 We prove mathematical ‘propositions’ ‘true’ (‘correct’) by ‘seeing’ that two expressions have the same meaning, which “must be manifest in the two expressions themselves” (6.23), and by substituting one expression for another with the same meaning. Just as “one can recognize that [‘logical propositions’] are true from the symbol alone” (6.113), “the possibility of proving” mathematical propositions means that we can perceive their correctness without having to compare “what they express” with facts (6.2321; cf. RFM App. III, §4).