## Peirce’s 1870 “Logic Of Relatives” • Comment 10.10

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

 (25)

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

 (26)

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 $L \subseteq X \times Y$ to the corresponding triadic being and loving relation $L \subseteq X \times X \times Y,$ which is then composed in a specific way with a dyadic serving relation $S \subseteq X \times Y$ so as to determine the dyadic relation $L,\!S \subseteq X \times Y.$  Table 27 schematizes the associated constraints on tuples.

$\text{Table 27.} ~~ \text{Conjunction Via Composition}$
$\mathit{1}$ $\mathit{1}$ $\mathit{1}$
$L,$ $X$ $X$ $Y$
$S$   $X$ $Y$
$L,\!S$ $X$   $Y$
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