 Thirdly, the definition of the concept of natural number exploits the notion of the ancestral of the relation of succession: x bears the succession-ancestral relation to y just in case y is at most finitely many steps of succession away from x. (As already made clear, any apparent circularity in this definition, deriving from the adverbial gloss ‘finitely’, turns out, upon closer inspection of the definitions used, to be just that: merely apparent.) The concept “z is a natural number” is then defined as “either 0 is z, or 0 bears the succession-ancestral relation to z”. And this is what allows the neo-Fregean logicist to derive the principle of mathematical induction for the natural numbers. The reader of this survey article will be spared the formal details. 