Well, I believe it took mankind centuries to come to terms with things like irrational numbers (think I read some guy almost got killed by Greek clique for putting forth idea of diagonal of a square), and infinities, and even zero ha!

You won't get a better meaning of 3, I guess it's not possible beyond the schools of thought he lists out, but the formal def as {0, {0,1}, {0,1,2}} is pretty pure and we can at least all understand and communicate about such things much more precisely