5.43 It is scarcely credible that from a fact p infinitely more others should follow, namely ~~p, ~~~~p, etc.. And it is no less remarkable that the infinite number of propositions of logic (of mathematics) follow from half a dozen “primitive propositions.”

All propositions of logic say the same thing however. Namely, nothing.

Wittgenstein suggests leaving out any translation of “von vornherein” (“from the very beginning”) in the first sentence here. See Letters to Ogden, p. 31. Those propositions follow from p, of course, but the idea that they are different facts is not credible (i.e. false?). Logic and mathematics cannot be derived from primitive propositions of logic. Now what about Wittgenstein’s own elementary propositions?