 The over-arching theme is that we can redeem Frege’s key philosophical insights concerning (natural and real) numbers and our knowledge of them, despite Russell’s discovery of paradox in Frege’s own theory of classes. That paradox notwithstanding, numbers are still logical objects, characterized by methods or principles of abstraction—which of course cannot be as ambitious as Frege’s Basic Law V. These principles afford a distinctive form of epistemic access to numbers. The usual mathematical axioms governing the two kinds of numbers are to be derived as results in (higher-order) logic—essentially following Frege’s deductive plan. These derivations will exploit appropriate definitions of the primitive constants, functions, and predicates of the brand of number theory concerned. (For example: 0, 1; s, +, ×; &lt;; N(x); ℝ(x).) 