Re: Wooden Ploughs, impredicativity

["Dan Fiscus" <***>]

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