Peirce’s 1870 “Logic of Relatives” • Comment 8.2
I continue with my commentary on CP 3.73, developing the Othello example as a way of illustrating Peirce’s formalism.
In the development of the story so far, we have a universe of discourse characterized by the following equations:
![\begin{array}{*{15}{c}} \mathbf{1} & = & \mathrm{B} & +\!\!, & \mathrm{C} & +\!\!, & \mathrm{D} & +\!\!, & \mathrm{E} & +\!\!, & \mathrm{I} & +\!\!, & \mathrm{J} & +\!\!, & \mathrm{O} \\[6pt] \mathrm{b} & = & \mathrm{O} \\[6pt] \mathrm{m} & = & \mathrm{C} & +\!\!, & \mathrm{I} & +\!\!, & \mathrm{J} & +\!\!, & \mathrm{O} \\[6pt] \mathrm{w} & = & \mathrm{B} & +\!\!, & \mathrm{D} & +\!\!, & \mathrm{E} \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7B%2A%7B15%7D%7Bc%7D%7D++%5Cmathbf%7B1%7D+%26+%3D+%26++%5Cmathrm%7BB%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BC%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BD%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BE%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BI%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BJ%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BO%7D++%5C%5C%5B6pt%5D++%5Cmathrm%7Bb%7D+%26+%3D+%26++%5Cmathrm%7BO%7D++%5C%5C%5B6pt%5D++%5Cmathrm%7Bm%7D+%26+%3D+%26++%5Cmathrm%7BC%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BI%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BJ%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BO%7D++%5C%5C%5B6pt%5D++%5Cmathrm%7Bw%7D+%26+%3D+%26++%5Cmathrm%7BB%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BD%7D+%26+%2B%5C%21%5C%21%2C+%26++%5Cmathrm%7BE%7D++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=1&c=20201002)
This much forms a basis for the collection of absolute terms to be used in this example. Let us now consider how we might represent an exemplary collection of relative terms.
Consider the genesis of relative terms, for example:
![\begin{array}{l} ^{\backprime\backprime}\, \text{lover of}\, \underline{~~~~}\, ^{\prime\prime} \\[6pt] ^{\backprime\backprime}\, \text{betrayer to}\, \underline{~~~~}\, \text{of}\, \underline{~~~~}\, ^{\prime\prime} \\[6pt] ^{\backprime\backprime}\, \text{winner over of}\, \underline{~~~~}\, \text{to}\, \underline{~~~~}\, \text{from}\, \underline{~~~~}\, ^{\prime\prime} \end{array}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7Bl%7D++%5E%7B%5Cbackprime%5Cbackprime%7D%5C%2C+%5Ctext%7Blover+of%7D%5C%2C+%5Cunderline%7B%7E%7E%7E%7E%7D%5C%2C+%5E%7B%5Cprime%5Cprime%7D++%5C%5C%5B6pt%5D++%5E%7B%5Cbackprime%5Cbackprime%7D%5C%2C+%5Ctext%7Bbetrayer+to%7D%5C%2C+%5Cunderline%7B%7E%7E%7E%7E%7D%5C%2C+%5Ctext%7Bof%7D%5C%2C+%5Cunderline%7B%7E%7E%7E%7E%7D%5C%2C+%5E%7B%5Cprime%5Cprime%7D++%5C%5C%5B6pt%5D++%5E%7B%5Cbackprime%5Cbackprime%7D%5C%2C+%5Ctext%7Bwinner+over+of%7D%5C%2C+%5Cunderline%7B%7E%7E%7E%7E%7D%5C%2C+%5Ctext%7Bto%7D%5C%2C+%5Cunderline%7B%7E%7E%7E%7E%7D%5C%2C+%5Ctext%7Bfrom%7D%5C%2C+%5Cunderline%7B%7E%7E%7E%7E%7D%5C%2C+%5E%7B%5Cprime%5Cprime%7D++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=1&c=20201002)
We may regard these fill-in-the-blank forms as being derived by a kind of rhematic abstraction from the corresponding instances of absolute terms.
The following examples illustrate the relationships that exist among absolute terms, relative terms, relations, and elementary relations.
-
The relative term
can be derived from the absolute term
by removing the absolute term
Iago is a lover of Emilia, so the relate-correlate pair
is an element of the dyadic relation associated with the relative term
-
The relative term
can be derived from the absolute term
by removing the absolute terms
and
Iago is a betrayer to Othello of Desdemona, so the relate-correlate-correlate triple
is an element of the triadic relation associated with the relative term
-
The relative term
can be derived from the absolute term
by removing the absolute terms
and
Iago is a winner over of Othello to Iago from Cassio, so the elementary relative term
is an element of the tetradic relation associated with the relative term
Resources
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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