Hi John,

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 large concept. 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.

Bruno

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*.

http://iridia.ulb.ac.be/~marchal/


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