 Similarly, in saying that “[t]he logic of the world” is shown by tautologies and true mathematical equations (i.e., #2), Wittgenstein may be saying that since mathematics was invented to help us count and measure, insofar as it enables us to infer contingent proposition(s) from contingent proposition(s) (see 6.211 below), it thereby reflects contingent facts and “[t]he logic of the world”. Though logic—which is inherent in natural (‘everyday’) language (4.002, 4.003, 6.124) and which has evolved to meet our communicative, exploratory, and survival needs—is not invented in the same way, a valid logical inference captures the relationship between possible facts and a sound logical inference captures the relationship between existent facts.