Post : Peirce's 1870 “Logic Of Relatives” • Comment 10.10
http://inquiryintoinquiry.com/2014/04/24/peirces-1870-logic-of-relatives-%E2%80%A2-comment-10-10/
Posted : April 24, 2014 at 12:00 am
Author : Jon Awbrey
Peircers,
The last of the three examples involving the composition of triadic relatives with dyadic relatives
is shown again in Figure 25.
Figure 25. Lover that is a Servant of a Woman
☞http://inquiryintoinquiry.files.wordpress.com/2014/04/lor-1870-figure-18.jpg
The hypergraph picture of the abstract composition is given in Figure 26.
Figure 26. Anything that is a Lover of Anything and a Servant of It
☞http://inquiryintoinquiry.files.wordpress.com/2014/04/lor-1870-figure-26.jpg
This example illustrates the way that Peirce analyzes the logical conjunction, we might even say the
''parallel conjunction'', of a pair of dyadic relatives in terms of the comma extension and the same
style of composition that we saw in the last example, that is, according to a pattern of anaphora
that invokes the teridentity relation.
If we lay out this analysis of conjunction on the spreadsheet model of relational composition, the
gist of it is the diagonal extension of a dyadic ''loving'' relation L ⊆ X × Y to the corresponding
triadic ''being and loving'' relation L ⊆ X × X × Y, which is then composed in a specific way with a
dyadic ''serving'' relation S ⊆ X × Y so as to determine the dyadic relation L,S ⊆ X × Y.
Table 27 schematizes the associated constraints on tuples.
Table 27. Conjunction Via Composition
...... | 1 | 1 | 1 |
====================
L, ... | X | X | Y |
S .... | . | X | Y |
L,S .. | X | . | Y |
Regards,
Jon
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