"G. Frege" <email@example.com> wrote in message news://firstname.lastname@example.org... > On Sun, 06 Apr 2003 18:28:35 GMT, "Poker Joker" <Poker@wi.rr.com> wrote: > > > > > Even if you are correct, it doesn't change the fact > > that Phil's questions uncovered alot of confusion > > amongst the people who responded negatively to him. > > > ??? > > > > > The negative responders obviously had set theory > > and Peano arithmetic intertwined and thay obviously > > couldn't point out that the terminology was causing > > confusion amonst themselves and Phil. The same > > confusion existed on both sides of the discusion. > > > Well. Actually the Peano axioms can be PROVED in set theory. Hence it doesn't > really matter (here) if we start our argumentation with the Peano axioms or just > with set theory. > > (Of course "set theory" is more "fundamental" or "basic".)
You could put it that way and many people do. In actuality though, PA is more "basic" partly proven by what you say. ZFC implies PA, but not the other way around, so there must be more to ZFC and therefore it less basic. That is why it DOES matter where you start your argumentation. You may not be able to get to where you want to go if you start with PA. "There are an infinite number of naturals." is unreachable from PA. So is its converse.