Locke and Newton on Space and Time (with Ed Slowiik)

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5.1 INTRODUCTION

It is well known that Isaac Newton’s conceptions of space and time as absolute—“without reference to anything external” (Principia, p.# 408)—was anticipated, and probably in$uenced, by a number of %gures among the earlier generation of seventeenth-century natural philosophers, including Pierre Gassendi, Henry More, and Newton’s own teacher Isaac Barrow.1 &e absolutism of Newton’s contemporary and friend, John Locke, has received much less attention, which is unfortunate for several reasons. First, Locke’s views of space and time undergo a dramatic evolution that mirrors the overall absolutist trend of the era. Second, there are good reasons to suppose that Locke was in$uenced late in this evolution by Newton’s Principia, which he read and reviewed shortly a'er its 1687 publication. &ird, despite the in$uence of Newton, Locke retains a skeptical attitude concerning our empirical knowledge of absolute space and time. He is especially cautious about absolute time, bucking a widespread tendency to treat time as strongly analogous to space. &eir disagreement about the measure of absolute time, we will suggest, re$ects a deeper disagreement in the philosophy of science. While Locke counts as scienti%c knowledge only ideas and demonstrations derivable from immediate experience, Newton endorses a more theory-driven brand of empiricism, which holds that our best explanations of the phe-nomena provide genuine knowledge that goes beyond what we can directly observe.

1 See Baker (1932), Burtt (1952), Koyré (1957), Grant (1981). References to Principia are to Newton (1999).

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5.2 THE EVOLUTION OF LOCKEAN!TIME

Locke’s views about space and time pass through three stages. In the earliest dra' (‘A’) of the Essay (1671, in Locke 1990), he initially adopts a stern empiricist stance on the much-disputed problem of the vacuum. &is he says is a ‘question of existence’ that cannot be resolved by conceptual analysis. Supporters and opponents of ‘Cartes’ each have compelling arguments because they begin from di=erent conceptions of body; but neither side can prove to us “that Body exists, or what it is that exists, but for that we are le' only to our senses to discover to us as far as they can” (‘A,’ pp.#45–46).2 Yet later in ‘Dra' A,’ where extension and duration are used to illustrate the problem of in%nity, Locke seems to side with the Cartesians. He argues that our idea of an end-less body must be negative because the idea of a bounded body is positive. As Locke recognizes, this applies to the idea of in%nite extension generally only because body is “the thing most properly capable of extension” (‘A,’ p.#79).

Later the same year, in the more detailed ‘Dra' B’ (in Locke 1990), Locke repudi-ates this Cartesian reduction of extension to body. Having gotten our ideas of %xed lengths and durations from bodily rulers and periodic changes, we are able to extend these ideas to space and duration absent of body or change:

Having once got the idea of the sun’s annual motion . . . we can apply it in our thoughts to duration where no motion is nor supposed to be nor no such appearances of the sun at all. As having got in our minds the idea of a foot, a yard or a mile or so on, from the o'en sight of bodies we are conversant with, we can apply in our thoughts the ideas of these lengths to those distances beyond the con%nes of the world where there are no bodies at all. (‘B,’ p.#243)

Not only may we extend duration and extension ‘in our thoughts’ beyond the limits of actual motions and bodies, Locke further asserts that we %nd it di>cult to conceive extension constrained within the same limits as body:#“every one who will go about it may easily conceive in his mind the beginning of motion though not at all duration . . . so also in his thoughts he may set limits to body but not to extension” (‘B,’ p.#244). But although we can (or must) mentally apply our bodily measures of duration and extension beyond their sensory origins, Locke declines to reify empty space and time.

2 As Rogers (1966, pp.#209–210) notes, Boyle had adopted the same empiricist attitude to the question of the vacuum in New Experiments Physical-Mechanical, Touching the Spring of the Air (1660). Locke himself rarely appealed to experiments in support of his later acceptance of space distinct from body. Rogers (1979, p.#71) notes that Locke invokes one of Boyle’s air-pump experi-ments in ‘Dra' C’ of the Essay, but removes this mention from the published Essay, apparently because he had wrongly interpreted#it.


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()( Locke and Newton on Space and#Time

We can be sure there always was time since God always existed, but “we can never come to know that that in%nite space whereof we have the idea is %lled with body which is the only reall thing that exists and has extension that we know” (‘B,’ p.#253). His %rst-considered position is therefore that time and space are conceptually, but not really, distinct from enduring and extended things.

&e unreality of empty space and time is emphasized in a journal composed during a 1676–1677 visit to Montpellier (in Locke 1936, herea'er ‘Journal’). Locke opens the 27 March entry with a single-word paragraph, ‘Rain’, and then conducts a suitably dis-mal thought experiment. A#man le' alone a'er the world’s annihilation could imagine the “space it %lled” before; but this imaginary space is nothing “real or positive”:

For space or extension separated in our thoughts from body seems to have no more real existence than number has without anything to be numbered and one may as well say that the number of the sea sand does exist and is something the world being annihilated as that the space or extension of the sea does exist or is any thing a'er such an annihilation. (‘Journal,’ p.#77)3

&e analogy with number indicates that Locke still regards space as supervenient on matter—“[both] only a=ections of real existences, the one of any being whatsoever the other only of material beings” (‘Journal,’ p.#77).4 But a more detailed journal entry a few months later (June 1676)#shows he has begun to conceive of space and time as real relations among things rather than mere conceptual abstractions. &us, he introduces the generic notion of ‘distance’ relation applicable to both space and time. In the case of extension, distance is “a simple relation arising [between] two bodies or beings that do not immediately touch one another” (‘Journal,’ p.#78). In the case of duration, it is “the relation between two things which have existed one before another” (‘Journal,’ p.#79). Although this distance “cannot be said properly to have partes ex partes” it nev-ertheless is “not barely an imaginary thing but really a relation between two separate beings”. Speci%cally noting his departure from ‘Des Cartes’, he insists that the ‘nuda relatio’ that constitutes space “though measurable by body is no more thereby body than duration, being measurable by motion, is therefore motion” (‘Journal,’ p.#78). So

3 Hobbes employed a very similar thought experiment many years earlier in order to distinguish between body and ‘imaginary space’. De Corpore (1655; 2.7.1–2); English Works (1839–1845), 2.1.91–94. Locke almost never mentioned Hobbes’s work and owned only Leviathan and the Problemata physica (an attack on Boyle’s account of the air pump). See Rogers (1998, ch.#5).4 Compare Descartes:#“&ere is no real distinction between quantity and extended substance; the distinction is merely a conceptual one, like that between number and the thing numbered” (1985, Vol. 1, p.#226).


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his second settled view is remarkably Leibnizian:#“distance I#suppose to be the relation of two bodies near or remote to one another . . . were there no beings at all we might truly say there was no distance” (‘Journal,’ p.#96).

Besides accounting for our irresistible tendency to conceive of space and time intervening between bodies and motions, Locke also notes a theological virtue of his relationism. Opponents of the Aristotelian/Cartesian reduction of space to extension, from Scotus to Barrow, were reluctant to attribute full reality to space and time for fear of introducing something in%nite and uncreated apart from God. Locke claims that his distinction between body and distance resolves these “doubts which have perplexed the learned” since it makes it “intelligible that distance may be something though it be not body and though it be something it is not yet uncreated” (‘Journal,’ pp.#79–80). It is something because it really separates bodies but it is not uncreated because it does not exist until those bodies do. Locke acknowledges that the essential bodily ‘betweeness’ of space implies that, strictly speaking, there are no “greater or less” parts in the space we conceive of before or beyond the %nite extension of the entire world, since God has created no bodies to ground these relations:#“it can never truly be said that that the utmost super%ces of the world is a foot distant from any thing if there be nothing really existing beyond it” (‘Journal,’ p.#102). Nevertheless, space is no longer merely a conceptual abstraction from the extension of body:#it is a real distance between bodies though not real except as between bodies.

According to the notebooks, then, space absolutely void of body “seems not to be any real thing” (‘Journal,’ p.#100). A#decade later, in the published Essay of 1690 (1975), Locke has gone over to a realist view of empty space. &e following remark from the chapter on ‘Simple Modes of Space’ o=ers a stark choice between his former relation-ism and Scriptural authority:

But whether any one will [i] take Space to be only a relation resulting from the existence of other beings at a distance; or whether they will [ii] think the words of the most knowing King Solomon, the Heaven and the Heaven of Heavens can-not contain #ee, or [iii] the more emphatical ones of the inspired Philosopher St. Paul, In Him we live, move and have our Being, are to be understood in a literal sense, I#leave every one to consider. (II, xiii,#26)

Locke seems to take both Scriptural passages as favoring realism over his former rela-tionism. Paul’s pantheism presumably makes space an attribute of God and therefore independent of any created bodies. &e relevance of Solomon’s words are made clearer when Locke invokes them again in the third chapter on space and time, ‘Duration and Expansion, considered together’. As usual, he notes that when the mind consid-ers the ‘extremity and bounds’ of all body “it %nds nothing to hinder its progress into


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()? Locke and Newton on Space and#Time

this endless expansion” (II, xv, 2). To those who would insist that “beyond the bounds of body there is nothing at all”, Locke’s own former view, he replies, “Solomon, whose understanding was %lled and enlarged with Wisdom, seems to have other thoughts when he says the Heaven and the Heaven of Heavens cannot contain #ee” (ibid.). &e clear implication is that space beyond the heavens, and presumably time before cre-ation, are real because God dwells there and then. Whereas the relational view allowed space and time to be created along with bodies, on the Essay conception they have become the place and duration of God himself:# “God, everyone easily allows, %lls Eternity; and it is hard to %nd a reason why anyone should doubt that he likewise %lls Immensity” (II, xv, 3). So Locke is ultimately convinced that spatial realism or absolut-ism is philosophically tenable and theologically preferable to relationism.5

It is also worth noting that his former anti-realist language is conspicuously absent from the Essay treatments of space and time. Locke is now derisive of the ‘imaginary space’ label he had formerly embraced—“as if it were nothing because there is no Body existing in it” (II, xv, 4)—and introduces the special term ‘expansion’ for “space in general with or without solid matter possessing it” (II, xiii, 26). And he now attributes inherent dimension and quantity to our idea of empty space:#“we sometimes speak of Place, or Distance or Bulk of in the great Inane beyond the con%nes of the world, when we consider so much of that space as is equal to or capable to receive a body of any assigned dimensions, as a cubic foot” (II, xv,#7).

His embrace of temporal absolutism in the Essay is even stronger. He attributes to duration itself, as distinct from its sensible measures, an intrinsic rate:#“We must carefully distinguish betwixt duration and the measures we make use of to judge of its length. Duration in itself is to be considered as going on in one constant, equal, uni-form course” (Essay, II, xiv, 21).6 He insists just as strongly as Newton on the distinc-tion between “those uniform Boundless Oceans of Duration and Space” and “certain

5 So we do not agree with Ayers that Locke remains “ambivalent or agnostic” as between rela-tionism and absolutism in the Essay (1990, Vol. 1, p.#233). On early modern conceptions of God’s relation to space and time, see Gorham (2008, 2011a, 2011b) and Slowik (2009,#2012).6 So we cannot accept Rogers’ assertion that “Locke never accepted Newton’s absolutist posi-tion on space” (1978, p.#221). Referring to Newton’s account in the Principia of how the ‘com-mon people’ conceive space and time, “solely with reference to the objects of sense perception” (Principia, p.#408), Rogers remarks that “Locke’s view of space and time was, and remained, that of the ‘common people’ ” (1978, p.#222, n14), which is the relationist view, according to Newton (1999, 409). See also Aaron (1971, pp.#156–157). We are much more sympathetic with Gibson’s (1960, ch. 10)#account of Locke’s views of space and time, though we think Locke’s pre-Essay relationism is far more coherent and uni%ed than Gibson’s portrayal, and we think the in$uence of Newton on Locke’s mature view is more ambiguous than Gibson indicates. See also Ayers (1990, Vol. 1, ch.#26).


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%xed points in sensible beings we reckon, and from them we measure out portions of those in%nite quantities” (II, xv,#5).7

To summarize the evolution of Locke’s space/time ontology:#(i)#the 1671#“Dra's” accept the Cartesian view that only body is extended in reality, but also introduce a clear conceptual distinction between space/time and body/change, (ii) the Montpellier notebooks of the late 1670s develop a systematic theory of distance as a real but mere relation between bodies, and (iii) the Essay of 1690 embraces absolute space and time, grounded on God’s literal immensity and eternity.

5.3 INFLUENCE OF NEWTON?

Locke read the Principia very shortly a'er its publication since he wrote an anony-mous review for Bibliotheque Universelle & Historique in 1688. And he was still revis-ing the space and duration sections of the Essay upon his return from Holland the next year since an example mentions “this present year 1689” (II, xv, 30). However, neither the review itself, nor the notes Locke took while studying the Principia,8 say anything about absolute space and time. In fact, aside from modest digressions on the geometri-cal method, the nature of attraction and repulsion, and Cartesian vortices, the review consists mainly of section headings from the Principia.9

&e 1685#‘Dra' C’ of the Essay is obviously pertinent since its composition is just prior to Locke’s encounter with the Principia.10 On the one hand, he already char-acterizes expansion and duration as uniform, boundless, and in%nite, distinguishes them from their sensible measures, place and time, and associates them with God’s immensity and eternity. On the other hand, in 1685 he still prefers to speak of the “pre-conceived Ideas of imaginary space & duration” (18:11), whereas in the corresponding sentence of the published Essay, the quali%cation ‘imaginary’ is deleted (II, xv, 8). Here is another example of a#shi':

Dra! C: “&e idea of extension of any body is so much of Imaginary Space as that bulk of that body takes up as lies between the extremities of it. And place is so much of that Imaginary Space as lies between it and the other known body” (18:11).

7 It is true that Locke understands our grasp of the in%nity of absolute space and time di=erently than Newton, as negative rather than positive. But this is not because he is dubious of Newton’s ‘absolute, true and mathematical quantities.’ On the contrary, by the Essay he had embraced#them. 8 Rogers (1978, p.#222,#n14). 9 See Axtell (1965).10 Page references to ‘Dra' C’ are to Locke (1685).


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Essay:#“&e extension of any body is so much of that In%nite Space as the bulk of that body takes up. And place is the position of any body as considered at a certain distance from some other” (II, xv,#8).

In ‘Dra' C’ place and time denote the conventional ‘position as it were’ of %nite beings in in%nite space and duration (18:10), but in the Essay such positions seem to be objec-tive (II, xv, 5). Indeed, an entire paragraph against the absolutist notion of the ‘place of the universe’ as a whole (18:12) is replaced with a more conciliatory treatment in the Essay. &ough strictly speaking there is no “clear and distinct” idea of the universe’s place, nevertheless “the word Place has sometimes a more confused sense, and stands for that Space which any body takes up, and so the universe is in a Place” (II, xiii, 10; cf. 16:10,#11).11

So it is reasonable to conclude that Locke’s lingering scruples about the reality of absolute space and time were removed by his close and admiring study of Newton’s ‘never enough to be praised’ book. &e Principia was evidently not, however, the source for Locke’s crucial association of space and time with God’s immensity and eternity since Newton himself does not broach this question in the %rst edition of the Principia.12 Furthermore, as noted, Locke already had his ‘divine space-time’ in place before the two became friends in London shortly a'er Locke’s return from Holland in 1689. Yet somewhat earlier than Locke was coming to the conclusion that God %lls eternity and immensity, Newton was developing his own version of this doctrine in the unpublished De dravitatione et aequipondio $uidorum (c.#1685?).13 &ere is independent evidence that Locke was otherwise in$uenced by the content of De Grav:#his translator Pierre Coste reports that Newton personally explained to Locke De Grav’s voluntarist theory of body and that this was the source for the “dim and seeming” conception of ex nihilo creation hinted at in the second edition of the Essay (IV, x, 18).14 &ere are several notable parallels between De Grav and the penultimate and %nal dra's of the Essay, starting with the discussions of God’s

11 &is di=erence between the Essay and ‘Dra' C’ is also noted by Ayers (1990, Vol. 1, pp.#235–236).12 Perhaps it was Locke who in$uenced the elaborate ‘physico-theology’ of the Opticks and the 1713#‘General Scholium’. More likely, Cambridge Platonists like More and Raphson were a com-mon in$uence on both. And there are other, more direct, sources for Newton, especially his friend Samuel Clarke. See Koyré (1957), Copenhaver (1980), Janiak (2008), Slowik (2009,#2012).13 Page reference to De Grav (herea'er ‘DG’) are to Newton (2004).14 For discussion, see Bennett and Remnant (1978), Stein (2002), and Hill (2003), and Downing in this volume.


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relation to space and time.15 Both hold that space and time must be in%nite in order to accommodate#God:

Newton: “Space is eternal in duration and immutable because it is the emana-tive e=ect of an eternal and immutable being. If ever space had not existed, God would at that time have been nowhere” (DG, p.#26). “&e quantity of the existence of God is eternal in relation to duration; and in%nite in relation to the space in which he is present” (DG, p.#25).

Locke: “God, everyone easily allows, %lls Eternity; and it is hard to %nd a reason why anyone should doubt that he likewise %lls Immensity. His in%nite being is certainly as boundless one way as another” (II, xv,#iii).

More striking is the similar way each addresses the problem how a mind (such as God) could be extended without being divisible. Newton’s answer relies on a remarkable analogy with#time:

Thus the relation of duration to space is very different from that of body to space. For we do not ascribe different durations to the different parts of space, but say they all endure simultaneously. The moment of duration is the same at Rome and at London, on the earth and on the stars, and throughout the heavens. And just as we conceive any moment of duration to be diffused through all space, according to its kind, without any conception of its parts, so it is no more contradictory that mind can also in its own way be diffused (diffundi) throughout space without any conception of parts. (DG, p.#25).

Locke ventures the same analogy in ‘Dra' C’ and the published Essay. A'er observ-ing that “this present moment is common to all things, that are now in being, and equally comprehends that part of their existence as much as if they were but one single being”, Locke further comments:# “Whether Angels and Spirits have any analogy to this, in respect of expansion, is beyond my Comprehension” (II, xv, 11). Locke treats the notion that minds relate to space like moments do as the conjecture of a brilliant friend:#worthy in equal parts of consideration and caution.

15 De Grav, especially its ‘physico-theology’, has been much discussed lately. See, for example, Carriero (1990), Janiak (2008), Slowik (2009), Gorham (2011a, 2011b), Ducheyne (2011), Kochiras (2012), McGuire and Slowik (2013), and Schliesser (2013a, 2013b).


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()C Locke and Newton on Space and#Time

5.4 THE MEASURE OF ABSOLUTE!TIME

In deference to God and Newton, Locke overcomes his empiricist hesitations about the ontology of absolute space and time. But on the question of time’s measure he remains skeptical. We measure expansion and duration by sensible standards that we take to be invariant in the relevant respect:#solid ‘parcels of matter’ in the case of expansion and ‘successive appearances’ (mental or physical) in the case of duration. But in both ‘Dra' C’ and, somewhat less vehemently, in the published Essay, Locke emphasizes a special di>culty about the measurement of time. We can lay our chosen parcel of matter directly against another extended thing but “in the measuring of duration this cannot be done because no two di=erent parts of succession can be put together to measure one another” (II, xiv, 18). He concludes:#“Since no two portions of duration can be brought together it is impossible ever certainly to know their equality” (Ibid.).

In his running commentary on the Essay, Leibniz questions this supposed asym-metry:#“We certainly cannot say, either, that a measure of space, such as a yard, which is kept in wood or metal ever remains the same” (New Essays, p.#153).16 But this misses Locke’s point. We cannot be sure that this wooden stick remains a yard, but we can be sure its extension is equal to another stick, at any given time, by bringing them together and directly examining them. However we cannot bring this hour of clock-time together with the last to see if they coincide. We can, of course, see whether two clocks are synchronized. But this would not show that two parts of duration are equal since both clocks measure the same part of duration. We could even say that, at any instant, any given body is necessarily an accurate measure of the expansion it occupies. But there is no question of measuring duration at an instant since time is inherently ‘$eet-ing’, as Locke says (ii, xiv, 18). So we cannot be sure over time whether our clocks, synchronized or not, are regular. In ‘Dra' C’, Locke makes this point explicit about the best clock of his day, namely the pendulum:

For however we may certainly know that two diadrams of two pendulums that move together in our sight are sensibly equal to one another & it be probable that all of the diadrams of the same pendulum are equal to one another yet we can never be certain that any two successive diadrams of the same pen-dulum are exactly so because we never put them together to measure them. (1685,#17:26)

If we demand direct sensory con%rmation of the equality of temporal intervals, as Locke seems to, our demand can never be met. In Locke’s view, the primary source

16 Page reference to New Essays are to Leibniz (1996).


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of this special di>culty of measuring time is not its one-dimensionality but rather its inherently successive being. Since the parts of measured time cannot be simultane-ously coincident, unlike any dimension of spatial measure, we can never have direct con%rmation that these parts compose a uniform measure.

&ere is a di=erent conceptual problem about void space vs. empty time where dimensionality is crucial. Recall that Locke, in his relationist phase, denied any objec-tive quantity in extramundane void space:#“it can never be truly said that the utmost super%ces of the world is a foot distant from any thing, if there be nothing really exist-ing beyond it” (‘Journal’, p.#102). But this does not preclude a determinate quantity for a local vacuum since this quantity can be determined by surrounding it in two or three dimensions with a sensible body. But nothing similar is available for time:#if an interval of time is absolutely empty of successive change, nothing %xes its length, even if it is bounded on both sides by such change. &is other aspect of the problem of temporal measure Leibniz perceives clearly:

If there were a vacuum in space one could establish its size. But if there were a vacuum in time, i.e. duration without change, it would be impossible to estab-lish its length. It follows from this that we can refute someone who says that if there is a vacuum between two bodies then they touch, since two opposite poles within an empty sphere cannot touch—geometry forbids it. But we could not refute any one who said that two successive worlds are contiguous in time so that one necessarily begins as soon as the other ceases with no possible interval between them. (New Essays, II,#xv)17

Leibniz correctly identi%es dimensionality as the source of the di=erence:# “if space were only a line, and bodies were immobile, it would also be impossible to establish the length of the vacuum between two bodies” (Ibid.). But, as we have seen, Locke is not worried about the possibility of measuring empty time but rather the uncertainty of any temporal measure, given the successive parts of time cannot be compared.

We believe these kinds of asymmetries between temporal and spatial measure help account for a notable feature of the development of ideas of absolute space and time prior to Newton, especially in the seventeenth century. As Nicholas Jolley has observed, “philosophical theories that seem primarily tailored to space are o'en said to apply mutatis mutandis to the case of time.”.18 An important reason philosophers such as Gassendi and Barrow argued by analogy about the nature of time from already

17 See also Bennett (1966, pp.#175–176), Gorham (2012).18 Jolley (2006, p.#128). See also von Leyden (1968, p.#259).


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()E Locke and Newton on Space and#Time

established features of space, is that certain in$uential thought experiments in support of void space cannot be adapted to empty time.19 Scotus, for example, argued that God could annihilate the earthly elements while leaving the heavens intact:#“&erefore, the concave surface of the heavens could remain and nevertheless contain no body”.20 But, as Leibniz observed, the corresponding thought about empty time has much less#force.

&is relative weakness of temporal absolutism is evident in Newton as well. In De Grav he invokes the traditional ‘annihilation’ argument for the void:#“we cannot believe it [extension] would perish if God should annihilate a body; it follows that extension does not inhere as an accident in some subject” (DG, p.#22). But he o=ers no independent argument for empty time, other than to insist it is “possible to suppose that universal nothingness (nihil omnino) endures” (DG, p.#26). &e arguments for absolute space and time in the Principia’s ‘Scholium’ to the Laws seem to have a dif-ferent structure as well. In the Principia absolute space and motion are distinguished from their relative counterparts in order to explain inertial e=ects in the famous rotating bucket and globes. But the distinction between absolute time and its relative measures is not demanded by a causal argument, but rather because we are always attempting to “correct” the measures by appeal to more regular motions like astro-nomical cycles and the pendulum (Principia, p.#410).21 But even if such corrections presuppose the ideal of a perfectly uniform clock, it is hard to see how they establish the existence of an insensible duration without reference to anything external—any more than the pursuit of maximally rigid measuring rods depend on the existence of absolute space.22

In any event, for the moment we are not concerned with the ontology of absolute time but its measure. Like Locke, Newton acknowledges, “it is possible that there is no perfectly uniform motion by which time may have an exact measure” (Principia, p.#410). However, unlike Locke, he also thinks an exact measure of time is possible, even without having to ‘bring together’ its parts. Consider his connected globes spin-ning in an “immense vacuum”. Newton observes that the increase or decrease in their absolute rotation “could be known from the increased or decreased tension of the cord” (Principia, p.#414). And from unvaried tension we could presumably infer the rotation was uniform. &at is, we could know this clock to be perfectly regular, with-out having to ‘bring together’ its successive rotations, simply by examining the forces present. Even more directly, as we will see, Newton demonstrated the isochrony of

19 See Gorham (2012).20 Quaestiones quodlbetales, II, ch. 11, n7. Quoted in Cross (1998, p.#207).21 Schliesser aptly labels this conception of absolute time a ‘regulative ideal’ (2013b, p.#90).22 For a more detailed account, see Gorham (2012). For recent accounts that diverge from this reading, see DiSalle (2006), and Schliesser (2013b).


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cycloidal pendulums in the Principia from rather modest mathematical and dynamical assumptions.

But Locke’s reading of the Principia failed to persuade him about the reliability of such measures. A#passage added to the Essay (post-Principia) strongly echoes the Newtonian ontology of absolute time:#“Duration in itself is to be considered as going on in one constant, equal, uniform course” (II, xiv, 21). And he grants Newton’s point about using the pendulum to ‘correct’ traditional clocks:#“Men have of late made use of the Pendulum as a more steady and regular motion than that of the sun” (II, xiv, 21). Yet, despite the well-known work on pendulum isochrony by Galileo, Huygens, and Newton—Locke, of course, admired (the ‘great’) Huygens and discussed the Principia with him in Rotterdam—he still insists we can never know whether distinct pendu-lum swings are equal. For one thing, “the medium in which the pendulum moves is not constantly the same” (Ibid.). &is di>culty was already well known to Newton who devoted considerable energy to the calculation of pendular oscillations in various media (Principia, Book II, Section 6).23 But Locke also raises an additional skeptical concern about the pendulum:

If anyone should be asked how he certainly knows that two successive swings of a pendulum are equal, it would be very hard to satisfy himself that they are infallibly so, since we cannot be sure that the cause of that motion, which is unknown to us, shall always operate equally. (II, xiv,#21)24

It is tempting to suppose that Locke is merely calling attention to the idealization of physical laws, as compared with the complexity of actual systems. We can’t be sure that the motion of the pendulum is not a=ected by varying forces:#the wind, subtle motions in the base, and so on. But this would fail to explain his unrelenting insistence that in order to be sure of the equality of successive pendulum swings we would need to ‘bring together’ two parts of duration. Such bringing together is not required to ascertain, at any given time, that we’ve accounted for all relevant forces.

We would like to suggest that Locke’s point is a deeper, Humean one:#not simply that we can’t ever know all the causes that operate; we can’t even know the causes ‘oper-ate equally’ over time. Despite his admiration for the incomparable Mr. Newton, Locke

23 See Schliesser (2013b) for a brief, but thorough and perceptive, account of the physical, meta-physical, and experimental aspects of Newton’s philosophy of time, as well as his debts to Galileo and Huygens.24 Oddly, Ayers quotes the %nal words of this passage in support of the view that for Locke our temporal judgments presuppose unchanging laws (1990, Vol. 1, p.#232). On the contrary, Locke’s clear point is that we are not entitled to any such presumption.


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considers scienti%c knowledge of the laws governing motion beyond us. One reason is well known:#we do not, according to Locke, know the ‘real essences’ of bodies (owing to their remoteness and/or minuteness), and we can therefore not grasp how their properties, powers, and operations follow from those essences in the same way we can grasp geometrical ideas.25 An additional cause of ignorance is the “want of a discover-able connections between those ideas which we have” of bodies (IV, iii, 28). Our igno-rance of the connections among our ideas of bodies is again contrasted with geometry, where we cannot conceive the connections “to be possibly mutable or depend on an arbitrary power” (IV, iii, 29). &is ignorance extends even to the fundamental rules governing physical motion:

[t] he original Rules and Communications of Motion being such, wherein we can %nd no natural connection with any ideas we have, we cannot but ascribe them to the arbitrary will and good pleasure of the Wise Architect . . . &e things that as far as our observation reaches, we constantly %nd to proceed regularly, we may conclude, do act by a law set them; but yet by a law that we know not. Whereby though causes work steadily, and e=ects do constantly $ow from them, yet their connection and dependencies, being not discoverable in our ideas, we have but an experimental knowledge of them. (IV, iii,#29)26

Since we %nd no natural ‘connections and dependencies’ among our ideas concern-ing the motions of bodies, the only law from which we can know they proceed is the inscrutable divine will. Locke concludes:#“Several e=ects come every day within the notice of our senses, of which we have so far Sensitive Knowledge; but the cause, man-ner and certainty of their production we must be content to be ignorant of ” (Ibid., cf. IV, xii, 12). However successful are Newton’s laws of the ‘communications of motion’ in accounting for the association between rotational motion and centrifugal force, and the regular motion of the pendulum, they do not reveal to us any ‘natural connection’ among our ideas. And for this reason it is impossible to be certain these associations will continue to $ow from their hidden and arbitrary cause, ultimately God’s will. So lacking a means of directly bringing together and comparing the parts of duration we must settle for the “seeming equality” of certain successive appearances lodged in our memory, along “with the concurrence of other probable reasons, to persuade us of

25 “ . . . whilst we are destitute of senses acute enough to discover the minute particles of bodies, and to give us ideas of their mechanical a=ections, we must be content to be ignorant of their properties and ways of operation” (IV, iii, 25; cf. IV, iii, 26; IV, xii,#9).26 See also #oughts Concerning Education (Locke 1989, p.#303). See McCann (1985, pp.#245, 257–258), Downing (1997, pp.#304–305), Anstey (2011, p.#147).


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their equality” (II, xv, 21). But the “highest probability amounts not to certainty, with-out which there can be no true knowledge” (II, iii, xiv; cf. IV, xii, 10 and IV, xvi,#6).27

For Newton it is not necessary that we perceive necessary connections among our ideas of bodies in order to be sure how they will operate going forward. It is enough that we derive laws of their operation from the fundamental forces that a=ect them:#“&e basic problem of philosophy seems to be to discover the forces of nature from the phe-nomena of motions and then to demonstrate the other phenomena from these forces” (Principia, p.#382). Consider his speci%c treatment of the pendulum in the Principia. Following Huygens, he proves in Proposition 51 of Book I#that cycloidal pendulums with di=erent amplitudes will be isochronous (have the same period). It follows from this, in Locke’s terms, that successive ‘diadrams’ of a single pendulum will have equiva-lent duration. Besides geometrical considerations about cycloids, Newton’s proof of isochrony relies on a very minimal physical assumption:#“the centripetal force tending from all directions to the center of a globe is in each individual place as to the distance of that place to the center” (Principia, p.#552). &at is, Newton assumes that the force that accelerates a body along its arc to the low point of a pendulum will at all times, and for all distances, be proportional to its distance to the center of the earth. From this he proves that the parts of the arcs of di=erent lengths will “vanish simultaneously”, so that bodies with di=erent arcs “will arrive at the same time at the perpendicular” (Principia, p.#553). In Book II (Section 6), where he treats of ‘simple pendulums’ with real masses, Newton relies on the Second Law of Motion to calculate actual rates of acceleration both in vacuums and in various media. &ese assumptions are unobjec-tionable and well supported of course; nevertheless they presuppose that nature is uni-form in certain de%nite ways, something Locke is unwilling to admit as certain.

&e question then arises, what entitles Newton to this presumption? On this point, Newton makes plain his inductivism, at least in later editions of the Principia. &e &ird Rule of Philosophizing states, “qualities that belong to all bodies on which experiments

27 In the later works like the Notes Concerning Education (1693), the Conduct of the Human Understanding (published 1706), and a letter to Stilling$eet (published 1699), Locke seems more willing to grant Newton’s philosophy the status of ‘knowledge’, as Stein (1990, pp.#31–33) and Winkler (2008) have emphasized. But, as Lisa Downing has e=ectively argued, he is using ‘knowledge’ in a looser sense not inconsistent with the cautious epistemology of the Essay (Downing 1997, p.# 292). Furthermore, it is Newton’s success as a mathematician rather than a natural philosopher that Locke tends to praise (Domski 2011; cf. Anstey 2003, 2011). In the second and subsequent editions of the Essay, he notes that Newton does not rely on ‘maxims’ but rather ‘intermediate ideas’ in the mathematical formalism of his demonstration of ‘so many new truths’ (IV, vii, 11). But it seems it is the geometrical proofs rather than the laws of nature that Locke is applauding:#“the agreement or disagreement of the ideas” (II, vii, 3). And in the fourth edition he weakened his proscription against action at a distance, presumably to accommodate gravity (II, viii,#11).


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can be made should be taken as belonging to all bodies universally” (Principia, p.#795). Contrary to Locke and Descartes, he thinks gravitation and inertial force have at least as strong empirical claim for universality as impenetrability and extension.28 Since experiments have uniformly con%rmed, at least to a high degree of approximation, the laws of force and motion for planets, comets, and the sea, we can be con%dent that the behavior of all bodies will conform to these laws, including the speci%c phenomena demonstrated from these laws, such as pendulur isochrony. Newton’s primary defense of the &ird Rule is simply that it is required for empirical science:#“For the qualities of bodies can be known only through experiments”. &e assumption that “nature is always simple and consonant with itself ” (Principia, p.#795) is not an empirical law in itself but rather a pre-condition for science of nature that the Principia exempli%es.29 So, a'er listing the various qualities that fall under the rule, he emphasizes:#“this is the founda-tion of all natural philosophy” (Principia, p.#796). In other words, Newton takes it for granted that natural or experimental philosophy delivers genuine knowledge. &ere is no question, as there is for Locke, whether induction itself is reliable since induction is the sine qua non of empirical knowledge. &us, he o=ers Cotes the following terse justi%cation for the &ird Rule:#“if we break that rule, we cannot a>rm any one law of nature:#we cannot so much as a>rm that matter is impenetrable. Experimental phi-losophy reduces all phenomena to general rules and looks upon the rules to be general when they hold generally in phenomena” (2004, pp.#120–121).30

28 In an early dra' of the &ird Rule, the principle of generality is applied to “laws (and ‘proper-ties’)” rather than simply ‘qualities’. See McGuire (1995, p.#89).29 We accept McGuire’s argument that the &ird Rule is also a principle of ‘transduction’ from observable things to their unobservable constituents (1995, ch. 2). But Newton clearly also emphasizes the ‘uniformity’ of nature over space and time along with the macro-micro analogy. And only the former would explain the disagreement with Locke about time’s measure; indeed Locke accepts the latter principle, as McGuire notes. Although McGuire does not consider the &ird Rule a primarily inductive principle, he does acknowledge that “his belief in the uniformity of nature, an unquestioned and primary commitment, is certainly fundamental to his whole phi-losophy of nature” (McGuire 1995, p.#254; cf. Shapiro 2004 and Finocchiaro#1974).30 “And thus Nature will be very conformable to herself and very simple” (Opticks, Query 31; Newton 2004, p.#135). “Although the arguing from experiments and observations by inductions be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of ” (Opticks, second English edition; Shapiro 2004, p.#197). “&at third rule is the rule of induction. And without it no proposition can become general in Natural Philosophy” (Dra' letter to Conti, for Leibniz. See McGuire 1995, p.#86). “Nature would not be consistently simple and consistent with itself [unless] the qualities on which it is allowed to make experiments, as many of them as are found to be immutable, apply in common to all bodies” (Dra' 2 of Rule II. See McGuire 1995, p.#243). “In this experimental philosophy, propositions are deduced from the phenomena and made general by induction” (‘General Scholium’, Principia, p.#943). On Newton’s rather loose notion of ‘deduction’ from the phenomena, see Shapiro (2004, pp.#211–213).


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5.5 CONCLUSION

One man’s modus ponens is another man’s modus tollens. Locke and Newton agree that Newtonian natural philosophy counts as knowledge only if induction beyond immediate experience is reliably truth-preserving. Newton’s positive, scienti%c empiri-cism takes it for granted that an empirical theory with universal empirical support is right until shown otherwise:#“certainly idle fantasies ought not to be fabricated reck-lessly against the evidence of experiments” (Principia, p.#795). &is is the upshot of his Fourth Rule of Philosophizing:#“Propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses” (Principia, p.#796). As the %nal proviso of the Rule makes explicit, Newton remains a falliblist. But Locke’s negative, sensationalist empiricism, with its skepticism about real essences, the uniformity of nature, and the ends of God, leads him to pes-simistic conclusion that in the end “natural philosophy is not capable of being made a science” (IV, xii,#10).31

&eir respective views of time’s measure follow from these divergent standards of empirical knowledge. Just as the absolute place of the sensible universe must remain a ‘confused’ idea for Locke (II, xii, 10), so must the uniform duration of measured time. Neither can be derived from immediate sensation. But if instead we count an idea as empirically supported so long as it is successfully applied to physical systems using the laws of our most empirically successful theory, the relation between absolute time and its relative measure is perfectly empirical. For it corresponds to the distinction between the durations of inertial vs. accelerated motions—“an ideal clock that keeps absolute time is simply an inertial clock” as Robert DiSalle observes.32 We can then use the laws of motion to determine whether a given motion is really ‘accelerated or retarded’. But solving the problem in this sense requires that we give inductively supported physical theory at least as much authority as the immediate experience, intuition, and demon-stration favored by Locke and traditional philosophy. In Newton’s hands, the concept of absolute time becomes in e=ect ‘theory-laden’, or as Howard Stein puts it, “part of

31 In his recent, path-breaking treatment of Locke’s philosophy of science, Peter Anstey empha-sizes that despite his skepticism about natural philosophy ever being made a full science, Locke is nevertheless committed to ‘experimental philosophy’, i.e., to the use of experiment and obser-vation in natural philosophy rather than speculation and hypotheses (2011, pp.# 3–5, 25–30). However, as Shapiro recently has pointed out (2004), Newton too is explicitly allied with the ‘experimental philosophy’ in this sense. As we see it, the di=erence between them concerns how much knowledge beyond immediate observation the experimental philosophy provides. Locke is pessimistic and skeptical; Newton is optimistic yet falliblist.32 2006,#p.#39.


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Newton’s theoretical apparatus”.33 We would put the point slightly di=erently:#absolute time is measurable because we presume we have a %rm grip on the universal laws that govern its measuring devices. Locke was unwilling to grant this priority to natural phi-losophy:#the ‘underlabourer’ modesty of the Essay’s Epistle is somewhat disingenuous. And so for him the problem of absolute time—like those of gravitational attraction, bodily cohesion, mind-body interaction, and so on—remained unsolved.

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Locke and Newton on Space and Time (with Ed Slowiik)

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