tag:blogger.com,1999:blog-3891434218564545511.post3829632989149115799..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: Guessing strategies and causal finitismAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-6020622330953645682015-02-10T07:08:37.298-06:002015-02-10T07:08:37.298-06:00Yes, there are issues about events.
No, this is n...Yes, there are issues about events. <br />No, this is not rearrangement. The obvious method yields infinitely many losses and wins. The Choice method yields infinitely many wins and finitely many losses, in a series that *absolutely* converges to infinity.<br />Perhaps a better way to do this is to make the payoffs be pleasures and pains. Obviously better to get infinitely many pleasures and finitely many equal pains at these times than infinitely many of both.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-85033467582676083322015-02-10T06:01:52.494-06:002015-02-10T06:01:52.494-06:00Another question on causal finitism: to apply it, ...Another question on causal finitism: to apply it, you have to be able to recognize causes and events. Metaphysics is not my area, but this is surely not uncontroversial. For example: if all is flux, events are arbitrary. Perhaps you could say something about the metaphysics you have in mind.<br /><br />On the problem: I am a bit confused about the setup. To make sure I understand: you are supposed to have had an infinite past life, to have bet on all the past rolls, and to be going to bet on the remaining 365 rolls. The alternative rules, “Choice-based” or “always bet no”, are supposed apply to all the bets, past and future.<br /><br />Isn’t the apparent paradox just a variation on the Analysis 101 trick of adding infinite series in different orders? When the sums are infinite (as here), anything goes. For any particular infinite sequence of rolls, for any sufficiently large number of bets, the Choice-based method is better. For any particular finite group of bets, averaged over sequences of rolls, always betting “no” is better. A puzzle, but not a contradiction. I see no need to invoke causal finitism here (though you certainly could).IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-84461968649948789702015-02-09T14:16:20.263-06:002015-02-09T14:16:20.263-06:00Here's a strategy not dependent on the Axiom o...Here's a strategy not dependent on the Axiom of Choice that dominates the "always guess 'no' (=non-six)" strategy and sometimes is strictly better.<br /><br />If you've seen infinitely many non-sixes, guess "no". Otherwise, guess "yes".<br /><br />In worlds where you get only finitely many non-sixes, this strategy beats "always guess 'no'". In other words, it gives the same result.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.com