But getting anywhere on the lower track will kill infinitely many people. You cannot kill finitely many people on the lower track. Well, unless you derail at exactly the first. On the upper track, a stop at any point will have killed only finitely many.
One person can only be on the spot for one number. As soon as more than one gets killed, that would mean that the trolley has traversed some distance, which implies that it has killed an infinite number of people. That is impossible in any finite timespan under the aforementioned assumption. Thus the only logical conclusion is that it gets stuck after the first person is killed, at the exact spot the first number is mapped to.
I guess there could also be a different solution when you look at the problem from a different angle. Treating infinity with this little mathematical care tends to cause paradoxes.
In any non-empty, finite interval on the real number line, there are uncountably infinitely many numbers = people in this thought experiment. If you think of physical space as continuous, we cross infinitely many points in any finite movement.
I’d like to see one of the numerous paradoxes you refer to.
But getting anywhere on the lower track will kill infinitely many people. You cannot kill finitely many people on the lower track. Well, unless you derail at exactly the first. On the upper track, a stop at any point will have killed only finitely many.
One person can only be on the spot for one number. As soon as more than one gets killed, that would mean that the trolley has traversed some distance, which implies that it has killed an infinite number of people. That is impossible in any finite timespan under the aforementioned assumption. Thus the only logical conclusion is that it gets stuck after the first person is killed, at the exact spot the first number is mapped to.
I guess there could also be a different solution when you look at the problem from a different angle. Treating infinity with this little mathematical care tends to cause paradoxes.
In any non-empty, finite interval on the real number line, there are uncountably infinitely many numbers = people in this thought experiment. If you think of physical space as continuous, we cross infinitely many points in any finite movement.
I’d like to see one of the numerous paradoxes you refer to.