 We are not saying that when \(f(1)\) holds and when \(f(c + 1)\) follows from \(f(c)\), the proposition \(f(x)\) is therefore true of all cardinal numbers: but: “the proposition \(f(x)\) holds for all cardinal numbers” means “it holds for \(x = 1\), and \(f(c + 1)\) follows from \(f(c)\)”. (PG 406)