When it comes to motion, there is a standard way of understanding the absolute versus relative terminology: relative motion is motion of a body with respect to other bodies, and absolute motion is motion of a body independent of its relations to other bodies (but perhaps in relation to absolute space and time instead). I take this to be uncontroversial. The idea of motion as relative to other bodies was familiar (from Descartes, among others), and much discussed, and moreover this is the one distinction that Newton himself explains in detail. He uses it in the same way for space, time, and place as he does for motion, and absolute motion is further spelled out in terms of absolute space and absolute time. Newton is clear about this terminology, and I take it that his readers would have understood his use of the terms in the way that is now standard. Absolute time is independent of material bodies, whereas relative time is an aspect of material bodies or of the relations among them.

The terms “true” and “apparent” have meanings that would already have been familiar to Newton’s readers from the dispute over the Copernican system, so some historical context is useful. The Copernican dispute concerns whether the system of the world is geocentric or heliocentric or whether there is no fact of the matter. Book III of Newton’s Principia is called “The System of the World,” and this is where Newton marshals the resources developed in Books I and II to give his answer to the Copernican question. Addressing this question is the overall purpose of the Principia, and the Copernican dispute is therefore the appropriate context for understanding what Newton means by the terminology “true and apparent” in the Principia.

Within this dispute, those in the geocentric and heliocentric camps shared a commitment to true motion, as distinct from apparent motion: whatever the apparent motion of a given body (e.g., the Sun moving across the sky), and of which there may be many (depending on the position of the observer), there is nevertheless a unique motion that is the true motion of that body. Thus, for geocentrists and heliocentrists alike, one motion is singled out as not mere appearance, but proper to the body, and this is its true motion. The distinction between true and apparent motion comes to the fore in the Copernican dispute because of the obvious conflict in Copernicus’s system between the appearances (it appears to us, observing from Earth, that the Sun moves around a stationary Earth) and the true motions described in the theoretical system (the Earth in motion around a stationary Sun), but even those astronomers committed to a geocentric theory made the distinction between the apparent motions of the heavenly bodies (how their motions appear to us) and their true motions.

With these distinctions in hand (between absolute versus relative and true versus apparent) there remains the issue of the relationship between them. For example, Descartes sought to give a relative account of true motion, whereas Newton sought to define true motion in terms of absolute motion. In his Principles II.25, Descartes (1991) defined true motion in terms of the relative motion of a body with respect to the immediately surrounding bodies (themselves considered to be at rest), and thereby sought to identify the one true relative motion proper to the body (i.e., its true motion) from the many relative motions that this body in the plenum undergoes. One of the things that Newton tried to do in the scholium to the definitions in the Principia was to show that true motion should be identified not with relative motion but with absolute motion, where for Newton absolute motion is motion with respect to absolute space and absolute time.

So these distinctions, and also I think the terminology, were already out there for the case of motion. Newton gathers them together, sets them out as two distinct pairs, and standardizes them across space, time, place, and motion. If this is the right way to approach the terminology,^{[1]} then the contrast between true and apparent time is the following. Just as true motion is unique and proper to the body (or system of bodies) in question, in contrast to being a property of the appearances, so too true time is unique and proper to the body (or system of bodies) in question, a property of the body or system itself rather than of the appearances. We can illustrate the idea as follows. The relative motions of the Sun and Moon with respect to the Earth give rise to their apparent motions with respect to the fixed stars, as viewed from Earth. Each apparent motion may be used as a clock for the Earth- Sun-Moon system, and therefore each gives rise to an apparent time (apparent solar time and apparent lunar time respectively). But these “clocks” do not tick regularly with respect to one another, and therefore the true time of the Earth-Sun-Moon system (if any such exists) remains to be determined.

The terminology of “mathematical” and “common” has its origins not in discussions of motion, but in the treatment of time in mathematical astronomy. In the scholium, Newton writes that absolute time is distinguished from relative time by the equation of common time. We can therefore begin our investigation of what is meant by “common time,” and by the contrasting term “mathematical time,” by looking at the equation of common time. Common time, in this context, is time on which a metric is imposed by means of material clocks, for the purposes of our common life; it is the division of the passage of time into intervals by which the rhythm of our lives is marked out, and has no more precision, nor any other properties, than those needed for this purpose.^{[2]} In the seventeenth century, apparent solar time (of which more below, see section 5) was used as the basis of common time. By contrast, the equation of common time was used by astronomers to construct a time parameter suitable for the purposes of mathematical astronomy (as explained below, section 5). This time parameter has precise mathematical properties (it is metrical, it is continuous, and so forth), and in later sections of this paper I will stress the importance of Newton’s time parameter being metrical. This time parameter was of no interest or use to anyone except mathematical astronomers. For Newton’s intended readership, well versed in the problems ofhorology and mathematical astronomy (especially Huygens), this terminology of mathematical and common time would have been readily understood.

I claim, therefore, that all six terms in the three distinctions have meanings that are prior to, and external to, the project of the Principia. What is new with Newton is stating them all explicitly as contrasts like this, stating them all together, and applying them uniformly and systematically across time, space, place, and motion.

If this is right, then all three distinctions are associated with independent questions concerning the nature and structure of time. Is time absolute or relative ? Is time true or apparent ? Is time mathematical or common? Moreover, as I will argue in what follows, each distinction has empirical import (section 5), all three conceptual distinctions are needed for setting up the project of the Principia (section 6), and therefore each of the three questions becomes subject to empirical investigation (see also section 6). The upshot is that, at the very least, there are more open empirical questions concerning time than Schliesser’s interpretation of this terminology would allow. But there is much more than this. In making these distinctions explicit for the first time, and in tying them to the details of empirical enquiry, Newton makes the questions about the nature and structure of time more fine-grained, and transforms the process by which we are to address them. I will argue (section 8) that all three distinctions engage with familiar metaphysical questions concerning the nature and structure of time, and so those questions themselves become empirically tractable in Newton’s hands. His work in the Principia thus constitutes an important transformation in the appropriate methodology for pursuing the metaphysics of time.

[2] It would be interesting to know whether there is any connection between this use of the term “common time,”and that in music (current at the time), where 4/4 time was considered “imperfect” and was known as “common time,” whereas time signatures with a three-measure (e.g., 3/4 time) were considered “perfect” (in accordance with the Trinity).