A chain of effects is an effect.
An effect requires a cause.
A chain of effects thus requires a cause.
This is a logically sound argument. However, when we talk about infinity, there is always a prior chain of effects that can act as a cause. Wrestling with infinities, we can often construct scenarios which end in apparent contradictions (such as your infinite army chain who shoot when the next person in line tells them to - how could it possibly start?). The contradictions in question are not necessarily logical contradictions. They can simply be counter-intuitive conclusions, that are nevertheless mathematically provable.
See Hilbert's Hotel: http://en.wikipedia.org/wiki/Hilbert%27s...rand_Hotel
An effect requires a cause.
A chain of effects thus requires a cause.
This is a logically sound argument. However, when we talk about infinity, there is always a prior chain of effects that can act as a cause. Wrestling with infinities, we can often construct scenarios which end in apparent contradictions (such as your infinite army chain who shoot when the next person in line tells them to - how could it possibly start?). The contradictions in question are not necessarily logical contradictions. They can simply be counter-intuitive conclusions, that are nevertheless mathematically provable.
See Hilbert's Hotel: http://en.wikipedia.org/wiki/Hilbert%27s...rand_Hotel
