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.

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

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

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

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.

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

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

Peirce’s 1870 Logic of Relatives • Part 1 • Part 2 • Part 3 • References

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Peirce Matters • Laws of Form • Peirce List (1) (2) (3) (4) (5) (6) (7)

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