CSMKIII202).42ThereissimplynoindicationthatSpinozamakesanysuchexception.

Spinoza is retaining an important aspect of Descartes’ usage of‘Extension’—namely,thatitidentifiesthe(principal)attributeofbodies.Butheunderstandsthemeaningofthetermdifferently.PerhapswemightimagineSpinozatobeusingtheword‘Extension’thewaythatone might use ‘material’ (or ‘materialism’) instead of ‘physical’ (or‘physicalism’), the formerbeingwell-entrenched,evenafter learningfromthephysiciststhatthephysicalincludesmorethanjustmatter.

§4 Conclusion

IfSpinozadoesnotmean“spatialextension”whenhewrites‘Extension’,thenwhatdoeshemean?IarguedinthelastsectionthatweshouldnottakeSpinoza’sreluctancetodefineExtensionasalicensetoassumethathemeantwhatDescartesmeantbyit.Inconclusion,I’lloffersomereasonswhyweshouldnotexpectSpinozatodefineitatall.

Extension,likeThought,isanattribute,whichtheEthicsdefinesas“whattheintellectperceivesofasubstance,asconstitutingitsessence”(EId4,G II 45/C 408). But in an early letter toOldenburg, Spinozadefines anattribute as “whatever is conceived through itself and initself,sothatitsconceptdoesnotinvolvetheconceptofanotherthing”(Ep.2toOldenburg,GIV7/C165).There,GodalreadyisdefinedasaBeingconsistingof infiniteattributes.Spinozagoeson toofferanexample:“Forexample,Extensionisconceivedthroughitselfandinitself,butmotionisnot.”

Whatdoes itmeanthatanattributemustbe“conceived throughitself”?ThereisasuggestionofatleastoneoftheimplicationsofthisphraseintheShort Treatise.There,Spinozaisobjectingtoaclaimthatanylegitimatedefinitionmustbegivenbygenusanddifference.ButSpinozaobjects that if this is true, thenone canknownothing.Hereasons that if this is true, “then we can never know perfectly the

42. FormoreonSpinoza’scritiqueofappliedmathematics, seePeterman2012andSchliesser2014.



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tryingtoaskafterthenatureordefinitionofanotherattribute:Thought.Perhaps it is clearer in this case that an answer is not forthcoming,andthat “Thought” is justabasickindof thing.Thisdoesnot itselfmeanthattheattributeofExtensionisnotspatialextension;itmaybethat thebasickindof thing issomethingwithspatialcharacteristics,and that its “immediate manifestation … to the intellect” is themanifestationofsomethingwiththosecharacteristics.Butifitisnot,and “Extension”means somethingelse,we shouldnotbe surprisedifitcannotbedefinedinanymorebasicterms.Ifthat’sright,thentotalkabout“Extended”natureisjusttotalkaboutmaterialorphysicalnature, andby Extended things Spinoza justmeans something likematerialorphysicalthings.

Ofcourse,todiscovertheimplicationsofthisforSpinoza’sphysicsisamuchmorecomplicatedproject;thisisjusttogesturetowardananswertoaquestionthattheearliersectionsofthispaperarelikelytoraise.ThereislotsofinterestingworktobedoneinfiguringoutthedetailsofSpinoza’saccountofthephysical(andalso,verylikely,thepreciseextent towhichhewasnotable towork themout).Here, IhopeonlytohaveofferedsomereasonstothinkthatSpinoza’scritiqueofCartesianphysicsstartsmuchdeeperthanmostinterpretershavethought:intheveryunderstandingofthephysicalitself,asfirstandforemostpossessingthepropertyofbeingextendedinspace.

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