Re: Precursors of Category Theory

Re:http://inquiryintoinquiry.com/2014/01/03/precursors-of-category-theory-3/
Re:https://www.facebook.com/groups/peircesociety/permalink/405042642965067/

Peircers,

My reply to a reader’s question on Facebook may be worth including here —

“I will now say a few words about what you have called Categories, but for which I prefer the 
designation Predicaments, and which you have explained as predicates of predicates.” (CP 4.549).

That is a difficult passage, partly because Peirce conducts the discussion in dialogue form, so one 
may question whether he is putting a variant of his own words in the mouth of the other or merely 
using the other as a foil to be corrected.  I have chosen to go with the first option until some 
evidence proves it untenable.

The word “monadic” is a predicate of predicates.  It holds of all predicates that express a simple 
quality of things.  The comprehension or intension of a monadic predicate is a property that things 
can have independently of reference to other things.  The extension of a monadic predicate is the 
set of things that have that property in common.

Likewise, “dyadic” is a predicate of predicates, holding of all 2-place predicates, properties, or 
relations, and “triadic” is a predicate of predicates, holding of all 3-place predicates, 
properties, or relations.

In their purely mathematical aspect, Firstness, Secondness, and Thirdness are simply what all 
monadic, dyadic, and triadic relations, respectively, have in common.  Of course the plot thickens 
when we turn to phenomenology because that requires us to ask whether there is anything about the 
phenomenon in view that makes a particular relational model more apt than any other.

Regards,

Jon

-- 

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