[FOM] Godel Sentences
Arnon Avron
aa at tau.ac.il
Thu Aug 28 05:12:53 EDT 2003
>
> All such issues raised have long been resolved - decades ago. I'm sure that
> Godel knew exactly how to handle them already in the 1930's. One has to be
> creative to think of some issue that needs to be addressed that hasn't
> already (see below).
I did not try to be creative here. On the contrary. I kept asking, and
more than once, for references to relevant works (and got none so far).
> In particular, it is well known how to give very minimal conditions on an
> encoding of syntax so that any Godel sentence relative to any such encoding
> is equivalent to any Godel sentence relative to any other encoding. This is
> most well known and most obvious in the case of extensions of PA = Peano
> Arithmetic.
>
> The conditions needed are extremely weak and well known. End of story!?
Again, in my messages I wrote at least twice that I am sure that such
conditions exist, and ask for references. I could certainly find some
myself, but why reinventing the wheel and devote time and energy
to things that are well-known? One of the benefits I expect
from something like FOM is getting this kind of information.
So this might be the end of this particular story if you tell me
(and perhaps some other few people in the list who might also not know)
what are these well-known conditions (it should not take more than
10-15 lines, I believe) and/or provide appropriate references!
As to the main issue of the discussion. I repeat that according to
the definition of a Godel sentence you gave in your previous posting
(and I certainly take you as an authority on the subject)
Con_T is a Godel sentence for T - and it certainly does not
"speak about itself". End of this story!?
Arnon Avron
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