[lisper]

> If by symbol you mean something different than variable, then I might agree,

Well, the real question is what Curtis means by symbol, as the answer he gave is rather cryptic. But since he specifically raised the issue of "gensyms", that seems to be a reference to a standard Lisp function that generates symbols, a first-class Lisp data structure, at run-time or, more usually, at macro-expansion time. Since Curtis has complained about macros in the past, I assumed this was what he was referring to. "Symbols" that exist only in the textual representation of the language and not as first-class data types are usually called "identifiers" rather than symbols precisely to avoid this sort of confusion.

In any case, it is an elementary exercise to define a formal computational system equivalent to the lambda calculus that uses integers rather than identifiers. Instead of λx.x you write λn where n is an integer. 0 refers to the value bound by the innermost scope, 1 to the value bound by the next outer scope, and so on. So, for example, λx.λy.x becomes λλ1. But of course, no one does this because it's completely pointless.