1 returns 1 as its identity, but how?

(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: lawrence@krubner.com, or follow me on Twitter.

In math, we take identity for granted. But this is really very complex. I am willing to believe that 1 knows it is 1, but how does it communicate that the function that calls it? This is something that I’ve been thinking about a lot lately. Or maybe I am wrong about what it knows. How does 1 know it is 1? Does it engage in self-reflection? If so, how? Wouldn’t self-reflection be a function? But how can a function get the identity of 1 if 1 has to call a function to discover what its own identity is? This seems to me an important paradox, yet I’m not able to discover much about it on the Internet. People seem comfortable resolving this issue by sidestepping it: just define the identity of a number as its value. But that breaks down sometimes, doesn’t it?