Post : Peirce's 1870 “Logic Of Relatives” • Comment 11.1
http://inquiryintoinquiry.com/2014/04/29/peirces-1870-logic-of-relatives-%e2%80%a2-comment-11-1/
Posted : April 29, 2014 at 12:12 pm
Author : Jon Awbrey
Peircers,
We have reached a suitable place to pause in our reading of Peirce’s text — actually, it’s more like
a place to run as fast as we can along a parallel track — where I can pay off a few of the
expository IOUs I’ve been using to pave the way to this point.
The more pressing debts that come to mind are concerned with the matter of Peirce’s “number of”
function that maps a term t into a number [t], and with my justification for calling a certain style
of illustration the ''hypergraph picture'' of relational composition. As it happens, there is a
thematic relation between these topics, and so I can make my way forward by addressing them together.
At this point we have two good pictures of how to compute the relational compositions of arbitrary
dyadic relations, namely, the bigraph representation and the matrix representation, each of which
has its differential advantages in different types of situations.
But we do not have a comparable picture of how to compute the richer variety of relational
compositions that involve triadic or any higher adicity relations. As a matter of fact, we run into
a non-trivial classification problem simply to enumerate the different types of compositions that
arise in these cases.
Therefore, let us inaugurate a systematic study of relational composition, general enough to
articulate the “generative potency” of Peirce’s 1870 Logic of Relatives.
Regards,
Jon
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