>and I do
>remember that one way of understanding Godel's theorem has been to assert
>that all languages (= representational systems whether mathematical,
>logical, or natural) are incomplete in the sense that paradoxes of this
>kind can occur. Further, I seem to remember that one way of resolving such
>a paradox is to talk _about_ it in a meta-language: a superordinate symbol
>system.
>
>And at that point my knowledge gives out. Can anyone else help us?
Godel showed that, in the syntax of any reasonably expressive axiomatic
system, a formula can be written that is true, but not provable within that
system.
Turing's formulation of the 'halting problem' would lead us to essentially
the same conclusion.
When examined carefully. Godel's result applies to a particular, fixed
axiomatic system.
There are almost certainly some truths whose statements are so complicated
that no human being could grasp them in full detail, and the Godel
sentences would probably fall into that category.
Cheers,
Jack
Jack Adams-Webber Tel: 905 (688) 5544 [x 3714]
Department of Psychology Fax: 905 (688) 6922
Brock University E-mail: jadams@spartan.ac.brocku.ca
St. Catharines, Ontario
CANADA L2S 3A1
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