Post : Peirce's 1870 “Logic Of Relatives” • Comment 10.8
http://inquiryintoinquiry.com/2014/04/22/peirces-1870-logic-of-relatives-%e2%80%a2-comment-10-8/
Posted : April 22, 2014 at 5:30 pm
Author : Jon Awbrey
Peircers,
There’s a critical transition point that we find in sight of Peirce’s 1870
Logic of Relatives and
it's a point that turns on the teridentity relation.
In the next example of relational composition, let's substitute the relation t
= taker of ─── for
Peirce's relation o = owner of ───, simply for the sake of avoiding conflicts in the symbols we use.
In this way, Figure 17 is transformed into Figure 22.
Figure 22. Giver of a Horse to a Taker of It
☞http://inquiryintoinquiry.files.wordpress.com/2014/04/lor-1870-figure-221.jpg
The hypergraph picture of the abstract composition is given in Figure 23.
Figure 23. Anything that is a Giver of Anything to a Taker of It
☞http://inquiryintoinquiry.files.wordpress.com/2014/04/lor-1870-figure-23.jpg
If we analyze this in accord with the spreadsheet model of relational
composition, the core of it is
a particular way of composing a triadic ''giving'' relation G ⊆ X × Y × Z with
a dyadic ''taking''
relation T ⊆ Y × Z in such a way as to determine a certain dyadic relation (G ∘
T) ⊆ X × Z.
Table 24 schematizes the associated constraints on tuples.
Table 24. Another Brand of Composition
..... | 1 | 1 | 1 |
===================
G ... | X | Y | Z |
T ... | . | Y | Z |
G ◦ T | X | . | Z |
So we see that the notorious teridentity relation, which I have left
equivocally denoted by the same
symbol as the identity relation 1 , is already implicit in Peirce’s discussion
at this point.
Regards,
Jon
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