On 13 Feb 2013, at 02:28, Russell Standish wrote:
On Tue, Feb 12, 2013 at 11:05:37AM -0800, Craig Weinberg wrote:
When we talk about a Bp, relating to consciousness is that we are
making an
assumption about what a proposition is. In fact, if we look
closely, a
proposition can only be another level of B. p is really nothing but
a group
of sub-personal Beliefs (logarithmically nested as B^n) which we are
arbitrarily considered as a given condition...but there is no given
condition in actual experience. All experiences are contingent upon
what
the experiencer is capable of receiving or interacting with.
I don't really follow your remaining comments, but I agree with you
that the p in the Theatetical definition of knowledge makes me
uncomfortable, post Popper.
That is why I like to sum up Popper by "in Science there are only
belief, never knowledge per se".
It is related to the modesty/Löbianity of the correct machines, and
the fact that the genuine mystical machines are mute on their knowledge.
Unfortunately this leads to vocabulary problem (only) for some
Popperians.
I'm happy for Bp & p to apply to mathematical knowledge, with B
semantically equivalent to "prove", but when it comes to scientific
knowledge, requiring absolute truth in things seems a step too far.
Well, actually it was a problem that Bp & p could work for Bp = "I
prove p", because most scientists believe that this makes knowledge
equivalent with belief or proof for/by the correct machine.
It takes some understanding of Gödel's theorem to realize that, even
for the correct machine, and despite the fact that Bp is equivalent
with Bp & p (prove the same arithmetical p), they obey different
logics. So only G* proves Bp <-> Bp & p, the machine, nor G, can't
prove that equivalence, and this makes Bp & p obeying a different
logic (indeed the modal logic S4 defining the classical notion of
knowledge).
A machine cannot prove that Bf is equivalent with Bf & f, without
contradicting Gödel's second incompleteness theorem.
But I have no constructive suggestions as to how to modify
Theatetus :(.
In "conscience and mécanisme" I argue in detail that the acceptance of
the classical theory of knowledge (S4) which we get back by applying
Theaetetus' definition of knowledge on Gödel's provability predicate)
is the only one which can make sense of the "dream argument" in
metaphysics. We can know that we are dreaming, but we cannot know
that we are awake, and that is a key to get the platonist idea that we
might be in a sort of cave/matrix (in the digital setting).
Bruno
Cheers
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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
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