In the discussion of similarity relations similarity is typically taken to be reflexive -- in fact, it's the one property that's nearly universally agreed upon. But not everyone thinks similarity is always reflexive.

Consider "similarity with respect to color" and the claim that

(1) The number 2 is similar in color to itself.

Critics of the reflexivity view argue that (1) is false since the number two has no color (under the plausible assumption that abstract objects can't possess a color).

I don't quite have the intuition that the sentence is false. Rather it strikes me as infelicitous, involving something like a presupposition failure. Some theories of presupposition argue that presupposition failures result in meaninglessness. Since (1) would then not be assigned a proposition, it would not constitute a counterexample to reflexivity.

What options are available to the defender of the reflexivity view to block the falsity of "the number 2 is similar in color to itself" (either by rendering it meaningless or otherwise truth-value-less) or to argue that its falsity doesn't threaten reflexivity? Are there similar problems that I might look to for additional ideas?

  • To say that anything is similar to itself in any way (numbers, colors, whatever) is already meaningless. Similarity is not defined mathematically, but Griceanly. One object is not similar to itself, unless similar to is defined mathematically as encompassing identical to; this is not the case in English. My car is not "similar to" my car; it is my car. – jlawler Oct 17 '20 at 16:40

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