The diagonal arguments by Cantor, Gödel and Turing constitute fundamental results that demonstrate limits to what is mathematically possible. These results can easily appear to us as limits that must hold, as if they were laws of nature that govern the ideal world of platonic numbers and logic, giving them an “ultraphysical” appearance of rigidity and hardness. In all three cases, Wittgenstein critically examines the formal ideal of consistency and points out that the conclusions of the diagonal arguments only seem ...