 The orthographic similarities between the first-order induction schema and the second-order induction axiom have an unfortunate tendency to obscure the important differences between them. The latter is a sentence in the language, whereas the former is just a recipe for generating sentences. Nor are they inferentially equivalent: the set of instances of the first-order induction schema is logically weaker than the second-order induction axiom. That is, there are sentences of first-order arithmetic that can be deduced from the second-order induction axiom (together with the other axioms of arithmetic, which are common to first-order and second-order arithmetic) but not from the instances of the first-order induction schema (see Shapiro 1991: 110).