Shakespeare's observations on the mathematics of relations

SYMMETRY

A relation R is symmetric if whenever a stands in relation R to b, then b also stands in relation R to a. Shakespeare uses the supposed symmetry of relations such as "by" and "near" to comic effect in the following dialogue from Twelfth Night, Act III, Scene I:

Viola: Dost thou live by thy tabor?
Clown: No, sir, I live by the church.
Viola: Art thou a churchman?
Clown: No such matter, sir: I live by the church; for I do live at my house, and my house doth stand by the church.
Viola: So thou mayst say, the king lies by a beggar, if a begger dwell near him; or, the church stands by the tabor, if thy tabor stand by the church.

(Compare the discussion on the asymmetry of spatial relations in Chapter 2 of Claude Vandeloise's book Spatial Prepositions, English translation published by University of Chicago Press, 1991.)

TRANSITIVITY

A relation R is transitive if whenever a stands in relation R to b, which in turn stands in relation R to c, then a stands in relation R to c. Curiously enough, Shakespeare has an observation on the supposed transitivity of the relation "servant of" later on in the very same scene, Twelfth Night, Act III, Scene I:

Viola: You're servant's servant is your servant, madam.

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