[This is the middle section from a draft article on "Newton's Philosophy of Time" commissioned for a *Blackwell Companion on the philosophy of time*, edited by Adrian Bardon and Heather Dyke. The preceding section provides historical context with treatment of Galileo and Huygens; the subsequent section provides a closer analysis of Newton's metaphysics. Comments very welcome.--ES][1]
The main aim of the *Principia* is according to Newton, “to determine true motions from their causes, effects, and apparent differences, and, conversely, of how to determine from motions, whether true or apparent, true causes and effects. For to this was the purpose for which I composed the following treatise,” (Scholium to the Definitions; Newton 1999: 413-14).[2] In particular, from measurement Newton infers forces, which he treats as such “true causes and effects,” of accelerations. This (theory-mediated) measurement(s) as well as the laws of motion on which it is predicated presupposes a conception of time.

Newton’s most extensive explicit treatment of his conception of time in the *Principia* occurs in the Scholium to the definitions. He introduces the topic as follows, “Although time, space, place, and motion are very familiar to everyone, it must be noted that these quantities are popularly conceived solely with reference to the objects of sense perception. And this is the source of certain preconceptions; to eliminate them it is useful to distinguish these quantities into absolute and relative, true and apparent, mathematical and common.” (Newton 1999: 408) So, time is a quantity. In order to elucidate its nature Newton introduces a three-fold distinction. The popular conception that Newton wishes to dispel is presumably the Aristotelian “notion of time’s depending on the motions or existence of the material world,” (Clarke to an unknown correspondent, 1998: 114. Clarke goes on to cite Newton’s scholium to the definitions approvingly.)[3] While much of the scholium is devoted space, place, and motion, Newton begins with time:

“Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and external measure (exact or nonuniform) of duration by means of motion; such a measure—for example, an hour, a day, a month, a year—commonly used instead of true time.” (Newton 1999: 408)

As Richard Arthur has shown, Newton’s conception of uniform flowing time is deeply indebted to Christian Epicureans such as Gassendi and Charleton perhaps mediated by his (more nominalistically inclined) teacher, Barrow.[4] It is, however, not immediately obvious what Newton means by “Absolute, true, and mathematical” time. This only gets elucidated (after Newton has offered more informative definitions of space, place, and motion) a few paragraphs down in the Scholium:

“In Astronomy, absolute time is distinguished from relative time by the equation of common time. For natural days, which are commonly considered equal for the purpose of measuring time, are actually unequal. Astronomers correct this inequality in order to measure celestial motions on the basis of a truer time. It is possible that there is no uniform motion why time may have an exact measure. All motions can be accelerated and retarded, but the flow of absolute time cannot be changed. The duration or perseverance of the existence of things is the same, whether their motions are rapid or slow or null; accordingly, duration is rightly distinguished from its sensible measures and is gathered from them by means of an astronomical equation. Moreover, the need for using this equation in determining when phenomena occur is proved by experience with a pendulum clock and also by eclipses of the satellites of Jupiter.” (Newton 1999: 410)

So, “absolute” time is captured by the astronomical equation of time (as Newton was familiar with from the work of Huygens and later Flamsteed). The equation of time is derived from and simultaneously corrects ordinary (“for example, an hour, a day, a month, a year”) sensible measures. The equation of time is a measure of true time, but explicitly not identical to it. So, while the equation of time is absolute and (presumably) mathematical, it is not true time. Newton has the following idea in mind.

It is by now a familiar fact from scholarship on Newton that he recognized something akin to an inertial frame of reference (see, especially, his treatment of a system of bodies sharing a common acceleration in corollary 5 and, especially, 6 to the Laws of Motion; Newton 1999: 423).[5] But it is has been less remarked upon that Newton treats the equation of time as something akin to a shared ‘temporal frame.’ In particular, a corrected equation of time governs the temporal frame of the solar system. As he writes in the original, suppressed version of the final part of the *Principia*, *The System of the World: demonstrated in an easy and popular manner*: “That the Planets, in respect of the fixed Stars, are revolved by equable motions about their proper aces. And that (perhaps) those motions are the most fit for the equation of time.” (Newton 1740: 58) It’s only an equation that governs temporal relations among the *whole *system of fixed stars (including the solar system) that would closely approximate true time. (This is unavailable to human observers; I return to this issue in next section.)

To put the nub slightly differently. From the vantage point of Newton’s dynamics, he needs absolute and mathematical time in order to identify and assign accelerations to moving bodies in a consistent fashion. From this perspective true time is an unnecessary addition to his conceptual framework of absolute and mathematical time. One way to put this point is that in the first edition of the *Principia *(that is, without the addition of the General Scholium), "true" time could have been understood not as an ontological posit, but as a regulative principle that can be successively approximated by astronomical equations (absolute and mathematical time).[6] This makes sense of Newton's use of the measure being both revisable and "truer."

But even in the scholium to the definitions, Newton provides enough of a hint to suggest that he had other, theological uses for “true time” in sight: “if the meanings of words are to be defined by usage, then it is these sensible measures which should properly be understood by the terms, ‘time’, ‘space’, ‘place,’ and motion’, and the manner of expression will be out of the ordinary and purely mathematical if the quantities being measured are understood here. Accordingly those who there interpret these words as referring to the quantities being measured do violence to the Scriptures. And they no less corrupt mathematics and philosophy who confuse true quantities with their relations and common measures.” (Newton 1999: 413-414) Newton is responding to unnamed authors that argue from the truth of the Copernican hypothesis to the falsity of scripture.[7] This is not the place to explore the full details of Newton’s argument,[8] but the passage is a forceful reminder that time, space, place, and motion also have metaphysical roles to play in Newton’s theology. I turn to a discussion of these now.

Preliminary Notes
[1] My discussion here is very indebted to generous, private correspondence with Niccolo Guicciardini as well as my joint work with Chris Smeenk (forthcoming) “Newton’s Principia” *Oxford Handbook of the History of Physics*, edited by J. Buchwald and R. Fox, Oxford: Oxford University Press.
[2] Newton’s most devastating criticism of Descartes is that in his conceptual apparatus, “Cartesian motion is not motion, for it is has no velocity, no determination, and there is no space or distance traversed by it.” (Newton 2004: 20)
[3] It’s unclear how Newton read Descartes’ conception of time. See Gorham (2007) "Descartes on Time and Duration" *Early Science and Medicine*, Volume 12, Number 1, pp. 28-54(27) for brilliant revisionary….
[4] Richard T.W Arthur (1995) “Newton's fluxions and equably flowing time,” *Studies In History and Philosophy of Science Part* A, 26(2), June, 323-351.
[5] Any modern discussion of Newtonian space-time is deeply indebted to H. Stein (1967). What follows has been inspired, in part, by a recent paper, N. Huggett (2012) “What did Newton mean by Absolute Motion?” *Interpreting Newton*, edited by A. Janiak & E. Schliesser, Cambridge: Cambridge University Press, which has shown the fruitfulness to attending to a distinction between absolute and true motions in the scholium
[6] Elsewhere, I have argued that philosophic framing of the Principia changes dramatically between the first and second editions, see “On Reading Newton as An Epicurean: Kant, Spinozism and the Changes to the Principia” Studies in the History and Philosophy of Science: Series A (forthcoming);
[7] See Spinoza’s treatment of the Biblical passages at Theological Political Treatise 6.55; III/92. I have explored Newton’s and Newtonian responses to Spinoza in my (2012) “The Newtonian Refutation of Spinoza” in *Interpreting Newton*, ed. By A. Janiak & E. Schliesser, Cambridge: Cambridge University of Press; “On Reading Newton as An Epicurean”; “Spinoza and the Newtonians on Motion and Matter (and God, of course)” (under review).
[8] See A. Janiak….

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