“Most of us believe it is trivial to verify that one and one are equivalent to 2. However, in careful examination, this matter is actually vastly more complex than it superficially appears — as are many matters that we ordinarily trivialize.

The truth that the statement 1 + 1 = 2 depends upon the establishment of an appropriate context in which such abstractions as numbers devoid of being-as-such may be said to exist and be manipulated according to rules.

This is not really the same as the world, where, for example, one penny and another, while being two pennies, are not -equivalent- to two, because each penny has a rather bizarre uniqueness, and they cannot share the same temporal and spatial extent, identity, or unity that literal equivalence seems to demand — except as a convenient abstraction.

Therefore, to my view, the sense in which they are equivalent to two is narrow, and the sense in which they have nothing to do with such perspectives is broad. This latter sense is, in effect, ‘more true’ than the numeric abstraction… and not slightly… but by many orders of magnitude.

We should respect this strange and exclusionary aspect of our habit, but not so much as to mistake it for reality. It is a toy. A powerful and possibly predictive one, but it and reality are not and cannot be synonymous. What one and one actually are equivalent to remains at least as mysterious as it is obvious, and, in my view, the mystery naturally overwhelms the abstraction.

What, after all, is ‘one’?”

— an anonymous informant