> 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.
