Re: Daniel Everett • Polyunsaturated Predicates

DE:

Among the several ideas Peirce and Frege came up with was the idea of a predicate before and after it is linked to its arguments.  Frege called the unlinked predicate unsaturated.  But Peirce built this into a theory of valency.  An unsaturated predicate in Frege’s system is a generic term, a rheme, in Peirce’s system.  So in Peirce’s theory all languages need generic terms (rhemes) to exist.  Additionally, thru his reduction thesis (a theorem proved separately by various logicians) Peirce set both the upper and lower bounds on valency which — even to this day — no other theory has done.

Dear Daniel,

In using words like “predicate” or “relation” some people mean an item of syntax, say, a verbal form with blanks substituted for a number of subject terms, and other people mean a mathematical object, say, a function from a set to a set or a subset of a cartesian product

It would be a great service to understanding if we had a way to negotiate the gap between the above two interpretations.

To be continued …

Resources

• Relation Theory
• Survey of Relation Theory

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