All of Andrew Jacob Sauer's Comments + Replies

Sorry to necro this here, but I find this topic extremely interesting and I keep coming back to this page to stare at it and tie my brain in knots. Thanks for your notes on how it works in the logically uncertain case. I found a different objection based on the assumption of logical omniscience:

Regarding this you say:

Perhaps you think that the problem with the above version is that I assumed logical omniscience. It is unrealistic to suppose that agents have beliefs which perfectly respect logic. (Un)Fortunately, the argument doesn't really depend

Rot13:

Gur vzcnpg bs na rirag ba lbh vf gur qvssrerapr orgjrra gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba tvira pregnvagl gung gur rirag jvyy unccra, naq gur pheerag rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba.

Zber sbeznyyl, jr fnl gung gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba vf gur fhz, bire nyy cbffvoyr jbeyqfgngrf K, bs C(K)*H(K), juvyr gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba tvira pregnvagl gung n fgngrzrag R nobhg gur jbeyq vf gehr vf gur fhz bire nyy cbffvoyr jbeyqfgngrf K bs C(K|R)*H(K). Gur vzcnpg bs R orvat gehr, gura, vf gur nofbyhgr inyhr bs gur qvssrerapr bs gubfr gjb dhnagvgvrf.

The proof doesn't work on a logically uncertain agent. The logic fails here:

Examining the source code of the agent, because we're assuming the agent crosses, either PA proved that crossing implies U=+10, or it proved that crossing implies U=0.

A logically uncertain agent does not need a proof of either of those things in order to cross, it simply needs a positive expectation of utility, for example a heuristic which says that there's a 99% chance crossing implies U=+10.

Though you did say there's a version which still works for logical ... (read more)

Seems to me that if an agent with a reasonable heuristic for logical uncertainty came upon this problem, and was confident but not certain of its consistency, it would simply cross because expected utility would be above zero, which is a reason that doesn't betray an inconsistency. (Besides, if it survived it would have good 3rd party validation of its own consistency, which would probably be pretty useful.)