I have argued that Newton is very deliberate when he sets out his three distinctions between absolute and relative, true and apparent, and mathematical and common time: each distinction is different, and each is needed for setting up the project of the Principia. I have also argued that all three distinctions mark open empirical questions in the context of the Principia (though I make no claim that this was Newton’s own view). The questions of whether time is absolute or relative, true or apparent, and mathematical or common become empirically tractable in the context of the project of the Principia (or some such project). Moreover, the significance of this conclusion is not local to the Principia. If we read the Principia as making a contribution to Descartes’s “metaphysical physics,” then we can read the moves that Newton is making as contributions to that metaphysical project, albeit via a very different epistemology and methodology. Read in this light, we see that Newton’s distinctions are connected to questions concerning the nature and structure of time. Newton transformed the methodology by which these questions should be addressed, providing empirical purchase on them and rendering them empirically tractable. Prior to Newton, questions such as whether time is relative (depending on the actual motions of bodies) or absolute (independent of these motions), and whether there is one time or many, were questions that could be tackled independently of the details of empirical enquiry. In the wake of the Principia, this is no longer the case: any legitimate exploration of these questions must take into account the kind of detailed empirical enquiry pursued in the Principia. Philosophical progress has been made.
In addition to these specific conclusions concerning an appropriately empiricist metaphysics of time, there is a more general methodological message that is perhaps worth highlighting. Disputes in philosophy of time over how to understand the significance of special relativity, for example, are hampered by difficulties over how to read the developments in physics as contributions to philosophy. Disputes arise as to whether the philosophical challenges posed by relativity of simultaneity in special relativity can be safely ignored by philosophers since special relativity is a false theory, and over whether, even if special relativity is to be taken into account, the dispensability of a privileged present in special relativity implies anything about the existence or otherwise of a privileged present, metaphysically. These disputes seem to me poorly framed, because they fail to read special relativity itself as arising through a diachronic process of philosophical engagement with our everyday concepts of space and time, a process that has clarified and transformed those concepts (see DiSalle 2006). The example I have discussed in this paper is Newton’s work on duration, and I have said nothing about simultaneity, which is more of a hot topic in contemporary metaphysics. But similar work to that which I have done here can be done for simultaneity. The question of whether time flows is another topic that has received attention recently, and, as my remarks on mathematical time above indicate, I think that attention to the role of this claim in Newton’s project help clarify how such a claim should be understood. By reading developments in physics as a part of the history of philosophy, we can make visible the ways in which physics contributes to the conceptual clarifications and transformations of the very questions that we are asking about time, and the means by which aspects of our oldest questions concerning time are rendered empirically tractable.
The Oxford Handbook of Philosophy of Time (2011) and the Blackwell Companion to the Philosophy of Time (2013) both contain sections written by metaphysicians (on such topics as presentism, persistence, fatalism, and tense) and sections written by philosophers of physics (on time in classical and relativistic physics, and in cosmology and quantum gravity). Though I have little empirical evidence to offer you, I am doubtful how much each group of philosophers reads one another’s chapters: if cross-referencing is anything to go by, they are not really talking to one another, and one reason is their differing methodologies. A more historically driven methodology, in which both philosophy and physics are read diachronically as contributions to our ongoing philosophical conversation, would enable both parties to speak to one another in more fruitful ways.