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 
use of Peirce's categories, my uninformed feeling being that Chomsky did not. 

 As to Peirce,

"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, 
"Forever is a long time, especially near the end." -Woody Allen

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