This limited anti-infinitism means that I do not need to worry about arguments in favor of actual infinities such as the following:
- The actual existence of an infinite future.
- The actual existence of mathematical infinities.
- The intuitively very plausible possibility of a simultaneous infinity of objects. At least, it's plausible to me.
In fact, my worry is not so much about an actual infinite as such, but about infinitely many causal influences coming together.
Initially, when I came to the Grim Reaper argument against an infinite past, I found the anti-infinitist conclusion very counterintuitive. But now it has become clear to me that it's not: for it's not that counterintuitive to think that absurdities can result if an infinite number of causal influences can work together. My pro-infinitist intuitions were based on non-causal mathematical considerations. But I can, if I wish, retain those intuitions.
In fact, I can even retain the intuition that there could have been an infinite past, as long as this does not imply a backwards-infinite causal chain. Consider, for instance, a world that consists of a multiverse of universes. The first universe is one year old. The second universe is two years old. The third is three years old. And so on. The world as a whole has an infinite past. But as long as there isn't the wrong kind of causal dependence between the universes, such an arrangement need not imply the kind of infinity in causal influence that my arguments lead me to think is problematic.
This strengthens the Kalaam argument by showing that the premises can be weakened: the Kalaam argument only needs the kind of causal anti-infinitism that I now cautiously accept.