 And, of course, as we’ve seen, Frege supposed that there is a domain of special logical objects (courses of values), among which he defined, and – until confronted by Russell’s paradox – took himself to have proved facts about, extensions and natural numbers (1884, 1893/1903).  Logic, then, is not purely formal, from Frege’s point of view, but rather can provide substantive knowledge of concepts and objects.