 This is the core of Wittgenstein’s life-long formalism. When we prove a theorem or decide a proposition, we operate in a purely formal, syntactical manner. In doing mathematics, we do not discover pre-existing truths that were “already there without one knowing” (PG 481)—we invent mathematics, bit-by-little-bit. “If you want to know what \(2 + 2 = 4\) means”, says Wittgenstein, “you have to ask how we work it out”, because “we consider the process of calculation as the essential thing” (PG 333). Hence, the only meaning (i.e., sense) that a mathematical proposition has is intra-systemic meaning, which is wholly determined by its syntactical relations to other propositions of the calculus.