[Inquiry] Re: Logic Of Relatives

[Jon Awbrey]

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LOR.  Note 43

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We have reached in our reading of Peirce's text a suitable place to pause --
actually, it is more like to run as fast as we can along a parallel track --
where I can due quietus make of a few IOU's that I've used to pave my way.

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
by the name of 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 2-adic relations, namely,
the bigraph and the matrix representations, 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 3-adic
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 explicate the "generative potency" of Peirce's 1870 LOR.

Jon Awbrey

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