On 30 Aug 2009, at 18:55, Bruno Marchal wrote:
> Not at all. Most theories can formally determined their Gödel
> sentences, and even bet on them.
> They can use them to transform themselves into more powerful, with
> respect to probability, machines, inheriting new Gödel sentences, and
> they can iterate this in the constructive transfinite. A very nice
> book is the "inexhaustibility" by Torkel Franzen.

I mean "povability".   (the "b" is too much close to the "v" on my  

> Machine can determined their Gödel sentences. They cannot prove them,
> but proving is not the only way to know the truth of a proposition.
> The fact that G* is decidable shows that a very big set of unprovable
> but true sentences can be find by the self-infering machine.

found. I guess.

I am so sorry for my english.


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