On 14 Sep 2017, at 05:49, Brent Meeker wrote:
On 9/13/2017 4:24 AM, Bruno Marchal wrote:
On 11 Sep 2017, at 19:21, Brent Meeker wrote:
On 9/11/2017 1:22 AM, Bruno Marchal wrote:
On 10 Sep 2017, at 22:25, Brent Meeker wrote:
On 9/10/2017 10:24 AM, Bruno Marchal wrote:
So I assume elementary arithmetic; I prove the existence of the
universal number(s), then I define a notion of rational belief
"scientific belief", (Plotinus discursive reasoner) by Gödel's
(sigma_1 arithmetical) beweisbar Bp. That makes sense, due to
incompleteness which prevent provability to be a notion of
knowledge.
This seems problematic to me. I understand why you do it;
because you want knowledge to be true belief (not just true
provable belief). But this does violence to the usual meaning
of knowledge (c.f. Getteir for example).
Yes. Incompleteness makes provability into belief instead of
knowledge. Gödel mention this already in 1933.
It means that given some undecidable proposition one of us can
assert it and the other deny it, and then one of us will know
it. ??
Ih he proves it (correctly or not).
But that is inconsistent with your definition of "know" = "true
belief". You are really using "know" = "true and proven".
Gödel already saw that "prove" is not a knowledge predicate. So
what remains is a notion of rational belief, and "knowledge" is
defined by that rational belief when conjuncetd to the truth. Here,
the truth is simply the "0th-person view", that the arithmetical
truth (and eventually only the tiiny sigma_1 part, that is the
universal dovetailing).
So does Bp not mean "beweisbar p"?
Bp means (usually) "beweisbar p".
Knowable(p) is Bp & p.
G* knows Bp <-> (Bp & p), but G does not, and that makes the
(important) difference.
With p sigma_1, G* knows p <-> Bp, but again, G does not prove that,
and again, this explains the difference, from the machine's persective.
Which is closer to Gettier's "caused true belief".
Yes, but it is "justified" true belief. "cause" appeal to the
physical, and thus needs the pov with the occurence of
"Dt" ("assumed" consistency).
Gettier says "justified" means a causal, though perhaps indirect,
connection (and I've discussed it with him personally).
I can agree. Justification is logical, non physical, and eventually
sigma_1 justification is a form of causality, but for physical
causality we need something like K~K~(K~K~ (p -> q)), with Kx = Bx &
Dt, p and q sigma_1. Physics is given by the S4Grz1, Z1* and X1* logics.
Which is close to nonsense to me, because he use the word
"transcend" like if observation could lead correctly to such
judgment. he is very coherent in his materialism, and he is force
to eliminate consciousness in that process.
He doesn't eliminate consciousness, he says it is the conclusion of
competition between modules of the brain constructing narratives to
explain perceptions.
Yes. Even himself realizes at some point that this explains
consciousness away. It invokes the solution to the "easy problem", and
nothing more, which is basically the "modern" method to put the "hard
problem" (the antique mind-body problem) under the rug. He does not
eliminate the narrative on consciousness, but still ignore its meaning.
Bruno
Brent
Brent
Bruno
Brent
Knowledge is Bp & p, which is impossible if p is not provable
(~Bp). We just cannot know an undecidable (by us) proposition,
by definition, although we can bet on it, but then it is
different kind of knowledge (closer to Bp & Dt).
That we can know for bad reason is the ultimate lesson of the
dream argument. People like Malcom who dislike Mechanism are
forced into disbelieving the existence of consciousness in
dreams, as he did.
Bruno
Brent
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