## 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.

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

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

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

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.

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

### Resources

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