On Thursday, February 27, 2014 10:28:33 AM UTC-5, John Gabriel wrote: > > You cannot use this N if you require that Peano defines it. > > > > Correct. >
> > > > Where does he axiomatize that the difference is always 1? > > > > > Nowhere. That is just a property of the addition function, which itself can be constructed from Peano's axioms. > > > > Nonsense. That is absolute hogwash. There is no such thing as an addition function, never mind a property of the addition function. >
So, we do NOT have 2+2=4?
> > > In order to define the addition function, you need the objects first. >
You can use the set N, the successor function S, the rules of logic and the axioms of set theory to formally construct the addition function.