
Re: A finite set of all naturals
Posted:
Aug 13, 2013 12:19 PM


Nam Nguyen <namducnguyen@shaw.ca> writes: <snip> >>>> Ben Bacarisse wrote: (quoting Nam) <snip> >>>>> Def03a: even1(x) <> Ey[x=y+y] >>>>> Def03b: even2(x) <> Ey[x=2*y] >>>>> Def03c: even(x) <> (even1(x) \/ even2(x)) <snip> > ... _an odd number can not be defined without addition_ while > an even number can (as per Def03b above).
odd(x) <> ~Ey[x=2*y]
In what sense does your definition of even2 avoid addition, where this one of odd does not?
Personally, I'd say that both this and Def03b use addition since multiplication in PA is usually defined using addition, but my view of what "without addition" means is not the issue here.
<snip>  Ben.

