definition of time travel in philosophy

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In This Article Expand or collapse the "in this article" section Time Travel

Introduction, general overviews.

• David Lewis’s Analysis, Its Forerunners and Critics
• Gödel and the Ideality of Time
• Models and Issues from Relativity
• Models and Issues from Quantum Theory
• Causal Loops and Probability
• Time Travel in Many Worlds and the Autonomy Principle
• Travel in Dynamic Time and Multi-Dimensional Time
• General Metaphysical Issues

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Time Travel by Alasdair Richmond LAST REVIEWED: 26 October 2015 LAST MODIFIED: 26 October 2015 DOI: 10.1093/obo/9780195396577-0295

Time travel is a philosophical growth industry, with many issues in metaphysics and elsewhere recently transformed by consideration of time travel possibilities. The debate has gradually shifted from focusing on time travel’s logical possibility (which possibility is now generally although not universally granted) to sundry topics including persistence, causation, personal identity, freedom, composition, and natural laws, to name but a few. Besides metaphysical discussions, some time travel works draw on the philosophies of science, spacetime, and computation. Some interesting forerunners notwithstanding, serious physical interest in time travel begins with Gödel’s 1949a demonstration that general relativity permits space-times that are riddled with closed timelike curves (“CTCs” henceforth). A key philosophical text on time travel is Lewis 1976 and its argument for the logical possibility of certain backward time travel journeys and even for the possibility of casual loops. Lewis concludes that time travel could occur in a possible world, albeit perhaps a strange world that would feature (or seem to feature) strange restrictions on actions. In Lewis’s analysis, a traveler can arrive in the past of the same history they come from provided that the traveler’s actions on arrival are consistent with the history that they come from. So other worlds or multiple temporal dimensions are not necessary to make time travel consistent. Granted, the physics, persistence conditions, agency, and epistemology of agents in such worlds might look weird indeed. Since Lewis, philosophical time travel questions include the following: given that a traveler into the past cannot create any paradoxical outcomes on arrival, what then would stay their hand? Are the constraints on a traveler’s actions admissible within our ordinary understanding of physical law or human agency? Is time travel compatible with dynamic time or even with the existence of time itself? Can backward time travel be physically possible within a single history? If a time traveler meets another stage of him- or herself, is the traveler in two places at once, and what theory of persistence can cope with this puzzling multiplication? Can time-travel spacetimes resolve otherwise intractable computational problems?

Despite several hundred philosophical and scientific articles, book chapters, and Internet resources devoted to philosophical problems posed by time travel, there is currently no full-length monograph or anthology on the subject. The best introduction to the topic in general so far is chapter 8 of Dainton (second edition 2010), Dainton 2010 being the best general philosophical resource available on time and space. The key work is Lewis 1976 , a defense of the logical possibility of backward time travel, from which a large number of subsequent treatments take their cue. A useful overview, albeit largely from a physical science perspective, is Nahin 1999 . Also largely physical in emphasis but comprehensive and thorough is Earman 1995 . Richmond 2003 surveys philosophical work on time travel to date. Arntzenius 2006 details the problems of free action and nomological constraint posed by backward time travel. Arntzenius and Maudlin 2005 is helpful on (especially) problems of physical law. Carroll 2008 is perhaps the best single online resource available on any aspect of time travel. Le Poidevin 2003 is a highly commendable introduction to the philosophy of time in general but especially good on problems of time travel. Bourne 2006 offers some useful arguments and clarifications centered on Gödel’s arguments about time travel and the relations between time travel and the status of times themselves. Earman and Wüthrich 2006 offers scientifically well informed but approachable and philosophically cogent discussions of what physics might, and might not, allow by way of time travel.

Arntzenius, Frank. “Time Travel: Double Your Fun.” Philosophy Compass 6 (2006): 599–616.

DOI: 10.1111/j.1747-9991.2006.00045.x

Entertaining survey of the philosophical terrain around time travel that concentrates particularly on the constraints on action likely to be suffered by travelers in the past. An excellent introduction to the nomological contrivance problem and more. Available online for purchase or by subscription.

Arntzenius, Frank, and Tim Maudlin. “ Time Travel and Modern Physics .” In Stanford Encyclopedia of Philosophy . Edited by Edward N. Zalta. 2005.

Notably acute survey of physical possibilities for time travel, including detailed arguments that backward time travel threatens to create correlations that conflict with standard quantum predictions.

Bourne, C. A Future for Presentism . Oxford: Oxford University Press, 2006.

DOI: 10.1093/acprof:oso/9780199212804.001.0001

Although primarily devoted to defending presentism, chapter 8 offers one of the best treatments of Gödel’s ideality argument around and pp. 132–134 offer some interesting sidelights on the possible compatability of time travel and presentism.

Carroll, John W. A Time Travel Website . 2008–.

Extremely thorough, engagingly-written, well-designed, and continually evolving online resource that offers helpful discussions, well-chosen readings, and helpful animations to boot.

Dainton, Barry. Time and Space . 2d ed. Durham, NC: Acumen, 2010.

Revised and expanded edition of Dainton’s classic 2001 introduction to the philosophy of space and time. Can be highly recommended but notable here for its extensive, essential treatments of time travel, relativity, and Gödel’s “ideality” argument.

Earman, John. “Recent Work on Time Travel.” In Time’s Arrows Today . Edited by Steven F. Savitt, 268–310. Cambridge, UK: Cambridge University Press, 1995.

DOI: 10.1017/CBO9780511622861

Thorough discussion of the then-current state of play in the philosophical and physical literature on time travel. This is still a valuable resource.

Earman, John, and Christian Wüthrich. “ Time Machines .” In Stanford Encyclopedia of Philosophy . Edited by Edward N. Zalta. 2006.

Comprehensive discussion of physical resources for time travel, among other intriguing suggestions, develops the view that physically realistic time machines might be uncontrollable even if they become a possiblility.

Le Poidevin, Robin. Travels in Four Dimensions: The Enigmas of Space and Time . Oxford: Oxford University Press, 2003.

Engaging and clearly written introduction to the philosophy of space and time. Often offers problems and discussions that lend themselves to time travel interpretation. An excellent introductory and pedagogical resource.

Lewis, David. “ The Paradoxes of Time Travel .” American Philosophical Quarterly 13 (1976): 145–152.

The philosophical time travel work. Includes Lewis’s discrepancy definition of time travel: the most useful by far. Invokes the notion of compossibility to disambiguate “Grandfather paradox” arguments and argues that backward time travel and causal loops can occur in (nonbranching) possible worlds. Usefully distinguishes between replacement change and counterfactual change. (This is often cited and sometimes rebutted but never refuted.)

Nahin, Paul. Time Machines: Time Travel in Physics, Metaphysics and Science Fiction . 1st ed. New York: American Institute of Physics, 1999.

DOI: 10.1007/978-1-4757-3088-3

Engaging and comprehensive attempt at surveying all the scientific, philosophical, and fictional literature on time travel. Perhaps slightly more at ease with physics and fiction than with philosophy, but this is a detailed and thorough treatment.

Richmond, Alasdair. “Recent Work: Time Travel.” Philosophical Books 44 (2003): 297–309.

DOI: 10.1111/1468-0149.00308

Survey of the time travel debate from Lewis 1976 onward, sketching links with debates in persistence, philosophy of spacetime and temporal topology. Available online by subscription.

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1000-Word Philosophy: An Introductory Anthology

Philosophy, One Thousand Words at a Time

Time Travel

Author: Taylor W. Cyr Category: Metaphysics Word Count: 1000

Time travel is familiar from science fiction and is interesting to philosophers because of the metaphysical issues it raises: the nature of time, causation, personal identity, and freedom, among others. [1]

It’s widely accepted that time travel to the future is possible, but the possibility of backward time travel remains hotly debated. [2] This article will sketch some models of backward time travel (hereafter simply “time travel”) before addressing the main objections to its possibility. [3]

1. Models of Time Travel

According to the standard model of time travel, time is linear so a time traveler’s journey may be depicted along a single timeline, with some events that occur earlier in the timeline’s being experienced as later by the traveler: [4]

On another model, time travel results in the creation of a new universe that branches out from the same trunk (shared past) as the original:

A third model of time travel maintains that there is a second temporal dimension, and so, in addition to times, there are “hyper-times.” [5] On this model, time is more like a plane than like a line, and a time traveler may, in returning to an earlier time, reach that time at a later hyper-time, with the result that the aforementioned time bears different properties at the different hyper-times: [6]

2. Changing the Past

It is natural to suppose that time travel would change the past, which many believe is impossible. Changing the past would require that the past have a certain property at one “time” and then lack that property at another “time.” This is incoherent on the standard model of time travel, which maintains that time is linear (there is no “second time around”), so the standard model precludes changing the past.

But time travel doesn’t require changing the past. We may distinguish changing the past from affecting the past, where the latter requires only that the time traveler’s travels have effects in the past. [7] For example, suppose a time traveler finds her younger self and attempts to convince herself not to time travel. [8] Assuming the standard model of time travel, she will fail to prevent herself from time traveling, but the attempt will affect how the past was “all along,” so to speak. From the outside, the scene will look like an ordinary conversation between two people, but, assuming the time traveler remembers the scene, she will remember an older version of herself trying to convince her not to time travel. [9]

Moreover, according to the other two models of time travel, one and the same time may exist in two different universes or hyper-times, and so it isn’t obviously incoherent to state that some past time may have a property at one “time” (either in one universe, or at one hyper-time) that it lacks at another “time” (in another universe, or at another hyper-time). [10]

3. Causal Loops

Consider some events from the television show Lost . [11] At one point, Richard gives a compass to Locke, telling him to return it the next time they meet. Locke then travels back in time, sees a younger Richard, and returns the compass, which Richard keeps until he gives it to Locke in the aforementioned meeting.

The Lost compass is strange. It was not created in the usual way—in fact, it has no creator! It appeared (with Locke) at time t1 (when it was given to Richard), remained with Richard at a later time t2, and then was given to Locke at t3, when Locke set out for t1, resulting in a “causal loop.” At each time t1-t3, there is a causal explanation for the compass’s presence by reference to the prior stage in the loop. But no explanation can be given for the loop itself. (Where did the compass come from to begin with? There is no answer.)

Now, if such cases are impossible, this might cast doubt on the possibility of time travel. As David Lewis says in response, however, such cases “are not too different from inexplicabilities we are already inured to” such as “God, or the Big Bang, or the decay of a tritium atom,” all of which are “uncaused and inexplicable” (1976: 149).

Note that this objection assumes the standard model of time travel, since these strange loops do not necessarily result from time travel on the other models. Moreover, it may be possible for there to be cases of time travel that don’t generate causal loops even assuming the standard model. [12]

4. Time Travelers’ Abilities

Suppose Tim time travels and attempts to kill his Grandfather before his parents are conceived. Assuming Tim has a gun, is a good shot, etc., it would seem that Tim can kill Grandfather. But Tim can’t kill Grandfather, for doing so would preclude his own existence. Tim both can and can’t kill Grandfather: that’s a contradiction, so we should give up the assumption that led to it, namely that time travel is possible.

This is the Grandfather Paradox, and it is the main objection to the possibility of time travel. Here are two responses, both of which assume the standard model of time travel. [13]

First, one might understand “can” claims like “Tim can kill Grandfather” as claims about what is possible in view of certain facts—and which facts are held fixed is determined by the context of utterance. [14] For example, in view of Tim’s possession of a gun, his reliable aim, etc., it is true that Tim can kill Grandfather. But if we also hold fixed the fact that Grandfather lives , then Tim’s killing Grandfather isn’t possible, and thus he can’t kill Grandfather. So, there is no contradiction; it is true that Tim can kill Grandfather holding certain facts fixed, and it is false holding more fixed, but the claim is not both true and false in the same context. [15]

A second approach denies that Tim can kill Grandfather. [16] This denial follows from certain independently motivated views of agents’ abilities, and it avoids the Paradox by restricting the freedom of time travelers.

5. Conclusion

Perhaps time travel is (metaphysically) possible, but it doesn’t follow that it’s technologically feasible, or that it will ever actually occur. Only time will tell.

[1]   While not the first philosophical discussion of time travel, David Lewis’s classic 1976 essay “The Paradoxes of Time Travel” popularized the subject in metaphysics. For a recent philosophical discussion of time travel—an excellent summary of several facets of the debate, as well as some new developments—see Wasserman (2018).

[2]   By “possibility” I mean metaphysical possibility—consistency with the laws of metaphysics, such as the laws of causation, identity, etc. For more on the discussion of the various senses of possibility we might be asking about in connection with time travel, see Wasserman (2018, chapter 1), and see the rest of the same book for a summary of the debate about the metaphysical possibility of backward time travel.

[3]   There are other objections, but there isn’t space to consider all of them here. One objection concerns its likelihood rather than its possibility . As we will see below, there are certain things that it would seem time travelers cannot do, and so if time travelers attempted the impossible, something would prevent them from succeeding (perhaps the time traveler would have a change of heart, or perhaps she would slip on a banana peel, or…). Horwich (1987) argues that since backward time travel would result in such improbable events, this casts doubt on the likelihood of time travel. See Smith (1997) for discussion and a response to Horwich.

[4]   See the first figure. Reprinted from Wasserman (2018, chapter 3) with permission of Ryan Wasserman and Oxford University Press.

[5]   For developments of the hyper-time model, see Meiland (1974), Goddu (2003), and van Inwagen (2010).

[6]   If we graphed the two dimensions of time on a plane, with the temporal dimension along the x- axis and the hyper-temporal dimension along the y -axis, as in the third figure, time travel would amount to moving leftward (back in time) and upward (forward in hyper-time).

[7]   As Brier explains, “One cannot change the past or undo what has been done. Rather, what is at issue is whether one can affect the past; that is, by a present action cause something to have happened which would not have happened otherwise” (1973: 361).

[8]   For a simple example of this from science-fiction, see the film Interstellar . After leaving Earth, Cooper is able to send messages back in time, and he uses his first message to try to get his daughter to make him stay on Earth, as seen here .

[9]   For another example of affecting (but not changing) the past, see J. K. Rowling’s Harry Potter and the Prisoner of Azkaban . An especially excellent case of time travel occurs toward the end of the book when Hermione takes Harry back in time, allowing him to save himself from Dementors. In the film version, we see Harry attacked by (but saved from) Dementors here , and then we see Hermione take Harry back in time here , and finally, we see Harry save himself here .

[10]   It is contentious whether these models of time travel really allow for changing the past. See Smith (1997, 2015) and Baron (2017) for arguments against, and see Law (Forthcoming) for a response.

[11]   The first of these occurs in the third episode of season five, “Jughead,” from 39:44-41:19,  and the second scene occurs in the first episode of season five, “Because You Left,” from 29:30-34:34.

[12]   For example, suppose I travel back in time by twenty seconds but set my machine to a destination on the other side of the planet. Presumably, my appearance in the past will not have any causal consequences across the globe, despite its occurring twenty seconds earlier than my departure, and thus no causal loop will be generated. For a similar example, see Hanley (2004: 130).

[13]   On the other models, there is no reason to think that Tim can’t kill Grandfather, for doing so would preclude Tim’s future birth in the new timeline (the new branch or hyper-time), but Grandfather would not have been killed in the original, and thus Tim is still born in that timeline.

[14] See Kratzer (1977).

[15]   While Lewis’s (1776: 149-152) influential response to the Paradox also relies on the Kratzer semantics for “can,” his proposed resolution is slightly different, for he sees the fact that Grandfather lives as one that it would be illegitimate to hold fixed. Holding it fixed, he thinks, amounts to “fatalist trickery,” as such a fact “is an irrelevant fact about the future masquerading as a relevant fact about the past” (1976: 151).

[16]   See Vihvelin (1996).

Baron, Sam (2017). “Back to the Unchanging Past,” Pacific Philosophical Quarterly 98: 129–147.

Brier, Bob (1973). “Magicians, Alarm Clocks, and Backward Causation,” Southern Journal of Philosophy 11: 359-364.

Goddu, G. C. (2003). “Time Travel and Changing the Past (or How to Kill Yourself and Live to Tell the Tale),” Ratio 16: 16-32.

Hanley, Richard (2004). “No End in Sight: Causal Loops in Philosophy, Physics, and Fiction,” Synthese 141: 123-152.

Horwich, Paul (1997). Asymmetries In Time: Problems In the Philosophy of Science . Cambridge, MA: MIT Press.

Kratzer, Angelika (1977). “What ‘Must’ and ‘Can’ Must and Can Mean,” Linguistics and Philosophy 1: 337-355.

Law, Andrew (Forthcoming). “The Puzzle of Hyper-Change,” Ratio .

Lewis, David (1976). “The Paradoxes of Time Travel,” American Philosophical Quarterly 13: 145-152.

Meiland, Jack (1974). “A Two-Dimensional Passage Model of Time for Time Travel,” Philosophical Studies 26: 152-173.

Smith, Nicholas J. J. (1997). “Bananas Enough for Time Travel?” The British Journal for the Philosophy of Science 48: 363-389.

Smith, Nicholas J. J. (2015). “Why Time Travellers (Still) Cannot Change the Past,” Revista Portuguesa de Filosofia 71: 677–694.

van Inwagen, Peter (2010). “Changing the Past,” in D. Zimmerman, ed., Oxford Studies in Metaphysics , vol. 5. Oxford: Oxford University Press.

Vihvelin, Kadri (1996). “What Time Travelers Cannot Do,” Philosophical Studies 81: 315-330.

Wasserman, Ryan (2018). Paradoxes of Time Travel . New York: Oxford University Press.

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Translation

This essay has been translated into Italian for the Italian cultural magazine  L’Indiscreto .

About the Author

Taylor W. Cyr is an Assistant Professor of Philosophy at Samford University. His main research interests lie at the intersection of ethics and metaphysics, including such topics as free will, moral responsibility, death, and time. His work has appeared in such journals as Ethics , Philosophical Studies , Philosophical Quarterly , and Erkenntnis . TaylorWCyr.com

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The Philosophy of Time: Study the Nature of Past, Present, and Future

Time is difficult to understand and even more difficult to explain. Do you ever wonder what it means?

Time is something we deal with every day. We usually characterize as split between past, present, and future. The progression of time is embodied in our experience—the future becomes the present, and the present becomes the past. In fact, it is impossible to talk about movement and dynamics without the concept of time and its progression. Though our perception of time is similar to our perception of space, time is a far more philosophically demanding topic.

The Nature of Time

What is time ? This phenomenon can seem mysterious. Indeed, time, on the one hand, is omnipresent and in some sense omnipotent (contrary to the well-known Arab saying, “Everything in the world fears time, yet time fears the pyramids ,” there will likely be an end to the pyramids as well).

On the other hand, although we all intuitively understand what it is, it seems almost impossible to give a precise and comprehensive definition of the concept of time.

One way of thinking of time as “a universal form of change.” “Universal” in this formulation means all-encompassing because any changes are really possible only within time.

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“Form” in the definition means that time resembles a kind of transparent vessel that can be filled with any content. In other words, the changes can be very diverse, but the passage of time in which they occur seems invariably uniform and inexorable.

Finally, taking a look at the concept of “change,” we come to the flip side of the coin. It seems that while change is inconceivable without time, time is also inconceivable without change. Indeed, the imaginary stoppage of time is associated with the complete freezing of life and the universe.

So, time is the world’s common denominator; one might say—the main currency of reality. We experience it in different ways: sometimes, we consider the past as something lost and regret it; we try to use the present wisely so that our future will be better; and at times, we eagerly await what is coming next.

The First Mentions of Time in Philosophy

One of the first philosophers who began to think about the nature of time was Plato . The time he characterizes in his treatise Timaeus as “a moving likeness of eternity.” For Plato, time is a characteristic of an imperfect dynamic world, where there is no good but only the desire to possess it. Time thus reveals a moment of incompleteness and inferiority. Eternity, on the contrary, is a characteristic of the static and perfect world of the gods.

Aristotle further developed this understanding of time, defining it as a “measure of movement.” This interpretation was enshrined in his Physics , and it laid the foundation for the natural sciences’ understanding of time. He raises the question of evidence of the existence of time and reproduces a dialectical approach here: the past no longer exists, the future does not yet exist, and the present is the moment of the unity of being and non-being.

This dialectical approach led Aristotle to study the connection between time and motion. The thinker showed that time, although not identical to movement, is nevertheless inseparable from movement. Aristotle defines time as “the number of motions in relation to the past and the future,” and as a “measure of movement and rest.”

Later, at the beginning of the Middle Ages, Augustine developed the concept of subjective time. He described time as a mental phenomenon of changing perceptions. Augustine distinguishes three parts of time: present, past, and future.

Newton Vs. Einstein

Over the past hundred or so years, a real revolution has taken place in the scientific understanding of time. Indeed, until the beginning of the 20th century, physics and everyday consciousness were dominated by Isaac Newton’s postulate of absolute mathematical time.

According to it, time flows at the same speed throughout the universe and is in no way dependent on physical or any other processes that occur in it.

For example, if it’s six in the evening in good old England and it’s time to drink tea. This means that somewhere in the Andromeda nebula, thousands of light-years away, it’s also six in the evening! This understanding of time fits well with our everyday experience; it’s intuitive.

That is why the special theory of relativity, developed in 1905 by Albert Einstein , was a real shock for the scientific world. Its presentation goes beyond the scope of this essay, so we will emphasize only a few key points.

Firstly, according to this theory, time does not exist in isolation but forms a single whole with space (hence the expressions “space-time” and “space-time continuum”).

Secondly, time, like other physical quantities, is relative, and so the speed of its flow depends on the reference point. That is, in an object that moves (for example, in a spaceship), the clock will run slower than in a stationary one. However, such so-called relativistic effects are significantly manifested only at speeds close to the speed of light in a vacuum (about 300 thousand kilometers per second), which is considered limiting in the theory of relativity .

Hence, for example, the well-known twin paradox: when one of the twin brothers goes into space on a ship and spends a couple of years there, flying at near-light speed, after returning home, he can see that entire decades have already passed on Earth!

But Einstein’s trampling of Newton’s theories did not stop there. Newton’s law of universal gravitation assumes an infinite rate of propagation of the gravitational force. However, based on the postulate about the limit of the speed of light, which we have already mentioned, this is impossible. Because of this, Einstein had to develop his own theory of gravity, which grew into the general theory of relativity.

With regard to time, its conclusions are perhaps even more impressive than those of the special theory. Time, it turns out, is inextricably linked not only with space but also with matter! In particular, the gravitational force of physical bodies is able to slow down time again, and if gravity is strong enough, it can even…stop it! The latter phenomenon is characteristic of so-called “black holes”—cosmic objects that are the last phase of the evolution of massive stars.

Immanuel Kant’s Theory of Time

In the world of philosophy, Immanuel Kant was a pretty big deal when it comes to our understanding of time. He believed that time wasn’t something that just existed on its own, but rather it was a feature of the mind. Think of it like this—your brain doesn’t just reflect the world around you in a perfectly accurate way; instead, it organizes everything into different categories so you can understand what you’re seeing. And one of those categories is time. So for Kant, time isn’t some concrete thing that’s just out there; instead, he saw it as an “empty form,” which might sound kind of weird and unintuitive at first.

But let us explain—somewhere in your brain, a “time-keeping” mechanism helps us see things as happening within a specific timeline. Without this mechanism, we might not be able to make sense of events in the same way—everything would just be happening all at once.

But maybe you’re thinking: “OK, so Kant thought we create time with our minds—why does that matter?” Well, here’s another thing he believed: when we think about time (and space, too), we’re not just passively observing the world around us—we’re actively engaging with it through our thoughts and experiences.

To put it another way, imagine you’re at a concert. The music plays on stage, and you experience each song as happening one after another. But suppose your best friend was also at the concert but sitting in a different section than you were. In that case, they’d have a totally different experience because they would hear and see everything differently thanks to their unique perspective. This is kind of how Kant sees time, too—everyone experiences things slightly differently based on how their minds process information.

So while Newton might have approached time more like an objective universal law of nature, Kant saw it more as something that was constantly being shaped by our own thoughts and actions.

Past, Present, Future: The Dimensions of Time

Let’s start with the past. For some philosophers (like Hegel ), the past is something that’s already happened and can’t be changed. It’s like a book that’s already been written—you can’t go back and erase or rewrite what happened in it.

Others (like Nietzsche ) saw things a little differently—they believed that the past isn’t set in stone; instead, how we remember it changes depending on our current situation and perspective.

The present is where things get tricky: some modern philosophers don’t think that time actually exists at all! Instead, they believe that everything is happening all at once (kinda like watching a movie frame-by-frame), but our brains process everything as if it were continuous time.

Then others see the present as an important moment for making decisions that will shape our future.

The future is like looking into a crystal ball; even though nobody knows what will happen next, every action taken in both real life and fiction paves the way toward an unknown tomorrow.

Some philosophers (like Heidegger ) thought that the future was something we could sort of “reach out and grab” by making choices in the present—like reaching for something today that will help us tomorrow. Others believe in a more fatalistic view, where the future is predetermined, and we’re all just along for the ride.

So, What Is the Concept of Time in Philosophy?

When it comes to philosophy, time has been explored from all angles: past, present, future, and everything in between! But through all these different schools of thought, there are a few key things we can say for sure about what time actually is (and isn’t).

First off, most philosophers agree that time isn’t some kind of universal force. It’s not like gravity or electricity—you can’t measure it the same way you can measure distance or speed. Time doesn’t exist independently; instead, it’s more like a tool we use to make sense of the world around us.

Some philosophers think that time might be an illusion altogether—sort of like how a mirage in the desert appears to be real even though it’s not really there. Instead, they believe that everything is always happening at once, even though that’s not how it seems to us.

Other philosophers see time as an essential part of human experience—something that shapes our memories and connects us. Think about it: without shared ideas about what time means (like “day” or “year”), how would we organize ourselves as a society? How would we know when to start school or work? So in this way, time is both a personal and social construct.

What is Time? St Augustine on Temporality and Consciousness

By Viktoriya Sus MA Philosophy Viktoriya is a writer from L’viv, Ukraine. She has knowledge about the main thinkers. In her free time, she loves to read books on philosophy and analyze whether ancient philosophical thought is relevant today. Besides writing, she loves traveling, learning new languages, and visiting museums.

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Paradoxes of Time Travel

Ryan Wasserman, Paradoxes of Time Travel , Oxford University Press, 2018, 240pp., $60.00, ISBN 9780198793335.

Reviewed by John W. Carroll, North Carolina State

Wasserman's book fills a gap in the academic literature on time travel. The gap was hidden among the journal articles on time travel written by physicists for physicists, the popular books on time travel by physicists for the curious folk, the books on the history of time travel in science fiction intended for a range of scholarly audiences, and the journal articles on time travel written for and by metaphysicians and philosophers of science. There are metaphysics books on time that give some attention to time travel, but, as far as I know, this is the first book length work devoted to the topic of time travel by a metaphysician homed in on the most important metaphysical issues. Wasserman addresses these issues while still managing to include pertinent scientific discussion and enjoyable time-travel snippets from science fiction. The book is well organized and is suitable for good undergraduate metaphysics students, for philosophy graduate students, and for professional philosophers. It reads like a sophisticated and excellent textbook even though it includes many novel ideas.

The research Wasserman has done is impressive. It reminds the reader that time travel as a topic of metaphysics did not start with David Lewis (1976). Wasserman (p. 2 n 4) identifies Walter B. Pitkin's 1914 journal article as (probably) the first academic discussion of time travel. The article includes a description of what has come to be called the double-occupancy problem, a puzzle about spatial location and time machines that trace a continuous path through space. The same note also includes a lovely passage, which anticipates paradoxes about changing the past, from Enrique Gaspar's 1887 book:

We may unwrap time but we don't know how to nullify it. If today is a consequence of yesterday and we are living examples of the present, we cannot unless we destroy ourselves, wipe out a cause of which we are the actual effects.

These are just two of the many useful bits of Wasserman's research.

Chapter 1 usefully introduces examples of time travel and some examples one might think would involve time travel, but do not (e.g., changing time zones). There is good discussion of Lewis's definition of time travel as a discrepancy between personal and external time, including a brief passage (p. 13) from a previously unpublished letter from Lewis to Jonathan Bennett on whether freezing and thawing is time travel. I had often wonder what Lewis would have said; now I know what he did say!

Chapter 2 dives into temporal paradoxes deriving from discussions of the status of tense and the ontology of time (presentism vs. eternalism vs. growing block vs. . . . ). Here, Wasserman also includes the double-occupancy problem as a problem for eternalism -- though it is not clear that it is only a problem for eternalism. Then he turns to the question of the compatibility of presentism and time travel, the compatibility of time travel and a version of growing block that accepts that there are no future-tensed truths, and finally to a section on relativity and time travel. The section on relativity is solid and seems to me to pull the rug out from under some earlier discussions. For example, Lewis's definition of time travel is shown not to work. It also becomes clear that presentism and the growing block are consistent with both time-dilation-style forward time travel and traveling-in-a-curved-spacetime "backwards" time travel.

Chapters 3 and 4 cover the granddaddies of all the time-travel paradoxes: the freedom paradoxes that include the grandfather paradox, the possibility of changing the past, and the prospects of such changes given models of branching time, models that invoke parallel worlds, and hyper time models. Chapter 4 gets serious about Lewis's treatment of the grandfather paradox and Kadri Vihvelin's treatment of the autoinfanticide paradox (about which I will have more to say).

Chapter 4 also includes discussion of "mechanical" paradoxes that, as stated, do not require modal premises about what something can and cannot do, and no notion of freedom or free will. (See Earman's bilking argument on p. 139 and the Polchinski paradox on p. 141.) Wasserman introduces modality to these paradoxes, but I would have liked them to be addressed on their own terms. As I see it, these paradoxes are introduced to show that backwards time travel or backwards causation in a certain situation validly lead to a contradiction. On their own terms, for these arguments to be valid, the premises of the arguments themselves must be inconsistent. How can one make trouble for backwards time travel if the argument is thus bound to be unsound?

Chapter 5 takes on the paradoxes generated by causal loops or more generally backwards causation including bilking arguments, the boot-strapping paradox (based on a presumption that self-causation is impossible), and the ex nihilo paradox with causal loops and object loops (i.e., jinn) that seem to have no cause or explanation.

Chapter 6 deals with paradoxes that arise from considerations regarding identity, with a focus on the self-visitation paradox from both perdurantist and endurantist perspectives. I was surprised to learn that Wasserman had defended an endurantist-friendly property compatibilism -- similar to my own -- to resolve the self-visitation paradox. I was then delighted to find out that he cleverly extends this sort of compatibilism to the time-travel-free problem of change (i.e., the so-called, temporary-intrinsics argument).

The outstanding scientific issue regarding backwards time travel is whether it is physically possible. There is no question that forwards time travel is actual, or even whether it is ubiquitous. There is also not much question that backwards time travel is consistent with general relativity. Still, we await more scientific progress before we will know whether backwards time travel really is consistent with the actual laws of nature. In the meantime, there is still much to be said about Lewis's treatment of the grandfather paradox and Vihvelin's stated challenge to that treatment in terms of the autoinfanticide paradox.

I will start by being somewhat critical of Lewis's approach. For his part (pp. 108-114), Wasserman does a terrific job of laying out Lewis's position as a metatheoretic discussion of the context sensitivity of 'can' and 'can't'. My concern is that not enough attention is given to the 'can' and 'can't' sentences that turn out true on the semantics. The semantics works only by a contextual restriction of possible worlds based on relevant facts -- the modal base -- associated with a conversational context. In meager contexts, false 'can' sentences will turn out true too easily. For example, suppose two people are having a conversation about Roger. Maybe all the two know about Roger is his name and that he is moving into the neighborhood. So, the proposition that Roger doesn't play the piano is not in the modal base. So, according to Lewis's semantics applied to 'can', 'Roger can play the piano' is true in this context. That seems wrong. This would be an unwarranted assertion for either of the participants in the conversation to make. Notice it is also true relative to the same meager context that Roger can play the harpsichord, the sousaphone, and the nyatiti. Quite a musician that Roger! [1]

Interestingly, though this problem arises for 'can', it does not arise for other "possibility" modals. For example, notice that, with the meager context described above, there is a big difference regarding the assertability of 'Roger could play the piano' and of 'Roger can play the piano'. Similarly, there is also no serious issue with regard to 'Roger might play the piano'. 'Could' and 'might' add tentativeness to the assertion that seems called for. There also seems to be no problem for the semantics insofar as it applies to 'is possible'. 'It is possible that Roger plays the piano' rings true relative to the context. But 'Roger can play the piano'? That shouldn't turn out true, especially if Roger is physically or psychologically unsuited for piano playing.

This issue has been frustrating for me, but Wasserman's book has me leaning toward the idea that what is needed is a contextual semantics that includes a distinguishing conditional treatment of 'can' of the sort Wasserman suggests:

(P1**) Necessarily, if someone would fail to do something no matter what she tried, then she cannot do it (p. 122).

This is a suggestion made by Wasserman on behalf of Vihvelin. I find (P1**) as a promising place to start in terms of the conditional treatment.

Speaking of Vihvelin, her thesis is "that no time traveler can kill the baby that in fact is her younger self, given what we ordinarily mean by 'can'" (1996, pp. 316-317). Vihvelin cites Paul Horwich as a defender of a can-kill solution, what she calls the standard reply :

The standard reply . . . goes something like this: Of course the time traveler . . . will not kill the baby who is her younger self . . . But that doesn't mean she can't . (Vihvelin 1996, p. 315)

Vihvelin's doing so is appropriate given what Horwich says about Charles attending the Battle of Hastings: "From the fact that someone did not do something it does not follow that he was not free to do it" (1975, 435). In contrast, it strikes me as odd that Vihvelin (1996, p. 329, fn. 1) also attributes the standard reply to Lewis. I presume that she does so based on some comments by Lewis. He says, "By any ordinary standards of ability , Tim can kill Grandfather," (1976, p. 150, my emphasis) and especially "what, in an ordinary sense , I can do" (1976, p. 151, my emphasis). So, admittedly, Vihvelin fairly highlights an aspect of Lewis's view as holding that, in the ordinary sense of 'can', Tim can kill Gramps. And I can see how this is a useful presentation of Lewis's position for her argumentative purposes.

Nevertheless, I take Lewis's talk of ordinary standards or an ordinary sense to just be a way to identify the ordinary contexts that arise with uses of 'can' in day-to-day dealings, where the possibility of time travel is not even on the table. Simple stuff like:

Hey, can you reach the pencil that fell on the floor?

Sure I can; here it is.

More importantly, we have to keep in mind that the basic semantics only has consequences about the truth of 'can' sentences once a modal base is in place. To me, the fact that Baby Suzy grows up to be Suzy is exactly the kind of fact that we do not ordinarily hold fixed. Lewis's commitment to the semantics does not make him either a can-kill guy or a can't-kill guy.

What is the upshot of this? There is a bit of underappreciation of Lewis's approach in Wasserman's discussion of Vihvelin's views. The pinching case on p. 119 provides a way to make the point. Consider:

(a) If Suzy were to try to kill Baby Suzy, then she would fail.

(b) If Suzy were to try to pinch Baby Suzy, then she would fail.

According to Wasserman, Vihvelin thinks that even in ordinary contexts (a) and (b) come apart (p. 119, note 32) -- (a) is true and (b) is false. As I see it, a natural context for (a) includes the fact that Baby Suzy grows up normally to be Suzy. That is a supposition that is crucial to the description of the scenario and so is likely to be part of the modal base. No canonical story or suppositions are tied to (b), though Vihvelin stipulates that Suzy travels back in time in both cases. We are not, however, told a story of Baby Suzy living a pinch-free life all the way to adulthood. We are not told whether Suzy decided go back in time because Baby Suzy deserved a pinch for some past transgression. My point is that the stories affect the context. So, with parallel background stories, (a) and (b) need not come apart.

I am not sure whether Wasserman was speaking for himself or for Vihvelin when he says about (a) and (b), "Self-defeating acts are paradoxical in a way other past-altering acts are not" (p. 120). Either way, I disagree. Lewis gives a more general way to resolve the past-alteration paradoxes that is not obviously in any serious conflict with Vihvelin's many utterances that turn out true relative to the contexts in which she asserts them. Wasserman also says, "The only disagreement between Lewis and Vihvelin is over whether Suzy's killing Baby Suzy is compatible with the kinds of facts we normally take as relevant in determining what someone can do" (p. 117). That is an odd thing for him to say. Lewis sketches a semantic theory that provides a framework for the truth conditions of 'can' and 'can't' sentences. He is not in disagreement with Vihvelin. For Lewis, there is one specification of truth conditions for 'can' that gives rise to both 'can kill' and 'can't kill' sentences turning out true relative to different contexts. Indeed, it is tempting to think that Vihvelin takes the fact that Baby Suzy grows up to be Adult Suzy as part of the modal base of the contexts from which she asserts the compelling 'can't-kill' sentences.

That all said, Wasserman's book is a significant contribution. There are those of us who focus a good chunk of our research on the paradoxes of time travel for their intrinsic interest, and especially because they are fun to teach. That is contribution enough for me. But, ultimately, from this somewhat esoteric, fun puzzle solving, we also learn more about the rest of metaphysics. The traditional issues of metaphysics: identity-over-time, freedom and determinism, causation, time and space, counterfactuals, personhood, mereology, and so on, all take on a new look when framed by the questions of whether time travel is possible and what time travel is or would be like. Wasserman's book is a wonderful source that spotlights these connections between the paradoxes of time travel and more traditional metaphysical issues.

Cargile, J., 1996. "Some Comments on Fatalism" The Philosophical Quarterly 46, No. 182 January 1996, 1-11.

Gaspar, E., 1887/2012. The Time-Ship: A Chronological Journey . Wesleyan University Press.

Horwich, P., 1975. "On Some Alleged Paradoxes of Time Travel" The Journal of Philosophy 72, 432-444.

Lewis, D., 1976 "The Paradoxes of Time Travel" American Philosophical Quarterly 13, 145-152.

Pitkin, W., 1914. "Time and Pure Activity" Journal of Philosophy, Psychology and Scientific Methods 11, 521-526.

Vihvelin, K., 1996. "What a Time Traveler Cannot Do" Philosophical Studies 81, 315-330.

[1] This criticism was first presented to me by Natalja Deng in the question-and-answer period for a presentation at the 2014 Philosophy of Time Society Conference. Later on, I found a parallel challenge in work by James Cargile (1996, 10-11) about Lewis's iconic, 'The ape can't speak Finnish, but I can'.

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2 Temporal Paradoxes

• Published: November 2017
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Chapter 2 surveys the various theories of time and explores their consequences for the possibility of time travel. Section 1 introduces the traditional debates over tense and distinguishes between three different views of temporal ontology: eternalism, presentism, and the growing block theory. Section 2 discusses eternalism and the double-occupancy paradox. Section 3 focuses on presentism and various versions of the “no destination” objection. Section 4 looks at the growing block theory and the worry that time travel would allow for future indeterminacy to creep back into the past. Finally, sections 5 and 6 look at the special and general theories of relativity and consider their implications for our understanding of time travel.

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Time Travel Philosophy

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4. Time in Physics

A. newtonian cosmology, b. special relativity, c. general relativity, d. quantum interpretations, 5. causation, a. the grandfather paradox, b. causal loops, 6. personal identity.

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Newton’s Views on Space, Time, and Motion

Isaac Newton founded classical mechanics on the view that space is distinct from body and that time passes uniformly without regard to whether anything happens in the world. For this reason he spoke of absolute space and absolute time , so as to distinguish these entities from the various ways by which we measure them (which he called relative spaces and relative times ). From antiquity into the eighteenth century, contrary views which denied that space and time are real entities maintained that the world is necessarily a material plenum. Concerning space, they held that the idea of empty space is a conceptual impossibility. Space is nothing but an abstraction we use to compare different arrangements of the bodies constituting the plenum. Concerning time, they insisted, there can be no lapse of time without change occurring somewhere. Time is merely a measure of cycles of change within the world.

Associated with these issues about the ontological status of space and time was the question of the nature of true motion. Newton defined the true motion of a body to be its motion through absolute space. Those who, before or shortly after Newton, rejected the reality of space, did not necessarily deny that there is a fact of the matter as to the state of true motion of any given body. They thought rather that the concept of true motion could be analyzed in terms of the specifics of the relative motions or the causes thereof. The difficulty (or, as Newton alleged, the impossibility) of so doing constituted for Newton a strong argument for the existence of absolute space.

In recent literature, Newton's theses regarding the ontology of space and time have come to be called substantivalism in contrast to relationism . It should be emphasized, though, that Newton did not regard space and time as genuine substances (as are, paradigmatically, bodies and minds), but rather as real entities with their own manner of existence as necessitated by God's existence (more specifically, his omnipresence and eternality).

1. Overview of the Scholium

2.1 the void, 2.2 aristotle's doctrines, 2.3 sixteenth-century innovations, 2.4 charleton and the seventeenth-century revival of atomism, 3. descartes' innovation.

• 4. Newton's Manuscript: De Gravitatione …

5.1 Arguments for Absolute Time

5.2 direct arguments for absolute space, 5.3 the arguments from properties, causes, and effects, 5.4 discriminating in practice between absolute and apparent motion, 6.1 what the major impediments are, 6.2 why they are indeed impediments, 7. newton's legacy, other internet resources, related entries.

Today, Newton is best known as a physicist whose greatest single contribution was the formulation of classical mechanics and gravitational theory as set out in his Philosophae Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ), first published in 1687, and now usually referred to simply as “Newton's Principia ”. Newton's views on space, time, and motion not only provided the kinematical basis for this monumental work and thus for the whole of classical physics up until the early twentieth century, but also played an integral role in Newton's general system of philosophy and theology (largely developed prior to the Principia ). Because Newton never drafted a treatise on, or even a digest of, this general system, his stature as one of the great philosophers of the seventeenth century, indeed, of all time, is no longer widely appreciated.

A “Scholium” at the beginning of the Principia , inserted between the “Definitions” and the “Laws of Motion”, lays out Newton's views on time, space, place, and motion. He begins by saying that, since in common life these quantities are conceived of in terms of their relations to sensible bodies, it is incumbent to distinguish between, on the one hand, the relative, apparent, common conception of them, and, on the other, the absolute, true, mathematical quantities themselves. To paraphrase:

• Absolute, true, and mathematical time , from its own nature, passes equably without relation to anything external, and thus without reference to any change or way of measuring of time (e.g., the hour, day, month, or year).
• Absolute, true, and mathematical space remains similar and immovable without relation to anything external. (The specific meaning of this will become clearer below from the way it contrasts with Descartes' concept of space.) Relative spaces are measures of absolute space defined with reference to some system of bodies or another, and thus a relative space may, and likely will, be in motion.
• The place of a body is the space which it occupies, and may be absolute or relative according to whether the space is absolute or relative.
• Absolute motion is the translation of a body from one absolute place to another; relative motion the translation from one relative place to another.

Newton devotes the bulk of the Scholium to arguing that the distinction between the true quantities and their relative measures is necessary and justified.

It is evident from these characterizations that, according to Newton:

• space is something distinct from body and exists independently of the existence of bodies,
• there is a fact of the matter whether a given body moves and what its true quantity of motion is, and
• the true motion of a body does not consist of, or cannot be defined in terms of, its motion relative to other bodies.

The first of these theses was a point of major contention in 17th-century natural philosophy and one assailed by Newton's critics such as Leibniz, Huygens, and Berkeley. The second was not in general dispute. Descartes, Leibniz, and Berkeley all believed that, to put it in somewhat scholastic terms, the predicate ‘ x is in true motion’ is a complete predicate in the sense that it holds or fails to hold for any given body. (Huygens, at least in his post- Principia views, constitutes a special case.) Thus, for those who denied the first thesis, it was necessary to secure a definition, or an analysis, of what it means for a body be in true motion (and what determines the quantity of that motion), so as to be as adequate to the facts as Newton's characterization of true motion. The figures mentioned above all deemed that motion relative to other bodies is a necessary condition for true motion, although not, by itself, a sufficient condition.

Over the course of years, the consensus in the 17th and early 18th Centuries on thesis (2) was lost sight of, and it became common to characterize Newton's opponents as denying that there is a fact of the matter as to whether a body is in true motion and maintaining instead that all motion is merely relative motion . Thus, modern readers expect that Newton's Scholium on space, time, and motion should be read as arguing not only thesis (1) above, but also thesis (2), that all motion is not merely relative motion, but that some motions are true and absolute. Newton's arguments concerning motion, however, are designed to show, not that true motion is distinct from merely relative motion (which is granted by all), but rather that the only feasible analysis of true motion requires reference to absolute places, and thus the existence of absolute space.

In particular it has been assumed that Newton's so-called “rotating bucket experiment”, together with the later example of a pair of globes connected by a chord and revolving about their center of gravity, is supposed to argue, or provide evidence for, the existence of true, or absolute, motion. Not only is this false, but the two cases have distinct purposes in the framework of the Scholium. The rotating bucket experiment is the last of five arguments from the “properties, causes, and effects of motion” designed to show cumulatively that an adequate analysis of true motion must involve reference to absolute space. In contrast, the example of the revolving globes is intended to illustrate how it is that, despite the fact that absolute space is invisible to the senses, it is nonetheless possible to infer the quantity of absolute motion of individual bodies in various cases.

2. The Legacy from Antiquity

The most important question shaping 17th-century views on the nature of space, time and motion is whether or not a true void or vacuum is possible, i.e., a place devoid of body of any sort (including rarified substances such as air). Ancient atomism, dating back at least to the pre-Socratic philosopher Democritus (5th century, B. C.), held that not only is such possible, but in fact actually exists among the interstices of the smallest, indivisible parts of matter and extends without bound infinitely. Following Plato, Aristotle rejected the possibility of a void, claiming that, by definition, a void is nothing, and what is nothing cannot exist.

According to Aristotle, the universe is a material plenum, finite in extent, bounded by the outermost sphere of the fixed stars. Beyond that there is no void, i.e., empty places, since, as Aristotle defines ‘place’, the place of something is the outermost of “the innermost motionless boundary of what contains it.” Hence, since there are no boundaries outside the outermost celestial sphere, there are no places or space outside of it.

Time, according to Aristotle, is just the measure of motion, where by ‘motion’ he means change of any sort, including qualitative change. In order to define the uniformity of time, that is, the notion of equal intervals of time, Aristotle was guided by astronomical practice, which in antiquity provided the most practical and accurate measures of time. He identified uniform motion with the rate of motion of the fixed stars, a choice for which he found a dynamical justification in his celestial physics.

“Local” motion is but one species of motion, viz., change of place. Motion, in general, he defined as the actualization of potentiality, a notion commonly held in the 17th century to be so obscure as to be either useless or meaningless. However, as far as local motion is concerned, there is no difficulty as to what constitutes the true or absolute motion of a body in a finite geocentric universe. Indeed, elementary substances in the sub-lunar realm (earth, air, fire, and water) move of their own accord either up or down, i.e., toward the center or away from the center by their very nature. The celestial realm, beginning with the orbit of the moon, consists of an interlocking network of celestial spheres composed of a fifth element (aether), which by its nature is disposed to circular motion about the center of the of universe (i.e., the center of the earth). If the motion of this substance is taken to be the measure of time, the celestial spheres necessarily rotate uniformly. Since the net motion of an embedded sphere is the sum of its natural motion superimposed on the natural motions of the spheres in which it is embedded, and since the axes of rotation are in general set at slightly different angles in order to account for why the sun does not move on the celestial equator and the planets and the moon do not move strictly on the ecliptic (i.e., the path of the sun against the fixed stars), the motions of the moon, planets, and even the sun are not necessarily uniform. However, since the sphere of the fixed stars is embedded in no other celestial sphere in motion, the motion of the fixed stars is de facto the measure of all motion.

The motions spoken of so far are all natural motions of the substances in questions, motions induced by the body being the very substance that it is. In contrast, other motions, in which the cause of the motion is external rather that internal to the body, Aristotle subsumed under the concept of violent motion. Violent motion required for its continuation the constant application of an external cause.

Although Aristotle's views dominated medieval scholasticism, there occurred a renewed interest in atomism in the early 17th Century. Apart from general factors such as the Renaissance, Humanism, and the Reformation, specific innovations of the 16th Century made it attractive. Although Copernicus' introduction of a helio-static system was motivated by a strict adherence to Aristotle's dynamics of celestial spheres, it brought into question his terrestial physics. Galileo's telescopic observations of the surface of the moon and his discovery of moons orbiting about Jupiter brought into question the very distinction between the terrestial and the celestial. Moreover, the visibility of an abundance of new stars, apparently without end, suggested that the universe may in fact be without bound.

An important representative of the revival of atomism and its concomitant views concerning the void is Walter Charleton's Physiologia Epicuro-Gassendo-Charltoniana: Or a Fabrick of Science Natural, upon the Hypothesis of Atoms, “Founded by Epicurus, Repaired by Petrus Gassendus, Augmented by Walter Charleton” , which appeared in English in 1654, twelve years after Newton's birth. It is a text with which Newton became familiar as an undergraduate, and some of the core theses concerning time and space later put forth in the Principia and various unpublished manuscripts in Newton's hand can be found in Charleton. These include:

• that time and space are real entities even though they fit neither of the traditional categories of substance or accident (i.e., property of a substance),
• that time “flow[s] on eternally in the same calm and equal tenor,” while the motion of all bodies is subject to “acceleration, retardation, or suspension”,
• that time is distinct from any measure of it, e.g., celestial motion or the solar day,
• that space is “absolutely immoveable” and incorporeal,
• that bodies, or “Corporeal Dimensions” are everywhere “Coexistent and Compatient” with the “Dimensions” of the parts of space they occupy,
• that space distinct from body existed before God created the world and that God's omnipresence is his literal presence everywhere, and
• that motion is the translation or migration of body from one place, as an immovable part of space, to another.

Charleton's arguments for his views concerning time have much the same tenor as those given by Newton in the Principia . In marked contrast, though, those for empty, immense, and immutable space are quite different. Charleton appeals to the explanation of such phenomena as rarefaction and condensation, the differences in “degrees of Gravity” of bodies, and the numerous ways in which bodies can interpenetrate at the micro-level in terms of solubility, absorption, calefaction, and diverse chemical reactions. However, Charleton does not introduce the terminology of “relative” time, “relative” spaces, or “relative” places, and nowhere raises concerns regarding true (absolute) motion versus merely relative motion. Oddly enough, although Charleton occasionlly mentions and criticizes Descartes with regard to other matters, no note of the fact is made that Descartes, a decade earlier, had proposed explanations, in detail or in outline, for just these sorts phenomena according to a system of nature in which the world is completely filled with matter and in which space distinct from body cannot exist. Descartes, it can be justly said, is the founder of the other main school of the “mechancal philosophy” of the 17th Century, which stood in direct opposition to atomism on the issue of the possibility of a vacuum and which adapted the Aristotelian doctrines on the nature of time, space, and motion to the new world view.

Although avowedly anti-Aristotelian in many regards, particularly on the view, shared with atomists, that all qualitative change on the macroscopic scale is reducible to the rearrangement and/or motion of matter on the microscopic scale, it was Descartes' ambition to carry out this program by retaining what is essentially Aristotle's notion of Prime Matter. The pure elements (earth, air, fire, and water) of Aristotle's physics could mutate into one another by alteration of the fundamental qualities definitive of them. These were the four haptic qualities of hot, cold, wet, and dry. Because of this, there had to be something distinguishable, at least in thought, from qualities that persist during elemental alteration. This quality-less substratum is what Aristotle referred to simply as matter, or as it is often called, Prime Matter, in order to avoid confusion with the macroscopically identifiable, quality-laden, homogenous portions of everyday objects. Unlike atomists, who attributed at least the quality of hardness (impenetrability) to the ultimate particles of matter, Descartes argued that matter, or synonymously, body [corpus] has no qualities whatsoever, but only quantity, i.e., extension. In other words, body and extension are literally one and the same [res extensa]. An immediate corollary is that there can be no vacuum, for that would require an extended region devoid of body --- a manifest contradiction. The task, then, was to show how all apparent qualities can be explained in terms of the infinite divisibility and rearrangement of extension with respect to itself. The task was grand indeed, for its goal was to develop a unified celestial and terrestrial physics that could account equally for the ductility of metals, magnetic attraction, the tides, the mechanism of gravity, the motion of the planets, the appearance and disappearance of comets, and the birth and death of stars (supernovae).

Descartes published his system of the world in 1644 as the Principles of Philosophy ( Principia Philosophae ). Part II of the Principles lays out the thesis of the identity of space (extension) and matter, develops a definition of motion in the “true, or philosophical sense”, and sets out the fundamental dynamical laws of his system. Motion, according to “the truth of the matter”, is defined to be “the translation of one part of matter, or one body, from the vicinity of those bodies, which are immediately contiguous to it and are viewed as if at rest, to the vicinity of others.” In consequence, Descartes points out, each body has a single motion proper to it (in contrast to the numerous relative motions that can be ascribed to it depending on which other bodies are selected in order to determine its place). It is this single proper motion that figures in his laws of motion. Of particular importance for Descartes' entire system, is that a body in circular motion has an endeavor [conatus] to recede from the center of rotation.

4. Newton's Manuscript De Gravitatione …

This fact, together with Descartes' contention that a body also participates in the motion of a body of which it is a part, makes it difficult to reconcile Descartes' system of the world with his definition of proper motion. Newton concluded that the doctrine is in fact self-refuting and that, where Descartes needed to, he had surreptitiously helped himself to a notion of space independent of body, particularly in order to assign the desired degree of centrifugal conatus to the planets and their satellites as they are swept about by celestial vortices of “subtle” matter.

The untitled and unfinished manuscript which begins “De Gravitatione et aequipondio fluidorum et solidorum …”, written perhaps a decade or more before the Principia , consists for the most part of an extensive and scathing critique of Descartes' doctrine of motion. The document, published for the first time in (Hall and Hall, 1962), is well worth the study for a glimpse at the development of Newton's thinking at a relatively young age. It manifestly embraces the doctrines of space and time later codified in the Principia . Notable, as well, is that each of the five arguments from the properties, causes and effects of motion advanced in the Scholium has a clearly identifiable antecedent in De Gravitatione . (See Rynasiewicz 1995 for details.) This makes it clear the extent to which the Scholium is concerned to argue specifically against the Cartesian system (as pointed out by Stein 1967), which Newton perceived to be the only other viable contender at the time.

5. Newton's Scholium on Time, Space, Place and Motion

The Scholium has a clearly discernible structure. Four paragraphs marked by Roman numerals I–IV follow the opening paragraph, giving Newton's characterizations of time, space, place and motion, respectively, as summarized in the third paragraph of Section 1 above. If we were to extend Newton's enumeration to the remaining paragraphs, then paragraphs V–XII constitute a sustained defense of the distinctions as characterized in I–IV. Paragraph XIII then states the general conclusion that the relative quantities are genuinely distinct from the respective absolute quantities and makes comments on the semantic issue of the meanings of these terms in the Bible. There follows one remaining, and quite extensive paragraph [XIV], which takes up the question how in practice one can ascertain the true motions of bodies and concludes: “But how we are to obtain the true motions from their causes, effects and apparent differences, and vice-versa, will be explained at length in the treatise that follows. For that is the end to which I composed it.”

In what follows, links have been inserted to the text of the Scholium according to the extended enumeration suggested above. Clicking on a link will open a new window in such a way that the reader can navigate back and forth between a given paragraph of the text and the commentary elucidating that paragraph.

Paragraph V appeals to the fact that astronomy distinguishes between absolute and relative time in its use of the so-called equation of time. This serves to correct for inequalities in the commonly adopted standard of time, the solar day, which most people mistakenly believe to be uniform. The solar day, defined as the period of time it takes the sun to return to zenith, varies by as much as 20 minutes over the course of a year. The standard of correction in the equation of time used in Ptolemaic astronomy was based upon the assumption that the sidereal day—the period of time it takes a fixed star to return to zenith—is constant, because the celestial sphere on which the fixed stars are located should not be assumed to speed up and slow down. With the demise of the Ptolemaic system and Aristotelian cosmology, this rationale was no longer compelling, and at least some astronomers, most notably Kepler, called into doubt whether the rate of rotation of the earth remained constant over the course of the year. (Kepler considered that its rotation would be faster when closer to the sun due to an excitatory effect of the sun.) Thus, the issue of the correct measure of time occupied considerable attention in 17th Century astronomy, especially because the ability to measure the rate of rotation of the earth is equivalent to the problem of determining longitude, which, for sea-faring nations, was critical for navigation (and hence military and economic dominance). Huygens' pendulum clock provided the first terrestrial candidate for a decently accurate measure of uniform time. Newton mentions this, as well as the eclipses of the moons of Jupiter, an alternative method based on Kepler's period law.

The invocation of the need for an equation of time in astronomy is not just an appeal to a well entrenched scientific practice. In the course of his discussion, Newton explains why he thinks the need is justified. Although he will argue in Book III of the Principia that the diurnal rotation of the earth is uniform, this is a contingent fact. It could have been otherwise. Indeed, it could have been that there are no uniform motions to serve as accurate measures of time. The reason is that all motion is subject to being accelerated or retarded (by the application of external forces). In contrast, absolute time (which is nothing other than duration or the perseverance of the existence of things) remains the same, whether the motions be be swift, slow, or null.

Paragraph VI defends the thesis of the immobility of (absolute) space, which against the backdrop of Descartes, clearly means that the parts of space, just as the parts of time, do not change their relation with respect to one another. Newton argues that the parts of space are their own places, and for a place to be moved out of itself is absurd. A more expansive antecedent of this argument occurs in De Gravitatione , applied specifically to time: if yesterday and tomorrow were to interchange their temporal relations with respect to the remainder of time, then yesterday would become today, and today yesterday. Thus, Newton held an interestingly holistic identity criterion for the parts of space and time.

Newton devotes five full paragraphs to justifying his characterization of the distinction between absolute and relative motion. The first three present arguments from properties of absolute motion and rest, the next presents an argument from their causes, and the final an argument from their effects. The force of these has confused modern commentators for a combination of reasons which, historically, are difficult to untangle. Since only those not already prejudiced by those commentaries, directly or indirectly, will find what follows unusual, it is best to defer an autopsy of those reasons until Section 6, after an exposition of the arguments.

Suffice it to say for the moment that it is a common misunderstanding that in these arguments Newton intends to develop empirical criteria for distinguishing cases of absolute motion from merely apparent motion and thereby to disprove the thesis that all motion is merely relative motion. To the contrary, the arguments take as their point of departure the assumption, common to Cartesian and Aristotelian philosophy, that each body has a unique state of true motion (or rest). Throughout the arguments, the terms ‘true motion’ and ‘absolute motion’ are treated synonymously. At issue is whether true motion (and rest) can be reduced to some special instance of relative motion (or rest) with respect to other bodies. In announcing at the outset of these arguments that “absolute and relative rest and motion are distinguished by by their properties, causes, and effects”, Newton indicates his intent to show that they cannot, at least if true motion and rest are to have those features we generally associate, or ought to associate, with them.

Argument 1 from Properties [ Paragraph VIII ] Property : Bodies that are truly at rest are at rest with respect to one another. Conclusion : True rest cannot be defined simply in terms of position relative to other bodies in the local vicinity.

Reasoning : Suppose there were a body somewhere in the universe absolutely at rest, say far away, in the region of the fixed stars, or even farther. (Whether or not that body might ever be observed doesn't enter into what follows.) Clearly it is impossible to know just from considering the positions of bodies in our region relative to one another whether any of these latter bodies maintains a fixed position with respect to that hypothetical distant body. To amplify, let B be one of the local bodies, C the relative configuration over time of the set of local bodies, and A the far distant body at absolute rest. The specification of C alone fails to establish the position of B relative to A over time. In particular, C fails to establish whether B is relatively at rest with respect A, which, by the property stated above, is a necessary condition for B to be absolutely at rest. Hence, specification of the local configuration C underdetermines whether or not B is at absolute rest. Thus the conclusion: it is impossible to define what it is for a body such as B to be at absolute rest [i.e., to give necessary and sufficient conditions for when it is that B is at rest] simply in terms of how B fits into the local configuration C.

Argument 2 from Properties [ Paragraph IX ] Property : If a part of a body maintains a fixed position with respect to the body as a whole, then it participates in the motion of the whole body. Conclusion : True and absolute motion cannot be defined as a translation from the vicinity of (the immediately surrounding) bodies, viewing the latter as if they were at rest.

Reasoning : Newton first introduces two considerations that can be taken either to support, or to illustrate, or to amplify upon the import of the stated property. The first is that if a part of a rotating body is at rest relative to the body as a whole, it endeavors to recede from the axis of rotation. The second is that the impetus of a body to move forward arises from the combination of the impetus of its parts.

From the property it follows that if those bodies surrounding a given body move (either rotationally or progressively forward as a fixed configuration) while the surrounded body is at rest relative to the surrounding ones, then the surrounded body partakes in the (true) motion of the group of surrounding bodies. Hence, if the surrounding bodies move truly, then so does the surrounded body. But according to the (Cartesian) definition of motion—which identifies the true motion of a body with its transference from the vicinity of immediately surrounding bodies, regarding the surrounding bodies to be as though they are at rest—it would have to be said (wrongly) that the surrounded body is truly at rest. Hence that definition is untenable.

Argument 3 from Properties [ Paragraph X ] Property : Anything put in a moving place moves along with that place, and hence a body participates in the motion of its place when it moves [relatively] away from that place. Conclusion : The complete and absolute motion of a body cannot be defined except by means of stationary places.

Reasoning : From the property, the [relative] motion of a body out of a given place is only part of the motion of the body if the place in question is itself in motion. The complete and true motion of the body consists of its motion relative to the moving place added vectorially to whatever motion the place may have. Should the place be moving relative to a place which is in turn moving, then the motion of that place must be added, and so on. Barring infinite regress, the sum must terminate with a motion relative to a stationary place.

Addended Argument : After deriving this conclusion, Newton amplifies upon the consequences. The only places that are stationary are all of those that that stay in fixed positions with respect to one another from infinity to infinity, and since these always remain stationary, they make up what Newton calls immobile absolute space.

The Argument from Causes [ Paragraph XI ] Causes : the forces impressed upon bodies. The major premise is that application of a [non-zero net] force on a body is both a necessary and sufficient condition for either generating or altering its true motion. More specifically: (A) Impressed force is a necessary condition for generating or altering true motion (but not, as remains to be shown, merely relative motion). (B) Application of a [non-zero net] force is a sufficient condition for the generation or alteration of true motion (but not, as will be shown subsequently, merely relative motion). Conclusion : The true motion of an individual body cannot be defined as any particular sub-instance of its motion relative to other bodies.

Reasoning : Newton seeks to establish that application of a positive net force to a body is neither a necessary not a sufficient condition for the generation of motion relative to other bodies. The two lines of reasoning are given separately, call them ‘Prong A’ and ‘Prong B’, respectively.

Prong A : To be established is that, although an impressed force is necessary for the generation or alteration of true motion in a body, it is not necessary for the generation of motion relative to other bodies. The reasoning is quite simple: pick a given body and merely apply the same [accelerative] force to all other bodies in question. These other bodies will then remain in the same relative configuration with respect to one another, but a relative motion with respect to the original body [to which no force has been applied] will either be generated or altered.

Prong B : To be established is that, although an impressed force is sufficient for the generation or alteration of true motion in a body, it is not sufficient for the generation of motion relative to other bodies. Again, the line of reasoning is quite straightforward. Consider an arbitrarily given body amongst a system of bodies and simply apply the same [accelerative] force to all bodies in question. Then, despite the fact that a force has been impressed upon the originally given body, there is neither generation nor alteration of relative motion with respect to the remaining bodies.

The Argument from Effects [ Paragraph XII ] Effects : the forces of receding from the axis of rotational motion [centrifugal endeavor]. The major premise is that the centrifugal endeavor of bodies [or parts of bodies] to recede from the axis of rotation is directly proportional to the quantity of the true circular motion. Conclusion : True rotational motion cannot be defined as relative rotation with respect to the surrounding bodies.

Reasoning : The line of reasoning is in fact parallel to the preceding argument from causes, although this may not be completely perspicuous due to the fact that the correlates of the two prongs above are here stages of a single on-going experimental situation, the so-called “rotating bucket” experiment, which, Newton intimates, he actually performed. In order to set up this experiment, one suspends a bucket using a long cord and by turning the bucket repeatedly, winds up the cord until it is strongly twisted, then fills the bucket with water. During the course of the experiment, the degree to which the water tries to climb up the sides of the bucket is used as a measure of its centrifugal endeavor to recede from the center. Newton uses the experiment to establish that centrifugal endeavor is neither a necessary condition nor a sufficient condition for the existence of relative circular motion [of the water] with respect to its surroundings [the bucket].

Stage 1 : When the bucket is first released, it rotates rapidly with respect to the rest frame of the experimenter while the water remains at rest with respect to the experimenter. In other words, there is rapid relative motion of the water with respect to the bucket. However, the surface of the water remains flat, indicating that it has no tendency to recede from the axis of relative rotation. Thus, the existence of centrifugal endeavor in the parts of a body is not a necessary condition for the body to be rotating relative to its surroundings. That is, such relative rotation with respect to immediately adjacent bodies need not produce any centrifugal endeavor in the parts of the body to recede from the axis of relative rotation.

In the further course of the experiment, as the bucket continues to rotate, the water gradually begins to rotate with it, and as it does so, begins to climb up the sides of the bucket. Eventually, according to Newton, the water acquires the same rotation of the bucket relative to the lab frame, at which point we have the following situation.

Stage 2 : The water and the bucket are at relative rest, yet the water has achieved its highest ascent up the sides of the bucket, indicating a maximum centrifugal endeavor to recede from the axis of common rotation. Hence, the existence of centrifugal endeavor is not a sufficient condition for the presence of relative circular motion between a body and its surroundings, i.e., if a body, or rather its parts, have a centrifugal endeavor to recede from a central axis, it does not follow that there is a relative circular motion of the body with respect to its immediate surroundings.

Astrophysical Application . After deriving the conclusion, Newton uses the premises of the first two arguments from properties, together with the premise of the argument from effects, to critique the vortex theory of planetary motion. According to that theory, each of the planets (and most notably the earth) is relatively at rest with respect to the “subtle” matter of the celestial vortex of our own sun. Hence, according to Descartes' own definition of true motion (as well as his explicit insistence), they have no true motion. However, it is manifest that they do not maintain fixed positions with respect to one another. So, according to the property invoked in the first argument, they cannot [all] be truly at rest. Moreover, from the property invoked in the second argument, they partake in the circular motion of the solar vortex [assuming that motion to be true motion, as Descartes implicitly assumed]. Finally, because they would accordingly participate in the true circular motion of this hypothetical vortex, they should have an endeavor to recede from the axis of its rotation.

This completes the sequence of arguments from the properties, causes, and effects of motion. The next paragraph [ XIII ] states the cumulative conclusions of the arguments marshalled beginning with the arguments for absolute time in paragraph V: “Hence relative quantities are not the quantities themselves, whose names they bear, but are only sensible measures of them (either accurate or inaccurate), which are commonly used in place of the quantities they measure.” Having made his case, Newton comments on the ordinary language meaning of the terms for these quantities in order to address contemporary issues of dogma and heresy.

Galileo's condemnation by the Catholic Church for asserting that the earth is in motion was still recent history at the time Newton composed the Principia . Descartes, who lived in reach of Papal authority and feared similar fate, had found a clever way of espousing Copernicanism without falling prey to accusation of heresy. According to his definition of motion “properly speaking”, he contends, the earth is truly at rest.

In Newton's system of the world as set out in Book III of the Principia , the earth patently moves absolutely. In anticipation, Newton indicates how to reconcile this with scripture by observing that, if usage determines the meanings of words, then in ordinary discourse (including the Bible) the terms ‘time’, ‘space’, ‘place’, and ‘motion‘ are properly understood to signify the relative quantities; only in specialized and mathematical contexts do they denote the absolute quantities. (Keep in mind Newton's title, The Mathematical Principles of Natural Philosophy .) He proceeds to chastise Descartes on two counts, first for doing violence to the scriptures by taking them to refer to the absolute quantities, and second, for confusing the true quantities with their relative measures.

Having argued his case that true motion consists in motion with respect to absolute space, and thus having dealt to his satisfaction with the metaphysics of motion, Newton turns in the final paragraph of the Scholium to epistemological strategies available on his account. On an Aristotelian or Cartesian account, one can directly observe the allegedly absolute motion of a body if both it and its immediate surroundings are visible. In contrast, because the parts of absolute space are not directly accessible to the senses, it is very difficult, Newton confesses, to ascertain the true motion of individual bodies and to discriminate them in practice from the apparent motions. “Nevertheless,” he remarks in a rare moment of wit, “the situation is not entirely desperate.” Evidence is available in part from apparent motions, which are the differences of true motions, and in part from the forces, which are the causes and effects of true motions.

Newton illustrates with an example. Imagine a pair of globes, connected by a cord, revolving about their common center of gravity. The endeavor of the globes to recede from the axis of motion is revealed by the tension in the cord, from which the quantity of circular motion can be estimated. Furthermore, whether the direction of their revolution is clockwise or counterclockwise can be detected by applying forces to opposite faces of the globes to see whether the tension in the cord increases or decreases. All this can be done in empty space where no other bodies are present to serve as points of reference.

Suppose now that, in addition to the globes, there is second system of bodies maintaining fixed positions with respect to one another (for example, the fixed stars). If the two systems are in a state of relative rotation, one cannot gauge from just the relative rotation, which, if either, is at rest. However, from the tension in the cord connecting globes, one can establish whether the relative rotation is due entirely to the absolute rotation of the system of globes. Supposing so, the second system of bodies can then be exploited to provide an alternative technique for determining whether the globes revolve in a clockwise or counterclockwise direction—one simply consults the direction of rotation relative to the stationary system.

At this point Newton cuts off the Scholium, explaining that the whole point of having written the treatise to follow is to show how to infer the true motions from their causes, effects, and apparent differences, and conversely the causes and effects from either the true or the apparent motions.

6. Common Impediments to Understanding the Scholium

As remarked in Section 5.3 above, the purpose of the arguments from properties, causes, and effects has been widely misunderstood in both the historical and philosophical literature, and as a consequence, so too the relation of these to the example of the revolving globes in the final paragraph. Some diagnosis as to why may help those readers already steeped in tradition to overcome certain prejudices they bring to the Scholium and may also serve to further illuminate the framework in which Newton and his contemporaries struggle with the problem of motion.

(1) Newton's stated intention in the Scholium is to maintain that absolute space, time, and motion are genuinely distinct from their relative counterparts. For the case of space, this clearly amounts to arguing the existence of an entity distinct from body in which bodies are located—something denied by relationists. Similarly, for the case of time, this involves arguing the existence of an entity distinct from the succession of particular events in which the events are located—again, something denied by relationists. It may seem then as a matter of course that, for the case of motion, Newton should argue for existence of something denied by relationists, presumably, absolute motion.

(2) It would amount to a virtual petitio principii were Newton to rest a case for absolute motion on the existence of absolute space. Hence, one would expect him to appeal to various physical phenomena that might provide independent warrant. Now it is well known that Newton's laws satisfy the principle of Galilean relativity, according to which there can be no experimental test to determine whether a system is at rest or in a state of uniform rectilinear motion. However, Newton's laws do support a distinction between inertial and non-inertial motion in that they predict, in non-inertial frames, the appearance of so-called “fictitious forces,” for instance, centrifugal forces in rotating frames, resulting in a tendency for bodies to recede from the axis of rotation. Since this is exactly the effect involved in the rotating bucket experiment, it is tempting to interpret Newton as marshaling it as a case in which this phenomenon suggests independent warrant for the existence of absolute motion.

(3) Moreover, since the same effect is operative in the example of the revolving globes, it is hard to see why that example does not serve the very same purpose. In fact, in his famous critique of Newton in the Science of Mechanics , Ernst Mach, in quoting from the Principia , cut out all of the intervening text to make it appear as though the two are but variant examples in the development of a single argument.

(4) Finally, the choice of language in Motte's 1729 translation, which is the basis for the most widely available twentieth century English translation by Cajori, tends to reinforce the presumption that the arguments from properties, causes, and effects seek to identify phenomena that empirically distinguish absolute from (merely) apparent motion. In the Cajori version, the conclusions of the first three arguments, the arguments from the properties of motion and rest, read:

• … it follows that absolute rest cannot be determined from the position of bodies in our regions. [ Paragraph VIII ]
• …the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest; [ Paragraph IX ]
• Wherefore, entire and absolute motions can be no otherwise determined than by immovable places; [ Paragraph X ]

Thus, it is tempting to assume that both the argument from causes and the argument from effects are likewise concerned to identify an empirical signature of absolute motion by which it can be distinguished from (merely) apparent motion. (Reading the arguments in this fashion, only the argument from effects, which deals with the centrifugal effects of circular motion, appears to help Newton's cause—a commonly registered complaint.)

It will be more illuminating to respond to these in reverse order.

(Ad 4) It is an artifact of Motte's translation that the Latin verb definiri (passive infinitive) is rendered occasionally as ‘be determined’ rather than as ‘be defined’. According to seventeenth-century English usage, either choice is acceptable. In appropriate contexts, the two function as synonyms, as in the Euclidean axiom, “Two points determine a line.” Motte's practice conforms with this. The conclusion of the argument from effects, ‘definiri’ is translated as ‘be defined’:

And therefore this endeavor does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. [ Paragraph XII ]

If one now goes back and substitutes ‘be defined’ for ‘be determined’ into the conclusions from the arguments from properties quoted above, they take on, to the modern ear, a different meaning. They make claims as to what constitutes an adequate definition of the concepts of true, or absolute, motion and rest.

(Ad 3) We have already seen how paragraph XIII signals the conclusion, not just of the arguments from properties, causes, and effects, but the direct arguments for absolute time and absolute space as well, which, altogether, Newton takes establish the ontological distinction between the absolute and the relative quantities. That the next paragraph, in which the globes are introduced, concerns a different, epistemological issue would be apparent were it not for another artifact of the Motte translation, this time involving the Latin verb ‘distinguere’. Newton uses the word again and again, almost thematically, in characterizing and arguing for the ontological distinction between the absolute and the relative quantities; and Motte renders it in English as ‘to distinguish’. Unfortunately, the English verb appears in the Motte translation one more time at the start of the final paragraph:

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent;

But in the Latin, the word ‘distinguere’ is nowhere to be found. Rather, the sentence reads:

Motus quidem veros corporum singulorum cognoscere, & ab apparentibus actu discriminare , difficillimum est;

Thus, to the Latin reader, it is clear that Newton is moving on to a different consideration.

(Ad 2) What has been said in connection with (4) suffices against the false expectations developed in (2). However, there may remain some sense that, even on a proper reading, Newton tried to bluff his way past the principle of Galilean relativity. Newton indeed acknowledges the principle, though not by name, in Corollary V to the laws of motion:

The motions of bodies in a given [relative] space are the same among themselves whether that space is at rest or moves uniformly in a straight line without uniform motion.

And there is no reason to think that he did not appreciate the limitation it poses for experimentally differentiating between absolute rest and uniform motion in a straight line. A particular instance of Corollary V is the solar system as a whole. Assuming the absence of external forces, it follows (from Corollary IV to the laws) that the center of gravity of the solar system is either at rest or moves uniformly in a straight line. But which? Because of Corollary V, when Newton wishes to attribute a definite state of motion to the center of mass of the solar system in Book III, he must introduce the hypothesis that “The center of the system of the world is at rest.” Should this not be some source of embarrassment?

Apparently not. Immediately following the hypothesis, he writes:

This is conceded by everyone, although some contend it is the earth, others the sun, that is at rest in the center. Let us see what follows from this.

According to Newton, the attribution of a state of absolute rest to one or the other of these bodies is universally taken for granted. What does confound all conventional wisdom in what follows is that neither the earth nor the sun is at rest, but rather the center of gravity of the solar system.

(Ad 1) Although arguing that absolute space and absolute time are distinct from any relative spaces and relative times involves, in each case, arguing for the existence of an additional entity, it does not follow that, in arguing that absolute motion is distinct from relative motion, Newton is obliged to argue yet another existence claim. Unfortunately, the term ‘absolute motion’ is prone to be read in two distinct ways. On one reading, it means, as a matter of stipulative definition, ‘change of absolute place’. In this sense of ‘absolute motion’, the existence of absolute motion (or more precisely, the possibility of the existence of absolute motion) follows immediately from the existence of absolute space and absolute time. As indicated before, nothing further needs to be said. On the other reading, ‘absolute motion’ is synonymous with ‘true motion’. And as we have just seen, Newton finds no reason to doubt that his audience does not grant that a body is either truly at rest or truly in motion. The venerable tradition that takes motion and rest to be contraries has yet to be questioned. So it is not incumbent on Newton make a case for the reality of absolute motion in the sense of true motion. What is incumbent is for him to argue that true motion just is change of absolute place. And that is the purpose of the arguments from properties, causes, and effects.

Newton's views on space, time, and motion dominated physics from the 17th Century until the advent of the theory of relativity in the 20th Century. Nonetheless, these views have been subjected to frequent criticism, beginning with contemporaries, such as Leibniz and Berkeley, and continuing on to the close of the 19th Century, most notably with Ernst Mach, whose writings influenced Einstein. In the early twentieth century, Newton tended to be cast as a metaphysical dogmatist by the early philosophical interpreters of relativity, in particular Hans Reichenbach. Unfortunately, that stigma has tended to linger.

More recent scholarship reveals a more sober picture of why Newton felt fully justified in positing absolute space, absolute time, and absolute motion. Moreover, the novel feature of special relativity, the rejection of absolute simultaneity—something that never occurred to any of Newton's earlier critics—necessitated only that absolute space and absolute time be replaced with an absolute space-time (Minkowski spacetime). And although Einstein's development of general relativity was in large part motivated by a desire to implement a general principle of relativity, to wit that all motion is relative motion, that it succeeds in doing so was questioned shortly after the theory was introduced. As for the question of the absoluteness of space-time in general relativity, it no longer has the character of something which acts without being acted upon, as Einstein himself pointed out. The space-time metric tensor not only encodes for spatiotemporal structure, but also represents the gravitational potentials, and thus gravitational energy. By Einstein's famous equation for the equivalence of energy and mass, it follows that the gravitational field possesses mass. Only, since gravitational energy can not be localized in terms of an energy density tensor, but is possessed by the field holistically, neither can this mass be localized. Thus, philosophical controversy as to whether space-time can exist without matter becomes tendentious according whether one counts the gravitation field as something material or not.

Thus, the question whether the revolution in our views about space and time in the last century vindicates Newton's critics as more philosophically astute becomes a misplaced one. The distinction between what counts as matter in contrast to empty space presupposed in the earlier debates has been eclipsed by possibilities undreamt of before the introduction of modern field theory and relativity. [ 1 ]

Primary Sources

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• The Newton Project
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• Papers of Isaac Newton (Cambridge University Library)
• Andrew Motte's 1729 translation of the Principia
• Voltaire on Descartes and Newton

Aristotle, Special Topics: natural philosophy | Clarke, Samuel | Descartes, René: life and works | Newton, Isaac | Newton, Isaac: Philosophiae Naturalis Principia Mathematica | Newton, Isaac: philosophy | space and time: absolute and relational space and motion, post-Newtonian theories | space and time: the hole argument

Acknowledgments

I'd like to thank John Norton for observations which led to many improvements.

Copyright © 2011 by Robert Rynasiewicz < ryno @ lorentz . phl . jhu . edu >

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