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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 16:00, 6 November 2007
, 16:00, 6 November 2007→Commentary Note 10.10: markup
===Commentary Note 10.10===
===Commentary Note 10.10===
Figure 8 depicts the last of the three examples involving the composition of 3-adic relatives with 2-adic relatives:
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Figure 8. Lover that is a Servant of a Woman
Figure 8. Lover that is a Servant of a Woman
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The hypergraph picture of the abstract composition is given in Figure 14.
The hypergraph picture of the abstract composition is given in Figure 14.
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Figure 14. Anything that's a Lover of Anything and that's a Servant of It
Figure 14. Anything that's a Lover of Anything and that's a Servant of It
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This example illustrates the way that Peirce analyzes the logical conjunction,
This example illustrates the way that Peirce analyzes the logical conjunction, we might even say the "parallel conjunction", of a couple of 2-adic 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.
we might even say the "parallel conjunction", of a couple of 2-adic 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
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 2-adic "loving" relation ''L'' ⊆ ''X'' × ''Y'' to the corresponding 3-adic "loving and being" relation ''L'', ⊆ ''X'' × ''X'' × ''Y'', which is then composed in a specific way with a 2-adic "serving" relation ''S'' ⊆ ''X'' × ''Y'', so as to determine the 2-adic relation ''L'',''S'' ⊆ ''X'' × ''Y''. Table 15 schematizes the associated constraints on tuples.
of relational composition, the gist of it is the diagonal extension
of a 2-adic "loving" relation L c X x Y to the corresponding 3-adic
"loving and being" relation L_, c X x X x Y, which is then composed
in a specific way with a 2-adic "serving" relation S c X x Y, so as
to determine the 2-adic relation L,S c X x Y. Table 15 schematizes
the associated constraints on tuples.
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Table 15. Conjunction Via Composition
Table 15. Conjunction Via Composition
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