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"?
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).
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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