tag:blogger.com,1999:blog-3891434218564545511.post2362146137141300824..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: A principle about infinite sequences of decisionsAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-83066681619788670632022-11-09T17:34:48.619-06:002022-11-09T17:34:48.619-06:00If so, then I guess, that any and every finite amo...If so, then I guess, that any and every finite amount of slices will do for Eve, as long as she doesn't go for any amount of slices with cardinality equal to the cardinality of the set of all natural numbers. If she is ought to maximise her utility AND there is no certain bound or limit to that maximisation of a finite amount of slices of Satan's apple, then go figure, what such a "maximum" in this case might be.<br /><b>As for me I will take an arbitrary amount of percentage below 100% of that pie, I mean, of that <i>"Satan's apple"</i> with an arbitrary finite amount of slices.</b><br />Thank you very much.Kritschhttps://www.blogger.com/profile/13025223721628879816noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-46005818062435378922022-11-09T14:37:46.574-06:002022-11-09T14:37:46.574-06:00Yup, in the story, taking all the even-numbered sl...Yup, in the story, taking all the even-numbered slices, or all the prime-numbered slices, or all the power-of-two-numbered slices will get you kicked out of paradise. Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-37297739136059262862022-11-09T08:49:22.156-06:002022-11-09T08:49:22.156-06:00"But if she greedily takes infinitely many, s...<i>"But if she greedily takes infinitely many, she is kicked out of paradise, an outcome so bad that the whole apple does not outweigh it."</i><br /><br />How about taking only the slices with even numbers?<br />Is she then also doomed to leaving paradise, just because she took an infinite amount of slices from Satan's apple, but not exactly the whole (100%) apple?!?<br /><b>∑n∈ℕ(1/2^n)/2=1/(1-1/2)·1/2=1 (=100% of Satan's apple)<br />≠ ∑m∈ℕ(1/2^(2m))/2=∑m∈ℕ(1/4^m)/2=1/(1-1/4)·1/2=2/3 (≈66.67% of Satan's apple)</b><br /><br />Is Hilbert's Hotel not capable of accommodating new guests, just because all and every room is currently occupied?<br />From the wiki article for <a href="https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel" rel="nofollow">"Hilbert's paradox of the Grand Hotel"</a>:<br /><i><b>Analysis</b><br />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....</i><br /><br />And these are the problems/propositions, which philosophers are hung up on these days.Kritschhttps://www.blogger.com/profile/13025223721628879816noreply@blogger.com