of the paradox by casting it as an algorithm to be executed in natural time emphasizes the difference between the existence of a set and the process of constructing the set, a difference that echoes Prigogine’s [@prigogine1981], [@prigogine1984 p. 320] distinction between being and becoming. In the algorithmic construction of the set, the size of the set oscillates between $n$ and $n+1$, sizes that correspond to “doesn’t” and “does”. Most well known paradoxes are similar to Russell’s in that they involve self-reference. However, Yablo [@yanofsky2013 pp. 24-25] has demonstrated one that is non-self-referential; but it, too, yields an oscillation (true, false, true, false …) if executed as an algorithm.

Incompleteness
--------------

Whereas Russell discovered a paradox that cast doubt on the possibility of demonstrating that mathematics is a purely syntactical system, both G[ö]{}del and Turing came up with proofs that even to the extent that it *is* syntactical, it is impossible to demonstrate that it is. G[ö]{}del showed that even for a relatively limited deductive system there were true statements that couldn’t be proven true within the system. In order to prove those statements, the system would have to be enlarged in some way, for example with additional axioms. But 