ABSTRACT
Peano’s three indefinables are 0, finite integer* and successor of. It is assumed, as part of the idea of succession (though it would, I think, be better to state it as a separate axiom), that every number has one and only one successor. (By successor is meant, of course, immediate successor.) Peano’s primitive propositions are then the following. (1) 0 is a number. (2) If a is a number, the successor of a is a number. (3) If two numbers have the same successor, the two numbers are identical. (4) 0 is not the successor of any number. (5) If s be a class to which belongs 0 and also the successor of every number belonging to s, then every number belongs to s. The last of these propositions is the principle of mathematical induction.
