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# THREE DISTINCTIONS

Newton’s Principia (published in 1687) opens with a series of definitions of the terms that he will use, including “quantity of matter,” “quantity of motion,” “inherent force of matter,” and so forth. Immediately following these definitions he turns his attention to time, space, place, and motion, in a scholium that begins as follows (Newton 1999, 408):

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.

The literature has largely focused on absolute versus relative motion, and absolute space, with comparatively little discussion of time,[1] and nothing that I know of about why Newton has this three-fold set of distinctions.

However, Schliesser’s (2013) discussion of Newton on time was inspired by Huggett (2012), who offered an interpretation of the distinction between absolute and true motion.[2] I differ from both in my interpretation of the terminology, and therefore in the distinctions that Newton is drawing. In this paper I focus on the case of time.

Newton introduces his discussion of time as follows:

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 (precise or imprecise) of duration by means of motion; such a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time. (Newton 1999, 408)

Thus, Newton is explicit in applying to time the three distinctions of absolute versus relative, true versus apparent, and mathematical versus common. What does he mean by these distinctions, and why do they matter?

According to Schliesser (2013), the terminology of “absolute” and “true” marks a distinction between time as a theoretical construct, arrived at from empirical considerations and applied in the context of the project of the Principia (absolute time), versus time as it occurs in metaphysical and theological discussions (true time). He writes,

True time is an unnecessary addition to Newton’s conceptual framework of absolute and mathematical time given the particular problems addressed in the Principia. (91)

And he goes on,

Newton introduces more conceptual distinctions than are required by his physical theory; his dynamics requires no more than absolute (mathematical) time as a contrast to “relative, apparent, and common time” without resort to “true” time. (92)

On Schliesser’s view, while it plays an important role in Newton’s overall philosophy of time, “true” time (and therefore the contrast between true and apparent time) has no place in the empirical project of the Principia.

I disagree. And what is at stake here is not merely Newton exegesis: resolving the terminological issue has implications for which questions concerning the nature and structure of time Newton’s empirical project is capable of addressing. In other words, what is at stake is the metaphysical reach of his empirical methods. I think, contra Schliesser, that all three of Newton’s conceptual distinctions between absolute and relative, true and apparent, and mathematical and common time, have empirical import (section 5) and are necessary for the project of the Principia (section 6). Moreover, I maintain that these distinctions bear on long-standing philosophical questions concerning the nature and structure of time (sections 7 and 8). As a consequence, these questions become subject to empirical investigation in a manner not possible prior to the relevant philosophical innovations of Newton’s Principia.

In the following section I discuss Schliesser’s approach in some more detail, before turning to my preferred approach in section 4, below. [3]

whereas for Schliesser “absolute time” is a mathematical construct, a time parameter in our physical theory by which we seek to place a measure on the passage of true time, I will argue below that “absolute” and “true” are both to be understood as characteristics of time, characteristics that will both be represented in an appropriate time parameter of an adequate physical theory.

Schliesser’s proposal is that absolute time is a theoretical construct obtained from our observations of the heavenly bodies and their relative motions via the equation of time (of which more below). He writes,

As a first approximation, we can say that “absolute” time is approximated by our clocks (or some other measure of relative time) corrected by the astronomical equation of time ... allowing thus a measure of true time. (2013, 90)

On this view, the empirical basis of “absolute time” is such that it extends spatially only so far as the bodies in our planetary systems whose relative motions we observe (with respect to the background of the fixed stars). True time, by contrast, is that which we are seeking to approximate in our construction of absolute time, and, according to Schliesser, it extends from infinity to infinity. Moreover, insofar as there is always room for improvement in the process by which we construct absolute time, we can think of it as a “regulative ideal.”

Schliesser’s “absolute time” is needed for the project of the Principia because what Newton is trying to do in the Principia is to determine whether our planetary system is geocentric or heliocentric, and in order to solve this problem he needs to be able to assign accelerations to bodies in our planetary system in a unique and consistent way. This latter task requires a single time parameter relative to which the bodies in our planetary system are assigned their motions. Furthermore, for the purposes of the project, the spatial extent of this time parameter need be only so far as the observed bodies in our planetary system, and this is consistent with the empirical basis from which the time parameter is constructed.

For Schliesser, our empirically constructed (absolute) time is only approximately accurate compared to metaphysical (true) time, and it has limited spatial extent. When Newton introduces true time, in addition to absolute time, he does not thereby introduce any new empirical questions, because true time is answerable to the demands of Newton’s rational theology and not to empirical considerations. The only open empirical question concerns the spatial extent of absolute time: will the time parameter appropriate for our planetary system turn out to be appropriate for treating bodies outside our planetary system?

This is one way to read the distinctions, and to think about their significance for philosophy of time. I agree up to a point. I agree that Newtonian absolute time should not be conflated with Newtonian true time. I agree that, for the purposes of the Principia, Newton does not need his time parameter to extend from infinity to infinity. I agree that the spatial reach of Newton’s time parameter in the Principia is an empirical matter. However, I do not think that, for Newton, “absolute” and “true” mark Schliesser’s distinction between a spatially limited empirical time parameter and a theologically motivated, infinitely extended “time.”

Initial doubts about Schliesser’s interpretation arise when we notice that in the scholium Newton does not make the positive assertion that absolute, true, or mathematical time are eternal in duration, nor does he assert that space is infinite, and nor does he assert that each moment of time extends from infinity to infinity. We are familiar with these claims from other places in Newton’s writings, but in this part of the text, where Newton is setting out what is needed for the project of the Principia, no such positive claims are made.

Moreover, the distinction that Schliesser draws is not one that we find doing work for Newton in his argument in the Principia, such that he has reason to mark it by means of a terminological distinction. As evidence for this, consider that Newton has just as good reasons to think that his absolute time extends to the physics of the distant stars and to the planetary systems around distant stars (if any such exist) as he does to think that his laws of motion and law of universal gravitation apply to such bodies, and he does not make the solar system the boundary of applicability for these latter. Newton worried about how we extend our knowledge to bodies beyond the reach of our experiments, and this worry is explicitly addressed in his Rule 3 of Reasoning, added to Book 3 in the second edition of the Principia (Newton 1999, 795):

Those qualities of bodies that cannot be intended and remitted and that belong

to all bodies on which experiments can be made should be taken as qualities of

all bodies universally.

This rule plays a crucial role in enabling Newton to extend results from terrestrial experiments to the celestial bodies of the solar system. In applying Rule 3 to bodies beyond the solar system, we would certainly be wise to be tentative given the flimsiness (even non-existence) of our empirical evidence, but there is nothing in Newton’s writings to indicate a sharp cut-off at the outer edges of the solar system such that we should not consider distant stars to be bodies. On the contrary, the possibility of other worlds around other Suns, governed by the same laws, is very much part of Newton’s thinking. For example, there is a manuscript5 in which Newton asserts that the fixed stars are bodies just like our Sun: they are formed into spheres by their own gravity, and since they are bodies, they are, by definition, subject to the laws of motion. It seems to me that the distinction Schliesser draws is not important for Newton’s purposes.

Finally, the contexts in which Newton extends moments of time to spatial infinity are generally also those in which he is talking about God’s presence in the world, rather than those in which he is concerned with methods of reasoning from the phenomena.

In my opinion, we have good reason to suspect that Newton was careful not to overreach empirically when he was setting out his accounts of time and space in the scholium (i.e., at the outset of the empirical project of the Principia). There is therefore reason to doubt that the inclusion of “true time” is an “unnecessary addition” (Schliesser 2013, 91). In the following section I propose an alternative interpretation of the terminology, in which each of his three distinctions—absolute versus relative, true versus apparent, and mathematical versus common—are relevant and important for the project of the Principia.

• [1] Arthur 1995; Gorham 2012; McGuire 1978; Palmerino 2013.
• [2] The disagreements that I have with Schliesser and Huggett are small compared to the overall content of theirpapers, from which I learned much. As so often happens, the many points of agreement and enlightenmentI pass over in silence, to focus on what we may learn from a point on which we disagree.
• [3] schliesser’s ACCOUNT OF NEWTON ON TIME Schliesser (2013) argues that we should distinguish absolute time from true time,and I think he is right that the two terms are not synonymous for Newton. However,

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