Le 16-févr.-06, à 21:58, [EMAIL PROTECTED] a écrit :
I should have said that Bp & p seems wrong, not that it's too simple.
I was trying to say that it seems wrong to say that Bp & p gets us
further than Bp, i.e. provability + truth is more than provability.
In order for Bp & p > Bp, it seems to me that we would have to have
access to truth (p) directly, we would have to *know* that we've
proved something to be true, not just that we've been consistent. In
order to be *sound* we have to be given "true truth" for our reasoning
to start with (and then of course be then be consistent with it).
This is similar to why I don't think that knowledge is simply true
first believe that the soul = the intellect. Exercise: what is wrong?
Answer tomorrow :-) (+ answers to Danny and Ben).
I don't know what you're trying to get at with soul = intellect. To
me the intellect is simply at the same par with provability and
reason. The intellect has to be given true truth in order for it to
come up with true truth (if it reasons consistently). More than that,
the intellect has to be given true truth and know that it was given
true truth, in order to reason its way to more true truth and know
that it has done so.
To sum up with logician's tools: G* can prove that Bp and Bp & p are
equivalent (p representing any proposition written in some language
understandable by the machine, for example numbers and addition +
multiplication symbols in case the machine is a Peano Arithmetic
prover. Godel showed how to define the provability "B" with numbers and
addition and multplication symbols and Penao axioms indeed).
With the Plotinian vocabulary: The divine intellect know that the soul
and the intellect are the same machine having the same discourse, but
neither the soul nor the intellect can know of believe that, so that
they differ from their point of view.
You can guess (unlike Plotinus) some inescapable tension between the
soul and the intellect. The intellect is the humble and modest one. It
is a scientist. The intellect is aware that either he can say
crackpots-thing or it is consistent that he will say crackpots things
(cf ~Bf -> ~B(~Bf) is equivalent with Bf v DBf). On the contrary, the
soul looks a bit like an arrogant entity which never doubt, which
pretend to be always right and, the more unnerving, is always right.
Now with the sound machine, the divine intellect know that the soul and
the intellect (terrestrial) have the same discourse, but neither the
soul nor the terrestrial intellect can ever believe or know that