Causal finitism says that nothing can have infinitely many things in its causal history. Suppose causal finitism is false. Then surely the following scenario is possible:
- There has always been a lamp.
- There is a backwards infinite sequence of flips of the lamp switch at times t−1>t−2>t−3>....
- Each time the switch was flipped, the lamp state flipped between on and off.
- All lamp state changes are explained by switch flips, and are not overdetermined by any other causes.
So if the Principle of Sufficient Reason is necessarily true, RTL is impossible, and hence causal finitism is true.