>So the constructivist position would be that we must remain open to the
>possibility that positivism may be "functional", but we can never know for
>sure--except that if positivism is functional we could know for sure.
>The following statement is true: the preceding statement is false?
Yes, that's another twist on the sort of bind that I had in mind when I
talked of the Boeotian Paradox: which, as I understand, goes as follows:
"All Cretans are liars", being a statement made by a Cretan.
>There is something about this that reminds me vaguely of Godel's theorem
>(which I don't claim to understand well enough to say more about).
No, I don't either, but incomplete knowledge (i.e. a strong component of
ignorance!) has never prevented me from offering my 2-cent's worth to a
forum like this, in the hope that another colleague will add his/her 2
cents in some constructive fashion!
So here's a hopefully relevant bit. I seem to recall that Russell tackled
the paradox by talking about it in terms of "levels of language" 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?
Specifically, can anyone remember how Russell tackled the Boeotian paradox,
in such a way that we might apply the same rationale to the
"constructivism" paradox which I posited in my last mailing and which Tim
has responded to?
Devi Jankowicz.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%