ABSTRACT
According to Gottlob Frege and many logicists since his time, the principle of mathematical induction is a consequence of the definition of natural number. Let “Nu” mean “a is a natural number”
and let A(x) be an open sentence. Then we can take the principle as a rule of inference that enables us to go from the premises
A(O) Nu + [A(a) -+ A(&)]
Nt
to the conclusion A(t), for any term t. In effect, Frege defined “ Nu” as
VF([FO A V’x(Fx - F(G))] - Fu]
and then, given his logic (a form of second-order logic), the principle of induction is indeed a derived rule.
