On 2/9/2011 8:02 AM, Bruno Marchal wrote:
On 08 Feb 2011, at 21:08, Brent Meeker wrote:
On 2/8/2011 8:47 AM, Bruno Marchal wrote:
On 07 Feb 2011, at 20:52, Andrew Soltau wrote:
(Is the 'intensional' referred to here the 'attach' you used in
Not really, although it is related.
"Intensional" refers to the fact that if you define a provable(x) by
beweisbar(x) and x', where x' denote the proposition which has x as
Gôdel number, you define a probability "predicate",
You mean "provability predicate" don't you?
Yes I mean "provability". It is unfortunate that the "v" and "b" are
so close on my keyboard. I also apologies for my many spelling
mistakes and my style which can go very bad when I have to answer many
posts, at time where time is a bit missing ...
Given that you are defining 8 basic points of view in the abstract,
applied to " intensional variants of the current provability
predicate of the machine with or without some oracle", it sounds a
bit, well, abstract. Could you be a bit more specific?
I try to be more specific in sane04. May be we should start from
that. Or search hypostasis or hypostases in the archive, or
"guardian angel", etc.
Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993).
Read perhaps the Theaetetus by Plato.
In short you can say that I model "belief" or "opinion" by "formal
You mean "formal provability"? Mind your "p"s and "v"s. :-)
You mean my "b"s and "v"s, I guess :-)
Yes, again I meant "formal provability". That error is annoying
because, if Bp, is a shorthand for "provability(p)", Bp & Dp plays the
role of a formal probability (yes, with a "b"), indeed probability 1,
or maximal credibility.
I'm really sorry.
I define then knowledge, following Theaetetus by the true opinion
(Bp & p),
You've never said what your answer is to Gettier's example.
I did it, the saturday 29 Jan 2011, according to my computer. Let me
paste it again. It is probably too short. I have a full chapter on
this in "Conscience et Mécanisme". Tell me if you see the point, or if
I should make it clearer:
Apes fetus can
dream climbing trees but they do that with ancestors climbing the most
probable trees of their most probable neighborhoods since a long period.
With classical mechanism, I would say, that to know is to believe p when
"luckily" p is true,
> So what is your response to Gettier's problem? [Brent Meeker]
The answer is that, with comp, we cannot distinguish reality from
dream. We can know that we are dreaming (sometimes), but we cannot
ever know for sure in a public way that we are awaken.
Another fact related to this is that knowledge, consciousness and
truth are not machine-definable. If we are machine, we can use those
notion in theoretical context only.
In practice, as real life illustrates very often, we never know as
such that we know. We belief we know, until we know better.
The SAGrz logics is a logical tour de force. Here Gödel's theorem
gives sense to Theaetetus. S4Grz, the logic of (Bp & p) formalizes a
notion which is not even nameable by the machine, unless she
postulates comp and relies explicitly on that postulate, or better,
relies on the study of a simpler than herself machine.
In science, or in public, we never know, as such. Knowing is a pure
first person notion. But this does not mean that we cannot make
3-theory on such pure first person notion, as S4Grz illustrates
particularly well. Same remarks for feelings (Bp & Dt & p).
Hmmm? I guess I thought you hadn't answered because I don't grasp the
relevance of your answer. Gettier points out that one can believe a
true statement for reasons that have nothing to do with what makes the
statement true. In his example Bob buys a new car which is blue, but
while waiting for the car to be delivered he borrows a car which also
happens to be blue. Jim sees Bob driving this car and believes that Bob
has bought a new car which is blue. It is a true belief, but only by
accident. So it seems that there is a difference between true belief
and knowledge. Gettier proposes that the true belief must be causally
connected to the fact that makes it true in order to count as
knowledge. The analogy in arithmetic would be to believe something,
like Goldbach's conjecture, which may be true but is unprovable.
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