Peirces' categories are predicates of predicates, the categories containing
both extension(quanta) and intension (qualia).
This might be an impediment to a a materialistic view. I don't know. In my poor
understanding, Peirce limited
the categories to three to enable reduction to take place.
My uneducated understanding of that is predicates of predicates would be
something like
"John (subject) is a tall (qualia) man (quanta)"
Those more familiar with Chomsky's context-free grammar might inquire into
Chomsky's
use of Peirce's categories, my uninformed feeling being that Chomsky did not.
As to Peirce,
http://en.wikipedia.org/wiki/Categories_%28Peirce%29
"The first thing to extract from this passage is the fact that Peirce's
Categories, or "Predicaments",
are predicates of predicates. Meaningful predicates have both extension and
intension, so predicates of
predicates get their meanings from at least two sources of information, namely,
the classes of relations
and the qualities of qualities to which they refer. Considerations like these
tend to generate
hierarchies of subject matters, extending through what is traditionally called
the logic of
second intentions,[4] or what is handled very roughly by second order logic in
contemporary parlance,
and continuing onward through higher intensions, or higher order logic and
type theory."
Roger Clough, [email protected]
9/19/2012
"Forever is a long time, especially near the end." -Woody Allen
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