Peirce’s 1870 “Logic of Relatives” • Comment 10.10

Peirce’s 1870 “Logic of Relatives”Comment 10.10

The last of Peirce’s three examples involving the composition of triadic relatives with dyadic relatives is shown again in Figure 25.

Lover that is a Servant of a Woman

\text{Figure 25. Lover that is a Servant of a Woman}

The hypergraph picture of the abstract composition is given in Figure 26.

Anything that is a Lover that is a Servant of Anything

\text{Figure 26. Anything that is a Lover that is a Servant of Anything}

This example illustrates the way 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 we saw in the last example, that is, according to a pattern of anaphora invoking the teridentity relation.

Laying out the above analysis of logical conjunction on the spreadsheet model of relational composition, the gist of it is the diagonal extension of a dyadic loving relation L \subseteq X \times Y to a triadic being and loving relation L \subseteq X \times X \times Y, which is then composed with a dyadic serving relation S \subseteq X \times Y so as to determine a dyadic relation L,\!S \subseteq X \times Y.  Table 27 schematizes the associated constraints on tuples.

\text{Table 27. Relational Composition}~ L,S

Relational Composition Table L,S

Resources

cc: CyberneticsOntolog ForumStructural ModelingSystems Science
cc: FB | Peirce MattersLaws of Form • Peirce List (1) (2) (3) (4) (5) (6) (7)

This entry was posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization and tagged , , , , , , . Bookmark the permalink.

5 Responses to Peirce’s 1870 “Logic of Relatives” • Comment 10.10

  1. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

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  3. Pingback: Peirce’s 1870 “Logic Of Relatives” • Comment 1 | Inquiry Into Inquiry

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