Thanks for the interesting reply. This is the piece my friend was
thinking of:
https://www.mit.edu/people/dpolicar/writing/prose/text/epistemologicalNightmare.html
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.
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