Re: Kinds of knowledge was (RE: An elegant distinction (was Re: brz, or Plan B revisited (LONG)))

Staving Yahya:

>Still, I wonder whether it's possible to answer such a question
>in any natural language.   My doubts arise from the analogy of
>natural languages to formal systems, where the well-known
>theorem of Gödel tells us that no system can describe itself.
>(Or at least I think it does - that may be TOO loose a paraphrase.)
Gödel's Incompleteness Theorem states that any system of logic capable of
describing itself must either be unable to prove at least one true
statement, and therefore be incomplete, or be able to prove at least one
false statement, and therefore be inconsistent. This is because the
self-describing nature of the system enables you to formulate a proposition
equivalent to, "This system of logic cannot prove this statement." If the
statement is true, then it cannot be proven, and the system must be
incomplete. If not, then the system can prove a falsehood, and therefore
contains inconsistencies. Obviously, incomplete systems of logic are
preferable to inconsistent ones.

Pete

Replies