> > But an inductive set contains elements that are not subject to > induction? >
The definition in Jech corresponds with Dedekind's simply infinite set.
An inductive set is a set having an injection into itself such that at least one element has no pre-image under the injection and such that no chain of elements under successive application of the injection closes in the sense that a pre-image is also a successor.
It need not be "thin" in the sense of the ordinal numbers defined to be transitive and well-ordered by membership.
For purposes of representing arithmetic within formal set theory, the empty set is taken as that element with no pre-image in the formal statement of the axiom of infinity. Then, some transfinite initial segment of the ordinals is necessarily a subset of the set whose existence is assumed by the axiom.
Of course, no elements are subject to induction since the purpose of the existence axiom is to provide a domain for inductive arguments to be applied.
WM probably thinks the platinum bar in Paris is a meter long (by definition, if another bar of different length replaced the current bar, a great deal of "empirical data" would become untrue instantaneously -- it is just one of those things that cannot be falsified)