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Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
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More options Nov 14 2012, 8:46 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Wed, 14 Nov 2012 13:46:23 +0000
Local: Wed, Nov 14 2012 8:46 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Nam Nguyen wrote:
> >> H:  T = T1 + T2 + T3 + ....
> >>       where each Ti is in a collection K of formal systems (K isn't
> >>       necessarily finite).
> >>       .
> >> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
> >> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

> >> Proof: The proof for C1 or C2 is trivial and taken for granted here.

I tell you what, since the proofs are trivial write them down anyway.

And when you done that, you can deal with the long outstanding issues of
the interpretation of '=', the number of $\in$'s that set theory needs,
'x = x' always being an axiom of FOL= theories, and so on.

Not that this has anything to do with G\"odel's proof of G\"odel's
theorem, which you've never read, or any other version of G\"odel's
theorem.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 16 2012, 11:18 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Fri, 16 Nov 2012 21:18:06 -0700
Local: Fri, Nov 16 2012 11:18 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 14/11/2012 3:48 AM, Rupert wrote:

So modern formal systems such as Q, PA, ZF, ZFC, ... aren't outside
the scope of GIT which is what I assumed above.

You seem to contradict yourself from one moment to the other on MT0!

Then you're not confirming that MT0 is correct, or refuting it.

So I don't see how you'd be ale to see my explanation as to why
GIT is a logically invalid assertion.

Let me categorically say this: _There is NO logical sense_ in proving
a consistency of a T 'in some appropriate sense of "consistency
sentence"'.

The definition of inconsistency or consistency is _within proving in T_
_using rules of inference_ .

Let L1(<) and L2(e) are 2 languages each with a 2-ary predicate symbol.
Let:

T1a = {Axy[x < y] /\ ~Axy[x < y]}
T1b = {Axy[x < y] \/ ~Axy[x < y]}

T2a = {Axy[x e y] /\ ~Axy[x e y]}
T2b = {Axy[x e y] \/ ~Axy[x e y]}

If you'd like to prove T1a is inconsistent, you'd prove that in T1a,
_not_ in T2a, whether or not you could prove it so; and in this case
you could.

If you'd like to prove T1b is consistent, you'd prove that in T1b,
_not_ in T2b, whether or not you could prove it so; and in this case
you could _NOT_ .

To say that you could prove the undecidability of G(PA) in PRA is as
not conforming to the definition of consistency and as not logical
as to prove T1a is inconsistent using a proof in T2a!

In summary, you either clearly acknowledge MT0 as true or refute it.
Otherwise you'd not understand my proof that GIT is in invalid inference
in meta level.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 16 2012, 11:41 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Fri, 16 Nov 2012 21:41:10 -0700
Local: Fri, Nov 16 2012 11:41 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 14/11/2012 6:46 AM, Frederick Williams wrote:

> Nam Nguyen wrote:

>>>> H:  T = T1 + T2 + T3 + ....
>>>>        where each Ti is in a collection K of formal systems (K isn't
>>>>        necessarily finite).
>>>>        .
>>>> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
>>>> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

>>>> Proof: The proof for C1 or C2 is trivial and taken for granted here.

> I tell you what, since the proofs are trivial write them down anyway.

No need for me to respond further until you admit you were wrong
on the following.

You yourself voluntarily accused my expression:

"x > the greatest counter example of the Goldbach conjecture"

as "is not well-formed"

then I explained to you that it's a well-formed expression, using the
well-formed formula below to define it:

~cGC /\ Ay[~GC(y) -> (y < x)]

But then you didn't see that I've correctly answered your "is not
well-formed" assertion.

So, until you acknowledge that you were wrong - and ignorant of the
matter - and that my:

~cGC /\ Ay[~GC(y) -> (y < x)]

correctly expresses "x > the greatest counter example of the Goldbach
conjecture", there's no point to answer another question of yours.

There got to be closure from a question of yours, before we could
move to another one.

So, acknowledge that you were wrong before, with your "is not
well-formed" assertion, if you'd like to hear further answer
from me on any technical questions.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 16 2012, 11:59 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Fri, 16 Nov 2012 21:59:42 -0700
Local: Fri, Nov 16 2012 11:59 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 13/11/2012 7:35 AM, Frederick Williams wrote:

But you haven't technically explained to the ng as to _why_
~cGC /\ Ay[~GC(y) -> (y < x)] would make "x > the greatest
counterexample of the Goldbach conjecture" lose "its usual meaning"!

Again, _WHY_ ?

> An honest person would say something like:

> I see that "x > the greatest counter example of the Goldbach conjecture"
> will not do, and I shall replace it with '~cGC /\ Ay[~GC(y) -> (y < x)],
> where GC(e) <-> even(e) -> "e is a sum of 2 primes"'.

Just because you're an idiot and are technically incompetent to
understand ~cGC /\ Ay[~GC(y) -> (y < x)] would expresses:

"x > the greatest counter example of the Goldbach conjecture"

doesn't make my explanation wrong at all.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 1:45 am
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Fri, 16 Nov 2012 23:45:21 -0700
Local: Sat, Nov 17 2012 1:45 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 16/11/2012 9:18 PM, Nam Nguyen wrote:

Then again, it seems you and I aren't talking about the same thing.

I'm saying consistency of T means T can _not_ prove certain formulas,
while you're talking about T can prove some formulas, as in "prove
[...] own consistency sentences".

How would T's proving some formulas _conform_ with the consistency-
requirement that T can _not_ prove certain formulas?

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 3:13 am
Newsgroups: sci.logic
From: Rupert <rupertmccal...@yahoo.com>
Date: Sat, 17 Nov 2012 00:13:10 -0800 (PST)
Local: Sat, Nov 17 2012 3:13 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On Nov 17, 5:18 am, Nam Nguyen <namducngu...@shaw.ca> wrote:

I should have been a bit more careful. I apologize.

I thought that what was going on was that you were confusing the
object theory and the metatheory. But you can have a situation where
the metatheory and the object theory are in fact equal, and a proof in
the metatheory is a proof of a consistency sentence for the object
theory.

Why not?

It's not.

> In summary, you either clearly acknowledge MT0 as true or refute it.

It's wrong. You can prove the consistency of a first-order theory. You
can prove the consistency of Q in PRA, for example. You can read about
that in Shoenfield.

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More options Nov 17 2012, 3:14 am
Newsgroups: sci.logic
From: Rupert <rupertmccal...@yahoo.com>
Date: Sat, 17 Nov 2012 00:14:24 -0800 (PST)
Local: Sat, Nov 17 2012 3:14 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On Nov 17, 7:45 am, Nam Nguyen <namducngu...@shaw.ca> wrote:

Take the example of PRA proving the consistency of Q. For Q to be
consistent is for it to fail to prove certain formulas. But there is a
formula in the language of PRA which expresses the assertion that Q is
consistent. And PRA can prove this formula.

What's the problem?

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More options Nov 17 2012, 9:06 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 14:06:06 +0000
Local: Sat, Nov 17 2012 9:06 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Nam Nguyen wrote:
> But you haven't technically explained to the ng as to _why_
> ~cGC /\ Ay[~GC(y) -> (y < x)] would make "x > the greatest
> counterexample of the Goldbach conjecture" lose "its usual meaning"!

> Again, _WHY_ ?

Don't nag.  You sound like a fishwife.

In "x > the greatest counterexample of the Goldbach conjecture" what
logic governs that "the"?  There are various ways of dealing with
definite descriptions, which do you use?

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 9:09 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 14:09:47 +0000
Local: Sat, Nov 17 2012 9:09 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

In other words you can't prove it.  Have you stopped to wonder why you
can't prove it.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 9:41 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 14:41:12 +0000
Local: Sat, Nov 17 2012 9:41 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Nam Nguyen wrote:

> [...]

You're thick, aren't you?  I don't just mean that you're ignorant of
logic, that's obvious.  You're general-purpose, all-round thick.  Did
you really do a four year college degree in mathematics?

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 10:59 am
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 08:59:39 -0700
Local: Sat, Nov 17 2012 10:59 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 7:06 AM, Frederick Williams wrote:

> Nam Nguyen wrote:

>> But you haven't technically explained to the ng as to _why_
>> ~cGC /\ Ay[~GC(y) -> (y < x)] would make "x > the greatest
>> counterexample of the Goldbach conjecture" lose "its usual meaning"!

>> Again, _WHY_ ?

> Don't nag.  You sound like a fishwife.

> In "x > the greatest counterexample of the Goldbach conjecture" what
> logic governs that "the"?  There are various ways of dealing with
> definite descriptions, which do you use?

You're really incapable of understanding simple mathematical
expression, using L(PA).

Can you _express_ :

x > the greatest even prime

_without even knowing_ if there's the greatest even prime?

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 11:23 am
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 09:23:12 -0700
Local: Sat, Nov 17 2012 11:23 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 1:14 AM, Rupert wrote:

There are 2 problems that for various reasons you seem to have refused
to acknowledge; and I've already explained these 2 problems.

----------------> 1st problem.

A language expressing an assertion does _NOT equate_ to the
assertion being true or false, logically speaking.

For instance, in the thread where I defined cGC, you can
certainly use the same technique to define a similarly formed
formula that would express "There are infinitely many even primes",
whether or not there _actually_ are infinitely many even primes!

And I have already explained this viz-a-viz non-standard
interpretation of formula expression-truth. Would you
understand what I said there?

So a formula expressing "the assertion that Q is consistent" can
_NOT_ be equated to Q being _actually_ consistent, _if_ Q is so.
Logically speaking.

Formula semantic and formula semantic-truth are not (even) the same!

Is alive(Kennedy_Spirit) true or false?

----------------> 2nd problem.

I've already explained it: the problem is the FOL definition of
inconsistency, consistency of a T is _absolutely agnostic_ about
any theory other than T!

If you use a method to come up with what you'd call "proof" of
consistency but the method doesn't conform with FOL definition
of consistency then for sure that's a logically invalid method,
however well intended.

Why can't you acknowledge that simple fact?

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 11:48 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 16:48:34 +0000
Local: Sat, Nov 17 2012 11:48 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Express in what formal language?  Definite descriptions are handled in
different ways by different authors.

Meanwhile:
You:

> H:  T = T1 + T2 + T3 + ....
>      where each Ti is in a collection K of formal systems (K isn't
>      necessarily finite).
>      .
> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

> Proof: The proof for C1 or C2 is trivial and taken for granted here.

Me:
Really?  If T = T1 + T2 means that the predicates (etc) of T is the
union of those of T1 and T2 and the axioms of T is the union of those of
T1 and T2, and T is closed under logical consequence; then it's obvious
that T can be inconsistent though both T1 and T2 are consistent.  If
that's not what you mean by +, you need to say so.

And when you done that, you can deal with the long outstanding issues of
the interpretation of '=', the number of $\in$'s that set theory needs,
'x = x' always being an axiom of FOL= theories, and so on.

Do you think that these things go away just because you ignore them?  Do
you think that just because you insist ("Again, _WHY_ ?"), like a
will forget all the points that you have left unanswered?

Have you read G\"odel's paper yet?  No.  Or any other account of
G\"odel's incompleteness theorem?  No.  And will you continue to hold

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 11:53 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 16:53:35 +0000
Local: Sat, Nov 17 2012 11:53 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Nam Nguyen wrote:
> I've already explained it: the problem is the FOL definition of
> inconsistency, consistency of a T is _absolutely agnostic_ about
> any theory other than T!

> If you use a method to come up with what you'd call "proof" of
> consistency but the method doesn't conform with FOL definition
> of consistency then for sure that's a logically invalid method,
> however well intended.

How do you express that a theory T is consistent in a first order
language?  What symbols does the first order language have, and what
symbols does T have?

> Why can't you acknowledge that simple fact?

It's a mystery.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 12:11 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 10:11:36 -0700
Local: Sat, Nov 17 2012 12:11 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 9:48 AM, Frederick Williams wrote:

Didn't I just say " using L(PA)"?

> Meanwhile:

There's no "Meanwhile:", until we have a closure and that you admit
you were technically wrong in not acknowledging that:

~cGC /\ Ay[~GC(y) -> (y < x)]

would correctly express:

"x > the greatest counterexample of the Goldbach conjecture".

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 12:42 pm
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 17:42:02 +0000
Local: Sat, Nov 17 2012 12:42 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

PA is expressed in various languages.  I'm not sure that I've met one
which had definite descriptions.  That is not to say there isn't such a
language, but in the one that you have in mind what is the truth value
of

the x such that phi

if there is no x such that phi, or if there are a number of x's such
that phi?  You'll really have to tell me because I don't know.  One
possibility is that

the x such that phi

is never used in a formula unless it is first established that

there is just one x such that phi,

but that may not be a good idea since the theory of arithmetic being
considered is recursively undecidable.

> > Meanwhile:

> There's no "Meanwhile:", until we have a closure and that you admit
> you were technically wrong in not acknowledging that:

> ~cGC /\ Ay[~GC(y) -> (y < x)]

> would correctly express:

> "x > the greatest counterexample of the Goldbach conjecture".

If "~cGC /\ Ay[~GC(y) -> (y < x)]" has a definite truth value and "x >
the greatest counterexample of the Goldbach conjecture" doesn't, then
one can't correctly express the other.  I don't now if "x > the greatest
counterexample of the Goldbach conjecture" has a definite truth value
until you explain how you're handing definite descriptions.

When you've done that, you might want to address:
You:

> H:  T = T1 + T2 + T3 + ....
>      where each Ti is in a collection K of formal systems (K isn't
>      necessarily finite).
>      .
> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

> Proof: The proof for C1 or C2 is trivial and taken for granted here.

Me:
Really?  If T = T1 + T2 means that the predicates (etc) of T is the
union of those of T1 and T2 and the axioms of T is the union of those of
T1 and T2, and T is closed under logical consequence; then it's obvious
that T can be inconsistent though both T1 and T2 are consistent.  If
that's not what you mean by +, you need to say so.

And when you done that, you can deal with the long outstanding issues of
the interpretation of '=', the number of $\in$'s that set theory needs,
'x = x' always being an axiom of FOL= theories, and so on.

Do you think that these things go away just because you ignore them?  Do
you think that just because you insist ("Again, _WHY_ ?"), like a
will forget all the points that you have left unanswered?

Have you read G\"odel's paper yet?  No.  Or any other account of
G\"odel's incompleteness theorem?  No.  And will you continue to hold

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 1:15 pm
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 18:15:46 +0000
Local: Sat, Nov 17 2012 1:15 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Frederick Williams wrote:
> until you explain how you're handing definite descriptions.

handling, sorry.

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 3:39 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 13:39:37 -0700
Local: Sat, Nov 17 2012 3:39 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 10:42 AM, Frederick Williams wrote:

L(PA) in this case is L(0,S,<,+,*).

> but in the one that you have in mind what is the truth value
> of

>     the x such that phi

> if there is no x such that phi, or if there are a number of x's such
> that phi?  You'll really have to tell me because I don't know.

That's why you were wrong: you were confused between semantic and truth.

_Truth is NOT required_ here; we're talking about semantics, expression
of the L(PA) language, to express say "x > the greatest even prime"
using formulas.

Until you're clear of this semantic vs. truth confusion, you'd not
be able to understand and admit you're wrong here in believing that:

>>>>>> ~cGC /\ Ay[~GC(y) -> (y < x)] would make "x > the greatest
>>>>>> counterexample of the Goldbach conjecture" lose "its usual
>>>>>> meaning"

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 5:26 pm
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sat, 17 Nov 2012 22:26:49 +0000
Local: Sat, Nov 17 2012 5:26 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Since there's a "the" there, your language has a logical constant for
definite descriptions (typically "iota x F(x)" is read as "the x such
that F(x)".  What logic governs your iota?  Specifically, what if there
is no x such that F(x), or more than one?

Meanwhile don't forget:
You:

> H:  T = T1 + T2 + T3 + ....
>      where each Ti is in a collection K of formal systems (K isn't
>      necessarily finite).
>      .
> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

> Proof: The proof for C1 or C2 is trivial and taken for granted here.

Me:
Really?  If T = T1 + T2 means that the predicates (etc) of T is the
union of those of T1 and T2 and the axioms of T is the union of those of
T1 and T2, and T is closed under logical consequence; then it's obvious
that T can be inconsistent though both T1 and T2 are consistent.  If
that's not what you mean by +, you need to say so.

And when you done that, you can deal with the long outstanding issues of
the interpretation of '=', the number of $\in$'s that set theory needs,
'x = x' always being an axiom of FOL= theories, and so on.

Do you think that these things go away just because you ignore them?  Do
you think that just because you insist ("Again, _WHY_ ?"), like a
will forget all the points that you have left unanswered?

Have you read G\"odel's paper yet?  No.  Or any other account of
G\"odel's incompleteness theorem?  No.  And will you continue to hold

And don't pretend that I'm obliged to deal with your questions (which I
do) and that you are not obliged to deal with your backlog.  Shall I
tell you how easy it is to deal with it?  You just say: "I wish to
withdraw my claims about T = T1 + T2, the interpretation of '=', the
number of $\in$'s that set theory needs, 'x = x' being an axiom, etc,
etc."  Unfortunately you are too devious and dishonest to do so.  Do you
think people haven't noticed, or will just forget?

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 6:07 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 16:07:03 -0700
Local: Sat, Nov 17 2012 6:07 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 3:26 PM, Frederick Williams wrote:

So that's the source of your technical ignorance of the matter: you
don't seem to realize there's such thing as logical equivalence
of 2 (syntactically) different formulas or expressions.

x > the greatest even prime

is equivalent to:

There are finitely many even primes each of which is less than x.

See: there is _NO_ "the" there.

_One expression could be inferred from the other and vice versa_ .

Actually, have you ever heard of logical equivalence of formulas
or expressions?

> Meanwhile

As said before, there's _NO_ "Meanwhile" _UNTIL you acknowledge_
_you are technically wrong in the matter here_ .

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 8:05 pm
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sun, 18 Nov 2012 01:05:42 +0000
Local: Sat, Nov 17 2012 8:05 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

Your example is not interesting. "x > the greatest even prime" is just
the same as "x > 2".

More interesting is

"x > the greatest counterexample of the Goldbach conjecture"

which is after all what you wrote.  Are you trying to disown it
already?  How do you formalize it?  What axioms and rules govern your
formalization?

Note that there is no known numeral n such that

"x > the greatest counterexample of the Goldbach conjecture"

is equivalent to

"x > n".

If the Goldbach conjecture is true there is no such n, known or
unknown.  And if there are infinitely many counterexamples to the
Goldbach conjecture, what does "the greatest counterexample" mean in
that case?

Note that "x > the greatest even prime" is quite unproblematic, because
it is just the same as "x > 2" come what may.   I suspect you realize
that "x > the greatest counterexample of the Goldbach conjecture" is
problematic, and you have introduced "x > the greatest even prime"
because it isn't problematic, and you hope the Goldbach conjecture
problem will go away.  Actually, you can make it go away by saying:

"I admit that the 'the' in 'x > the greatest counterexample of the
Goldbach conjecture' is problematic, and my knowledge of logic is too
inadequate for me to know how to deal with it.  Therefore, whatever I
was saying about 'x > the greatest counterexample of the Goldbach
conjecture' I now withdraw."

Or you could say:

"I admit that the 'the' in 'x > the greatest counterexample of the
Goldbach conjecture' is problematic, and I shall learn about definite
descriptions and how to deal with it.  I may then return to the fray."

When you've dealt with that, you might want to address:
You:

> H:  T = T1 + T2 + T3 + ....
>      where each Ti is in a collection K of formal systems (K isn't
>      necessarily finite).
>      .
> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

> Proof: The proof for C1 or C2 is trivial and taken for granted here.

Me:
Really?  If T = T1 + T2 means that the predicates (etc) of T is the
union of those of T1 and T2 and the axioms of T is the union of those of
T1 and T2, and T is closed under logical consequence; then it's obvious
that T can be inconsistent though both T1 and T2 are consistent.  If
that's not what you mean by +, you need to say so.

And when you done that, you can deal with the long outstanding issues of
the interpretation of '=', the number of $\in$'s that set theory needs,
'x = x' always being an axiom of FOL= theories, and so on.

Do you think that these things go away just because you ignore them?  Do
you think that just because you insist ("Again, _WHY_ ?"), like a
will forget all the points that you have left unanswered?

Have you read G\"odel's paper yet?  No.  Or any other account of
G\"odel's incompleteness theorem?  No.  And will you continue to hold

You are truly stupid.  There is an easy way out of your difficulties.
First, admit that you know nothing about the formalization of "the" and
wish to give up on it.  Then just say: "I also wish to withdraw my
claims about T = T1 + T2, the interpretation of '=', the number of
$\in$'s that set theory needs, 'x = x' being an axiom, etc, etc."
Unfortunately you are too devious and dishonest to do so.  Do you think
people haven't noticed, or will just forget?

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

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More options Nov 17 2012, 8:41 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 18:41:25 -0700
Local: Sat, Nov 17 2012 8:41 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 6:05 PM, Frederick Williams wrote:

You're technically incompetent.

There are ways to express "x > the greatest even prime" without
requiring SS0 to be present in the formula. I already explain how
to do it: you're just not capable of understanding that _basic fact_ .

> More interesting is

>    "x > the greatest counterexample of the Goldbach conjecture"

> which is after all what you wrote.  Are you trying to disown it

Of course not. I always maintain that  ~cGC /\ Ay[~GC(y) -> (y < x)]
would express "x > the greatest counterexample of the Goldbach
conjecture". My example about "There are finitely many even primes
each of which is less than x" was meant to help you to understand
you error of a _basic fact_ .

> How do you formalize it?  What axioms and rules govern your
> formalization?

This is your 2nd utterly confusion: formula semantics expression
has nothing to do with _formalization needing axioms_ !

> Note that there is no known numeral n such that

>    "x > the greatest counterexample of the Goldbach conjecture"

> is equivalent to

>    "x > n".

You're really hopeless with all that idiotic rambling, while
not knowing what a language _formula expression_ is.

were wrong.
--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 17 2012, 8:54 pm
Newsgroups: sci.logic
From: Nam Nguyen <namducngu...@shaw.ca>
Date: Sat, 17 Nov 2012 18:53:58 -0700
Local: Sat, Nov 17 2012 8:53 pm
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On 17/11/2012 6:41 PM, Nam Nguyen wrote:

Seriously, Frederick. Why don't you bring my definition of cGC
and ask an informed poster or a Professor that you could talk to,
to see if my claim that ~cGC /\ Ay[~GC(y) -> (y < x)] would express
"x > the greatest counterexample of the Goldbach conjecture" is wrong,
and if so bring back their explanation and present it here for people
to see.

Until then you've shown you don't know a _very basic fact_ of
mathematical reasoning.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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More options Nov 18 2012, 4:56 am
Newsgroups: sci.logic
From: Rupert <rupertmccal...@yahoo.com>
Date: Sun, 18 Nov 2012 01:56:44 -0800 (PST)
Local: Sun, Nov 18 2012 4:56 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud
On Nov 17, 5:23 pm, Nam Nguyen <namducngu...@shaw.ca> wrote:

I don't understand your point. Just because I can write down a formula
doesn't mean it is true, no. But many would feel that if I can prove
it in PRA that's a pretty good reason for thinking it true. You may
perhaps feel differently, but in that case the onus is on you to tell
us which systems you do trust.

> ----------------> 2nd problem.

> I've already explained it: the problem is the FOL definition of
> inconsistency, consistency of a T is _absolutely agnostic_ about
> any theory other than T!

> If you use a method to come up with what you'd call "proof" of
> consistency but the method doesn't conform with FOL definition
> of consistency then for sure that's a logically invalid method,
> however well intended.

> Why can't you acknowledge that simple fact?

Again, I just don't get what your point is. As far as I can tell you
are talking incoherent nonsense.

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More options Nov 18 2012, 7:08 am
Newsgroups: sci.logic
From: Frederick Williams <freddywilli...@btinternet.com>
Date: Sun, 18 Nov 2012 12:08:36 +0000
Local: Sun, Nov 18 2012 7:08 am
Subject: Re: Uniting Forces: Email to Prof. Norman J. Wildberger on Politics,IneptitudeandFraud

The example "x > the greatest even prime" is of no interest.  You are
just trying to divert attention away from your failure to understand
that "the" is a logical constant that is regulated by axioms and/or
rules, and you need to say what those axioms and/or rules are.  What is
"the x s.t. F(x)" in the cases where no x Fs or more than one x Fs?

> > [...]

> were wrong.

Do you think that by snipping what follows I will forget about it?  Why
are such a cowardly, lying, devious little cunt?

You:

> H:  T = T1 + T2 + T3 + ....
>      where each Ti is in a collection K of formal systems (K isn't
>      necessarily finite).
>      .
> C1: Inconsistent(T) <=> (There exists a Ti: Inconsistent(Ti)).
> C2: Consistent(T)   <=> (For _any given_ Ti: Consistent(Ti)).

> Proof: The proof for C1 or C2 is trivial and taken for granted here.

Me:
Really?  If T = T1 + T2 means that the predicates (etc) of T is the
union of those of T1 and T2 and the axioms of T is the union of those of
T1 and T2, and T is closed under logical consequence; then it's obvious
that T can be inconsistent though both T1 and T2 are consistent.  If
that's not what you mean by +, you need to say so.

And when you done that, you can deal with the long outstanding issues of
the interpretation of '=', the number of $\in$'s that set theory needs,
'x = x' always being an axiom of FOL= theories, and so on.

Do you think that these things go away just because you ignore them?  Do
you think that just because you insist ("Again, _WHY_ ?"), like a
will forget all the points that you have left unanswered?

Have you read G\"odel's paper yet?  No.  Or any other account of
G\"odel's incompleteness theorem?  No.  And will you continue to hold

You are truly stupid.  There is an easy way out of your difficulties.
First, admit that you know nothing about the formalization of "the" and
wish to give up on it.  Then just say: "I also wish to withdraw my
claims about T = T1 + T2, the interpretation of '=', the number of
$\in$'s that set theory needs, 'x = x' being an axiom, etc, etc."
Unfortunately you are too devious and dishonest to do so.  Do you think
people haven't noticed, or will just forget?

--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting