Friday, February 28, 2014

Aristotle and Absolute Space and Time

In Aristotle's physics, is there an absolute space and time (or absolute motion and rest)? I've come across a number of places in which people assume that it does. Obviously, to some extent it depends on what you mean by absolute space and time. Suppose we use Newton's definition of absolute space and absolute time from the Principia:

I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth.

By these definitions Aristotle's physics has no absolute space and no absolute time -- indeed, in Aristotle's physics absolute space and absolute time are simply impossible. 'When' for Aristotle is by definition relative to motion; 'where' is by definition relative to body. This is why we get the kinds of discussions in physics that we find in the medieval scholastics; whenever they talk about time, they are always talking about clocks, and whenever they talk about space they are always talking about containers (in a broad sense of the term). Aristotle's physics has no absolute time or absolute space in Newton's sense; time is always relative to some clock and space is always relative to some container.

Indeed, given some of the way Newton phrases things, I actually wonder if Newton might be deliberately anti-Aristotelian here. Newton posits absolute space and absolute time because his physics crucially requires us to break away from the purely sensible -- Newtonian physics can explain a great many things, but it does so by abstraction from the sensible. Taking time itself, or space itself, to be a measure, as Aristotelian physics effectively does, from his perspective means that physical theories never talk about realities, but only about measurements. At least, this seems to be one of the ways his scholium on the subject can be read.

There is a sense, though, in which the Aristotelians admitted something that we could think of as absolute space and time. For while time is relative to clocks or changes and place to containers, the old Aristotelian universe had something capable of operating as a general clock or container: the primum mobile, which as that which has the first and most general change can serve as both a universal clock and a universal container. Time is necessarily relative to a change that can act as (in some sense) a clock -- but there happens to be a change that can be a clock for any other change. Place is necessarily relative to a body that can act as (in some sense) a container -- but there happens to be a body that can be a container for every other body. If by 'There is an absolute time' we meant 'There is a universal clock', and by 'There is an absolute space' we meant 'There is a universal container', the Aristotelians typically did hold that there was an absolute space and time. But this does need to be distinguished from Newton's sense; these things are relative, not absolute, space and time for Newton.

(The fact that Newton thinks of relative space and time as tied to the senses does complicate this conclusion somewhat, it should be said; the way in which the primum mobile works as a 'clock' or a 'container' in Aristotelian physics doesn't so obviously tie it to the senses. There are also some variations among Aristotelians, and there was some puzzlement arising from the fact that if place is relative to a container, the primum mobile is not in any place, which sounds a bit odd.)


  1. Timotheos1:07 PM

    I've found that something like this happens with Aristotle's notion of heavy and light; supposedly since Galielo showed that gravity affects things evenly, Aristotle was wrong. But given how Aristotle speaks of heavy and light, it's obvious that he's including density and not just gravity, otherwise we should take him to say that it is obvious by the senses that anti-gravity exists! If Galielo had wanted to be fair, he should have done expirements with an iron ball and a cork ball instead of a steel one.

  2. branemrys1:15 PM

    Yes, that's definitely a point where people fail to consider shifts of terms.

  3. Timotheos1:31 PM

    Also, I'm wondering if you think that Aristotle would have accepted Newton's idea of inertia; Newton seemed to think he did. Most of the supposed incompatibility comes from the fact that Aristotle thinks that motion in a void is literally impossible, since a void is impossible, so for continued motion you must have a mover, since there is always some finite resistance. And Newton didn't deny this, in fact, he affirmed that this was true. But there can be a true antecedent with a false consequent, and since Newton is trying to mathematically model nature, this is valuable to him, whereas Aristotle wouldn't care about this too much, since he's just giving an account of nature.

    What I'm wondering is whether Aristotle would have granted Newton the antecedent as true; he says that if motion were in a void, nothing would slow it down, thus it would move ad infinitum. (I'm paraphrasing from Book IV lecture 10 of Aristotle with Aquinas's commentary) Do you think he meant that the motion would thus be infinitely fast, which appears to be the common reading, at least on the internet, or just unending in one direction? If it's the latter, isn't this just Newton's principle?

  4. branemrys2:01 PM

    I haven't really thought about this in particular detail before, but Newton's 'inertia' is still literally inertness -- the explicit reason he gives for it is that body of itself doesn't act and for that reason is resistant to change. Newton's primary arguments on the subject seem to me to focus not on the void (despite having the obvious implications for what would happen in it) but on the nature of body.

    On the lecture 11 passage, without investigating in detail, my guess would be neither: the point seems to be not that it will continue unendingly in one direction nor that it would be endlessly fast, but simply that it would never be at rest, i.e., unendingly moving. I don't see any reason to accept the infinitely-fast interpretation, and while the passage itself could be read in an infinite-in-one-direction way, Aristotle immediately goes on to say that in a void things should move in every direction, which at least makes the infinite-in-one-direction interpretation awkward in context.


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