In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 3 Apr., 00:29, Virgil <vir...@ligriv.com> wrote: > > > The point being that removing one object from an infinite set does not > > diminish the infinite number left in the set > > That is a good point. Alas induction holds for every natural number.
No! It only holds for inductive sets:
One valid form of induction is:
There exists a set of objects, N, and a special object such that: 1. The special object is a member of N. 2. For every object in N there is a successor object also in N. 3. The special object is not a successor object of any object in N. 4. If successors of two objects in N are the same, then the two original objects are the same. 5. If any set contains The special object and the successor object of every object in N, then that set contains N as a subset.
There is no correct statement of the principle of induction that is incompatible with the above, at least none outside of Wolkenmuekenheim. --