Time v. kinesis

-Aristotle defines time as a sort of number. It’s any count of the parts of kinesis ordered by things like in front of and behind, stages of development, or relation to the parts of some other motion (a second hand, a pendulum, etc.)

-Making time a number is how A. avoids Zeno’s paradoxes, since time is always actually some unit and never actually a continuously divisible magnitude.

-Time is always many while kinesis is one. An hour can’t mature and a second can’t get to a destination. Both can only repeat.

-Kinesis is one from its goal, fulfillment or specification.

-Calculus or the theory of limits is not a response to Zeno. His theories are critiques of motion and time and approaching a limit is not a motion and takes no time. How long does a derivative take?

-Euclid I.4 is not a motion. How far apart are the triangles? How long does it take?

-Just because you imagine a line moving does not mean that lines move any more than measuring something in a dream makes it just that long.

-Descartes allows two things to be true in dreams: mathematics and the self.

Motion is continuous because it is infinitely divisible but time is continuous because it has no first or minimum unit.

-Time as such has a unit but not a minimum one while motion as such has no unit at all.  This is what A. means when he says that Zeno confuses potential divisions with actual ones. The actual divisions are whatever unit of time one chooses to take and its multiplications, not the potential divisions of motion that allow the time unit to be as small as one pleases.

 

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2 Comments

  1. Kristor said,

    May 14, 2016 at 3:03 pm

    James, I’d like to link to this post from my Journal, where I am chewing on it. But I can’t, because since it has no title, I can’t navigate to it or figure out a URL for it.

  2. May 14, 2016 at 8:27 pm

    I don’t understand this very well, but I just have a couple of questions:

    (i) It seems that ancient philosophers, like Aristotle and St. Augustine, seem to think that time depends upon motion (I think in the Confessions, Augustine says that if all bodies were not in motion, there would be no time). But I have a hard time of thinking about it like that. In modern times I think we think of time first, then motion. After all, motion is measured by “change in distance over change in time.” What’s the precise relationship between motion and time here?

    (ii) “Calculus or the theory of limits is not a response to Zeno. His theories are critiques of motion and time and approaching a limit is not a motion and takes no time. How long does a derivative take?”
    You’re right that motion and number aren’t the same thing, but couldn’t they respond by saying there is an essential ‘link’ between number and ‘motion’? Couldn’t someone like a Pythagorean say that calculus responds successfully to Zeno, since he says that all is essentially number (including motion)?


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