Part of what is at issue here, at least implicitly, is what constitutes a proof. It seems obvious that if a set is non-empty, then it must be possible to ‘choose’ an element from it (i.e., there must exist an element in it). Indeed, the obviousness of this is enshrined in the modern logical calculus by the way the inference principle of Existential Instantiation (EI) usually works: from ∃xPx one assumes Pc, where ‘c’ is a new constant, and reasons on that basis; whatever can be inferred from P(c) (as long as it does not itself contain the new constant ‘c’) is then taken to be inferable from ∃xPx alone. Furthermore, it is clear how this extends to finite sets (or finite extensions) by stringing together successive inferential steps. But how can such an inferential procedure be extended to infinite sets, if at all?