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Rodych 2018, §2.1: "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." Note, however, that Wittgenstein does not identify such deduction with philosophical logic; cf. Rodych §1, paras. 7-12.
Rodych 2018, §3.4: "Given that mathematics is a 'motley of techniques of proof' (RFM III, §46), it does not require a foundation (RFM VII, §16) and it cannot be given a self-evident foundation (PR §160; WVC 34 & 62; RFM IV, §3). Since set theory was invented to provide mathematics with a foundation, it is, minimally, unnecessary."
Rodych 2018, §2.2: "An expression quantifying over an infinite domain is never a meaningful proposition, not even when we have proved, for instance, that a particular number n has a particular property."
