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Newsgroups: sci.logic
From: Rupert <rupertmccal...@yahoo.com>
Date: Sun, 11 Nov 2012 05:28:29 -0800 (PST)
Local: Sun, Nov 11 2012 8:28 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 11月10日, 上午4时33分, Nam Nguyen <namducngu...@shaw.ca> wrote:
> On 09/11/2012 2:58 AM, Rupert wrote:
I don't get the question. What you gave is a wff in the first-order
> > On Nov 9, 5:51 am, Nam Nguyen <namducngu...@shaw.ca> wrote:
> >>>>> The concept "<" can be defined in terms of the other concepts. You
> >> If '<' is a defined symbol: (x < y) <-> Ez[x+Sz=y], then to you
> >> Ex[(0 < x) /\ (x < S0) ] <-> Ex[ Ez[0+Sz=x] /\ Ez[x+Sz=S0] ]
> >> ?
> >> You've not refuted that Godel's defined '<' is narrower than
> > There's nothing wrong with Goedel's definition of "<" in the context
> Then, why didn't you answer my question above?
language of arithmetic if < is included as a non-logical symbol, or if it is treated as a defined symbol and the abbreviations are eliminated. > >>>> Then, by the _semantic of_ the language of arithmetic of _the natural_
Not at all.
> >>>> _numbers_ , the semantic of '<' is: "numeral-less-than" and the formula > >>>> say Ax[0 <= x] would mean: "The numeral zero would equal to or be less > >>>> that any numeral x". > >>>> Then, no wonder why GIT is invalid: Godel _subverted_ the _meaning_ ,
> >>> Nonsense.
> >> That's not a refute; and my assertion would still remain.
> > As I correctly pointed out, you are talking nonsense.
> You're bluffing of course. You couldn't even answer my question above.
> >>>>>>> That's a large part of what
> >>>>>>> We say that P is omega-consistent if, given any well-formed formula
> >>>> But as alluded to above, how would you _range over the natural_
> >>>> And if you can _NOT_ then exactly what did you mean by the _concept_ of
> >>> I was just explaining what type 0 variables are. The concept of a type
> >> Except you've _not successfully_ given a definition for the phrase
> >> Now Godel said of the numerals (your "type 0 variables"?):
> >> "II. Variables of first type (for individuals, i.e. natural
> >> How would "purely syntactic" rhyme with "natural numbers" which is, in
> > The variables are syntactic objects. When we say that their
> >>> Specifying the intended model is irrelevant;
> >> So, the "natural numbers" you'd need to define your "purely syntactic"
> > You are confusing using natural numbers as surrogates for syntactic
> So now we have 2 more new buzz-words "surrogate" and "referent" that
> > I *don't* need to make
The first-order language of arithmetic is one possible metalanguage
> > any mention of natural numbers in the second sense in order to talk > > about syntax. > Really? So no one including Godel would need the language of arithmetic
you can use for talking about syntax. If you were doing this then you would not make any mention of the semantic properties of the object language, such as the fact that the referents of type 0 variables are natural numbers. I only mentioned this in order to make it clear what a type 0 variable was. > >> Because Godel's definition of a _general numeral instance_ _depends_
> > Discourse about natural numbers is effectively equivalent to discourse
> Except that "effectively equivalent" isn't a _precise_ technical term,
> >> Had Godel define a _general_ numeral _instance_ as the following
> >> In general, let 'S' be a unary function symbol, and '0' be an
> >> - Only '0' or 'S' could appear in t.
> Let me ask you this and hopefully you could give a straightforward
> Do you acknowledge that my definition of a general numeral above is
> Since this is one of the foundations of the back and forth arguments,
> I think we need a confirmation here, before we could technically go further. > --
> NYOGEN SENZAKI
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