 Thus, Wittgenstein adopts the radical position that all expressions that quantify over an infinite domain, whether ‘conjectures’ (e.g., Goldbach’s Conjecture, the Twin Prime Conjecture) or “proved general theorems” (e.g., “Euclid’s Prime Number Theorem”, the Fundamental Theorem of Algebra), are meaningless (i.e., ‘senseless’; ‘sinnlos’) expressions as opposed to “genuine mathematical proposition[s]” (PR §168). These expressions are not (meaningful) mathematical propositions, according to Wittgenstein, because the Law of the Excluded Middle does not apply, which means that “we aren’t dealing with propositions of mathematics” (PR §151). The crucial question why and in exactly what sense the Law of the Excluded Middle does not apply to such expressions will be answered in the next section.