Russell Standish wrote:

>Interesting, although I suspect the interpretation of "the ability to
>do something completely stupid" is more like asserting the truth of
>an unprovable statement than asserting the truth of a false
>statement. In modal logic, this would be (x & -[]x )  n'est-ce pas?


I would say it is asserting the possibility or consistency (instead of 
the truth) of some false but irrefutable statement: like <>[]f, which 
belongs to G* minus G, which means <>[]f is indeed a solution of 
x & -[]x, that is G* prove <>[]f & -[]<>[]f.  Note <>t is also a solution
of x & -[]x 
Of course the statement []f is false on the sound machines by 
definition! But <>[]f is true. The correct machine "suffers" from the 
consistency of inconsistency.


>Note an automaton cannot assert the truth of anything not provable
>from its axioms...


An "automaton" cannot even assert the truth of its provable assertions
in general. Except the one which has been proved. (Lob), so, ok.

But an automaton can *anticipate* or bet on the possibility 
(the consistency) of both what he/she/it can prove (G) and even some 
truth he/she/it  *cannot* prove (which truth can works as fruitful 
questioning or betting or hoping or fearing ...) (G*).
Or even quantum probabilising on. (Z1*).


Best Regards,


Bruno

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