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From: Aatu Koskensilta on 8 Aug 2010 16:54
Newberry <newberryxy(a)gmail.com> writes:

> This sentence:
>
> ~(Ex)(Ey)(Pxy & Qy). (3.3.1)
>
> Pxy means that x is the proof of y, where x and y are G�del numbers of
> wffs or sequences of wffs. Q has been constructed such that only one y
> = m satisfies it, and m is the G�del number of (3.3.1).

Proof in what theory?

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechen kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Newberry on 8 Aug 2010 20:56
On Aug 8, 1:54 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Newberry <newberr...(a)gmail.com> writes:
> > This sentence:
>
> >     ~(Ex)(Ey)(Pxy & Qy).       (3.3.1)
>
> > Pxy means that x is the proof of y, where x and y are Gödel numbers of
> > wffs or sequences of wffs. Q has been constructed such that only one y
> > = m satisfies it, and m is the Gödel number of (3.3.1).
>
> Proof in what theory?

How does it matter?
From: Don Stockbauer on 8 Aug 2010 21:01
On Aug 8, 7:56 pm, Newberry <newberr...(a)gmail.com> wrote:
> On Aug 8, 1:54 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
>
> > Newberry <newberr...(a)gmail.com> writes:
> > > This sentence:
>
> > >     ~(Ex)(Ey)(Pxy & Qy).       (3.3.1)
>
> > > Pxy means that x is the proof of y, where x and y are Gödel numbers of
> > > wffs or sequences of wffs. Q has been constructed such that only one y
> > > = m satisfies it, and m is the Gödel number of (3.3.1).
>
> > Proof in what theory?
>
> How does it matter?

Does any of this put food on the table?
From: Newberry on 9 Aug 2010 09:29
On Aug 9, 5:24 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote:
> In article <6b4407fe-f953-48eb-a22c-f9ab8de85...(a)g6g2000pro.googlegroups.com>,
> Newberry says...
>
>
>
> >On Aug 8, 1:54=A0pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> >> Newberry <newberr...(a)gmail.com> writes:
> >> > This sentence:
>
> >> > =A0 =A0 ~(Ex)(Ey)(Pxy & Qy). =A0 =A0 =A0 (3.3.1)
>
> >> > Pxy means that x is the proof of y, where x and y are G=F6del numbers o=
> >f
> >> > wffs or sequences of wffs. Q has been constructed such that only one y
> >> > =3D m satisfies it, and m is the G=F6del number of (3.3.1).
>
> >> Proof in what theory?
>
> >How does it matter?
>
> If it doesn't matter, then why would you object to my assuming that we
> are talking about PA?
>
> I've run rings around you, logically.

Hahahaha.

The question was what is Goedel sentence. The formula I exhibited is
Goedel's formula in many kinds of logic including PA. If we take PA to
be purely syntactic then we can re-interpret the formula. But if we
want a sound system it is obviously not going to be PA.

> --
> Daryl McCullough
> Ithaca, Ny

From: Newberry on 9 Aug 2010 10:22
On Aug 9, 6:33 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote:
> Newberry says...
>
> >The question was what is Goedel sentence. The formula I exhibited is
> >Goedel's formula in many kinds of logic including PA.
>
> If it is sufficiently similar to the Godel formula for PA, then it
> is nonsensical to say that it is neither true nor false.

Would you care to define "sufficiently similar" and show how your
conclusion follows?
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