Arguments against Kant's Temporal Finitism?
Posted: Sun May 05, 2013 4:26 pm
Has the universe been around forever, or did it have a beginning? Furthermore, does it even make sense to say that it has been around "forever"?
Kant observes,
Kant observes,
Consider the following before replying:If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in that world an infinite series of successive states of things. Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away, and that a beginning of the world is therefore a necessary condition of the world's existence.
- Albert Einstein thought Steady-State was reasonable and coherent.
- Fred Hoyle thought Steady-State was a grand idea.
- Kant wrote the above 120 years after the invention of infinitesimal calculus.
- We can assume that Kant was fully aware of Zeno paradoxes regarding runners who never finish races and arrows which are "everywhere stationary", and so on. And that he was aware of how calculus solves them.
- Regarding Zeno, summation of T / (2^n) as n -> inf, converges. A very transparent proof about epsilons and deltas shows that moving arrows are, in fact, never stationary anywhere. In other words, the derivative of a function exists and is coherent.
- However, Summation of n, as n -> inf, diverges. Summing all the seconds from from previous times yields a nasty divergence.
- Kant flubbed the ending of this passage. It is clear that what he really meant to communicate, was that a finite beginning time (Tb) is a necessary condition for the existence of the present moment. (not necessarily the existence of the "world").