Le 16-févr.-06, à 16:21, John M wrote:
since when do we think 'beweisbar' (provable) anything
within the domain of our knowledge-base which may have
connotations beyond it (into the unlimited)? Since
when do we want to speak about "Truth" in a general
sense? Our 'truth'? Our percept of reality?
I think "simple definitions" are limiting the validity
of the 'definition' into a narrower model.
My reasoning will work already with "arithmetical truth". This is non
trivial. Leibnitz, Hilbert, and many mathematicians before Godel would
have believed that arithmetical truth gives a narrower model, but after
Godel we know that we cannot formalized that notion in any effective
way. The fashion today consists even in considering it to be a too
But I will make clear (well I will try, or refer to some literature)
that what I say can be extended on much more large notion of truth.
I assure you John that the approach is everything but reductionnist.
Even just about numbers there is no effective TOE (by Godel).
Now, there are "angel" like Anomega (Analysis + Omega rule) which can
grasp the whole arithmetical truth, thanks to their infinite power, but
then they cannot grasp the whole analytical truth, and will suffer
similar limitation as the more terrestrial machines.
Here "truth" has nothing to do with any form of perception. We are in
Platonia, by hypothesis. We keep our eyes closed, if you want.
Note also that without "simple definition" we would not progress, and
would not been able to find our errors, or our limitations.
PS a) I answer Tom, and Ben tomorrow.
b) For those who read Plotinus, what I call "Angels", is what
Plotinus call "Gods". It corresponds just to loebian entities which
cannot been simulated by a computer. There is a chapter in Boolos 1993
describing Anomega, and showing it obeys to G and G*.