this post was submitted on 29 Oct 2024
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[โ€“] Samvega@lemmy.blahaj.zone 26 points 2 weeks ago* (last edited 2 weeks ago) (5 children)

"The struggle itself towards the heights is enough to fill a man's heart. One must imagine Sisyphus happy."

He will struggle to ask the infinite staff of the infinite hotel to move infinite occupants into another set of infinite rooms. After all:

It is also possible to accommodate a countably infinite number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and, in general, the guest occupying room n to room 2n (2 times n), and all the odd-numbered rooms (which are countably infinite) will be free for the new guests.

Even if Sisyphus is infinite and the boulder is infinite, they can be accommodated within an infinite space.

Hilbert's paradox is a veridical paradox: it leads to a counter-intuitive result that is provably true. The statements "there is a guest to every room" and "no more guests can be accommodated" are not equivalent when there are infinitely many rooms.

This struggle will, according to Camus, provide some meagre happiness to offset the fact he's stuck in a stupid, made up, unrealistic trolley problem; one which serves only to trap people within consequentialist moral thought as if that is the only ingredient for a moral decision, ignoring all other bases for moral decisions.

[โ€“] Malgas@beehaw.org 3 points 2 weeks ago

Even if Sisyphus is infinite and the boulder is infinite, they can be accommodated within an infinite space.

But not if they're uncountably infinite.

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