In a recent conversation, James enlightened me about the connection between functions and relations in first order logic. In this short post I'd like to share the insight. Functions, of course, are a certain kind of relation—a total, functional relation. In set theory we directly define functions that way, and in any first order logic we think of a function f(x) and the relation f(x) = y as representing the same thing. Yet there is a definite difference between the two: syntactically, they ...
