Complex sentence: A controversy that goes back to the early twentieth century concerns the issue of purely theoretic existence theorems, i.e., theorems depending on non-constructive foundational material such as the axiom of infinity, the axiom of choice, or the law of excluded middle.
Split into simpler sentences: A controversy that goes back to the early twentieth century concerns the issue of pure existence theorems. Such theorems may depend on non-constructive foundational material such as the axiom of infinity, the axiom of choice, or the law of excluded middle.