Found Sci (2013) 18:419448DOI 10.1007/s10699-011-9278-zNewtons Neo-Platonic Ontology of SpaceEdward SlowikPublished online: 8 July 2012 Springer Science+Business Media B.V. 2011Abstract ThispaperinvestigatesNewtonsontologyofspaceinordertodetermineitscommitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basisfor space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newtons theory has been famously championed by HowardStein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuirehave downplayed the inuence of Cambridge neo-Platonism on various aspects of Newtonsown spatial hypotheses. Both of these assertions will be shown to be problematic on variousgrounds, with special emphasis placed on Steins inuential case for a non-substantivalistreading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspectsof Newtons approach, most notably, his critical assessment of substance ontologies, that helpto distinguish his theory of space from his neo-Platonic contemporaries and predecessors.Keywords Newton Space Neo-Platonism SubstantivalismAmidthescholarlydebatesurroundingNewtonsnaturalphilosophy,twoseeminglyele-mentaryaspectsofhistheoryofspacehavebeen,hitherto,seldomquestioned:rst,thatNewton reckons space to be a form of independently existing substance or entity, a thesisoften dubbed substantivalism; and second, that Newtons view was deeply inuenced byhis seventeenth century neo-Platonic predecessors, especially Henry More, whose ontologyultimatelygroundstheexistenceofspaceuponanincorporealbeing, i.e., GodorWorldSpirit. A number of important investigations have begun to challenge even these ostensiblysafe assumptions concerning Newtons philosophy, however. Among these notable reapprais-als is the work of Stein (e.g., 1967, 2002) and DiSalle (e.g., 2002, 2006), who conclude thatthe content and function of Newtons concept of absolute space should be kept separatefromthequestionofNewtonscommitmenttosubstantivalism. Stein(2002)furthercon-tends, more controversially, that Newton does not sanction substantivalism apropos space. Arelated, albeit much more nuanced, interpretation that parts fromthe traditional substantivalistE. Slowik (B)Winona State University, Winona, MN, USAe-mail: ESlowik@winona.edu1 3420 E. Slowikreading may also be evident in an inuential early article by McGuire (1978a), who arguesthat space for Newton is the general condition required for the existence of any individualsubstance (1978a, 15).1Turning to the second of our traditional assumptions regard-ing Newtons spatial theory, Stein (2002, 269) rejects any significant neo-Platonic content;whereas McGuire had earlier conjectured that, though Platonic in character, the primaryinuence on Newtons ontology is Descartes Meditations, rather than the eclecticism ofRenaissanceNeo-Platonism, ofwhichwendlittleevidenceinDegravitatione(1983,152).2This essaywill examinetheontologyof Newtons spatial theoryinorder todeter-mine the adequacy of these non-substantivalist, anti-Platonist interpretations. While Sect. 1will introduce the main non-substantivalist strategies, Sects. 24 will be devoted toa lengthy critical examination of the strongest formof non-substantivalist interpreta-tion, in particular, the arguments offered in Stein (2002) that drawupon Newtonsearly unpublished tract, De gravitatione. As will be demonstrated, Newtons spatialtheory is not only deeply imbued in neo-Platonic speculation, contra the revisionisttrend, but theseneo-Platonicelementslikewisecompromiseanystrongnon-substantiv-alist interpretation. Throughout ourinvestigation, however, thespecicdetailsandsub-tletiesofNewtonsparticularbrandofneo-Platonismwill becontrastedwiththeontol-ogies of his contemporaries and predecessors, and by this means a more adequategraspof the innovations andforeword-lookingaspects of his theoryof space canbeobtained.1Substantivalism is itself a complex subject, with various explanations spotlighting different aspects of theconcept: e.g., Sklar (1974, 161), whose famous contribution focuses more on its status as an independentlyexisting entity, whereas Earman (1989, 1214) places greater emphasis on the topology of spacetime points. Adetailed exploration is beyond the bounds of this essay, but we will largely side with Sklars approach, mainlydue to the fact that spatial points/parts are not the central issue as to the neo-Platonic basis of Newtons spatialontology. Indeed, as will be demonstrated, the possible independent existence of space per se (and not just itspoints/parts) is the key feature as regards neo-Platonism. Moreover, since a substantivalist, or any other theoryof space approaching substantivalism, must address the question concerning howthe spatial points/parts relateto the whole of space, this issue is not the best means of determining a commitment to substantivalism (sincethereisnoclearprecedent,aswillbearguedinthecaseofNewton).However,ifforcedtogiveaquicksynopsis,then,followingSklarsdefinition,Newtonsspaceisnotsubstantivalist,sincespacenecessarilydepends on God; but it is substantivalist if independence only means independent of matter. The essaywill also argue that, while strong non-substantivalism fails (since Newtons space is deeply metaphysical andtheological in orientation), weak substantivalism is nonetheless a consistent interpretation (although difcultto corroborate). See, also, footnotes 4, 8, 9.2The ensuing analysis will attempt to demonstrate that Cambridge neo-Platonism and the (quite similar)Gassendi-Charleton philosophy is the primary inuence on Newtons ontology of space. McGuire comments,furthermore, on the question of [the Cambridge neo-Platonist] Henry Mores inuence on Newtons doctrineof extended space, concluding that it is minimal in the period from 1664 to 1668 (1983, 152; where thefour year span, 16641668, covers the then accepted period for the composition of Newtons major treatiseon the ontology of space, the De gravitationesee footnote 17 on the recent dating of this work). In con-trast, McGuire later concedes that a possible inuence on Newtons concept of emanation (see Sect. 2) isHenry More (1990, 105); and, in his most recent work (2000, 2007), he successfully pursues a number ofneo-Platonic threads in Newtons natural philosophy. Nevertheless, these post-1990 reappraisals fall short ofretracting McGuires earlier demotion of the Cambridge neo-Platonist inuence, and thus the justied author-ity of McGuires pre-1990 work is likely to give a misleading impression of his evolving conception of theseissues (if examined in isolation from the later output). In private discussion, McGuire has indeed conrmedthis potential mischaracterization of his overall Newton scholarship, adding that the newer dating of the Degravitationeprovided a crucialstimulustotheevolutionof hisviews.Finally,unlessotherwisenoted,allitalics in citations are from the original, and all references to neo-Platonism refer to the seventeenth centuryvarieties then popular in England.1 3Newtons Neo-Platonic Ontology of Space 4211 Two Non-Substantivalist Conceptions of Newtons Absolute SpaceBefore launching into an investigation of the specic details of their arguments, it would behelpful at this point to delineate the general strategies employed by the principle proponentsof a non-substantivalist interpretation.The rst claim is that, apart from his metaphysics, Newtons concepts of absolute spaceand time in the Principia (1999, 408415) are best regarded as definitions, or mathematicalconcepts or structures, required for the successful application of his physics, namely, for thethree laws of motion and the theory of gravity (and including the mathematical apparatus asso-ciated with these hypotheses). That is, Newton may have engaged in the sort of ontologicalspeculation on the nature of space common among seventeenth century natural philosophers,but the really important aspect of his overall theory is the realization that a spatio-temporalconcept belongs in physics just in case it is dened by physical laws that explain howit is to beapplied, and how the associated quantity is to be measured (DiSalle 2002, 51). A thoroughaccount of these definitional structures is beyond the scope of this essay, but they can be brieydiscussed: Newton erred in positing absolute space (spatial position) and absolute velocity,but he was correct as regards absolute time and absolute acceleration (and, hence, rotation).3We can label this strategy the weak non-substantivalist interpretation of Newtons physics,for it allows other approaches to his natural philosophy that take into account the metaphysi-cal disputes common in that era.4The weak reading gains credibility in the rst edition of thePrincipia (1687), which contains little, if any, metaphysics. Substance and God barelyappear in the rst edition of the Principiayet, later editions of the Principia (the GeneralScholium of the second edition, 1713), the later Queries to The Opticks, and various non-publishedwritings(tobediscussedbelow)doindeedpickuptheseontological themes,3That is, unlike the relationists (Descartes, Huygens, Leibniz, etc.), Newton understood that the motions andinteractions of material bodies could not be adequately treated by recourse to their relative motions alone(e.g., the famous bucket experiment in the Principia; 1999, 408415). Absolute spatial position and abso-lute velocity, however, would eventually be seen as overly rigid and unnecessary structures for an adequatetreatment of acceleration within the context of Newtonian physics. As DiSalle comments, a four-dimensionalspacetime structure equipped with an afne connection would have sufced for Newtons purposes (2002,35).4In reecting on the question, What concepts of time, space, and motion [in Newtons Principia] are requiredby a dynamical theory of motion?, DiSalle offers what is possibly his most forthright endorsement of theweak non-substantivalist line: Asking this question about Newtons theory does not deny its connection withhis profound metaphysical convictionsnot only about space and time, but about God and his relationshipto the natural world. On the contrary, it illuminates the nature of those convictions and their relationship toNewtons physics. For Newton, God and physical things alike were located in space and time. But space andtimealsoformedaframeworkwithinwhichthingsactononeanother,andtheircausalrelationsbecomeintelligible through their spatio-temporal relationsabove all, through their effects on each others state ofmotion. (2002, 38; emphasis added). While acknowledging Newtons profound metaphysical convictions,which include space, time, and God and his relationship to the natural world, DiSalle adds that space andtime also formed a framework for understanding the causal relationships among bodies. The implication ofthis assessment, arguably, is that the content or role of space and time for Newton may not be exhausted by theirconstructive function in his physics. The fact that DiSalle does not seriously engage the details of Newtonsmetaphysics in order to counter the traditional substantivalist line thus lends support for this weak readingalthough he does come close at times: Newton was not a substantivalist, at least not in the now-standard useof the term (emphasis added), since Newton was critical of substance ontologies, and he did not regard theparts of space as possessing an intrinsic individuality, whereas the modern substantivalist (often) does viewspacetime points as irreducibly basic existents (2006, 37; see, Sects. 3 and 4, and footnotes 1, 8, and 9, forrelated discussions). Once again, this appraisal leaves open the possibility that other notions of substance, notin the now-standard use of the term, might apply in Newtons case. The weak non-substantivalist reading ofDiSalle has been conrmed in private communication, moreover (2009). Incidentally, one of the rst mod-ern cases made for a weak non-substantivalist interpretation of Newton is Toulmin (1959), although Steinslandmark (1967, 277282) is better known (and also hints towards a strong non-substantivalist reading).1 3422 E. SlowikthustryingtoinferNewtonsoverallcommitmenttotheweakthesisremainsdifculttogauge.While the weak non-substantivalist interpretation will not be examined in depth in thisessay, one of the most meticulous investigations of Newtons concepts of space and motion,namely, Rynasiewicz (1995), would seem to be consistent with it. Stein (2002), on the otherhand, apparently sanctions a much stronger position, namely, that Newtons metaphysicaldeliberationsdonot, infact, advocateaformofsubstantivalismcall thisthestrongnon-substantivalist interpretation. Whereas the weak thesis is largely conned to Newtonshandling of the concepts of space, time, velocity, etc., as they appear in his physics, throughstressing their constructive and foundational role in setting up his physics, the strong thesisactuallyengagesNewtonsmetaphysicalwritingsinanattempttocountertheprevailingconsensus that Newton endorsed substantivalism. Stein claims that Newtons metaphys-icsofspaceisthat spaceis(somekindof)effect oftheexistenceofanything, andtherefore of the rst-existing thing (2002, 268). In essence, Stein interprets Newtons meta-physics as sanctioning a conception of space that does not t either substantivalism or itschief rival, relationism, which holds that space is merely the relations among physical ex-istentsindeed, theviewthat SteinattributestoNewtonisverymuchlikeSteinsownmetaphysical interpretation of space (spacetime), as a passage from an earlier essay makesclear: Stein claims that spacetime structures are an emanative effect of the existence ofanything (Stein 1977, 397), where the phrase in quotation marks, emanative effect, is anobvious allusion to Newtons spatial hypotheses (as will be explained below). If space isconceived as an effect of the existence of anything, as Stein regards both Newtons andhis own theory, then it is quite difcult to pin an ontology to this thesis, let alone a com-mitment to substantivalism. That is, space is not an independently existing substance/entitybecauseitdepends(insomemanner)ontheexistenceofanything,presumably,physi-cal bodies or elds, thus violating the independence clause for substances. But, neither isit a mere relation, since the domain (as the set of possible values) of the spatial relationsinagivenuniverseatanyinstantisnotlimitedtotheactualspatialrelationsamongthematerial existents at that instant, as it is under a strict relationism.5In short, Steins non-ontological interpretation of Newton,6like his own hypothesis of space, would seem to favora third-way (tertium quid) between the prevailing substantivalist and relationist ontolo-gies.75While a strict relationist connes space to the actual relations among existing objects, weaker forms of rela-tionism dene space as the actual and possible relations among existing objects. Yet, even on the these weakerforms, certain meaningful physical states-of-affairs would seem to be ruled out, such as a lone rotating body inan otherwise empty universe (because there is nothing relative to which it could rotate). These considerationsthus render even the weaker forms of relationismunacceptable for Newtons spatial theory (unless the possiblerelations include a bodys relations to earlier states of itself).6Throughout this essay, the term non-ontological as applied to Stein (2002) denotes a non-causal, non-being, and hence anti-neo-Platonic reading of Newtons spatial theory; a reading that is motivated more bymodern epistemology and the philosophy of science/physics than Early Modern metaphysics, since the causal,being, and neo-Platonic aspects of Newtons theory are systematically downgraded or rejected altogether fora sort of structuralist conception of space. See, also, footnotes 9 and 18.7Steins rejection of the traditional substantivalist and relationist ontologies is a leading theme throughout hiswork (e.g., 1967, 1977), although a thorough discussion is not relevant to our investigation. Further aspectsof Steins interpretation are critically examined in Slowik (2007), including a more detailed investigation ofthe substance/accident dichotomy in Newton, and the third-way notion of space.1 3Newtons Neo-Platonic Ontology of Space 4232 Newton and Strong Non-Substantivalism: Making the CaseInitially, thestrongnon-substantivalistanalysisofNewtonsspatialconceptslooksquitepromising. In the unpublished tract, De gravitatione, which most likely predates the Prin-cipia, Newton insists that space has its own manner of existing which is proper to it andwhich ts neither substance nor accident [i.e., property] (Newton 2004, 21). Space is not asubstance because it cannot act upon things, yet everyone tacitly understands this of sub-stance (21), nor is it an accident, since we can clearly conceive extension existing withoutanysubject,aswhenweimaginespacesoutsidetheworldorplacesemptyofanybodywhatsoever, (22). The substance/accident doctrine holds that all existents come in oneof two exclusive types: either self-dependent substances, or the properties that can only existwithin, or inhere in, a substance (see, e.g., Bolton 1998, 179). In contrast, Newton consis-tently refers to space as an affection (affectio) or attribute (attributa), which may signifyhis attempt to employ neutral terms without substance/accident overtones:8Space is an affection of a being just as a being (Spatium est entis quatenus ens affec-tio). No being exists or can exist which is not related to space in some way. God iseverywhere, created minds are somewhere, and body is in the space that it occupies;and whatever is neither everywhere nor anywhere does not exist. And hence it followsthat space is an emanative effect (effectus emanativus) of the rst existing being, for ifany being whatsoever is posited, space is posited. (25)Much of the ensuing investigation will attempt to unravel the complexities of this fairlyenigmatic passage.2.1Space as a Necessary Consequence or ResultBasedlargelyontheevidenceintheabovequote,SteincontendsthatNewtondoesnotderive his Idea of spaceits ontological status includedfrom his theology (as has oftenbeen claimed); for he tells us that if anything is posited, space is posited (Stein 2002, 268).Since God is the rst existing thing, space (in some sense) results from the existence ofGod (268), but this does not detract from Newtons general hypothesis that space (in somesense) results from the existence of anything (268). He adds:But this sense of the wordsimply a necessary consequence, with no connotation ofcausal efcacy or actionexactly ts the rest of what Newton says; indeed, thismeaning might have been inferred directly from Newtons words: [S]pace is an ema-native effect of the rst-existing being, for if I posit any being whatever I posit space:the second clause tells us precisely what the rst clause means. (269)8Newtons understanding of substance presumably draws from the wide variety of substance concepts preva-lent in the seventeenth century. For instance, some portions of his concept reect, say, the Cartesian line thatit is an entity that can exist independently of all other beings (except God, of course), but other elements ofhis concept introduce more novel ideas, such as the ability to act upon things. Overall, Newtons substanceconcept is difcult to accurately x relative to his contemporaries and predecessors, largely because he seldomprovides any details when employing this term. The same is true (in fact, more so) for his employment ofaffection and attribute, which seem to denote a property that is necessary for a beings existence, whereasan accident (such as red, triangular, etc.) is not. Newton refers to space as an attribute/affection of all being,while denying that it is an accident, thus demonstrating (apparently) its necessity for all being (more on thisbelow). See, once again, Bolton (1998), for these metaphysical categories, as well as Carriero (1990), for moreon Newtons use of affection.1 3424 E. SlowikSteins attempt to attribute a strong non-substantivalist conception of space to Newtonstands out rather clearly in this passage; for, stripped of its ontological connotations, spaceas an emanative effect becomes simply space as a necessary consequence or result of theexistence of anythingand, of course, it is just this type of non-ontological notion of spacethat Steins theory counsels, i.e., space as a non-causally generated fact, with little or noontological associations.9Howplausible are Steins arguments for the strong non-substantivalist thesis? While someoftheobjectionswill havetoawait thefollowingsections, whereintheontologyoftheCambridge neo-Platonists will be discussed in greater detail, there are a few difculties thatcan be raised directly. Above all, Newton never explicitly states that space is a necessary con-sequence or result, which is a description that, as noted above, seemingly equates space witha form of logical or conceptual fact, as opposed to an ontological, causal feature of existingbeings.10Presumably Newton would have emphasized this non-ontological notion of spacein a more lucid manner, since his application of the relevant terms, especially emanativeeffect, often parallels the decidedly ontological meaning given to these very same terms inearlier neo-Platonist tomes.Moreover,otherpassageswouldseemtosupportthetraditionalontologicalpictureofNewtons spatial theory. After dismissing a substance/accident ontology, Newton nonethe-less adds: much less may [space] be said to be nothing, since it is something more than anaccident, and approaches more nearly to the nature (naturam) of substance (Newton 2004,22). If Newtons concept of space, as Stein contends, is not ontological, then one would notexpect Newton to declare that spaces nature is closer to a substance than an accident. Putdifferently, if space is a non-ontological, necessary consequence of a beings existence, itwould seem to follow that Newton should reject any application of the substance/accidentdichotomy to spaceone would not expect, once more, that he would try to place the conceptsomewhere between these ontological positions.119There are also hints of a third-way structuralist rendering of space in Steins analysis of Newton. In the Degravitatione, it is claimed that the parts of space are individuated by their positions, so that if any two couldchange their positions, they would change their individuality at the same time and each would be convertednumerically into the other (Newton 2004, 25; see, also, the Scholium on space in time in the Principia, whichroughly makes the same argument, Newton 2004, 66). As regards this quotation, Stein reasons: This canbe taken, in rather modern terms, as saying that space is a structure, or relational system, which can beconceived of independently of anything else; its constituents are individuated just be their relations to oneanother, as elements of this relational system (Stein 2002, 272). A relational system [of the parts of space],as dened by Stein, is not to be confused with relationism, however. See, Slowik (2007), for more on thisissue.10In a later writing, Newton does refer to innite space and time as modes of existence in all beings, &unbounded modes &consequences of the existence of a substance that which is really necessary &substantiallyOmnipresent & Eternal (Koyr and Cohen 1962, 9697; see, also, Sect. 4.1). The use of the term conse-quences, in this passage, might be taken to support the non-ontological interpretation of Newtons conceptof spaceyet, it is used in conjunction with the basic ontological term, modes, which denotes the specicway in which a being manifests a general property (e.g., circular is a mode of shape). Consequently, it isnot clear whether this passage actually assists or harms the non-substantivalist cause.11This counter-argument is not conclusive, of course, since Newton may be merely relying on known onto-logical categories to describe a unique position. Stein, on the other hand, reads Newtons quote (that spaceis closer to substance) as pertaining to the rejection of an accident ontology: namely, in that [space] needsno subject to support its existence (2002, 267). Presumably, subject and support are used here tosignify an accidents inherence (support) in a substance or being (subject), for, if these terms refer generallyto any subject, then it would directly contradict Steins (later) claim that space results from the existenceofanything(268;whichnecessitatesasubject,ofcourse).Thisthesis,thatspaceneedsnosubjecttosupport its existence, thereby complements his non-ontological reading of emanative effect. Yet, as will bedemonstrated below, incorporeal spirit (God, or a world soul) is the subject required for Newtons space.1 3Newtons Neo-Platonic Ontology of Space 425On the whole, the best evidence for Steins interpretation appears in the quotation exam-ined at length above, where Newton claims that space is an emanative effect of the rstexisting being, for if any being whatsoever is posited, space is posited (Newton 2004, 25;Et hinc sequitur quod spatium sit entis primario existentis effectus emanativus, quia positoquolibet ente ponitur spatium, Newton 1962, 103), whereupon Stein reasons that the secondclause tells us precisely what the rst clause means (Stein 2002, 269). Yet, in the De grav-itatione, the term emanative effect is not used with reference to any being whatsoever,but only to God or the rst existing being. To avoid the obvious theistic implications, Steintakes the phrase, rst existing being, to pertain to any rst existing being, presumably even amere corporeal beingbut this interpretation strains credibility. On Newtons theology, onlyGod (or possibly a world soul) can qualify as the rst existing being, as the context of theDe gravitatione makes clear. Once again, the evidence for Newtons incorporeal ontologicalfoundation for space will emerge in more detail in the ensuing sections, where the distinctionbetween emanation and space as an attribute of being qua being will be explained, but anumber of important criticisms can be mentioned straight away.First, if Newtons concept of emanation is merely the claim that if any being whatsoeveris posited, space is posited, then one would expect a much more general application of theemanation concept to other beings, especially corporeal being. The fact that Newton neverentertains the possibility that space could emanate froma material body, or anything else thatis situated on the ontological chain of being below God (or a world soul) strongly suggeststhat Steins readings of emanative effect and rst existing being are much too broad.12Second, as regards Steins equating rst existing being with any rst existing being,a serious difculty resides in the historical fact that there were clear precedents among theearlierCambridgeneo-Platonistsforemployingsuchphrases, likerstexistingbeing,with reference to God alone. In Mores Enchiridium Metaphysicum (1679), there are severalnotable instances of such terms in his well-known comparison of the metaphysical titlesascribed to both God and spatial extension (see also De Smet and Verelst 2001 on this):For this innite and immobile extension will be seen to be not something merely real but something divine after we shall have enumerated those divine names or titleswhich suit it exactly, Of which kind are those which follow, which metaphysiciansattribute to First Being. Such as one, simple, immobile, eternal, complete, independent,existing from itself, subsisting by itself, incorruptible, necessary, immense, uncreated,uncircumscribed, incomprehensible, omnipresent, incorporeal, permeating and encom-passing everything, being by essence, being by Act, pure Act. (More 1995, 57)As is evident given the references to being by essence, being by Act, etc., Moresdiscussion of First Being relies heavily on concepts that can be traced back to AristotlesMetaphysics; in particular, the existence of an eternal, immovable rst substance requiredto ground the worlds lesser, nite, and mutable substances.13These traits of First Being,12The term emanative effect only appears three times in the De gravitatione. Besides Steins favorite ofthese three quotations (i.e., space is an emanative effect of the rst existing being, ), there are: [space] isas it were an emanative effect of God and an affection of every kind of being (21); and, space is eternal induration and immutable in nature because it is the emanative effect of an eternal and immutable being (26).13Inhisdepictionofthetraitsofinniteextension,Moreaddsthatitisnecessarythatitbeimmobile.Which is celebrated as the most excellent attribute of First Being in Aristotle (1995, 58). In the Metaphysics(Bk. XII, 1071b11071b10), Aristotle concludes that it is necessary that there should be an eternal unmov-able substance. For substances are the rst of existing things, and if they are all destructible, all things aredestructible (Aristotle 1984, 16921693). In short, the intended meaning of Newtons rst existing beingalmost certainly follows Mores usage, which, in turn, is based on Aristotles reasoning. More importantly, as1 3426 E. Slowiktherefore, are only applicable to God or a world soul, although Mores interesting point isthat most also apply to space: That which, however, is the rst Being and receives all oth-ers, without doubt exists by itself, since nothing is prior to that which sustains itself (59;emphasis added). Moreover, a similar use of language and concepts pervades Mores earlierworks, such as the crucial section on emanative causation in The Immortality of the Soul(1659) that refers to God as the First and primest Essence (1997b, 35). Accordingly, thehistorical context of the terms and phrases in Newtons work would seem to fatally undercutSteins reading.2.2Efcient Causation and Cambridge Neo-PlatonismAs Stein admits (2002, 271), his interpretation runs counter to the prevailing consensus amongEarly Modern and Newtonian scholars, who have concluded, by and large, that Newtonsspatial ontology is thoroughly imbued with neo-Platonic natural philosophy: see the com-mentaries by Burtt (1952, 261), Jammer (1993, 110), Koyr (1965, 89), Funkenstein (1986,96),Hall(2002),tonameonlyafew.EdwardGrantsassessmentisfairlyrepresentativeof this position: if space is Gods attribute, does that not imply it is somehow an accidentor property of God (1981, 243)? A notable exception to this line of reasoning, however,ispresented inan inuential earlyarticleby McGuire(1978a), which presentsa view ofNewtonsconceptofspacethatcanbeinterpreted,albeitonlysupercially,assimilartoSteins assessment. McGuire initially sides with a less ontological, more factual or conse-quential interpretation, arguing that space for Newton is the general condition required forthe existence of any individual substance including its characteristics (1978a, 15).The relation between the existence of a being and that of space is not causal, but oneof ontic dependence. Newton is dening one condition which must be satised so thatany being can be said to exist. In short, the phrase, when any being is posited, space isposited denotes an ontic relation between the existence of any kind of being and thecondition of its existence. (1978a, 15)Possibly prompted by Carrieros criticisms (1990), McGuire later qualied this account ofNewtons spatial theory, concluding that the relation between divine being and the innityof space can be seen (in a curious sense) as a causal dependency, and, moreover, one that hasa legacy in theological and philosophical thought (1990, 105).14It will be useful to explorethese issues in somewhat greater depth, for they shed light on a likely source of Newtonsdescriptive phrase emanative effect.McGuirecontendsthat thereisamedieval precedent for construingtherelationshipbetween God and space as under the rubric of efcient causation, yet, since the notionof an eternal and efcient cause does not involve any activity, production, or active efcacybetween it and its effect, it is difcult to distinguish natural or ontic dependence in these con-texts from the notion of causal dependence between eternal things (105). The difcultiesFootnote 13 continuedthe subsequent investigation of the De gravitatione will demonstrate, Newton likewise demands an innite,immobile rst existing being to ground the existence and extension of lesser, mobile entities.14McGuire (2007), following (1990, 105), likewise connects his earlier ontic dependence hypothesis withefcient causation: It seems evident that emanative causation, as Newton understands it, reects this rela-tionship between Gods necessary existence and spaces uncreated nature: space exists always because Godexists necessarily. Moreover, since the notion of an eternal and efcient cause does not necessarily involveactivity, production, creation, or active efcacy between it and its effect, the distinction between ontic andcausal dependence essentially collapses (123124).1 3Newtons Neo-Platonic Ontology of Space 427concern howcausation can link eternal things, namely, God, space, and time, which are nottemporally prior to one another. McGuire offers the example of Augustines foot eternallyembedded in dust, and thus eternally causing its footprint (105), as a characterization of thisspecial form of efcient causation. As pointed out above, Newtons inuential older contem-porary, Henry More, in his The Immortality of the Soul (1659), had employed the concept ofan emanative cause in just this manner in explicating the extension of immaterial substance.More contends that there exists a spatially extended, immaterial Secondary Substance thatis coextensive with the extension of material substance: he states that we have a rationallapprehension of that part of a Spirit which we call the Secondary Substance. Whose Exten-sion arising by graduall Emanation from the First and primest Essence [God] (1997b,35). More holds that an Emanative Effect is coexistent with the very Substance of that whichis said to be the Cause thereof , and explains that this Cause is the adequate and imme-diate Cause, and that the Effect exists so long as that Substance does exist (1997b, 33).While there remain significant differences between McGuires and Carrieros understandingof Newtons use of emanation,15they nonetheless concur that traditional ontological, andspecifically causal, issues are at play; indeed, both agree that there are a number of Scholasticand, not surprisingly, neo-Platonic precedents for Newtons handling of emanative causationas a unique type of efcient causation.16Stein criticizes the allegation that a form of neo-Platonic causation underlies Newtonsspatial hypotheses, however. Commenting that the grounds for thinking that Newtons the-ory of emanation is neo-Platonic, or Cambridge Platonic, are very weak (2002, 269), Steinasserts that emanation is distinct from creation for the neo-Platonists, and all being (exceptGod) is created; thus space is not created, and thus (presumably) not a being. Yet, as justdiscussed, there is a Scholastic form of causation that does t Newtons use of emanation(which he obtained via More). It is true that Newton lists uncreated (increata) among thecharacteristics of space (33); but, as Carriero (1990, 113115) explains, this use of uncre-ated is almost certainly due to the fact that, for Newton, the cause of a created being is priorin time, whereas an emanative cause is co-existent with (not temporally prior to) its effect.This interpretation of Newtons use of creation is corroborated in the De gravitatione when hedeclares that extension is not created (creatura) but has existed eternally (since extension isan emanative effect of an eternal being; 31). Equally important, Newtons hypothesis closelyfollows Mores reasoning, since More both denes an emanative cause as co-existent withits effect, as well as lists uncreated among the attributes of space (see Sect. 2.2).17Finally,15One of the main points of contention is how space relates to the divine essence. While various aspects ofthese traditionally theological issues will be discussed below, an in-depth examination is beyond the scope ofthis essay. Both commentators agree, however, that More likely inuenced Newtons quite similar hypothesis(McGuire 1990, 105; Carriero 1990, 112115; see, also, footnote 2).16While providing a brief synopsis of the natural philosophy of the Cambridge neo-Platonists is difcult,the central feature is probably the rejection of a purely mechanical account of the material world (i.e., thatall material phenomena can be completely explained through the interactions and impact of inert matter inmotion). Rather, the neo-Platonists appealed to God, or spirit, as an active agent, or foundational basis, forall natural phenomena. See, e.g., Garber et al. (1998). As mentioned above, Charletons natural philosophy,which is decidedly Gassendian at least as regards space, adopts an incorporeal basis for space, and thus isstrikinglysimilartoCambridgeneo-Platonisminmanyrespects,althoughthereareimportantdifferences(e.g., Newtons repudiation of a substance-accident metaphysics for space).17More is less forthcoming on the uncreated status of space in his earlier The Immortality of the Soul,although it is strongly implied in his discussion of emanative causation: By an Emanative Cause is under-stood such a Cause as merely by Being, no other activity or causality interposed, produces an Effect (1997b,32). Newtons list of the characteristic of space versus matter, in the De gravitatione, thus reveals a knowledgeof Mores later Enchiridion, rst published in 1671, as do many of the other features detailed in our investi-gation (namely, the being as being hypothesis, see Sect. 4 below). Indeed, it is highly unlikely that Newton1 3428 E. Slowikas Carriero also observes (114), while Newton states that space is uncreated, he never statesthat space is uncaused.Consequently, despite Steins best effort to argue for a non-ontological version of Newtonstermemanativeeffect, thehistorical context renderssuchaninterpretationextremelyimplausible. In short, since More also denes the spatial extension of incorporeal substanceas an emanative effect, and given that Mores hypothesis stands as a clear instance of hisneo-Platonic ontology, there can be little doubt as to the direct inspiration, and thus likelyintended meaning, of Newtons use of the identical phrase emanative effect.18Besides emanation, a veritable host of sixteenth and seventeenth century natural philos-ophersproposedotherhypothesesonthenatureofspacethatcloselyparallelNewtons,including many thinkers in England with whom he was directly acquainted (most impor-tantly, in addition to More, Isaac Barrow and Joseph Raphson). For instance, the idea thatspaceliesoutsidetheScholasticsubstance/accidentcategorieswasalmostcommonplaceinthesixteenthandseventeenthcenturies:Fonseca,Amicus,Bruno,Telesio,Patrizi,andGassendi, to name a few, all favored this notion, and, more significantly, theological con-cerns are heavily implicated in their respective views. These last two, Francesco Patrizi andPierre Gassendi, in addition to More, probably comprised the main source of inuence onNewtons developing views of space, although their inuence was likely obtained indirectlythrough More and Walter Charleton, Gassendis foremost English advocate. One can nd asurprising number of close similarities between the individual hypotheses of these naturalphilosophers and Newtons concept of space: for example, an atomistic or stoic cosmology,with a nite material world set within an innite, three-dimensional void space, is commonto all (except Patrizi, who lls empty space with light). Patrizi, like Newton, also emphasizesthe mathematical aspect of space, which can receive all geometric shapes, and further arguesthat, while neither substance nor accident per se, space is nevertheless a type of substancenot covered by the Scholastic categories; i.e., space is closer to the traditional concept ofsubstance (Brickman 1943, 241). With Gassendi, Patrizis ideas on space would be developedin a direction that would prove highly attractive to the later Cambridge neo-Platonists. OnGrants summation, space, for Gassendi, is an absolutely immobile, homogenous, inactive(resistenceless), and even indifferent three-dimensional void that exists by itself whether ornot bodies occupy all or part of it and whether or not minds perceive it (Grant 1981, 210).More importantly for our analysis, Gassendi holds that space is both uncreated and co-eter-nal with God, although, like many Scholastic predecessors, he also believes that God is inevery place while not actually extended in the same manner as body (see Sect. 4 below). Thepotential impiety involved in claiming some form of independent status for space wouldprove a source of concern for the Cambridge neo-Platonists, who nevertheless developedFootnote 17 continuedwas not familiar with this, quite important, work of Mores later years. The arguments for a later dating ofthe De gravitatione (in Dobbs 1991, 130146), i.e., after 1680, thereby gains support, since Newtons treatiseexhibits signs of several of Mores major works, including the Enchiridion. McGuire (1978a, 41, n. 27) hadearlier remained a bit circumspect about the inuence of Mores Enchiridion based on the earlier date suppliedby Hall and Hall for the De gravitatione (Newton 1962, 90), i.e., circa 1666; but McGuire has since advocatedthe later date (2007, 112). See, also, footnote 2.18Another instance of the use of emanation that parallels Newtons, although with respect to time, is employedby J. B. van Helmont, a natural philosopher in the early half of the seventeenth century who Newton had stud-ied. See, Ducheyne (2008). Finally, it should be noted that this essay does not take sides on the complex issuesassociated with causation in Newtons natural philosophy; e.g., whether emanative causation more closelyresembles an efcient or formal causea fruitful topic of further exploration, needless to say. The main pur-pose of the discussion of causation is to refute the idea, espoused in Stein (2002), that deates the ontologicalsignificance of the seventeenth century concepts linked to emanative causation (see footnotes 6 and 9).1 3Newtons Neo-Platonic Ontology of Space 429their respective spatial hypotheses roughly along Gassendian lines, at least as regards spacesindependence from body.19It is against this historical backdrop that any assessment of theimport of Newtons concept of space must be examined, especially the relationship betweenGod and space.3 Neo-Platonism and Determined Quantities of Extension3.1Is God Necessary for Newtons Spatial Theory?For the advocate of the strong non-substantivalist thesis, a possible rejoinder to the evidencepresented above would be to concede that ontological factors do play a major role in Newtonsspatial theory, but that these ontological factors need not be specifically theological in kind.That is, the strong non-substantivalist position might be compatible with a position that sim-ply argues that God is not required for the existence of space, as allegedly evident in his claimthat space is an affection of every kind of being (Newton 2004, 21).20This form of argu-ment may, in fact, lie at the center of Stein (2002); for, in defense of his approach, he insiststhat on the objective or ontological side, , Newtons doctrine about space and time, in thelight of his explicit statements, did not teach that space and time per se, or their attributes,depend upon the nature of God (297).21As regards the question, Can we conceive space19ThebestoveralltreatmentoftheseissuesstillremainsGrant(1981). TranslationsofPatrizisspatialhypotheses are provided in Brickman (1943). For Gassendis philosophy of space, see his Syntagma philo-sophicum (published posthumously in his Opera Omnia, 1658), parts of which are translated in Brush 1972,and Capek 1976. Gassendis ideas informthe main content of Charletons discussion of space in his, Physiolo-gia Epicuro-Gassendo-Charletoniana (1654), a work known to Newton (see footnote 27). In the Physiologia,Charleton comments on the possible charge of impiety that can be leveled at a theory, like his, that makesspace independent of God in various respects (6869). See, also, footnote 35.20Incidentally, thisversionofthestrongnon-substantivalistpositionstilldiffersfromtheweakvariety(explained in Sect. 1), since it continues to maintain that Newtons actual ontology of space is non-substantiv-alist. The weak version, in contrast, only claims that Newtons handling of his definitions and concepts relatedto Absolute space, etc., do not obligate substantivalism (or relationism), and thus Newtons approach pointsforward to a third-way conception of space that eschews the standard ontological dichotomy.21A similar interpretation of Stein (2002) has been put forward by Andrew Janiak: Stein (forthcoming) notes that Newtons view is not rst and foremost a theological one, for its rst premise is that space is anaffection of all entities. The fact that Gods innite and eternal existence makes it the case that space is inniteand eternal is logically parasitic on this rst premise. That is, given the logical structure of Newtons view,space would emanate from the rst existent, whatever that rst existent happened to be, because for Newtononcewepositanentitywepositspace.ThisjustmeansthatspatialityiswhatwemightcallfollowingGalileos discussion of the primary qualities of objectsa necessary accompaniment of the existence of enti-ties (Janiak 2000, 222, fn. 67). As will be explained, there is abundant evidence to support the idea that spaceis a necessary accompaniment of the existence of any being for Newtonyet, this viewwas practically stan-dard among Newtons predecessors and contemporaries (for More, Charleton, Raphson, etc., also acceptedit: see Sect. 4). However, the claim, space would emanate from the rst existent, whatever that rst existenthappened to be, is unsupportable: Newtons use of emanation in the De gravitatione, as well as its likelysource in More, link emanation to higher incorporeal/spiritual beings alone (see Sects. 3 and 4 below), and thusNewtons theology does indeed play a fundamental role in Newtons spatial theory. As with Stein, the abovequote tends to run together being as being and emanative causation (see Sect. 4.3), which are two distincthypotheses. Similar errors occur in Janiak (2008, Chap. 5), although he does strive to distance his reading fromsome aspects of Steins interpretation (155163): after arguing that the affection thesis entails the claim thatspace is an emanative effect of the rst existing being (142), and that space emanates from whatever entityis the rst to exist (146), he later goes on to claimthat an affection is not dependent upon particular objects forits existence (157)on the whole, such contradictions (which may be only apparent) make it rather difcultto determine the nature of Janiaks conclusions. In addition, he mistakenly conates emanative causation andcreation, the latter involving Gods will (see, footnote 17 above, where More clearly rejects this inference:1 3430 E. Slowikwithout God? (271), Stein cites a passage from Newtons critical assessment of Descarteshypothesis which equates spatial extension with matter:If we say with Descartes that extension is body, do we not manifestly offer a path toatheism, both because extension is not created but has existed eternally, and becausewe have an idea of it without any relation to God, and so [in some circumstances] itwould be possible for us to conceive of extension while supposing God not to exist?(Newton 2004, 31)22In commenting on this passage, Stein concludes that, for Newton, extension does notrequireasubjectinwhichitinheres,asaproperty;anditcanbeconceivedasexistentwithout presupposing any particular thing, God included (2002, 271).Yet, the problem with this rendering of Newtons statement, put simply, is that Newtonsconceiving space without God does not necessarily entail that Newton believed that spacecan exist without God. Indeed, a significant part of Newtons argument against Descartesontology is precisely this point: that it allows a conception of spatial extension, as the essen-tialpropertyofcorporealsubstance,withoutanyapparentconnectionto,orneedof,theconcept of God. In its place, Newton tentatively advances a neo-Platonic ontology in whichboth spatial extension and body depend upon God.3.2The Determined Quantities of Extension HypothesisNewtons contemplates a world wherein God directly endows spatial extension with bodilyproperties, such as impenetrability or color, without requiring an underlying corporeal sub-stance to house these accidents: If [God] should exercise this power, and cause some spaceprojecting above the earth, like a mountain or any other body, to be impervious to bodies andthus stop or reect light and all impinging things, it seems impossible that we should notconsider this space really to be a body from the evidence of our senses (Newton 2004,2728). If we accept this hypothesis, then Newton contends that we can dene bodies asdetermined quantities of extension which omnipresent God endows with certain conditions(28); the conditions being, rst, that these determined quantities are mobile, second, thattheycanbringaboutperceptionsinminds, andthree, thattwoormorecannotcoincide.Through this process, these bundles of quantities can exactly replicate our everyday expe-rience of material bodies without need of Descartes material substance, or the Scholasticnotion of prime matter (2731). These determined quantities, furthermore, are apparently sus-tained and moved through the exercise of the divine will alone, and Newton makes repeatedreferences to the relationship between the human mind and human body, on the one hand,and Gods will and determined quantities, on the other, to make this point:Since each man is conscious that he can move his body at will, , the free power ofmoving bodies at will can by no means be denied God, whose faculty of thought isinnitely greater and more swift. And for the same reason it must be agreed that God,by the sole action of thinking and willing, can prevent a body from penetrating anyspace dened by certain limits. (27)Footnote 21 continuedByanEmanativeCauseisunderstoodsuchaCauseasmerelybyBeing, nootheractivityorcausalityinterposed, produces an Effect, 1997b, 32).22The phrase in brackets, in some circumstances, is excluded from Steins translation. The differences arenot relevant to the above arguments against his overall position, however, so it will not be discussed.1 3Newtons Neo-Platonic Ontology of Space 431This passage hence foreshadows Newtons later description of space as Gods sensorium(in the Queries to the Opticks, Newton 2004, 127140), since the omnipresence of the divinewill is directly analogous to the omnipresence of human thought and sensation throughoutthe human bodye.g., just as humans can move their limbs at will, God can likewise movebodily quantities through space at will.Therefore, with respect to the citation provided by Stein, Newtons point is simply thatany theory, like Descartes, that links bodily extension to corporeal substance alone, such thatmental properties are excluded, is apt to mistakenly infer that extended, corporeal substancecan exist independently of GodWhy?: because the divine will is erroneously presumed tobe more akin to a mental property on the Cartesian scheme, such that it has little or no rela-tionship with the extension of corporeal substance. Newtons attempt to blur, or minimize,any sharp distinction between mind and body is, in fact, the method by which his determinedquantities of extension hypothesis (hereafter, DQE) avoids the atheistic implications of bothDescartes dualism of mental and material substance, as well as the Scholastics distinctionbetween prime matter and substantial form. The passage cited by Stein (in Sect. 3.1) is pre-ceded by an explanation that clearly shows that Newton rejects any theory, like Descartes,that ties body, and thus bodily extension, so exclusively to corporeal substance: For we can-not posit bodies of this kind [i.e., on the DQE thesis] without at the same time positing thatGod exists, and has created bodies in empty space out of nothing (31). For the Cartesiansand Scholastics, however:They attribute no less reality in concept (though less in words) to this corporeal sub-stance regarded as being without qualities and forms, than they do the substance ofGod, abstracted from his attributes. And hence it is not surprising that atheists ariseascribing to corporeal substance that which solely belongs to the divine. Indeed, how-ever we cast about we nd almost no other reason for atheismthan this notion of bodieshaving, as it were, a complete, absolute, and independent reality in themselves (32;emphasis added)Consequently, leaving aside issues of conceivability, the quote provided by Stein is notevidence that Newton actually accepts an ontology that allows extension, through its inti-mate connection with body, to be as it were, a complete, absolute, and independent realityin themselvesi.e., apart from Godrather, Newton argues at length that any theory thatallows such an autonomous conception of bodily extension is in serious error!Newtons neo-Platonic credentials are in evidence throughout his assault on these Carte-sian and Scholastic dualisms, moreover. Directly after the quote provided by Stein, he offersa number of further criticisms against strictly demarcating the incorporeal and the corporealvia Descartes distinction in substance:Nor is the distinction between mind and body in [Descartes] philosophy intelligible,unless at the same time we say that mind has no extension at all, ; which seems thesame as if we were to say that it does not exist, or at least renders its union with bodythoroughly unintelligible and impossible. Moreover, if the distinction of substancesbetween thinking and extended is legitimate and complete, God does not eminentlycontain extension within himself and therefore cannot create it; but God and extensionwould be two separate, complete, absolute substances, and in the same sense. But onthe contrary if extension is eminently contained in God, or the highest thinking being,certainly the idea of extension will be contained within the idea of thinking, and hencethedistinctionbetweentheseideaswillbesuchthatbothmaytthesamecreated1 3432 E. Slowiksubstance, that is, but that a body may think, and a thinking being be extended. (31;modied translation)One of the remarkable facets of Newtons assessment is that it looks forward to the Empir-icists skeptical analysis of substance,23but, for our purposes, the important question pertainsto the relationship between eminent containment and emanative causation, two separate, butsimilarly named, metaphysical hypotheses. While the evidence is rather sketchy, it is possiblethat Newton may regard the emanative causation of various accidents or attributes, such asextension, as an ontological consequence of their eminent containment in a higher incorpo-real being.24If Newton does accept this sort of metaphysical entailment, then his claimthat extension is eminently contained in God (in the above passage), renders the strongnon-substantivalistpositionquiteproblematic,includingtheversionthatonlyinsiststhatspace is not dependent on God.3.3The Question of Hierarchical DependenceAt this point, it would be benecial to examine Newtons concept of emanation as it pertainsto the neo-Platonic ontological hierarchy or ranking of beings, i.e., the notion that all types23Newtons DQE hypothesis in the De gravitatione, alongside his denial of a corporeal/incorporeal dichot-omy for substances and accidents/attributes, has Spinoza-like implicationsat least in the sense that Newtonstheory would seem to posit only one being/substance, God, such that lesser beings/substances are containedin, or are a part of, God. And, indeed, Newton makes this very claim in an unpublished tract from the 1690s:The most perfect idea of God is that he be one substance, simple, indivisible, live and making live, necessarilyexisting everywhere and always, understanding everything to the utmost, freely willing good things, by hiswill effecting all possible things, and containing all other substances in Him as their underlying principle andplace; a substance which by his own presence discerns and rules all things, just as the cognitive part of a manperceives the forms of things brought into his brain, and thereby governs his own body; (McGuire 1978b,123; emphasis added). On a similar theme, Sklars (1974) analysis of geometrodynamic theories of spacetimeprompted this definition of supersubstantivalism: not only does spacetime have reality and real structuralfeatures, but in addition, the material objects of the world, its totality of ordinary and extraordinary materialthings, are seen as particular structured pieces of spacetime itself (1974, 221). Needless to say, Newtons DQEhypothesis comes very close to supersubstantivalism, although the term spacetime in this quote would needto be substituted with the phrase Gods spatial extension. See, also, McGuire (2000) for a comparison withPlatos Timaeus. In fact, a possible explanation for the unpublished status of both the De gravitatione and Tem-pus et Locus (1978b) may partly reside in the strong hints of Spinozistic monism discernible in these works.24The distinction between eminent containment and emanative causation is somewhat vague in the literature,but, presumably they are distinct hypotheses, and perhaps can stand alone in a given ontology. For example,one can hold that God eminently contains the reality manifest in, say, a stone, but that Gods creation of a stonedoes not employ the emanationist model favored by many neo-Platonists, who often marshal an assortmentof light metaphors to describe the causal process whereby the higher-level entity (the light source) bringsabouttheexistenceoflower-levelentities(thelightitself,ortheshadow):e.g.,lower-levelbeingsareanimage of, or a radiation from, a higher-level being, which is a type of explanation frequent in Moresoeuvre (e.g., 1995, 135). Now, in the above citation, it is possible that Newton may be simply contending thatthe Cartesian dualism of mind and body undermines Descartes previous sanction of eminent containment.Newton claims that Cartesian dualism entails that God does not eminently contain extension within himselfandthereforecannotcreateitbut,asdisclosedinSect.2.2,Newtonrejectsthebeliefthatextensioniscreated, thus (leaving aside a mere lapse in terminology) the reference to eminent containment in this passageneed not imply that Newton actually accepts this thesis. On the other hand, a bit earlier in the De gravitatione,Newton remarks that created mind (since it is the image of God) is of a far more noble nature than body,so that perhaps it may eminently contain [body] in itself (30)and, importantly, the context strongly favorsthe view that Newton is elaborating his own view here. Consequently, Newton may accept some form of theeminent containment thesis. However, Newtons statements employing just emanative effect (see footnote12) and emanate (see Sect. 3.3) are alone sufcient to demonstrate his Cambridge neo-Platonist stance (andthus uphold the argument of this essay), regardless of the eminent containment issue. On the vexed issue ofeminent containment in Descartes, see, Gorham (2003).1 3Newtons Neo-Platonic Ontology of Space 433of being (such as matter, humans, angels, etc.) ll positions within a hierarchical relationshipof ontological dependence upon God. By this means, we may gain a better insight into hisalleged Cambridge neo-Platonism, for the ontological hierarchy of being is a central featureof neo-Platonic thought.First of all, Newton strikes a decidedly neo-Platonic note by allowing for the possibilityof a world soul, an immaterial being who governs the material world and who ranks justbelow God on the hierarchical chain. As disclosed in Sect. 2.2, More embraces a similarnotion, although Newtons endorsement is both more hesitant and mentioned specifically inthe context of his DQE hypothesis (to serve as the immaterial basis for the mobile, deter-mined quantities): some may perhaps prefer to posit a soul of the world created by God,upon which he imposes the law that definite spaces are endowed with corporeal properties,rather than to believe that this function is directly discharged by God (Newton 2004, 30).On the whole, Newtons De gravitatione would seem to favor some limited conception ofhierarchical dependence, at least among immaterial and material beings, for he states thatmind may eminently contain body:That we are created in Gods image, holy writ testies. And his image would shinemore clearly in us if only he simulated in the faculties granted us the power of creationin the same degree as his other attributes; nor is it an objection that we ourselves arecreated beings and so a share of this attribute could not have been equally granted tous. For if for this reason the power of creating minds is not delineated in any facultyof created minds, nevertheless created mind (since it is the image of God) is of a farmore noble nature than body, so that perhaps it may eminently contain [body] in itself.(30)There are several hints towards a neo-Platonist model of reality in this discussion, if onlyof a fairly weak and underdeveloped sort: e.g., minds are images of God, we share inGods attributes (to a lesser degree), and, mind may eminently contain matter because theformer has a more noble nature than the latter. Yet, like More and many other Cambridgeneo-Platonists, Newtons De gravitatione presents a material world that is, so to speak, spirit-infusedin fact, there appears to be a clear line of ontological descent, with God and hisattributes, which includes extension, situated at the top of the hierarchy, moving lower tohuman minds (and other lesser spirits), and terminating at the level of matter. Regarding thepossibility of a world soul, Newton adds a comments that strengthens this neo-Platonicreading:theworldshouldnotbecalledthecreatureofthatsoulbutofGodalone,whocreates it by constituting the soul of such a nature that the world necessarily emanates [fromit] (31). Throughout the De gravitatione, Newton places incorporeal beings (spirits, souls)at the top of the hierarchy, with the lower, corporeal world regarded as emanations fromtheseincorporeal beings. Finally, since these lesser beings have a share of Gods attributes, albeitto a lesser degree than Godand space is an attributeit must be the case that these beingsalso share in Gods attribute of spatial extension. An ontology that includes space among theattributes that God emanates is thus also implicated in Newtons hierarchy of immaterial andmaterial being, a point that will be developed further in the next section.3.4The DQE Hypothesis and Strong Non-Substantivalism: An AssessmentIn previous research of the De gravitatione tract, careful attention has seldom been devotedto the aspects of the DQE hypothesis that specifically concern the nature of space. Part of theexplanation for this oversight might be due to the explicit context in which the DQE hypoth-esis is rst introduced, namely, as an account of the nature of body, and notexplicitly, at1 3434 E. Slowikleaston the nature of space. Yet, if one desires to gain a better understanding of the ontolog-ical presuppositions of Newtons overall spatial theory, then the DQE hypothesis is of crucialimportance. In addition, although Newton states that his DQE hypothesis is uncertain, andthat he is reluctant to say positively what the nature of bodies is (Newton 2004, 27), thisshould not divert attention away from the only hypothesis that he has, in fact, developed.Not only is a significant portion of the De gravitatione allotted to the DQE hypothesis, but(as noted above) Newton makes repeated claims as to the superiority of this hypothesis incomparison with both the Cartesian and Scholastic alternatives: e.g., the usefulness of theidea of body that I have described [the DQE hypothesis] is brought out by the fact that itclearly involves the principal truths of metaphysics and thoroughly conrms and explainsthem (31). In summarizing the importance of this hypothesis, he adds: So much for thenatureofbodies,whichinexplicatingIjudgethatIhavesufcientlyprovedthatsuchacreation as I have expounded [the DQE hypothesis] is most clearly the work of God, and thatif this world were not constituted from that creation, at least another very like it could beconstituted (33). Nevertheless, since the endorsement of the DQE hypothesis does remaintentative, it is possible that other attempts to construct a theory of material bodies, but whichstill uphold Gods central role, may have been amenable to Newton.On the other hand, there is an interesting piece of indirect evidence that may support thecontention that Newton not only accepted the DQE hypothesis, even granting his expressedhesitation, but did so until well into his later years. In a footnote to Pierre Costes Frenchtranslation of Lockes Essay Concerning Human Understanding, third edition, Coste reportsthat Newton provided an account of the creation of matter, in 1710, that correlates with theDQE hypothesis in the De gravitatione (Koyr 1965, 92). While this report falls short ofconclusive proof, it should nevertheless assist in countering any effort to discredit or belittlethe importance of the DQE hypothesis. Less specic, but also important, is David Gregoryssummary of his conversations with Newton in 1705: He believes God to be omnipresent inthe literal sense for he supposes that as God is present in space where there is no body, heis present in space where a body is also present (Hiscock 1937, 29).In brief, what the DQE hypothesis reveals about Newtons ontology is that the Westernconception of God, or some spiritual entity at (or near) the hierarchical level of God, is theemanative cause of corporeal being, and perhaps eminently contains incorporeal being. Allof Newtons examples of emanative causation and eminent containment in the De gravitati-one, as revealed above, involve a mental/spiritual entity as the sourcei.e., God, the worldsoul, createdmindsand either matteror space asthe emanative effect or theeminentlycontained entity.25Thus, even apart from the question of Gods attribute of extension, sincebody is at (or near) the lowest rung in the hierarchy, and thereby depends for its existence onthese incorporeal beings, space cannot be the emanative effect of matter/body. Put slightlydifferently, emanative causation in the neo-Platonic tradition, and in the DQE hypothesis,ows down the hierarchical chain from spiritual beings to, ultimately, matter; and so itwould be highly unorthodox for Newton to have conceived spatial extension as the emana-tive effect of material being, especially given the deep disparity in Newtons characterizationof space and matter: extension is eternal, innite, uncreated, uniform throughout, not in theleast mobile, nor capable of inducing changes of motion in bodies or change of thought inthe mind; whereas body is opposite in every respect (33). Indeed, this simple hierarchicalrelationship between God and body, mediated via Gods attribute of extension, is very likely25In her collection of More extracts, MacKinnon summarizes the emanation concept as follows: The uni-verse of Neo-Platonism is formed by emanation from the One, through the descending stages of intelligence,the soul, and the world, with formless matter, or unreality, as the ultimate limit of the emanative power (More1925, 315).1 3Newtons Neo-Platonic Ontology of Space 435the underlying motivation for Newtons DQE hypothesis, since he constantly criticizes theopposition (i.e., Cartesians and Scholastics) for ascribing to corporeal substance that whichsolely belongs to the divine (31; see Sect. 3.2)and, once again, what the Cartesians andScholastics have been erroneously ascribing to corporeal substance is extension. Therefore,the strong non-substantivalists contention that, for Newton, space (in some sense) resultsfrom the existence of anything (Stein 2002, 268), is inconsistent with the details of theDQE hypothesisapparently only God, or an incorporeal being akin to a world soul, can bethe emanative cause of space.26Leaving aside the issue of incorporeal being, any interpretation that would posit matter asthe emanative origin of space is likewise unacceptable given the basic ontological relation-ship between body and space on the DQE hypothesis. Material bodies are, in effect, portionsof space that have been allotted certain empirical properties, such as impenetrability or color,and thus body presupposes spatial extensionbody cannot, therefore, be the emanative causeof space. Newton carefully highlights bodys dependence upon space in describing the DQEhypothesis: extension takes the place of the substantial subject in which the form of thebody [i.e., the determined quantities] is conserved by the divine will (29). It would be quiteodd, therefore, if Newton held that the determined quantities, as the forms or properties,were the ontological foundation of their own, as it were, substantial subject.We should return at this point to the topic of attributes and their dependence upon God.Throughout Newtons analysis in the De gravitatione, the dependence upon God of all possi-ble substances, attributes, or accidents is constantly acknowledged, and this includes space,of course:For certainly whatever cannot exist independently of God cannot be truly understoodindependentlyoftheideaofGod.Goddoesnotsustainhiscreaturesanylessthanthey sustain their accidents, so that created substance, whether you consider its degreeof dependence or its degree of reality, is of an intermediate nature between God andaccident. And hence the idea of it no less involves the concept of God, than the ideaof accident involves the concept of created substance. And so it ought to embrace noother reality in itself than a derivative and incomplete reality. Thus the prejudice justmentioned must be laid aside, and substantial reality is to be ascribed to these kinds ofattributes [i.e., extension], which are real and intelligible things in themselves and donot need to be inherent in a subject [i.e., an accident inherent in corporeal substance],ratherthantothesubject[i.e.,corporealsubstance]whichwecannotconceiveasdependent [upon God], much less formany idea of it. And this we can manage withoutdifculty if (besides the idea of body expounded above) we reect that we can conceiveof space existing without any subject when we think of a vacuum. And hence somesubstantial reality ts this. (3233; emphasis added)Since this passage claries to some degree the relationship between God and the attributeof extension, it is worth examining in closer detail. As described in Sect. 3.2, Newton rejectsthe Cartesian and Scholastic accounts because they foster a conception of corporeal substancethat appears to be independent of God (as well as incoherent). In its place, Newton championsa notion of extension as an affection or attribute of God, which naturally implies that the con-cept of extension, unlike corporeal substance, cannot be truly understood independently of26McGuire (1978a, 15) explores a hypothetical interpretation that would allow beings other than God toground the existence of space; yet, as disclosed in personal discussion, McGuires purpose was only to explorethe implications of an emanationist ontology, and not to put forward the view that Newton actually acceptedthis hypothetical scenario. Unlike Stein, McGuire has always accepted that Newtons theology is central tounderstanding his theory of space (see, e.g., 1978a, 3839).1 3436 E. Slowikthe idea of God. In fact, having rejected corporeal substance, Newton argues that we shouldascribe some substantial reality to extension as opposed to corporeal substance. That spacecan exist in the absence of body in Newtons cosmology is also furnished as evidence againstassigning extension to corporeal substance. One should not, accordingly, construe the termsubject (subjecto) as referring to any subject, whether God or a lesser substance/beingrather, subject consistently refers to corporeal substance in these passages. It is only onthis interpretation that Newtons overall argument makes sense: it would not be consistentfor Newton to criticize the Cartesians and Scholastics for positing a conception of corporealsubstance that is independent of God,andthen put forward his own preferred thesis thatmakes spatial extension independent of all subjects, taken broadly, and thus God! Withrespect to the pivotal sentence italicized in this quote, we can give a more accurate renditionas follows: substantial reality is to be ascribed to the attribute of spatial extension, which isa real and intelligible thing-in-itself and does not need to be an accident inhering in corporealsubstance, rather than ascribe substantial reality to corporeal substance, which we cannotconceive as dependent upon God, much less form any coherent idea of it. Implicit in thisstatement, of course, is the idea that the substantial reality of the attribute space is dependentupon God, which is the basis for Newtons preference of the DQE hypothesis.Newtons DQE hypothesis is therefore quite clear in assigning to space a form of sub-stantial reality, an admission that may help to elucidate Newtons earlier claim that spaceapproaches more nearly to the nature of substance (22). In the passage quoted directlyabove, spaceisdeclaredtohavesomesubstantial reality, although, asanattributeofGod, it isobviouslyneitherasubstancenoranaccident (i.e., givenhisrejectionofthesubstance/accident dichotomyregardingspace). Thenon-substantivalist interpretationofNewtonis, accordingly, quitecorrect inclaimingthat Newtonsabsolutespaceisnot asubstance. Yet, given that space is emanative effect of a higher, incorporeal being, the sub-stantial reality that Newton does bestow upon extension makes it practically equivalentapproaches more nearlyto the traditional substance concept: not only can space exist inthe absence of all corporeal existents, but, on the DQE hypothesis, spatial extension replacescorporeal substance as the container of his mobile, determined bodily quantities (see, also,footnote 23). Therefore, despite a minor tactical victory in rejecting space as a substance, themore radical non-ontological and non-theological reading of Newtons spatial theory cham-pioned by the strong non-substantivalists is simply not upheld under a close scrutiny of therelevant texts.4 Neo-Platonism and the Ontology of Space: More, Charleton, NewtonNotwithstanding the evidence presented in Sects. 2 and 3, the strong non-substantivalistswould likely counter that the traditional ontological conception of Newtons spatial theorycannot satisfactorily explain two of its important features (while the non-substantivalist inter-pretation can): rst, why did Newton utilize affections/attributes in place of the more familiaraccidents, as manifest in his well-known statement that Space is an affection of a being justas a being (2004, 25)?; and second, why is space associated with being just as a being(ens/entis quatenus ens)? In this section, a more detailed comparison of Newton, More, andCharleton, will help to shed light on these mysteries. As will be argued, the second questiondiscloses a predominate feature of the spatial ontologies of late seventeenth century Englishnatural philosophy, which Newton shares with both More and Charleton, whereas the rstquestion is indicative of Newtons general discontent with the substance/accident distinction,and in this manner marks a point of departure away from Mores ontology towards the line1 3Newtons Neo-Platonic Ontology of Space 437favored by Gassendi-Charleton. The rationale for focusing on the these two philosophers,More and Charleton, is that: rst, their inuence on Newton is well-documented; and sec-ond, they represent the two dominant positions in Newtons time on the relevance of the sub-stance/accident dichotomy for space (with Charleton sponsoring Gassendis popular solution;see Sect. 2).274.1Extension and AccidentsIf one seeks a rationale for Newtons characterization of space as an attribute (or affection),a likely candidate is the potential metaphysical difculties associated with classifying spaceas an accident. In Mores later, Enchiridion Metaphysicum (1671), space is an accident ofGod in the traditional substance/accident sense, although More uses the term attribute, andsometimes affection, instead of accident:The real attribute of some real subject can be found nowhere else except where in thesame place there is some real subject under it. And, indeed, extension is the real attri-bute of a real subject . Indeed, we cannot not conceive a certain immobile extensionpervading everything to have existed from eternity and really distinct, nally, frommobile matter. Therefore, it is necessary that some real subject be under this extension,since it is a real attribute. (More 1995, 5657)More is thereby led to conclude that spatial extension must be the attribute of an incor-poreal substance, and, while the details are not explicit, More seems to embrace the notionthat attributes inhere in substances: extension indeed is in the real subject (1995, 68).28In contrast, Walter Charletons popular tract, although quite similar to Mores views in manyways, nevertheless parts company with More by declaring that space is neither substance noraccident, since it is more general than those two (Charleton 1654, 66), an opinion earlieradopted by Gassendi (1972, 384).2927See, Westfall (1962), and McGuire (1978a), on the references within Newtons work to More and Charleton.Newtons early notebook, Quaestiones quaedam Philosophicae (16611665, Cambridge University Library,Ms Add. 3996, folios 88135), contains evidence that he had read, at the least, both Charletons Physiologia,as well as Mores, The Immortality of the Soul.28More tends to complicate his hypothesis that space is Gods attribute by often referring to space as anincorporeal substance; e.g., in the ensuing section of the Enchiridion, he reasons that his theory utilizes theverysamewayofdemonstrationwhichDescartesappliestoprovingspacetobeasubstance,althoughitbe false in that he would conclude it to be corporeal (More 1995, 57). More rejects Descartes theory ofspace for many of the very same reasons that Newton provides in the De gravitatione (and other works); forinstance, that Descartes theory cannot account for possibility of a vacuum (which is conceivable). An earlyformulation of this argument appears in An Antidote against Atheism (1655): If after the removal of corporealmatter out of the world, there will be still Space and distance, in which this very matter, while it was there, wasalso conceived to lye, and this distant Space cannot but be something, and yet not corporeal, because neitherimpenetrable nor tangible, it must of necessity be a substance Incorporeal, necessarily and eternally existent (More 1997a, 338). Mores penchant for conating space as Gods attribute and space as identicalto Gods substance stands out clearly in this last quote, and it may have prompted Newtons more carefulattempts to deny the latter (see below).29Besides Newtons contemporary, Joseph Raphson (see, Koyr 1957, Chap. 8), another Cambridge neo-Platonistwhoheldthatspaceisanattribute/accident ofGodisRalphCudworth(see, Grant1981, 230).However,thePatrizi-Gassendisolution,thatspaceisneitheraccidentnorsubstance,wasquitepopularinEngland: besidesCharletonandBarrow, oneshouldaddtheearlierneo-PlatonicphilosophiesofWarnerandHill (see, Garber et al. 1998, 558561). For additional assessments of Mores spatial theory, see,Boylan (1980),Copenhaver(1980), and,forthetheologicalaspectsofNewtonstheory,Snobelen(2001).Palter (1987, 395398) argues that More did not inuence greatly Newtons criticisms of Cartesian motion(intheDegravitatione):thisishighlydebatable,sincecriticismofDescartestheoryofspace,time,and1 3438 E. SlowikWhilerejectingMoresaccidentconceptionofspace,NewtonsDQEthesis(fromtheDe gravitatione) does resemble Mores theory in that all extended things, whether body orspirit,necessitatetheinnitespatialextensiongroundedinGodsexistence.Throughout,Newtonrepeatedlyclaimsthatextensiondoesnot existasanaccidentinheringinsomesubject (2004, 22), and this argument also surfaces much later (17191720) in a paragraphhe intended for the Des Maizeaux edition of the Leibniz-Clarke correspondence:TheReader isdesiredtoobserve, that wherever inthefollowingpapersthroughunavoidable narrowness of language, innite space or Immensity & endless durationor Eternity, are spoken of as Qualities or Properties of the substance which is Immenseor Eternal, the terms Quality & Property are not taken in that sense wherein they arevulgarly, by the writers of Logick & Metaphysics applied to matter; but in such a senseas only implies them to be modes of existence in all beings, & unbounded modes &consequences of the existence of a substance which is really necessarily &substantiallyOmnipresent & Eternal; Which existence is neither a substance nor a quality, but theexistence of a substance with all its attributes properties & qualities, . (Koyr andCohen 1962, 9697)In his correspondence with Leibniz, Clarke had suggested that space is a property ofGod (2000, 19, 30), and this may have prompted Newton, in the above passage, to qualifyand correct Clarkes terminology and overall argument. Since the term property is likelyto be taken as synonymous with accident, and accidents are often regarded as contingentfeatures of a beings existence, Newton reminds the reader that space is not an accident, andthus space does not inhere in God in the way bodily accidents inhere in matter.Onthislastpoint,Carrieronotesthat,itisastandardtheologicalpositionthattherearenoaccidentsinGod(1990, 123), yet, afurthergraveproblemwithviewingspatialextensionasGodsaccidentisthatencouragesamonisticconceptionofspace,suchthatall lesser spatially extended entities partake of Gods extension, and hence are located orinhere in God. Leibniz raises some of these worries in the correspondence with Clarke: Ifinnite space is Gods immensity, therefore we must say, that what is in space, is in Godsimmensity, and consequently in his essence; Strange expressions; which plainly show, thatthe author makes a wrong use of terms (2000, 45; see, also, footnote 23). Furthermore, aswith mundane material objects, there is a tendency to conceive the inherence relationshipbetweenanaccidentanditssubjectinsuchamannerthatthesubject,inthiscase,God,takes on the accident, extension, along with all of the consequences normally associated withextension, e.g., divisibility, location, three-dimensionality. In the Enchiridion, More strivesto circumvent this dilemma by ascribing to space some of the same incorporeal features thatbelong to God, for example, that God and space are both simple, i.e., indivisible, such thatthey lack separable parts (More 1995, 58). It is not surprising, therefore, that More ultimatelyconcludes on the basis of these similarities (among God and space) that there are two types ofextension, namely, the divisible extension of corporeal matter and the indivisible extensionofincorporealspirit(withinnitespatialextensionbeinganattributeofthelatter;1995,Footnote 29 continuedmotion were a constant theme throughout Mores opus, and thus he likely inspired the more potent series ofcounterarguments that begin Newtons De gravitatione (albeit Newtons counterarguments are indeed moredeveloped and unique in numerous ways). However, Mores inuence on Newtons spirit-based ontology ofspace is a separate issue from Mores inuence on his critique of Cartesian motion.1 3Newtons Neo-Platonic Ontology of Space 439118: More additionally infers the existence of physical monads, which would constitutematters indivisible basic parts, 7181).304.2Nullibism and HolenmerismMores conclusion that all being is spatially extended is likewise supported by his rejectionof two popular hypotheses on the relationship between God and space: rst, he rejects thenullibist view favored by the Cartesians, among others, that God is nowhere in space; and,second, he rejects holenmerism (or holenmerianism), a belief common among the Scho-lastics, that God is whole in every part of space (which thereby guarantees that God is notdivisible even if matter and space are divisible; More 1995, 98148). Given the rejection ofthese two hypotheses, the seemingly inevitable outcome is that incorporeal spirit is extended,a conclusion also adopted by Newtons neo-Platonist contemporary, Joseph Raphson (see,Koyr 1957, Chap. 8).As with many of his spatial hypotheses, Newtons anti-nullibist reasoning closely followsMores. As rst disclosed in Sect. 2, Newton also reckons that both corporeal and incorporealbeing are extended, as the much quoted passage from the De gravitatione makes clear: afterdeclaring that, Space is an affection of a being just as a being, he explains that, No beingexists or can exist which is not related to space in some way. God is everywhere, createdmindsaresomewhere,andbodyisinthespacethatitoccupies;andwhateverisneithereverywhere nor anywhere does not exist (2004, 25). A bit further, he adds: If ever spacehad not existed, God at that time would have been nowhere; and hence he either createdspace later (where he was not present himself), or else, which is no less repugnant to reason,he created his own ubiquity (26). As for Gassendi and Charleton, both reject nullibism forthe same reasons as More, and thus their natural philosophy may have also been a sourcefor Newtons anti-nullibism: e.g., no substance can be conceived existent without Place andTime (Charleton 1654, 66). On the other hand, Gassendi accepts holenmerism (the divinesubstance is supremely indivisible and whole at any time and any place; 1976, 94); as does(presumably) Charleton (1654, 70).If Newton clearly articulates his anti-nullibist philosophy, his opinions on holenmerismare more difcult to discern. Indeed, the question as to the manner of Gods relation to exten-sionmaycomprisethemostcomplexandperplexingelementinhisspatialmetaphysics.Overall, numerous passages in the De gravitatione, as well as some later works, support aclose analogy between the extension of material beings and Gods extension. He begins byexplaining that [space and time] are affections or attributes of a being according to whichthe quantity of any things existence is individuated to the degree that the size of its presenceand persistence is specied (25). He then proceeds to compare the quantity of existenceamong God and created being: So the quantity of the existence of God is innite in rela-30Moreclaimsthatspaceisindiscerpible,whichmeansitcanbedividedinthought,butnotactually(by removing or tearing), and this explains why it is simple (1995, 123124). In addition, both More andCharleton believe that space is incorporeal, and this belief is based largely on the idea that the dimensions ofspace, like spirit, penetrate the dimensions of corporeal substance (More 1995, 123124; Charleton 1654,68). Newtons DQE hypothesis nicely captures this aspect of their philosophy, since bodies are just parts ofspace endowed with material propertiesconsequently, Newtons reference to the extension (diffusion) ofmind throughout innite space (see Sect. 4.2) also follows these earlier philosophies by closely associatingspace with a spiritual entity. Yet, while both More and Charleton incorporate two types of extension, i.e., anincorporeal extension that penetrates corporeal extension, Newtons DQE hypothesis is more parsimonious inthat it employs only one, namely, the divine attribute of extension. Indeed, Newton never (to the best of ourknowledge) refers to space as incorporeal (or immaterial, etc.), a quite significant fact that is noted byMcGuire as well (1978a, 42, n. 38).1 3440 E. Slowiktion to the space in which he is present; and the quantity of the existence of a created thingin relation to the size of its presence, it is as great as the space in which it is present (2526).This explanation suggests that God and created beings do not differ as regards extension,contra holenmerism, since the same, as it were, metricdubbed, quantity of existenceapplies equally to both, but with the important exception that God has an innite quantityof existence and created beings do not (or need not). Yet, quantity of existence is a fairlymysterious and undened notion in the De gravitatione, so it is difcult to draw a specicconclusion based on this use of terminology.In the subsequent passage, however, a better case can be made that Newton does side withMores anti-holenmerist strategy: lest anyone should for this reason imagine God to be likea body, extended and made of divisible parts, it should be known that spaces themselvesare not actually divisible (26). So, Newton not only fails to reject the claim that God isextended, but he also claims, along with More, that space is not really divisible. It wouldseem, therefore, that the Newton of the De gravitatione, like More, may have regarded theindivisibility of space as a solution to the controversy concerning Gods potential divisibility(see, also, Janiak 2000, 224). Newton rounds out this discussion by drawing an interestinganalogy between the extension of both Gods being and a temporal moment: And justas we understand any moment of duration to be diffused (diffundi) throughout all spaces,according to its kind, without any concept of its parts, so it is no more