Peirce's 1870 “Logic Of Relatives ” • Comment 11.1

Post   : Peirce's 1870 =93Logic Of Relatives=94 =95 Comment 11.1
http://inquiryintoinquiry.com/2014/04/29/peirces-1870-logic-of-relatives-%e=
2%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=92s text=
 =97 actually, it=92s more like =

a place to run as fast as we can along a parallel track =97 where I can pay=
 off a few of the =

expository IOUs I=92ve been using to pave the way to this point.

The more pressing debts that come to mind are concerned with the matter of =
Peirce=92s =93number of=94 =

function that maps a term t into a number [t], and with my justification fo=
r calling a certain style =

of illustration the ''hypergraph picture'' of relational composition.  As i=
t 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 co=
mpositions of arbitrary =

dyadic relations, namely, the bigraph representation and the matrix represe=
ntation, 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 variet=
y of relational =

compositions that involve triadic or any higher adicity relations.  As a ma=
tter of fact, we run into =

a non-trivial classification problem simply to enumerate the different type=
s of compositions that =

arise in these cases.

Therefore, let us inaugurate a systematic study of relational composition, =
general enough to =

articulate the =93generative potency=94 of Peirce=92s 1870 Logic of Relativ=
es.

Regards,

Jon

-- =


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