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Re: Who is too stupid to agree with Phil?
Posted:
Apr 12, 2003 9:25 AM
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"Lao Coon" <laocoon@fastmail.fm> wrote in message
news://Xns935B4F7B4A548laocoon@62.153.159.134...
> "Poker Joker" <Poker@wi.rr.com> wrote in
> news://FBKla.12771$B4.216514@twister.rdc-kc.rr.com:
>
> > "Lao Coon" <laocoon@fastmail.fm> wrote in message
> > news://Xns935BD8F96F0laocoon@62.153.159.134...
> >> "Poker Joker" <Poker@wi.rr.com> wrote in news://bRHla.12747$B4.202956
> >> @twister.rdc-kc.rr.com:
> >>
> >> >> > Where did you prove "if x has the property Q the x' also has the
> >> >> > property Q?"
> >> >> > Oh yeah... You didn't. You just said you could and then omitted
> >> >> > it.
> >> >>
> >> >> That's right. Isn't that intuitous to you?
> >> >
> >> > nope.
> >>
> >> see my other reply for the rest of the proof (i think it's complete)
> >>
> >> >> N(z) : z has the property of being a natural number
> >> >> H(z) : z has the property of having a successor
> >> >> L(z) : z has the property of being the "number of natural numbers"
> >> >
> >> > Could you explain this notation is the context of PA?
> >>
> >> Yes.
> >> N(z) means z is a natural number according to Peano 1 and 2
> >> H(z) means z has a successor as defined by Peano 2
> >> L(z) means z has the property of being the "number of natural
> >> numbers" (which is what we're looking at), this is any property Q in
> >> the context of Peano 5.
> >>
> >> >
> >> >> Now by definition, the number of natural numbers would have to be
> >> >> the biggest natural number, any smaller and it's not enough, any
> >> >> bigger
> >> and
> >> >> it's too much.
> >> >
> >> > I get it. It HAS TO BE. Why didn't you say so before. Let's
> >> > see if that always works: 2 HAS TO BE 3. Darn it. How did you
> >> > do that again? I can't make 2=3.
> >>
> >> I took the definition. You're out of luck though, 2 is not defined to
> >> be 3. If you want to propose another definition, please do.
> >
> > I'm not going spelling it all out for you, (I hope.) but
> > lets continue on:
> >
> > You said:
> > (1) L(z) means z has the property of being the "number of natural
> > numbers"
> > and
> > (2) the number of natural numbers would have to be the biggest
> > natural number, any smaller and it's not enough, any bigger
> > and it's too much.
> >
> > I claim you said (1) was the defining statement and (2) was
> > the "proof by IT HAS TO BE method." What am I getting wrong?
> >
> > This is not the only problem I see but its kind of
> > important.
>
> In (1) I just said what L(z) means. Namely that z has the property etc
> etc. So in (2) this property is defined.
LOL. Are you serious? You must know that a definition
is "what something means."
> We have to do this because we
> cannot of course proof that if x then x' do or do not have some
> _undefined_ property. you see?
All is not lost for you. You are half way to where you need
to be. You understand the "cannot prove" part. Now you
need to understand the "undefinable property" part.
Try to formalize your proof and you may see the rest.
> Lao
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