Kalaam Argument, II
I. Al Kindi:
- Argument 1: If you take away some from an infinite... Easy to get into trouble. Hilbert's hotel does better here.
- Argument 2: The insight is that the distance backwards is the distance forwards (shades of Heraclitus.)
- Idea: If there was an undifferentiated past time, then the universe's potentiality for change would have surely already been actualized?
II. The Grim Reaper paradox
- In finite time. One possible conclusion: A finite amount of time contains a finite number of moments. Another: Things may be not as compossible as they seem.
- Infinity consists in the impossibility of completing.
- But if so, then why assume that a sequence of times with the property there is a time one minute before each time is infinite?
IV. For the eternity of the world
- Kant's argument: No infinite empty time. (But the sliding over problem remains!)
- Aristotle's argument: Suppose that before t0, there was no time. This appears self-contradictory. (But is it?) But time requires motion. And motion requires things that move. Ergo, the world is eternal.