Peirce’s 1870 “Logic Of Relatives” • Comment 10.7

Here is what I get when I analyze Peirce’s “giver of a horse to a lover of a woman” example along the same lines as the dyadic compositions.

We may begin with the mark-up shown in Figure 19.

LOR 1870 Figure 8

If we analyze this in accord with the spreadsheet model of relational composition, the core of it is a particular way of composing a triadic giving relation G \subseteq T \times U \times V with a dyadic loving relation L \subseteq U \times W so as to obtain a specialized type of triadic relation (G \circ L) \subseteq T \times V \times W. The applicable constraints on tuples are shown in Table 20.

\text{Table 20.} ~~ \text{Composite of Triadic and Dyadic Relations}
  \mathit{1} \mathit{1} \mathit{1} \mathit{1}
G T U V  
L   U   W
G \circ L T   V W

The hypergraph picture of the abstract composition is given in Figure 21.

LOR 1870 Figure 21
This entry was posted in Graph Theory, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics and tagged , , , , , , , . Bookmark the permalink.

2 Responses to Peirce’s 1870 “Logic Of Relatives” • Comment 10.7

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

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

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