> On 5 May 2019, at 22:24, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > Thanks for the interesting reply.
You are welcome. > This is the piece my friend was thinking of: > > https://www.mit.edu/people/dpolicar/writing/prose/text/epistemologicalNightmare.html > > <https://www.mit.edu/people/dpolicar/writing/prose/text/epistemologicalNightmare.html> OK. Nice. I forgot that little piece of chef-d’oeuvre, which is indeed in the book "MIND’S I” edited by Dennett and Hofstadter. The closest book to the correct consequence of Mechanism. I would add pieces of Daniel Galouye’s book Simulacron III in a next possible edition. All books by Smullyan are good introduction to what I call the “theology of the machine”, mainly the theory G*, or qG*, or qG1* and their mandatory intensional variants. The most explicit one is “Forever Undecided” where the Gödel diagonal lemma, or Kleene’s second recursion theorem is “modelled” by a human visiting the island of night and knaves. Bruno > > Brent > > On 5/5/2019 9:59 AM, Bruno Marchal wrote: >>> On 2 May 2019, at 22:59, Brent Meeker <[email protected]> wrote: >>> >>> You probably know book my friend [Max] is seeking. >>> >>> Brent >>> >>> >>> >>> "I recall encountering in one of Raymond Smullyan’s books a thought >>> experiment that convinced me that it is possible to be mistaken about what >>> one believes. That is, one can say “I believe X” and be speaking falsely >>> even though one is not intentionally lying. Does anyone know what thought >>> experiment I’m dimly recalling, and which of his books it appears in?" >> One simple example, which plays a crucially important role in Mechanist >> Philosophy, since Plato (at least), appears in one of the last book by >> Raymond Smullyan: >> https://www.amazon.com/Gödelian-Puzzle-Book-Puzzles-Paradoxes/dp/0486497054 >> >> “Do you have rational evidence that you are now awake? Isn’t it logically >> possible that you are now asleep and dreaming all this? Well, I once got >> into an argument with a philosopher about this. He tried to convince me that >> I had no rational evidence to justify believing that I was now awake. I >> insisted that I was perfectly justified in being certain that I was awake. >> We argued long and tenaciously, and I finally won the argument, and he >> conceded that I did have rational evidence that I was awake. At that point I >> woke up.” >> >> Of course, that is, in a nutshell, the dream argument. >> >> With “belief" = “have rational evidence for”, below we have a generator of >> situation with "I believe X”, genuinely believed and wrong. (In fact, all >> consistent theories + the axiom that they are inconsistent). >> >> In his book “Forever Undecided” Smullyan explains Gödel’s theorem, in the >> frame of the Knight and Knaves island, leading his “reasoner of type 4”, >> whose beliefs includes >> >> [](A -> B) -> ([]A -> []B) >> []A -> [][]A >> >> And are close to the modus ponies rule (from a proof of A and a proof of A >> -> B, derive B) and the necessitation rule (from a proof of A derive []A). >> >> When such a reasoner met, on the knight-knave island, a guy telling him, you >> will never believe that I am a knight, will obey to the “theology” G*, in >> particular, Gödel’s and Löb’s theorems apply to him, and it will be >> consistent that he has false beliefs. >> >> I am not sure I remember more specific examples. >> >> Bruno >> >> PS I hope you don’t mind I sent this to the everything list, as both type 4 >> reasoners, rational belief, but also the dream argument plays a big role in >> Mechanism. I changed the name. >> >> >> > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/FB1B1EF0-2F11-4025-8F97-891408680037%40ulb.ac.be. For more options, visit https://groups.google.com/d/optout.
