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Science Forum Index » Logic Forum » Newberry's Theses
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| Newberry |
 Posted: Sun Apr 20, 2008 6:22 pm |
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1. Mathematics (excluding geometry) is analytic.
2. You cannot solve a paradox without first acknowledging that there
is one.
3. Goedel's result IS paradoxical.
4. The solution of the paradox consists of constructing a SEMANTICALLY
complete system of logic/arithmetic.
5. Nobody ever proved that any system capable of encoding all of
arithmetic must be semantically incomplete.
6. The so called "vacuously true" formulae are neither true nor false. |
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| Rupert |
| Posted: Sun Apr 20, 2008 11:06 pm |
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On Apr 20, 9:22 pm, Newberry <newberr...@gmail.com> wrote:
Quote: 1. Mathematics (excluding geometry) is analytic.
2. You cannot solve a paradox without first acknowledging that there
is one.
3. Goedel's result IS paradoxical.
Tell us a bit more about this one.
Quote: 4. The solution of the paradox consists of constructing a SEMANTICALLY
complete system of logic/arithmetic.
5. Nobody ever proved that any system capable of encoding all of
arithmetic must be semantically incomplete.
6. The so called "vacuously true" formulae are neither true nor false. |
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| Aatu Koskensilta |
| Posted: Mon Apr 21, 2008 3:29 am |
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On 2008-04-21, in sci.logic, Newberry wrote:
Quote: 3. Goedel's result IS paradoxical.
What is paradoxical about Godel's results?
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus |
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| Newberry |
| Posted: Mon Apr 21, 2008 3:57 am |
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On Apr 21, 1:29 am, Aatu Koskensilta <aatu.koskensi...@xortec.fi>
wrote:
Quote: On 2008-04-21, in sci.logic, Newberry wrote:
3. Goedel's result IS paradoxical.
What is paradoxical about Godel's results?
If you can figure out that the senetnce is true you must have computed
it somehow. And if T(G) then G. |
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| Newberry |
| Posted: Mon Apr 21, 2008 3:59 am |
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On Apr 21, 3:59 am, David C. Ullrich <dullr...@sprynet.com> wrote:
Quote: On Sun, 20 Apr 2008 21:22:33 -0700 (PDT), Newberry
newberr...@gmail.com> wrote:
1. Mathematics (excluding geometry) is analytic.
The fact that you exclude geometry shows you're confusing
geometry and physics. The Pythagorean Theorem does not
prove anything about what's going to happen when you measure
the sides of triangles in the actual physical world.
I do not claim anything about geometry. In fact I have explicitly
excluded it from any claims.
Quote: 2. You cannot solve a paradox without first acknowledging that there
is one.
3. Goedel's result IS paradoxical.
4. The solution of the paradox consists of constructing a SEMANTICALLY
complete system of logic/arithmetic.
5. Nobody ever proved that any system capable of encoding all of
arithmetic must be semantically incomplete.
6. The so called "vacuously true" formulae are neither true nor false.
David C. Ullrich |
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| Newberry |
| Posted: Mon Apr 21, 2008 4:03 am |
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On Apr 21, 5:52 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Quote: Newberry <newberr...@gmail.com> writes:
1. Mathematics (excluding geometry) is analytic.
In what sense do you mean this?
(1) Every axiom of mathematics (except geometrical axioms) are
analytic truths.
What is "axiom of mathematics"?
Quote:
(2) Every theorem is really a statement "From these axioms, P follows"
and such statements are analytic truths.
If (2), then geometry is no less analytic than any other mathematics.
So, perhaps you mean (1). Now, ZFC is a mathematical theory and
hence,
According to Newberry, the axiom of choice is an analytic truth.
Is this correct?
--
"They are anti-mathematicians, evil incarnate, dedicated to undermining
intellectual development in this area. If you never thought such
people could actually exist, outside of myths or legends, welcome to
the real world." --James S Harris on evil incarnate's Usenet presence |
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| Ross A. Finlayson |
| Posted: Mon Apr 21, 2008 4:20 am |
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Aatu Koskensilta wrote:
Quote: On 2008-04-21, in sci.logic, Newberry wrote:
3. Goedel's result IS paradoxical.
What is paradoxical about Godel's results?
How about, incompleteness says every system (strong enough to have
natural arithmetic) is inconsistent or incomplete, but each model of
those is a model of a Goedel theory where all the sentences are "this
sentence is provable", but then there's a sentence "this sentence is
provable", that is not one of those. That is, there's only one theorem
in the Goedel theory, and it's also outside the Goedel theory.
Self-referentially, that system proves, via the other form, its own
consistency in being incomplete. Then, it is thus inconsistent and
incomplete.
That's not very exact, basically Goedel's theory of theories is
inconsistent, or incomplete. Where it's incomplete, then there are true
statements about the objects of theory that don't include that all of
them are necessarily incomplete, because otherwise Goedel's theory of
theories would be complete, thus, by his own reckoning, inconsistent.
Ross F. |
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| elsiemelsi |
| Posted: Mon Apr 21, 2008 4:30 am |
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Aatu says
Quote: 3. Goedel's result IS paradoxical.
What is paradoxical about Godel's results?
--
i say
colin leslie dean has shown godel is paradoxical for 3 reasons
you obiviously after all this Aatu not even read deans book
http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
here is a tit bit
quote
GODEL IS SELF-CONTRADICTORY
But here is a contradiction Godel must prove that a system cannot be
proven to be consistent based upon the premise that the logic he uses must
be consistent . If the logic he uses is not consistent then he cannot
make a proof that is consistent. So he must assume that his logic is
consistent so he can make a proof of the impossibility of proving a system
to be consistent. But if his proof is true then he has proved that the
logic he uses to make the proof must be consistent, but his proof proves
that this cannot be done
--
Message posted using http://www.talkaboutscience.com/group/sci.logic/
More information at http://www.talkaboutscience.com/faq.html |
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| David C. Ullrich |
| Posted: Mon Apr 21, 2008 5:59 am |
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On Sun, 20 Apr 2008 21:22:33 -0700 (PDT), Newberry
<newberryxy@gmail.com> wrote:
Quote: 1. Mathematics (excluding geometry) is analytic.
The fact that you exclude geometry shows you're confusing
geometry and physics. The Pythagorean Theorem does not
prove anything about what's going to happen when you measure
the sides of triangles in the actual physical world.
Quote: 2. You cannot solve a paradox without first acknowledging that there
is one.
3. Goedel's result IS paradoxical.
4. The solution of the paradox consists of constructing a SEMANTICALLY
complete system of logic/arithmetic.
5. Nobody ever proved that any system capable of encoding all of
arithmetic must be semantically incomplete.
6. The so called "vacuously true" formulae are neither true nor false.
David C. Ullrich |
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| Jesse F. Hughes |
| Posted: Mon Apr 21, 2008 7:52 am |
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Newberry <newberryxy@gmail.com> writes:
Quote: 1. Mathematics (excluding geometry) is analytic.
In what sense do you mean this?
(1) Every axiom of mathematics (except geometrical axioms) are
analytic truths.
(2) Every theorem is really a statement "From these axioms, P follows"
and such statements are analytic truths.
If (2), then geometry is no less analytic than any other mathematics.
So, perhaps you mean (1). Now, ZFC is a mathematical theory and
hence,
According to Newberry, the axiom of choice is an analytic truth.
Is this correct?
--
"They are anti-mathematicians, evil incarnate, dedicated to undermining
intellectual development in this area. If you never thought such
people could actually exist, outside of myths or legends, welcome to
the real world." --James S Harris on evil incarnate's Usenet presence |
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| Aatu Koskensilta |
| Posted: Mon Apr 21, 2008 9:21 am |
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On 2008-04-21, in sci.logic, Newberry wrote:
Quote: If you can figure out that the senetnce is true you must have computed
it somehow. And if T(G) then G.
What does it mean to "compute" a sentence?
--
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus |
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| Jesse F. Hughes |
| Posted: Mon Apr 21, 2008 9:23 am |
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Newberry <newberryxy@gmail.com> writes:
Quote: On Apr 21, 5:52 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
Newberry <newberr...@gmail.com> writes:
1. Mathematics (excluding geometry) is analytic.
In what sense do you mean this?
(1) Every axiom of mathematics (except geometrical axioms) are
analytic truths.
What is "axiom of mathematics"?
An axiom in some field of mathematics, I suppose. I admit it seems
pretty implausible to claim that every axiom in every field of
mathematics (except geometry) is analytic. But I'm simply trying to
make sense of your first thesis.
What did you mean when you claimed that "mathematics is analytic"?
Quote: (2) Every theorem is really a statement "From these axioms, P follows"
and such statements are analytic truths.
If (2), then geometry is no less analytic than any other mathematics.
So, perhaps you mean (1). Now, ZFC is a mathematical theory and
hence,
According to Newberry, the axiom of choice is an analytic truth.
Is this correct?
No comment?
--
"I'm a very well-educated, successful, intelligent person. This is
insane to me that I have an armed guard outside my door when I've
cooperated with everything other than the whole solitary-confinement-
in-Italy thing." --A. Speaker, on the whole T.B.-quarantined thing |
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| Daryl McCullough |
| Posted: Mon Apr 21, 2008 11:37 am |
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Newberry says...
Quote: 1. Mathematics (excluding geometry) is analytic.
2. You cannot solve a paradox without first acknowledging that there
is one.
The flip side of this is that claiming that there is a paradox
when there provably is not is a sign of a lack of analytic skills.
Quote: 3. Goedel's result IS paradoxical.
No, it certainly is not.
--
Daryl McCullough
Ithaca, NY |
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| Daryl McCullough |
| Posted: Mon Apr 21, 2008 11:50 am |
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Newberry says...
Quote:
On Apr 21, 1:29=A0am, Aatu Koskensilta <aatu.koskensi...@xortec.fi
wrote:
On 2008-04-21, in sci.logic, Newberry wrote:
3. Goedel's result IS paradoxical.
What is paradoxical about Godel's results?
If you can figure out that the senetnce is true you must have computed
it somehow. And if T(G) then G.
What is paradoxical about that?
For some reason, you seem to have never understood
what Godel's theorem says, even though you make grand
claims about it. Godel starts with some
r.e. theory T axiomatizing arithmetic (for example,
T could be Peano Arithmetic). He constructs a statement
G in the language of T such that
G is true (as a statement about numbers)
<-> G is not provable by T
Godel never claimed that G was unprovable,
he claimed that T cannot prove G. (Unless
T is inconsistent: If T is consistent, then
G is true. If T is not consistent, then G is
false.)
There is nothing paradoxical here.
T does not prove G, but
T + Con(T) proves G
(where Con(T) is the statement
of arithmetic encoding the claim
that T is consistent).
--
Daryl McCullough
Ithaca, NY |
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| elsiemelsi |
| Posted: Mon Apr 21, 2008 12:56 pm |
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Daryl McCullough
Ithaca, NY says
"Godel never claimed that G was unprovable,
he claimed that T cannot prove G. (Unless
T is inconsistent: If T is consistent, then
G is true."
i say
colin leslie dean points out godel cannot tell us what makes a statement
true
thus his theorem is meaningless
peter smith
said
quote
"Gödel didn't rely on the notion
of truth"
and
http://assets.cambridge.org/97805218/57840/excerpt/9780521857840_excerpt.pdf
"Godel did is find a general method that enabled him to take any theory T
strong enough to capture a modest amount of basic arithmetic and
construct
a corresponding arithmetical sentence GT which encodes the claim ‘The
sentenceGT itself is unprovable in theory T’. So G T is true if and
only
if T can’t prove it
If we can locate GT
, a Godel sentence for our favourite nicely ax-
iomatized theory of arithmetic T, and can argue that G T is
true-but-unprovable,"
dean says if godel cant tell us what true is
then his theorem is meaningless nonsence
--
Message posted using http://www.talkaboutscience.com/group/sci.logic/
More information at http://www.talkaboutscience.com/faq.html |
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