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Topic: Induction is Wrong
Replies: 8   Last Post: Nov 30, 2012 5:55 PM

 Messages: [ Previous | Next ]
 Dan Christensen Posts: 8,219 Registered: 7/9/08
Re: Induction is Wrong
Posted: Nov 29, 2012 10:59 PM

On Nov 29, 9:27 pm, RussellE <reaste...@gmail.com> wrote:
> Andrew Boucher has developed a theory called General Arithmetic (GA):http://www.andrewboucher.com/papers/ga.pdf
>
> GA is a sub-theory of Peano Arithmetic (PA).
> If we add an induction axiom (IND) to the axioms of Ring Theory (RT)
> then
> GA is also a sub-theory of RT+IND. (We also need a weak successor
> axiom).
>
> Boucher proves Lagrange's four square theorem, every number is the sum
> of four
> squares, is a theorem of GA. Since the four square theorem is not true
> in the
> integers, the integers can not be a model for GA, PA, or RT+IND.
>
> GA also proves multiplication is commutative.
> It is well known there are non-commutative rings.
>
> Induction is wrong. It proves multiplication,
> as defined by the axioms of ring theory,
> must be commutative when this is not true.
>

Wrong. The set of integers, along with usual addition and
multiplication functions on the integers can be constructed starting
from Peano's Axioms (including induction) by using the axioms of logic
and set theory.

Dan

Date Subject Author
11/29/12 reasterly@gmail.com
11/29/12 J. Antonio Perez M.
11/29/12 Dan Christensen
11/30/12 quasi
11/30/12 Brian Q. Hutchings
11/30/12 Brian Q. Hutchings
11/30/12 quasi
11/30/12 Rupert
11/30/12 Brian Q. Hutchings