*The philosophical foundation of analytic knowledge*
Analytic knowledge is the set of expressions of formal or natural
language that are connected to the semantic meanings that make them
true.
Thus when we construe provability broadly within the Curry-Howard isomorphism, we understand that unprovable (within this body of
human knowledge BOHK) simply means untrue.
*I now prove that such a system cannot be incomplete in the Gödel sense* *There are two mutually exclusive possibilities*
(a) The BOHK can prove every instance of (formal system /expression)
pair that cannot be proved making the BOHK complete.
(b) The BOHK cannot prove some instances of (formal system /expression)
pairs cannot be proved, thus humans have no way to know that they cannot
be proved.
The BOHK cannot possibly be incomplete in the Gödel sense. It is either complete in the Gödel sense or its incompleteness cannot be shown.
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