Discussion:
Refuting Incompleteness and Undefinability Version(12) (World class expert coaching)
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peteolcott
2018-11-05 02:00:01 UTC
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A world class expert provided some coaching. They have published very much
in the field of Incompleteness and many related fields.

They changed this:
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))

into this:
∀F (F ∈ Formal_Systems & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)

I realized that Q is not needed if the following expression evaluates to False:
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))

The following analysis seems to refute Gödel 1931 Incompleteness as long as
the term "satisfiable" is interpreted using the conventional meanings of the
symbols within symbolic logic.

If G was Provable in F this contradicts its assertion: G is not Provable in F
If ~G was Provable in F this contradicts its assertion: G is Provable in F.
Since G is neither Provable nor Refutable in F it forms a Gödel sentence in F.

Because G is not satisfiable in any Formal System F, the Gödel sentence does not exist.

Copyright 2018 Pete Olcott
peteolcott
2018-11-05 02:07:26 UTC
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Post by peteolcott
A world class expert provided some coaching. They have published very much
in the field of Incompleteness and many related fields.
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))
L(F) means the language of formal system F.
Post by peteolcott
∀F (F ∈ Formal_Systems  & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
The following analysis seems to refute Gödel 1931 Incompleteness as long as
the term "satisfiable" is interpreted using the conventional meanings of the
symbols within symbolic logic.
If G was Provable in F this contradicts its assertion:  G is not Provable in F
If ~G was Provable in F this contradicts its assertion:  G is Provable in F.
Since G is neither Provable nor Refutable in F it forms a Gödel sentence in F.
Because G is not satisfiable in any Formal System F, the Gödel sentence does not exist.
Copyright 2018 Pete Olcott
Franz Gnaedinger
2018-11-05 07:47:22 UTC
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Post by peteolcott
Copyright 2018 Pete Olcott
Peter Olcott knows the absolute and complete and total truth, he is the author
of life and creator of life, he has hundred reasons to believe that he is God,
he creates our future minds in order that we can go on existing, he is both
a human being and God, he is the one Creator of the Universe (claims he made
in sci.lang). He proves Goedel wrong with word magic, but as he can't bamboozle
those who understand modern mathematical logic he applies the cancer strategy:
multiply multiply multiply, start ever more parallel threads unti the immune
system of a group collapses.
Arnaud Fournet
2018-11-05 14:10:42 UTC
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Post by peteolcott
A world class expert provided some coaching. They have published very much
in the field of Incompleteness and many related fields.
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))
∀F (F ∈ Formal_Systems & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
The following analysis seems to refute Gödel 1931 Incompleteness as long as
the term "satisfiable" is interpreted using the conventional meanings of the
symbols within symbolic logic.
If G was Provable in F this contradicts its assertion: G is not Provable in F
If ~G was Provable in F this contradicts its assertion: G is Provable in F.
Since G is neither Provable nor Refutable in F it forms a Gödel sentence in F.
Because G is not satisfiable in any Formal System F, the Gödel sentence does not exist.
Copyright 2018 Pete Olcott
ah, a new metastasis of Péter la Crotte garbage.
HOLY GHOST
2018-11-05 14:25:04 UTC
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[snip rant]
Force (graviton) = c^4 / Gravitational constant
Gravitational constant = c^4 / Force (graviton)

F = c^4 / G
G = c^4 / F

HOLY GHOST
peteolcott
2018-11-05 15:51:50 UTC
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sci.lang removed
sci.lang added back in.

Refuting Tarski / Gödel validates my ∀x True(x).
A complete and consistent True(x) anchors Truth Conditional Semantics.
Truth Conditional Semantics provides the basis for formalizing natural language.

https://academic.oup.com/jos/pages/About
https://academic.oup.com/jos/search-results?page=1&q=truth%20condition&fl_SiteID=5212&SearchSourceType=1&allJournals=1
Post by peteolcott
A world class expert provided some coaching. They have published very much
Does he or she have a name?
Post by peteolcott
in the field of Incompleteness and many related fields.
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))
L(F) means the language of formal system F.
∀F (F ∈ Formal_Systems  & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
The following analysis seems to refute Gödel 1931 Incompleteness as long as
Does he or she know that you have "refuted" the incompleteness theorem?
All that I had them do is verify that my formalized simplification of the
incompleteness theorem accurately represents a correct simplification of the
original theorem.

As long as my formalized simplification correctly sums up the essence of
the original theorem then refuting the simplification refutes the original
theorem by analogy.

The only semantic change that they made is the restriction that F must be
at least as expressive as Q. All of the other changes are purely syntactic,
making what I am saying easier to understand by using existing conventions,
yet not changing the meanings that I am conveying.
Post by peteolcott
the term "satisfiable" is interpreted using the conventional meanings of the
symbols within symbolic logic.
If G was Provable in F this contradicts its assertion:  G is not Provable in F
If ~G was Provable in F this contradicts its assertion:  G is Provable in F.
Since G is neither Provable nor Refutable in F it forms a Gödel sentence in F.
Because G is not satisfiable in any Formal System F, the Gödel sentence does not exist.
Copyright 2018 Pete Olcott
peteolcott
2018-11-05 16:42:39 UTC
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Post by peteolcott
A world class expert provided some coaching. They have published very much
in the field of Incompleteness and many related fields.
∀F ∈ Formal_Systems (∃G ∈ F (G ↔ ∃Γ ⊆ F ~(Γ ⊢ G)))
∀F (F ∈ Formal_Systems & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))
Your "world class expert" made an error. This formula is missing the parentheses needed to correctly mark the scope of the universal quantifier. As written, it only scopes over the antecedent, leaving the various instances of F in the consequent unbound.
Here is their cut-and-paste full reply:

We need to distinguish the language of formal system L(F) and the formal system F (often equated with the set of its theorems). Distinct systems may share the same language.

So the correct formalization would be something like:

∀F (F ∈ Formal_Systems & Q ⊆ F) → ∃G ∈ L(F) (G ↔ ~(F ⊢ G))

Q here is Robinson Arithmetic (the theorem fails for some weaker formal systems)

So does my reformulated adaptation of their reformulation have correct scoping?
∃F ∈ Formal_Systems ∃G ∈ L(F) (G ↔ ~(F ⊢ G))

Or do I need to say it this way?
∃F ∈ Formal_Systems (∃G ∈ L(F) (G ↔ ~(F ⊢ G)))
Jeff Barnett
2018-11-08 21:59:47 UTC
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peteolcott wrote on 11/8/2018 12:29 PM:
[CRAP FLUSHED]
As soon as my current reasoning has been sufficiently validated I will
have passed this credibility threshold to work with him.
I take the above to mean you are currently and, likely permanently
unemployed. If you trotted this nonsense in front of someone who
expected some legit work from you, it would be like igniting a fuse cap
in a dynamite factory.

Let's look at that patent you so proudly exhibited as an example of what
your mind could do: It was of interest to no one, it badly solved a
fairly trivial problem (reading a known font), and being excessively
complicated for no good reason.

You believe the programming language, C, is sufficiently formal to
codify all the universe's knowledge. Since one can't even write a
correctly behaving C program without specifying the compiler, it is
probably the world's worst choice.

Oh, by the way, for those wondering about the "him" in the "... to work
with him." in the replied-to text, it's Doug Lenat. I wonder if he knows
that his name and reputation are being bandied about by our resident
lunatic?
--
Jeff Barnett
peteolcott
2018-11-09 05:15:21 UTC
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       [CRAP FLUSHED]
As soon as my current reasoning has been sufficiently validated I will
have passed this credibility threshold to work with him.
I take the above to mean you are currently and, likely permanently unemployed. If you trotted this nonsense in front of someone who expected some legit work from you, it would be like igniting a fuse cap in a dynamite factory.
Let's look at that patent you so proudly exhibited as an example of what your mind could do: It was of interest to no one, it badly solved a fairly trivial problem (reading a known font), and being excessively complicated for no good reason.
You believe the programming language, C, is sufficiently formal to codify all the universe's knowledge. Since one can't even write a correctly behaving C program without specifying the compiler, it is probably the world's worst choice.
Oh, by the way, for those wondering about the "him" in the "... to work with him." in the replied-to text, it's Doug Lenat. I wonder if he knows that his name and reputation are being bandied about by our resident lunatic?
I think that I remember that you are technically competent, there is no evidence of that here.

Ad hominem is the first resort of the totally incompetent, and apparently the last resort of

the competent when they are stuck in rebuttal mode and encounter the unequivocally irrefutable.

One very excellent reviewer here got stuck in ad hominem for a short while until I made the challenge:

TRY AND FIND ANY SPECIFIC ERROR IN THE GIST OF ANY OF MY RECENT REASONING.

http://liarparadox.org/index.php/2018/11/09/simplifying-the-tarski-undefinability-sentence/

http://liarparadox.org/index.php/2018/11/04/godels-1931-incompleteness-theorem-as-simple-as-possible/
Jeff Barnett
2018-11-09 05:26:05 UTC
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Post by peteolcott
        [CRAP FLUSHED]
As soon as my current reasoning has been sufficiently validated I will
have passed this credibility threshold to work with him.
I take the above to mean you are currently and, likely permanently
unemployed. If you trotted this nonsense in front of someone who
expected some legit work from you, it would be like igniting a fuse
cap in a dynamite factory.
Let's look at that patent you so proudly exhibited as an example of
what your mind could do: It was of interest to no one, it badly solved
a fairly trivial problem (reading a known font), and being excessively
complicated for no good reason.
You believe the programming language, C, is sufficiently formal to
codify all the universe's knowledge. Since one can't even write a
correctly behaving C program without specifying the compiler, it is
probably the world's worst choice.
Oh, by the way, for those wondering about the "him" in the "... to
work with him." in the replied-to text, it's Doug Lenat. I wonder if
he knows that his name and reputation are being bandied about by our
resident lunatic?
I think that I remember that you are technically competent, there is no
evidence of that here.
Ad hominem is the first resort of the totally incompetent, and
apparently the last resort of
the competent when they are stuck in rebuttal mode and encounter the
unequivocally irrefutable.
One very excellent reviewer here got stuck in ad hominem for a short
TRY AND FIND ANY SPECIFIC ERROR IN THE GIST OF ANY OF MY RECENT REASONING.
http://liarparadox.org/index.php/2018/11/09/simplifying-the-tarski-undefinability-sentence/
http://liarparadox.org/index.php/2018/11/04/godels-1931-incompleteness-theorem-as-simple-as-possible/
Since you typically revise your documents daily or faster, just wait
until the 17th copy of each is released then run a diff. You don't need
my help or anyone else's to catalogue zillions of inconsistencies and
mistakes. I presume you know what I mean by diff. By the way, since you
continuously come to wrong conclusions in everything you write we know
there are errors within. N.B. That is the argument you use when you
refuse to read the things you criticize, I'll use it on you. Since you
have derived nonsense there are errors and you need to learn to policy
your own pile of poop.
--
Jeff Barnett
peteolcott
2018-11-09 05:27:50 UTC
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You believe the programming language, C, is sufficiently formal to codify all the universe's knowledge. Since one can't even write a correctly behaving C program without specifying the compiler, it is probably the world's worst choice.
I believe that a slightly adapted version of the YACC BNF provided on
the first page of this link is sufficient to encode any HOL expression
which can encode almost all of the knowledge in the world.

https://www.researchgate.net/publication/317953772_Provability_with_Minimal_Type_Theory

Doug Lenat's team is using CycL:
http://www.cyc.com/documentation/ontologists-handbook/

I still don't know how to compare two arbitrary length finite strings
of actual digits in any tree structured knowledge ontology.

Integers are represented in lambda calculus by the Church numerals.
Zero is represented by the lambda expression λfx.x, and other integers
are generated by the applying successor function λnfx.f(nfx) to an
existing integer n. In other words, n is represented by λfx.f(f(...f(fx)..))
where there are n fs on the right.

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