Russell dealt with the paradoxes generated by levels of logical types by
simply ruling self-referential statements out of order. This may work in
formal logic, but psychologically things are not so easy, which is why
Bateson reintroduced the concept as the double-bind.
My own response to the paradox is to note (with Godel, as I understand
him) that no logical system can ever be fully self-validating. Positivism
(which tends to generate its own paradoxes, most famously in physics)
asserts that it is possible to attain a point of view so transcendent (by
the careful application of appropriate methods) that it ceases to be a
point of view at all; constructivism asserts that every point of view is a
point of view. ONe cannot, from within either system, evaluate the
competing claims of both, since they rely upon different models of truth
(correspondence vs. coherence). To do that requires a realm of
meta-discourse--aesthetics.
I contend that the choice of metatheory is ultimately an aesthetic
one--that positivists find beauty in a world in which everything can be
known and proved, and nothing but chaos in the constructivist vision of
permanent uncertainty; constructivists revel in the idea of unlimited
possibility, and find the positivist world static and dull. Aesthetics
may be a fragile platform on which to build a world-view (or maybe not),
but its all we've got--an intuitive sense of "fit", harmony, and
balance. (Lewis Brandt wrote a delightful book which explores, among
other things, the aesthetics of psychological theory: Psychologists
Caught: A Psycho-Logic of Psychology, Univerisity of Toronto Press, 1981).
I'm beginning to sense a connection between constructivist or positivist
sensibilities and a preference for the Beatles or the Stones--which may
just mean it's getting late and I need to sign off.
Regards,
Tim Connor
<connort@pacificu.edu>
On Tue, 10 Oct 1995 anima@devi.demon.co.uk wrote:
> In response to a previous posting of mine, Tim Connor writes:
>
> >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.
>
>
>
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