[Inquiry] Re: Blocks On The Road Of Inquiry

[Jon Awbrey]

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BOTROI.  Note 10

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Peirce's Categories are categories of predicates, which is supposed
to be one of the reasons that he revived the old word "Predicaments"
as a synonym for his Categories.  If we stick to the sense intended,
this is the same thing as saying that the Categories are categories
of relations.  The reason why we need only three Categories is that
we need nothing higher than 1-adic, 2-adic, and 3-adic relations to
construct all the models of phenomena that we'd ever need to build.

In this way of viewing our Common Predicaments, Firstness is what
all 1-adic relations, or sets of elements treated as individuals,
have in common, Secondness is what all 2-adic relations, or sets
of ordered pairs have in common, and Thirdness is what all 3-adic
relations, or sets of ordered triples, have in common.

The astute decoder will no doubt pick up what I have telegraphed
in the foregoing paragraph, and this is just the circumstance of
a residual indeterminacy in the application of the Categories to
any domain of experience, on account of the interpretive play in
the will that permits one to treat a set of k-tuples as a set of
j-tuples for any j less than k.  So there is a j-ness of k-ness,
in this sense.  However, I will not insist on this subtlety, as
I sense far too great a risk of sophistry in it somewhere.

Jon Awbrey

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