A Pretty Dichotomy and True. — “Equality is a pretty lie because it pretends to assert commensurability with respect to incommensurable things. When we give up on the idea of equality though it is tempting to replace it with the idea of inequality. This is a mistake. Like its yin equality, the yang inequality carries with it a connotation of commensurability: two things which are unequal are quantitatively comparable along some axis, and one is greater than the other along that axis. So to conclude that (in a comparison of incommensurables) inequality is the case from the fact that equality is false is to make the same mistake that got us here in the first place.” 1
With due respect for the author, I must nonetheless disagree. No connotation of commensurability or quantifiability is carried within the concept of inequality per se. Whether or not two things are commensurable, they are unequal by dint of being in fact two things and not one and the same thing. (Incommensurability means we cannot tell of two things which is the better, the greater, etc, not that we do not know that they are unequal in some way.) “Incommensurable” is not a third option between “equal” and “unequal”. There is no third option. Either A or not-A, equal or unequal. Hence, giving up on the idea of the equality of things — i.e., regaining humble sanity — just means accepting their inequality, commensurable or not.
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1. Zippy Catholic, “All men are not created unequal”, Zippy Catholic (weblog), 14th November 2012.