Peirce’s 1870 “Logic of Relatives” • Comment 10.8

Peirce’s 1870 “Logic of Relatives”Comment 10.8

Our progress through the 1870 Logic of Relatives brings us in sight of a critical transition point, one which turns on the teridentity relation.

The markup for Peirce’s “giver of a horse to an owner of it” is shown again in Figure 22.

Giver of a Horse to an Owner of It

\text{Figure 22. Giver of a Horse to an Owner of It}

The hypergraph picture of the abstract composition is given in Figure 23.

Anything that is a Giver of Anything to an Owner of It

\text{Figure 23. Anything that is a Giver of Anything to an Owner of It}

If we analyze this in accord with the spreadsheet model of relational composition then the core of it is a particular way of composing a triadic giving relation G \subseteq X \times Y \times Z with a dyadic owning relation O \subseteq Y \times Z in such a way as to determine a specialized dyadic relation (G \circ O) \subseteq X \times Z.  Table 24 schematizes the associated constraints on tuples.

\text{Table 24. Relational Composition}~ G \circ O

Relational Composition Table G ◦ O

So we see the notorious teridentity relation, which I left equivocally denoted by the same symbol as the identity relation \mathit{1}, is already implicit in Peirce’s discussion at this point.

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 10.8

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

  2. Pingback: Peirce’s 1870 “Logic Of Relatives” • Overview | Inquiry Into Inquiry

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

  4. Pingback: Survey of Relation Theory • 4 | Inquiry Into Inquiry

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