On 27 Nov 2017, at 23:02, Brent Meeker wrote:
On 11/27/2017 10:19 AM, Bruno Marchal wrote:
The formal modal formula is B(Bp -> p) -> Bp.
It looks also like wishful thinking. If you succeed in convincing a
Löbian entity (whose beliefs are close for the Löb rule, or having
Löb's theorem for its bewesibar predicate) that if she ever
believes that some medication will work, then it work, then she
will believe the medication works!
But that's equivocating on "B". In the formula it means
beweisbar=prove not "believes". I think that is obfuscation.
Before Gödel, everyone thought that B was an operator for a knowledge
predicate. But after Gödel (1931), we know that B verifies all the
axiom of knowledge minus the key one (Bp -> p), making it into a
(rational) notion of belief. I could have defined by axiomatically
belief by:
The subject believes x + 0 = x, the subject believes x + s(y) = s(x +
y), etc.
If this applies to you, as I am sure it does, the results will apply
to you or any of your recursive computational continuations.
This would be ridiculous if that was used to model human psychology,
but it is not a problem for the derivation of the physical laws
(unless you believes that the universe depends conceptually of human
psychology, but that would be a rather strong coming back to the kind
of anthropomorphism we usually avoid here.
Bruno
Brent
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