Re: Wooden Ploughs, impredicativity

["Tim Gwinn" <***>]

Dan,
Great remarks - I agree completely.
Regards,
Tim

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Dan
> Fiscus
> Sent: Thursday, October 30, 2003 10:38 AM
> To: ***
> Subject: Re: Wooden Ploughs, impredicativity
>
>
> Tim Gwinn wrote:
> snip
> > Beyond doubt, pattern exists there, but it is
> > the kind of pattern we haven't yet learnt to see.
> snip
>
> Tim,
>
> Great post. Re: your debates with Pete - I think an important
> issue is that we may want to resist the temptation to make
> impredicativities go away or "resolve" them into some clear
> "specificity" as in predicate logic, true/false clean dichotomy,
> etc. Instead, I think if we begin to accept and embrace them
> as the general case, as with the complexity they're tied to, then
> we may start to see some totally new patterns.
>
> I like Bohr's quote as a guide - "A great truth is one for which
> the opposite is also a great truth." We might call these also
> complex truths and they are impredicative and require at
> minimum two models to describe. The type example is the
> particle-wave complementarity of light. Paradox is not only
> useful when it is resolved or goes away - it is useful also when
> it persists indefinitely.
>
> Some thoughts...
>
> Dan