On 5/7/23 1:43 PM, olcott wrote:
> Gödel's proof it relies upon a definition of incompleteness that
> requires formal systems to be able to prove self-contradictory
> expressions of language.
>
> > Kurt Gödel's incompleteness theorem demonstrates that mathematics
> > contains true statements that cannot be proved. His proof achieves
> > this by constructing paradoxical mathematical statements. To see how
> > the proof works, begin by considering the liar's paradox: "This
> > statement is false." This statement is true if and only if it is
> > false, and therefore it is neither true nor false.
> >
> > Now let's consider "This statement is unprovable." If it is provable,
> > then we are proving a falsehood, which is extremely unpleasant and is
> > generally assumed to be impossible. The only alternative left is that
> > this statement is unprovable. Therefore, it is in fact both true and
> > unprovable. Our system of reasoning is incomplete, because some truths
> > are unprovable.
> >
> > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>
> "14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof." (Gödel 1931:40)
>
> Does it make sense that formal systems are required to prove
> epistemological antinomies (AKA self-contradictory expressions) or
> should these expressions be rejected as non sequitur?
>

Note, Consistant Formal Systems will reject actual epistemological
antinomies as non-Truth Bearing, and thus your premise is incorrect.

Formal Systems, to be consistent, only need to be able to prove every
True statement, and disprove every False statement, since BY DEFINITION,
an epistemological antinomy can neither be True or False, a Formal Logic
system doesn't need (and in fact CAN'T) prove or disprove an
epistemological antinomy, because such a statement won't be a Truth
Bearer, and thus neither True or False.

The thing you seem to be too stupid to understand is that Godel doesn't
use the Liar's paradox in its paradox form where it IS an
epistemological antinomy, but has transformed it from being about the
truth of the statement (and thus the antinomy) to a statement about the
provability of the statement, which breaks the paradox.

The

> *The valid/sound deductive inference model seems to think that latter:*
> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C)  ↔ True(F, C))
> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔ NonSequitur(F, C))

Wrong, unless you mean COMPETE FORMAL SYSTEM,

Replace the "Prove" symbol, with the "Establishes" relationship, which
changes the requirement from a finite set of steps, to any (possibly
infinite) set of sets, and the statment holds for any formal system.

C is True in F, if there is a (possibly infinite) sequence of steps in F
from its Truth Makers

You are missing the fact that it is shown that it is possible for a
statement C to be TRUE, because there is a (possibly infinte) chain of
semantic connections from the Truth Makers of the system. through valid
logical inferances, to the statement C, but there might not be a valid
PROOF of the statement, which is a FINITE chain of semantic connections
from the Truth Makers of the system through valid logical inferences.

>
> *Non Sequitur*
> https://en.wikipedia.org/wiki/Formal_fallacy)
> In philosophy, a formal fallacy, deductive fallacy, logical fallacy or
> non sequitur[1] (Latin for "it does not follow")
>
> By simply disallowing symbolic logic to diverge from the valid/sound
> deductive inference model Gödel Incompleteness and Tarski Undefinability
> cease to exist.

Nope, because it DOESN'T, but only because you don't understand what a
sound or valid proof actually is, or the defintion of Truth.

>
> *Gödel, Kurt 1931*
> *On Formally Undecidable Propositions of Principia Mathematica*
> *And Related Systems*
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf)
>

Which just shows that you don't understand what you are reading.

Please point out to the step where he used an UNSOUND or INVALID logical
step. Not just where he says words that you disagree with, but performs
an actual logical step that is incorrect.

Your silence on this shows that you don't have a leg to stand on because
you are the one that doesn't hold to sound and valid logical inference
rules.

On 5/7/2023 3:00 PM, Richard Damon wrote:
> On 5/7/23 1:43 PM, olcott wrote:
>> Gödel's proof it relies upon a definition of incompleteness that
>> requires formal systems to be able to prove self-contradictory
>> expressions of language.
>>
>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>  > contains true statements that cannot be proved. His proof achieves
>>  > this by constructing paradoxical mathematical statements. To see how
>>  > the proof works, begin by considering the liar's paradox: "This
>>  > statement is false." This statement is true if and only if it is
>>  > false, and therefore it is neither true nor false.
>>  >
>>  > Now let's consider "This statement is unprovable." If it is provable,
>>  > then we are proving a falsehood, which is extremely unpleasant and is
>>  > generally assumed to be impossible. The only alternative left is that
>>  > this statement is unprovable. Therefore, it is in fact both true and
>>  > unprovable. Our system of reasoning is incomplete, because some truths
>>  > are unprovable.
>>  >
>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>
>> "14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof." (Gödel 1931:40)
>>
>> Does it make sense that formal systems are required to prove
>> epistemological antinomies (AKA self-contradictory expressions) or
>> should these expressions be rejected as non sequitur?
>>
>
> Note, Consistant Formal Systems will reject actual epistemological
> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>
> Formal Systems, to be consistent, only need to be able to prove every
> True statement, and disprove every False statement, since BY DEFINITION,
> an epistemological antinomy can neither be True or False, a Formal Logic
> system doesn't need (and in fact CAN'T) prove or disprove an
> epistemological antinomy, because such a statement won't be a Truth
> Bearer, and thus neither True or False.
>
> The thing you seem to be too stupid to understand is that Godel doesn't
> use the Liar's paradox in its paradox form where it IS an
> epistemological antinomy, but has transformed it from being about the
> truth of the statement (and thus the antinomy) to a statement about the
> provability of the statement, which breaks the paradox.
>
> The
>
>
>> *The valid/sound deductive inference model seems to think that latter:*
>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C)  ↔ True(F, C))
>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔ NonSequitur(F,
>> C))
>
> Wrong, unless you mean COMPETE FORMAL SYSTEM,
>
> Replace the "Prove" symbol, with the "Establishes" relationship, which
> changes the requirement from a finite set of steps, to any (possibly
> infinite) set of sets, and the statment holds for any formal system.
>
> C is True in F, if there is a (possibly infinite) sequence of steps in F
> from its Truth Makers
>
> You are missing the fact that it is shown that it is possible for a
> statement C to be TRUE, because there is a (possibly infinte) chain of
> semantic connections from the Truth Makers of the system. through valid
> logical inferances, to the statement C, but there might not be a valid
> PROOF of the statement, which is a FINITE chain of semantic connections
> from the Truth Makers of the system through valid logical inferences.
>
>>
>> *Non Sequitur*
>> https://en.wikipedia.org/wiki/Formal_fallacy)
>> In philosophy, a formal fallacy, deductive fallacy, logical fallacy or
>> non sequitur[1] (Latin for "it does not follow")
>>
>> By simply disallowing symbolic logic to diverge from the valid/sound
>> deductive inference model Gödel Incompleteness and Tarski Undefinability
>> cease to exist.
>
> Nope, because it DOESN'T, but only because you don't understand what a
> sound or valid proof actually is, or the defintion of Truth.
>
>>
>> *Gödel, Kurt 1931*
>> *On Formally Undecidable Propositions of Principia Mathematica*
>> *And Related Systems*
>>
>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf)
>>
>
> Which just shows that you don't understand what you are reading.
>

Try and find an example of this.

Tarski used the actual Liar Paradox to derive his comparable proof.
https://plato.stanford.edu/entries/goedel-incompleteness/#TarTheUndTru

> Please point out to the step where he used an UNSOUND or INVALID logical
> step. Not just where he says words that you disagree with, but performs
> an actual logical step that is incorrect.
>
> Your silence on this shows that

You have not yet understood the prerequisites.

> you don't have a leg to stand on because
> you are the one that doesn't hold to sound and valid logical inference
> rules.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/7/23 10:35 PM, olcott wrote:
> On 5/7/2023 3:00 PM, Richard Damon wrote:
>> On 5/7/23 1:43 PM, olcott wrote:
>>> Gödel's proof it relies upon a definition of incompleteness that
>>> requires formal systems to be able to prove self-contradictory
>>> expressions of language.
>>>
>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>  > contains true statements that cannot be proved. His proof achieves
>>>  > this by constructing paradoxical mathematical statements. To see how
>>>  > the proof works, begin by considering the liar's paradox: "This
>>>  > statement is false." This statement is true if and only if it is
>>>  > false, and therefore it is neither true nor false.
>>>  >
>>>  > Now let's consider "This statement is unprovable." If it is provable,
>>>  > then we are proving a falsehood, which is extremely unpleasant and is
>>>  > generally assumed to be impossible. The only alternative left is that
>>>  > this statement is unprovable. Therefore, it is in fact both true and
>>>  > unprovable. Our system of reasoning is incomplete, because some
>>> truths
>>>  > are unprovable.
>>>  >
>>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>
>>> "14 Every epistemological antinomy can likewise be used for a similar
>>> undecidability proof." (Gödel 1931:40)
>>>
>>> Does it make sense that formal systems are required to prove
>>> epistemological antinomies (AKA self-contradictory expressions) or
>>> should these expressions be rejected as non sequitur?
>>>
>>
>> Note, Consistant Formal Systems will reject actual epistemological
>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>
>> Formal Systems, to be consistent, only need to be able to prove every
>> True statement, and disprove every False statement, since BY
>> DEFINITION, an epistemological antinomy can neither be True or False,
>> a Formal Logic system doesn't need (and in fact CAN'T) prove or
>> disprove an epistemological antinomy, because such a statement won't
>> be a Truth Bearer, and thus neither True or False.
>>
>> The thing you seem to be too stupid to understand is that Godel
>> doesn't use the Liar's paradox in its paradox form where it IS an
>> epistemological antinomy, but has transformed it from being about the
>> truth of the statement (and thus the antinomy) to a statement about
>> the provability of the statement, which breaks the paradox.
>>
>> The
>>
>>
>>> *The valid/sound deductive inference model seems to think that latter:*
>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C)  ↔ True(F, C))
>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔
>>> NonSequitur(F, C))
>>
>> Wrong, unless you mean COMPETE FORMAL SYSTEM,
>>
>> Replace the "Prove" symbol, with the "Establishes" relationship, which
>> changes the requirement from a finite set of steps, to any (possibly
>> infinite) set of sets, and the statment holds for any formal system.
>>
>> C is True in F, if there is a (possibly infinite) sequence of steps in
>> F from its Truth Makers
>>
>> You are missing the fact that it is shown that it is possible for a
>> statement C to be TRUE, because there is a (possibly infinte) chain of
>> semantic connections from the Truth Makers of the system. through
>> valid logical inferances, to the statement C, but there might not be a
>> valid PROOF of the statement, which is a FINITE chain of semantic
>> connections from the Truth Makers of the system through valid logical
>> inferences.
>>
>>>
>>> *Non Sequitur*
>>> https://en.wikipedia.org/wiki/Formal_fallacy)
>>> In philosophy, a formal fallacy, deductive fallacy, logical fallacy
>>> or non sequitur[1] (Latin for "it does not follow")
>>>
>>> By simply disallowing symbolic logic to diverge from the valid/sound
>>> deductive inference model Gödel Incompleteness and Tarski Undefinability
>>> cease to exist.
>>
>> Nope, because it DOESN'T, but only because you don't understand what a
>> sound or valid proof actually is, or the defintion of Truth.
>>
>>>
>>> *Gödel, Kurt 1931*
>>> *On Formally Undecidable Propositions of Principia Mathematica*
>>> *And Related Systems*
>>>
>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf)
>>>
>>
>> Which just shows that you don't understand what you are reading.
>>
>
> Try and find an example of this.

What DO you correctly understand. You haven't shown ANY actual knowledge
of the paper, but only the ability to pull pieces out of it totally out
of context.

>
> Tarski used the actual Liar Paradox to derive his comparable proof.
> https://plato.stanford.edu/entries/goedel-incompleteness/#TarTheUndTru

Nope, he DERIVES the Liar Paradox as a statement that must be true if a
"Definition of Truth" per his rules exists (that is, if there is a
deterministic method that always determines in a finite number of
operations if a given statement is true or false).

Note that he says what he used to get to that step, it isn't a "premise"
of his proof, it is a conclusion derived as part of a proof by
contradiction, which you don't seem to understand as even being possible.

That the assumption of a definition exists leads to an impossible
conclusion shows that such a definition can not exist.

>
>> Please point out to the step where he used an UNSOUND or INVALID
>> logical step. Not just where he says words that you disagree with, but
>> performs an actual logical step that is incorrect.
>>
>> Your silence on this shows that
>
> You have not yet understood the prerequisites.

What Prerequisites? That we accept your flawed logic?

YOU are the one making the claim, so YOU have the burden of proof, and
untill you provide it, the claim that you haven't established you claim
is correct, and it is also correct to call you claim that you HAVE
established it a LIE.

You are just showing that you don't understand how formal logic works.
If you want to claim the fundamental logic that it is based on is some
how flawed, you first need to actually demonstrate the actual error, and
then you need to show that your alternate "logic" can actualy perform in
the desired fields.

You have just failed to do any of that.

In fact, the mere fact that you are claiming to rely on an inappropriate
field of philosophy shows how off you are. Epistimoligy doesn't tell us
by what method things are ACTUALLY True or False, but talks about how
*WE* can *KNOW* if something is true of false.

Unless you are going to try to argue that if no one know the truth of
something, that thing doesn't actually HAVE a Truth value, the fact that
you are confusing Knowledge with Truth shows you are just too stupid to
understand what you are actually talking about.

>
>> you don't have a leg to stand on because you are the one that doesn't
>> hold to sound and valid logical inference rules.
>

On 5/7/2023 3:00 PM, Richard Damon wrote:
> On 5/7/23 1:43 PM, olcott wrote:
>> Gödel's proof it relies upon a definition of incompleteness that
>> requires formal systems to be able to prove self-contradictory
>> expressions of language.
>>
>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>  > contains true statements that cannot be proved. His proof achieves
>>  > this by constructing paradoxical mathematical statements. To see how
>>  > the proof works, begin by considering the liar's paradox: "This
>>  > statement is false." This statement is true if and only if it is
>>  > false, and therefore it is neither true nor false.
>>  >
>>  > Now let's consider "This statement is unprovable." If it is provable,
>>  > then we are proving a falsehood, which is extremely unpleasant and is
>>  > generally assumed to be impossible. The only alternative left is that
>>  > this statement is unprovable. Therefore, it is in fact both true and
>>  > unprovable. Our system of reasoning is incomplete, because some truths
>>  > are unprovable.
>>  >
>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>
>> "14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof." (Gödel 1931:40)
>>
>> Does it make sense that formal systems are required to prove
>> epistemological antinomies (AKA self-contradictory expressions) or
>> should these expressions be rejected as non sequitur?
>>
>
> Note, Consistant Formal Systems will reject actual epistemological
> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>

Try and find an example of this. (I pasted it in the wrong place)

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/7/2023 10:06 PM, Richard Damon wrote:
> On 5/7/23 10:35 PM, olcott wrote:
>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>> On 5/7/23 1:43 PM, olcott wrote:
>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>> requires formal systems to be able to prove self-contradictory
>>>> expressions of language.
>>>>
>>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>>  > contains true statements that cannot be proved. His proof achieves
>>>>  > this by constructing paradoxical mathematical statements. To see how
>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>  > statement is false." This statement is true if and only if it is
>>>>  > false, and therefore it is neither true nor false.
>>>>  >
>>>>  > Now let's consider "This statement is unprovable." If it is
>>>> provable,
>>>>  > then we are proving a falsehood, which is extremely unpleasant
>>>> and is
>>>>  > generally assumed to be impossible. The only alternative left is
>>>> that
>>>>  > this statement is unprovable. Therefore, it is in fact both true and
>>>>  > unprovable. Our system of reasoning is incomplete, because some
>>>> truths
>>>>  > are unprovable.
>>>>  >
>>>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>
>>>> "14 Every epistemological antinomy can likewise be used for a
>>>> similar undecidability proof." (Gödel 1931:40)
>>>>
>>>> Does it make sense that formal systems are required to prove
>>>> epistemological antinomies (AKA self-contradictory expressions) or
>>>> should these expressions be rejected as non sequitur?
>>>>
>>>
>>> Note, Consistant Formal Systems will reject actual epistemological
>>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>>
>>> Formal Systems, to be consistent, only need to be able to prove every
>>> True statement, and disprove every False statement, since BY
>>> DEFINITION, an epistemological antinomy can neither be True or False,
>>> a Formal Logic system doesn't need (and in fact CAN'T) prove or
>>> disprove an epistemological antinomy, because such a statement won't
>>> be a Truth Bearer, and thus neither True or False.
>>>
>>> The thing you seem to be too stupid to understand is that Godel
>>> doesn't use the Liar's paradox in its paradox form where it IS an
>>> epistemological antinomy, but has transformed it from being about the
>>> truth of the statement (and thus the antinomy) to a statement about
>>> the provability of the statement, which breaks the paradox.
>>>
>>> The
>>>
>>>
>>>> *The valid/sound deductive inference model seems to think that latter:*
>>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C)  ↔ True(F, C))
>>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
>>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔
>>>> NonSequitur(F, C))
>>>
>>> Wrong, unless you mean COMPETE FORMAL SYSTEM,
>>>
>>> Replace the "Prove" symbol, with the "Establishes" relationship,
>>> which changes the requirement from a finite set of steps, to any
>>> (possibly infinite) set of sets, and the statment holds for any
>>> formal system.
>>>
>>> C is True in F, if there is a (possibly infinite) sequence of steps
>>> in F from its Truth Makers
>>>
>>> You are missing the fact that it is shown that it is possible for a
>>> statement C to be TRUE, because there is a (possibly infinte) chain
>>> of semantic connections from the Truth Makers of the system. through
>>> valid logical inferances, to the statement C, but there might not be
>>> a valid PROOF of the statement, which is a FINITE chain of semantic
>>> connections from the Truth Makers of the system through valid logical
>>> inferences.
>>>
>>>>
>>>> *Non Sequitur*
>>>> https://en.wikipedia.org/wiki/Formal_fallacy)
>>>> In philosophy, a formal fallacy, deductive fallacy, logical fallacy
>>>> or non sequitur[1] (Latin for "it does not follow")
>>>>
>>>> By simply disallowing symbolic logic to diverge from the valid/sound
>>>> deductive inference model Gödel Incompleteness and Tarski
>>>> Undefinability
>>>> cease to exist.
>>>
>>> Nope, because it DOESN'T, but only because you don't understand what
>>> a sound or valid proof actually is, or the defintion of Truth.
>>>
>>>>
>>>> *Gödel, Kurt 1931*
>>>> *On Formally Undecidable Propositions of Principia Mathematica*
>>>> *And Related Systems*
>>>>
>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf)
>>>>
>>>
>>> Which just shows that you don't understand what you are reading.
>>>
>>
>> Try and find an example of this.
>
> What DO you correctly understand. You haven't shown ANY actual knowledge
> of the paper, but only the ability to pull pieces out of it totally out
> of context.
>
>>
>> Tarski used the actual Liar Paradox to derive his comparable proof.
>> https://plato.stanford.edu/entries/goedel-incompleteness/#TarTheUndTru
>
> Nope, he DERIVES the Liar Paradox as a statement that must be true if a
> "Definition of Truth" per his rules exists
You have Tarski correctly. Tarski rejects that truth can be correctly
formalized because he can't prove that a non-truth bearer is true.

That is like rejecting Geometry upon the failure to prove that a circle
is a square.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/7/23 11:40 PM, olcott wrote:
> On 5/7/2023 3:00 PM, Richard Damon wrote:
>> On 5/7/23 1:43 PM, olcott wrote:
>>> Gödel's proof it relies upon a definition of incompleteness that
>>> requires formal systems to be able to prove self-contradictory
>>> expressions of language.
>>>
>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>  > contains true statements that cannot be proved. His proof achieves
>>>  > this by constructing paradoxical mathematical statements. To see how
>>>  > the proof works, begin by considering the liar's paradox: "This
>>>  > statement is false." This statement is true if and only if it is
>>>  > false, and therefore it is neither true nor false.
>>>  >
>>>  > Now let's consider "This statement is unprovable." If it is provable,
>>>  > then we are proving a falsehood, which is extremely unpleasant and is
>>>  > generally assumed to be impossible. The only alternative left is that
>>>  > this statement is unprovable. Therefore, it is in fact both true and
>>>  > unprovable. Our system of reasoning is incomplete, because some
>>> truths
>>>  > are unprovable.
>>>  >
>>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>
>>> "14 Every epistemological antinomy can likewise be used for a similar
>>> undecidability proof." (Gödel 1931:40)
>>>
>>> Does it make sense that formal systems are required to prove
>>> epistemological antinomies (AKA self-contradictory expressions) or
>>> should these expressions be rejected as non sequitur?
>>>
>>
>> Note, Consistant Formal Systems will reject actual epistemological
>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>
>
> Try and find an example of this. (I pasted it in the wrong place)
>
>

Its definitional. In a formal system, a statement is only a member of
that system if it is either True or False. A statement is only part of a
formal system if it is established true or false in that system.

Since Truth is based on having a (possibly infinite) series of valid and
sound inferences from the Truth Makers of a system to the Statement (or
to its complement for falsehood), and a self-referential statement can
NEVER have all of its premises established, since it is one of them,
that can never happen.

On 5/7/23 11:45 PM, olcott wrote:
> On 5/7/2023 10:06 PM, Richard Damon wrote:
>> On 5/7/23 10:35 PM, olcott wrote:
>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>>> requires formal systems to be able to prove self-contradictory
>>>>> expressions of language.
>>>>>
>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>>>  > contains true statements that cannot be proved. His proof achieves
>>>>>  > this by constructing paradoxical mathematical statements. To see
>>>>> how
>>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>>  > statement is false." This statement is true if and only if it is
>>>>>  > false, and therefore it is neither true nor false.
>>>>>  >
>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>> provable,
>>>>>  > then we are proving a falsehood, which is extremely unpleasant
>>>>> and is
>>>>>  > generally assumed to be impossible. The only alternative left is
>>>>> that
>>>>>  > this statement is unprovable. Therefore, it is in fact both true
>>>>> and
>>>>>  > unprovable. Our system of reasoning is incomplete, because some
>>>>> truths
>>>>>  > are unprovable.
>>>>>  >
>>>>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>
>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>
>>>>> Does it make sense that formal systems are required to prove
>>>>> epistemological antinomies (AKA self-contradictory expressions) or
>>>>> should these expressions be rejected as non sequitur?
>>>>>
>>>>
>>>> Note, Consistant Formal Systems will reject actual epistemological
>>>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>>>
>>>> Formal Systems, to be consistent, only need to be able to prove
>>>> every True statement, and disprove every False statement, since BY
>>>> DEFINITION, an epistemological antinomy can neither be True or
>>>> False, a Formal Logic system doesn't need (and in fact CAN'T) prove
>>>> or disprove an epistemological antinomy, because such a statement
>>>> won't be a Truth Bearer, and thus neither True or False.
>>>>
>>>> The thing you seem to be too stupid to understand is that Godel
>>>> doesn't use the Liar's paradox in its paradox form where it IS an
>>>> epistemological antinomy, but has transformed it from being about
>>>> the truth of the statement (and thus the antinomy) to a statement
>>>> about the provability of the statement, which breaks the paradox.
>>>>
>>>> The
>>>>
>>>>
>>>>> *The valid/sound deductive inference model seems to think that
>>>>> latter:*
>>>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ C)  ↔ True(F, C))
>>>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) ((F ⊢ ¬C) ↔ False(F, C))
>>>>> ∀F ∈ Formal_Systems ∀C ∈ WFF(F) (((F ⊬ C) ∧ (F ⊬ ¬C)) ↔
>>>>> NonSequitur(F, C))
>>>>
>>>> Wrong, unless you mean COMPETE FORMAL SYSTEM,
>>>>
>>>> Replace the "Prove" symbol, with the "Establishes" relationship,
>>>> which changes the requirement from a finite set of steps, to any
>>>> (possibly infinite) set of sets, and the statment holds for any
>>>> formal system.
>>>>
>>>> C is True in F, if there is a (possibly infinite) sequence of steps
>>>> in F from its Truth Makers
>>>>
>>>> You are missing the fact that it is shown that it is possible for a
>>>> statement C to be TRUE, because there is a (possibly infinte) chain
>>>> of semantic connections from the Truth Makers of the system. through
>>>> valid logical inferances, to the statement C, but there might not be
>>>> a valid PROOF of the statement, which is a FINITE chain of semantic
>>>> connections from the Truth Makers of the system through valid
>>>> logical inferences.
>>>>
>>>>>
>>>>> *Non Sequitur*
>>>>> https://en.wikipedia.org/wiki/Formal_fallacy)
>>>>> In philosophy, a formal fallacy, deductive fallacy, logical fallacy
>>>>> or non sequitur[1] (Latin for "it does not follow")
>>>>>
>>>>> By simply disallowing symbolic logic to diverge from the valid/sound
>>>>> deductive inference model Gödel Incompleteness and Tarski
>>>>> Undefinability
>>>>> cease to exist.
>>>>
>>>> Nope, because it DOESN'T, but only because you don't understand what
>>>> a sound or valid proof actually is, or the defintion of Truth.
>>>>
>>>>>
>>>>> *Gödel, Kurt 1931*
>>>>> *On Formally Undecidable Propositions of Principia Mathematica*
>>>>> *And Related Systems*
>>>>>
>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf)
>>>>>
>>>>
>>>> Which just shows that you don't understand what you are reading.
>>>>
>>>
>>> Try and find an example of this.
>>
>> What DO you correctly understand. You haven't shown ANY actual
>> knowledge of the paper, but only the ability to pull pieces out of it
>> totally out of context.
>>
>>>
>>> Tarski used the actual Liar Paradox to derive his comparable proof.
>>> https://plato.stanford.edu/entries/goedel-incompleteness/#TarTheUndTru
>>
>> Nope, he DERIVES the Liar Paradox as a statement that must be true if
>> a "Definition of Truth" per his rules exists
> You have Tarski correctly. Tarski rejects that truth can be correctly
> formalized because he can't prove that a non-truth bearer is true.

So, can YOU prove that a non-truth bearer is true?

Because he shows that if truth can be formalized, then the liar's
paradox MUST be a True statement.

>
> That is like rejecting Geometry upon the failure to prove that a circle
> is a square.
>

Nope, just shows your stupidity and not understanding the argument.

It seems the concept of the proof by contradiction is beyond you. He
shows that there can not be a "Definition of Truth" (per his definition
of what that is) because if there was, then it would require that the
liar's paradox be true, becuase it can be proven using the existance of
that definition.

That would be like in Geometry trying to add a new axiom/assumption to
the system, but finding out if you do that there exists a circle that is
a square.

On 5/8/2023 6:56 AM, Richard Damon wrote:
> On 5/7/23 11:40 PM, olcott wrote:
>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>> On 5/7/23 1:43 PM, olcott wrote:
>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>> requires formal systems to be able to prove self-contradictory
>>>> expressions of language.
>>>>
>>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>>  > contains true statements that cannot be proved. His proof achieves
>>>>  > this by constructing paradoxical mathematical statements. To see how
>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>  > statement is false." This statement is true if and only if it is
>>>>  > false, and therefore it is neither true nor false.
>>>>  >
>>>>  > Now let's consider "This statement is unprovable." If it is
>>>> provable,
>>>>  > then we are proving a falsehood, which is extremely unpleasant
>>>> and is
>>>>  > generally assumed to be impossible. The only alternative left is
>>>> that
>>>>  > this statement is unprovable. Therefore, it is in fact both true and
>>>>  > unprovable. Our system of reasoning is incomplete, because some
>>>> truths
>>>>  > are unprovable.
>>>>  >
>>>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>
>>>> "14 Every epistemological antinomy can likewise be used for a
>>>> similar undecidability proof." (Gödel 1931:40)
>>>>
>>>> Does it make sense that formal systems are required to prove
>>>> epistemological antinomies (AKA self-contradictory expressions) or
>>>> should these expressions be rejected as non sequitur?
>>>>
>>>
>>> Note, Consistant Formal Systems will reject actual epistemological
>>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>>
>>
>> Try and find an example of this. (I pasted it in the wrong place)
>>
>>
>
> Its definitional. In a formal system, a statement is only a member of
> that system if it is either True or False. A statement is only part of a
> formal system if it is established true or false in that system.
>

Thus when we hypothesize that a formal system is powerful enough to have
its own provability predicate in F then when G asserts its own
unprovability in F we understand that this would require a sequence of
inference steps in F that prove that they themselves do not exist.

> Since Truth is based on having a (possibly infinite) series of valid and
> sound inferences from the Truth Makers of a system to the Statement (or
> to its complement for falsehood), and a self-referential statement can
> NEVER have all of its premises established, since it is one of them,
> that can never happen.

Alternatively if an expression involves an infinite sequence of steps
then this sequence never resolves to true or false.

This sentence is not true.
It is not true about what?
It is not true about being not true.
It is not true about being not true about what?
It is not true about being not true about being not true...

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On Monday, May 8, 2023 at 10:54:58 AM UTC-5, olcott wrote:
> On 5/8/2023 6:56 AM, Richard Damon wrote:
> > On 5/7/23 11:40 PM, olcott wrote:
> >> On 5/7/2023 3:00 PM, Richard Damon wrote:
> >>> On 5/7/23 1:43 PM, olcott wrote:
> >>>> Gödel's proof it relies upon a definition of incompleteness that
> >>>> requires formal systems to be able to prove self-contradictory
> >>>> expressions of language.
> >>>>
> >>>> > Kurt Gödel's incompleteness theorem demonstrates that mathematics
> >>>> > contains true statements that cannot be proved. His proof achieves
> >>>> > this by constructing paradoxical mathematical statements. To see how
> >>>> > the proof works, begin by considering the liar's paradox: "This
> >>>> > statement is false." This statement is true if and only if it is
> >>>> > false, and therefore it is neither true nor false.
> >>>> >
> >>>> > Now let's consider "This statement is unprovable." If it is
> >>>> provable,
> >>>> > then we are proving a falsehood, which is extremely unpleasant
> >>>> and is
> >>>> > generally assumed to be impossible. The only alternative left is
> >>>> that
> >>>> > this statement is unprovable. Therefore, it is in fact both true and
> >>>> > unprovable. Our system of reasoning is incomplete, because some
> >>>> truths
> >>>> > are unprovable.
> >>>> >
> >>>> > https://www.scientificamerican.com/article/what-is-goumldels-proof/
> >>>>
> >>>> "14 Every epistemological antinomy can likewise be used for a
> >>>> similar undecidability proof." (Gödel 1931:40)
> >>>>
> >>>> Does it make sense that formal systems are required to prove
> >>>> epistemological antinomies (AKA self-contradictory expressions) or
> >>>> should these expressions be rejected as non sequitur?
> >>>>
> >>>
> >>> Note, Consistant Formal Systems will reject actual epistemological
> >>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
> >>>
> >>
> >> Try and find an example of this. (I pasted it in the wrong place)
> >>
> >>
> >
> > Its definitional. In a formal system, a statement is only a member of
> > that system if it is either True or False. A statement is only part of a
> > formal system if it is established true or false in that system.
> >
> Thus when we hypothesize that a formal system is powerful enough to have
> its own provability predicate in F then when G asserts its own
> unprovability in F we understand that this would require a sequence of
> inference steps in F that prove that they themselves do not exist.
> > Since Truth is based on having a (possibly infinite) series of valid and
> > sound inferences from the Truth Makers of a system to the Statement (or
> > to its complement for falsehood), and a self-referential statement can
> > NEVER have all of its premises established, since it is one of them,
> > that can never happen.
> Alternatively if an expression involves an infinite sequence of steps
> then this sequence never resolves to true or false.
>
> This sentence is not true.
> It is not true about what?
> It is not true about being not true.
> It is not true about being not true about what?
> It is not true about being not true about being not true...
> --
> Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

Woof!!! Woof!!!!

On 5/8/23 11:53 AM, olcott wrote:
> On 5/8/2023 6:56 AM, Richard Damon wrote:
>> On 5/7/23 11:40 PM, olcott wrote:
>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>>> requires formal systems to be able to prove self-contradictory
>>>>> expressions of language.
>>>>>
>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>>>  > contains true statements that cannot be proved. His proof achieves
>>>>>  > this by constructing paradoxical mathematical statements. To see
>>>>> how
>>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>>  > statement is false." This statement is true if and only if it is
>>>>>  > false, and therefore it is neither true nor false.
>>>>>  >
>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>> provable,
>>>>>  > then we are proving a falsehood, which is extremely unpleasant
>>>>> and is
>>>>>  > generally assumed to be impossible. The only alternative left is
>>>>> that
>>>>>  > this statement is unprovable. Therefore, it is in fact both true
>>>>> and
>>>>>  > unprovable. Our system of reasoning is incomplete, because some
>>>>> truths
>>>>>  > are unprovable.
>>>>>  >
>>>>>  > https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>
>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>
>>>>> Does it make sense that formal systems are required to prove
>>>>> epistemological antinomies (AKA self-contradictory expressions) or
>>>>> should these expressions be rejected as non sequitur?
>>>>>
>>>>
>>>> Note, Consistant Formal Systems will reject actual epistemological
>>>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>>>
>>>
>>> Try and find an example of this. (I pasted it in the wrong place)
>>>
>>>
>>
>> Its definitional. In a formal system, a statement is only a member of
>> that system if it is either True or False. A statement is only part of
>> a formal system if it is established true or false in that system.
>>
>
> Thus when we hypothesize that a formal system is powerful enough to have
> its own provability predicate in F then when G asserts its own
> unprovability in F we understand that this would require a sequence of
> inference steps in F that prove that they themselves do not exist.
>
>> Since Truth is based on having a (possibly infinite) series of valid
>> and sound inferences from the Truth Makers of a system to the
>> Statement (or to its complement for falsehood), and a self-referential
>> statement can NEVER have all of its premises established, since it is
>> one of them, that can never happen.
>
> Alternatively if an expression involves an infinite sequence of steps
> then this sequence never resolves to true or false.

But it can.

For instance, if it requires the testing of all natural numbers, each
one taking a finite number of steps, that that DOES resolve in an
infinite number of steps, and thus IS established in the logic system.

If there is no positive number that when put into the divide by 2 or 3x
+ 1 steps that never reaches 1, then the Collatz conjecture is true,
even if it can only be verifies by testing EVERY number (that is an
infinite number of them). Things like the Collatz conjecture MUST be
Truth Beares, as either a number with the property exists or it doesn't,
so if no such number exists, we can say it is true that no such number
exists (or all numbers do the opposite) even if we can't formally prove
that result.

The fact that you tiny brain can't handle how infinity works doesn't
keep infinite steps, that actually arrive at the connection, from
establishing a statement as True.

>
> This sentence is not true.
> It is not true about what?
> It is not true about being not true.
> It is not true about being not true about what?
> It is not true about being not true about being not true...
>

First, you are not working from the Truth Makers, so isn't even a proper
sequence of steps (You have shown this previous error in understanding
the definition of a semantic connection).

Second, this shows why Non-Truth-Bearers don't ever connect, even in an
infinite number of steps, between the truth makers and the statement.

Thirdly, this statement NEVER gets to the end, not even after an
infinite number of steps, so does't connect in an infinite number of
steps. There is a difference between ACTUALLY connecting, but needing an
infinite number of steps, and never connecting.

So, your use of a straw man just show how little you understand what you
are talking about.

Just like two parrallel lines (in plane Geometry) NEVER meet, but always
have the same distance between them, even "at infinity" (which you can
never actually get to in ordinary plane Geometry, it is only a limit,
just like when we are talking about domains like the Reals.

That differs from things like 1/x and 0, which DO meet "at infinity".

On 5/8/2023 6:20 PM, Richard Damon wrote:
> On 5/8/23 11:53 AM, olcott wrote:
>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>> On 5/7/23 11:40 PM, olcott wrote:
>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>>>> requires formal systems to be able to prove self-contradictory
>>>>>> expressions of language.
>>>>>>
>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>>>>  > contains true statements that cannot be proved. His proof achieves
>>>>>>  > this by constructing paradoxical mathematical statements. To
>>>>>> see how
>>>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>>>  > statement is false." This statement is true if and only if it is
>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>  >
>>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>>> provable,
>>>>>>  > then we are proving a falsehood, which is extremely unpleasant
>>>>>> and is
>>>>>>  > generally assumed to be impossible. The only alternative left
>>>>>> is that
>>>>>>  > this statement is unprovable. Therefore, it is in fact both
>>>>>> true and
>>>>>>  > unprovable. Our system of reasoning is incomplete, because some
>>>>>> truths
>>>>>>  > are unprovable.
>>>>>>  >
>>>>>>  >
>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>
>>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>>
>>>>>> Does it make sense that formal systems are required to prove
>>>>>> epistemological antinomies (AKA self-contradictory expressions) or
>>>>>> should these expressions be rejected as non sequitur?
>>>>>>
>>>>>
>>>>> Note, Consistant Formal Systems will reject actual epistemological
>>>>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>>>>
>>>>
>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>
>>>>
>>>
>>> Its definitional. In a formal system, a statement is only a member of
>>> that system if it is either True or False. A statement is only part
>>> of a formal system if it is established true or false in that system.
>>>
>>
>> Thus when we hypothesize that a formal system is powerful enough to have
>> its own provability predicate in F then when G asserts its own
>> unprovability in F we understand that this would require a sequence of
>> inference steps in F that prove that they themselves do not exist.
>>
>>> Since Truth is based on having a (possibly infinite) series of valid
>>> and sound inferences from the Truth Makers of a system to the
>>> Statement (or to its complement for falsehood), and a
>>> self-referential statement can NEVER have all of its premises
>>> established, since it is one of them, that can never happen.
>>
>> Alternatively if an expression involves an infinite sequence of steps
>> then this sequence never resolves to true or false.
>
> But it can.
>
> For instance, if it requires the testing of all natural numbers, each
> one taking a finite number of steps, that that DOES resolve in an
> infinite number of steps, and thus IS established in the logic system.
>

Count to infinity is not computable.

> If there is no positive number that when put into the divide by 2 or 3x
> + 1 steps that never reaches 1, then the Collatz conjecture is true,
> even if it can only be verifies by testing EVERY number (that is an
> infinite number of them). Things like the Collatz conjecture MUST be
> Truth Beares, as either a number with the property exists or it doesn't,
> so if no such number exists, we can say it is true that no such number
> exists (or all numbers do the opposite) even if we can't formally prove
> that result.
>

Maybe for these kind of things there are truths that can never be verified.

> The fact that you tiny brain can't handle how infinity works doesn't
> keep infinite steps, that actually arrive at the connection, from
> establishing a statement as True.
>
>>
>> This sentence is not true.
>> It is not true about what?
>> It is not true about being not true.
>> It is not true about being not true about what?
>> It is not true about being not true about being not true...
>>
>
> First, you are not working from the Truth Makers, so isn't even a proper
> sequence of steps (You have shown this previous error in understanding
> the definition of a semantic connection).
>

Self-contradictory expressions are not truth bearers you can either
comprehend that or fail to comprehend that.

> Second, this shows why Non-Truth-Bearers don't ever connect, even in an
> infinite number of steps, between the truth makers and the statement.
>

OK so we agree on this.

> Thirdly, this statement NEVER gets to the end, not even after an
> infinite number of steps, so does't connect in an infinite number of
> steps. There is a difference between ACTUALLY connecting, but needing an
> infinite number of steps, and never connecting.
>

OK so we agree on this too.

You still do not acknowledge that you understand that when G asserts its
own unprovability in F proving G requires a sequence of inference steps
in F that prove that they themselves do not exist.

*x := y means x is defined to be another name for y*
https://en.wikipedia.org/wiki/List_of_logic_symbols
This seem to be the only way that we get actual self-reference
all of the textbooks merely approximate self-reference with ↔

∃G ∈ F (G := (F ⊬ G))
There exists a G in F that proves its own unprovabilty in F
Maybe you have a more accurate way to translate the symbols.

> So, your use of a straw man just show how little you understand what you
> are talking about.
>
> Just like two parrallel lines (in plane Geometry) NEVER meet, but always
> have the same distance between them, even "at infinity" (which you can
> never actually get to in ordinary plane Geometry, it is only a limit,
> just like when we are talking about domains like the Reals.
>
> That differs from things like 1/x and 0, which DO meet "at infinity".

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/8/23 10:40 PM, olcott wrote:
> On 5/8/2023 6:20 PM, Richard Damon wrote:
>> On 5/8/23 11:53 AM, olcott wrote:
>>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>>> On 5/7/23 11:40 PM, olcott wrote:
>>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>>>>> requires formal systems to be able to prove self-contradictory
>>>>>>> expressions of language.
>>>>>>>
>>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that mathematics
>>>>>>>  > contains true statements that cannot be proved. His proof
>>>>>>> achieves
>>>>>>>  > this by constructing paradoxical mathematical statements. To
>>>>>>> see how
>>>>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>>>>  > statement is false." This statement is true if and only if it is
>>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>>  >
>>>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>>>> provable,
>>>>>>>  > then we are proving a falsehood, which is extremely unpleasant
>>>>>>> and is
>>>>>>>  > generally assumed to be impossible. The only alternative left
>>>>>>> is that
>>>>>>>  > this statement is unprovable. Therefore, it is in fact both
>>>>>>> true and
>>>>>>>  > unprovable. Our system of reasoning is incomplete, because
>>>>>>> some truths
>>>>>>>  > are unprovable.
>>>>>>>  >
>>>>>>>  >
>>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>>
>>>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>>>
>>>>>>> Does it make sense that formal systems are required to prove
>>>>>>> epistemological antinomies (AKA self-contradictory expressions)
>>>>>>> or should these expressions be rejected as non sequitur?
>>>>>>>
>>>>>>
>>>>>> Note, Consistant Formal Systems will reject actual epistemological
>>>>>> antinomies as non-Truth Bearing, and thus your premise is incorrect.
>>>>>>
>>>>>
>>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>>
>>>>>
>>>>
>>>> Its definitional. In a formal system, a statement is only a member
>>>> of that system if it is either True or False. A statement is only
>>>> part of a formal system if it is established true or false in that
>>>> system.
>>>>
>>>
>>> Thus when we hypothesize that a formal system is powerful enough to have
>>> its own provability predicate in F then when G asserts its own
>>> unprovability in F we understand that this would require a sequence of
>>> inference steps in F that prove that they themselves do not exist.
>>>
>>>> Since Truth is based on having a (possibly infinite) series of valid
>>>> and sound inferences from the Truth Makers of a system to the
>>>> Statement (or to its complement for falsehood), and a
>>>> self-referential statement can NEVER have all of its premises
>>>> established, since it is one of them, that can never happen.
>>>
>>> Alternatively if an expression involves an infinite sequence of steps
>>> then this sequence never resolves to true or false.
>>
>> But it can.
>>
>> For instance, if it requires the testing of all natural numbers, each
>> one taking a finite number of steps, that that DOES resolve in an
>> infinite number of steps, and thus IS established in the logic system.
>>
>
> Count to infinity is not computable.

Didn't say it was, but not all things that are True are Computable.

>
>> If there is no positive number that when put into the divide by 2 or
>> 3x + 1 steps that never reaches 1, then the Collatz conjecture is
>> true, even if it can only be verifies by testing EVERY number (that is
>> an infinite number of them). Things like the Collatz conjecture MUST
>> be Truth Beares, as either a number with the property exists or it
>> doesn't, so if no such number exists, we can say it is true that no
>> such number exists (or all numbers do the opposite) even if we can't
>> formally prove that result.
>>
>
> Maybe for these kind of things there are truths that can never be verified.

Right, which means can't be proven.

That shows your definition, where all truth must be provable, is INCORRECT.

>
>> The fact that you tiny brain can't handle how infinity works doesn't
>> keep infinite steps, that actually arrive at the connection, from
>> establishing a statement as True.
>>
>>>
>>> This sentence is not true.
>>> It is not true about what?
>>> It is not true about being not true.
>>> It is not true about being not true about what?
>>> It is not true about being not true about being not true...
>>>
>>
>> First, you are not working from the Truth Makers, so isn't even a
>> proper sequence of steps (You have shown this previous error in
>> understanding the definition of a semantic connection).
>>
>
> Self-contradictory expressions are not truth bearers you can either
> comprehend that or fail to comprehend that.

Right, But saying you aren't provable isn't being "Self-Contradictory".

You just are showing you don't understand that actual meaning of that word.

>
>> Second, this shows why Non-Truth-Bearers don't ever connect, even in
>> an infinite number of steps, between the truth makers and the statement.
>>
>
> OK so we agree on this.
>
>> Thirdly, this statement NEVER gets to the end, not even after an
>> infinite number of steps, so does't connect in an infinite number of
>> steps. There is a difference between ACTUALLY connecting, but needing
>> an infinite number of steps, and never connecting.
>>
>
> OK so we agree on this too.
>
> You still do not acknowledge that you understand that when G asserts its
> own unprovability in F proving G requires a sequence of inference steps
> in F that prove that they themselves do not exist.

You are still stuck on your lie that you can assert as true something
which can not be proven in that system.

You just agreed that some true statements can not be "verified"

>
> *x := y means x is defined to be another name for y*
> https://en.wikipedia.org/wiki/List_of_logic_symbols
> This seem to be the only way that we get actual self-reference
> all of the textbooks merely approximate self-reference with ↔

So, you REALLY don't understand logic. "↔" doesn't mean anything like
self-reference, it means always has the same truth value, even if just
as a coencident, or because the two sides derive from a common source
(but aren't the same statement).

>
> ∃G ∈ F (G := (F ⊬ G))
> There exists a G in F that proves its own unprovabilty in F
> Maybe you have a more accurate way to translate the symbols.

No, the statements says that there exists a G in F that STATES that G in
not provable in F.

Where is the "Proves" operator in that statement?

G isn't "Proving" that it is unprovable, it is just asserting it.

Note also, this isn't Godel's G, so mostly irrelevant. In Godel's proof,
G (in F) is just a statement about there not existing a natural number
that satisfies a particular relationship. It is only in Meta-F that we
get any of the meaning about "proving" statements,

>
>> So, your use of a straw man just show how little you understand what
>> you are talking about.
>>
>> Just like two parrallel lines (in plane Geometry) NEVER meet, but
>> always have the same distance between them, even "at infinity" (which
>> you can never actually get to in ordinary plane Geometry, it is only a
>> limit, just like when we are talking about domains like the Reals.
>>
>> That differs from things like 1/x and 0, which DO meet "at infinity".
>

On 5/9/2023 6:44 AM, Richard Damon wrote:
> On 5/8/23 10:40 PM, olcott wrote:
>> On 5/8/2023 6:20 PM, Richard Damon wrote:
>>> On 5/8/23 11:53 AM, olcott wrote:
>>>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>>>> On 5/7/23 11:40 PM, olcott wrote:
>>>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>>>> Gödel's proof it relies upon a definition of incompleteness that
>>>>>>>> requires formal systems to be able to prove self-contradictory
>>>>>>>> expressions of language.
>>>>>>>>
>>>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that
>>>>>>>> mathematics
>>>>>>>>  > contains true statements that cannot be proved. His proof
>>>>>>>> achieves
>>>>>>>>  > this by constructing paradoxical mathematical statements. To
>>>>>>>> see how
>>>>>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>>>>>  > statement is false." This statement is true if and only if it is
>>>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>>>  >
>>>>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>>>>> provable,
>>>>>>>>  > then we are proving a falsehood, which is extremely
>>>>>>>> unpleasant and is
>>>>>>>>  > generally assumed to be impossible. The only alternative left
>>>>>>>> is that
>>>>>>>>  > this statement is unprovable. Therefore, it is in fact both
>>>>>>>> true and
>>>>>>>>  > unprovable. Our system of reasoning is incomplete, because
>>>>>>>> some truths
>>>>>>>>  > are unprovable.
>>>>>>>>  >
>>>>>>>>  >
>>>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>>>
>>>>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>>>>
>>>>>>>> Does it make sense that formal systems are required to prove
>>>>>>>> epistemological antinomies (AKA self-contradictory expressions)
>>>>>>>> or should these expressions be rejected as non sequitur?
>>>>>>>>
>>>>>>>
>>>>>>> Note, Consistant Formal Systems will reject actual
>>>>>>> epistemological antinomies as non-Truth Bearing, and thus your
>>>>>>> premise is incorrect.
>>>>>>>
>>>>>>
>>>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>>>
>>>>>>
>>>>>
>>>>> Its definitional. In a formal system, a statement is only a member
>>>>> of that system if it is either True or False. A statement is only
>>>>> part of a formal system if it is established true or false in that
>>>>> system.
>>>>>
>>>>
>>>> Thus when we hypothesize that a formal system is powerful enough to
>>>> have
>>>> its own provability predicate in F then when G asserts its own
>>>> unprovability in F we understand that this would require a sequence of
>>>> inference steps in F that prove that they themselves do not exist.
>>>>
>>>>> Since Truth is based on having a (possibly infinite) series of
>>>>> valid and sound inferences from the Truth Makers of a system to the
>>>>> Statement (or to its complement for falsehood), and a
>>>>> self-referential statement can NEVER have all of its premises
>>>>> established, since it is one of them, that can never happen.
>>>>
>>>> Alternatively if an expression involves an infinite sequence of steps
>>>> then this sequence never resolves to true or false.
>>>
>>> But it can.
>>>
>>> For instance, if it requires the testing of all natural numbers, each
>>> one taking a finite number of steps, that that DOES resolve in an
>>> infinite number of steps, and thus IS established in the logic system.
>>>
>>
>> Count to infinity is not computable.
>
> Didn't say it was, but not all things that are True are Computable.
>
>>
>>> If there is no positive number that when put into the divide by 2 or
>>> 3x + 1 steps that never reaches 1, then the Collatz conjecture is
>>> true, even if it can only be verifies by testing EVERY number (that
>>> is an infinite number of them). Things like the Collatz conjecture
>>> MUST be Truth Beares, as either a number with the property exists or
>>> it doesn't, so if no such number exists, we can say it is true that
>>> no such number exists (or all numbers do the opposite) even if we
>>> can't formally prove that result.
>>>
>>
>> Maybe for these kind of things there are truths that can never be
>> verified.
>
> Right, which means can't be proven.
>
> That shows your definition, where all truth must be provable, is INCORRECT.
>
>>
>>> The fact that you tiny brain can't handle how infinity works doesn't
>>> keep infinite steps, that actually arrive at the connection, from
>>> establishing a statement as True.
>>>
>>>>
>>>> This sentence is not true.
>>>> It is not true about what?
>>>> It is not true about being not true.
>>>> It is not true about being not true about what?
>>>> It is not true about being not true about being not true...
>>>>
>>>
>>> First, you are not working from the Truth Makers, so isn't even a
>>> proper sequence of steps (You have shown this previous error in
>>> understanding the definition of a semantic connection).
>>>
>>
>> Self-contradictory expressions are not truth bearers you can either
>> comprehend that or fail to comprehend that.
>
> Right, But saying you aren't provable isn't being "Self-Contradictory".
>
> You just are showing you don't understand that actual meaning of that word.
>
>>
>>> Second, this shows why Non-Truth-Bearers don't ever connect, even in
>>> an infinite number of steps, between the truth makers and the statement.
>>>
>>
>> OK so we agree on this.
>>
>>> Thirdly, this statement NEVER gets to the end, not even after an
>>> infinite number of steps, so does't connect in an infinite number of
>>> steps. There is a difference between ACTUALLY connecting, but needing
>>> an infinite number of steps, and never connecting.
>>>
>>
>> OK so we agree on this too.
>>
>> You still do not acknowledge that you understand that when G asserts
>> its own unprovability in F proving G requires a sequence of inference
>> steps in F that prove that they themselves do not exist.
>
> You are still stuck on your lie that you can assert as true something
> which can not be proven in that system.
>
> You just agreed that some true statements can not be "verified"
>
>>
>> *x := y means x is defined to be another name for y*
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>> This seem to be the only way that we get actual self-reference
>> all of the textbooks merely approximate self-reference with ↔
>
> So, you REALLY don't understand logic. "↔" doesn't mean anything like
> self-reference, it means always has the same truth value, even if just

None-the-less

> as a coencident, or because the two sides derive from a common source
> (but aren't the same statement).
>
>>
>> ∃G ∈ F (G := (F ⊬ G))
>> There exists a G in F that proves its own unprovabilty in F
>> Maybe you have a more accurate way to translate the symbols.
>
> No, the statements says that there exists a G in F that STATES that G in
> not provable in F.

On 5/9/23 12:08 PM, olcott wrote:
> On 5/9/2023 6:44 AM, Richard Damon wrote:
>> On 5/8/23 10:40 PM, olcott wrote:
>>> On 5/8/2023 6:20 PM, Richard Damon wrote:
>>>> On 5/8/23 11:53 AM, olcott wrote:
>>>>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>>>>> On 5/7/23 11:40 PM, olcott wrote:
>>>>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>>>>> Gödel's proof it relies upon a definition of incompleteness
>>>>>>>>> that requires formal systems to be able to prove
>>>>>>>>> self-contradictory expressions of language.
>>>>>>>>>
>>>>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that
>>>>>>>>> mathematics
>>>>>>>>>  > contains true statements that cannot be proved. His proof
>>>>>>>>> achieves
>>>>>>>>>  > this by constructing paradoxical mathematical statements. To
>>>>>>>>> see how
>>>>>>>>>  > the proof works, begin by considering the liar's paradox: "This
>>>>>>>>>  > statement is false." This statement is true if and only if
>>>>>>>>> it is
>>>>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>>>>  >
>>>>>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>>>>>> provable,
>>>>>>>>>  > then we are proving a falsehood, which is extremely
>>>>>>>>> unpleasant and is
>>>>>>>>>  > generally assumed to be impossible. The only alternative
>>>>>>>>> left is that
>>>>>>>>>  > this statement is unprovable. Therefore, it is in fact both
>>>>>>>>> true and
>>>>>>>>>  > unprovable. Our system of reasoning is incomplete, because
>>>>>>>>> some truths
>>>>>>>>>  > are unprovable.
>>>>>>>>>  >
>>>>>>>>>  >
>>>>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>>>>
>>>>>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>>>>>
>>>>>>>>> Does it make sense that formal systems are required to prove
>>>>>>>>> epistemological antinomies (AKA self-contradictory expressions)
>>>>>>>>> or should these expressions be rejected as non sequitur?
>>>>>>>>>
>>>>>>>>
>>>>>>>> Note, Consistant Formal Systems will reject actual
>>>>>>>> epistemological antinomies as non-Truth Bearing, and thus your
>>>>>>>> premise is incorrect.
>>>>>>>>
>>>>>>>
>>>>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Its definitional. In a formal system, a statement is only a member
>>>>>> of that system if it is either True or False. A statement is only
>>>>>> part of a formal system if it is established true or false in that
>>>>>> system.
>>>>>>
>>>>>
>>>>> Thus when we hypothesize that a formal system is powerful enough to
>>>>> have
>>>>> its own provability predicate in F then when G asserts its own
>>>>> unprovability in F we understand that this would require a sequence of
>>>>> inference steps in F that prove that they themselves do not exist.
>>>>>
>>>>>> Since Truth is based on having a (possibly infinite) series of
>>>>>> valid and sound inferences from the Truth Makers of a system to
>>>>>> the Statement (or to its complement for falsehood), and a
>>>>>> self-referential statement can NEVER have all of its premises
>>>>>> established, since it is one of them, that can never happen.
>>>>>
>>>>> Alternatively if an expression involves an infinite sequence of steps
>>>>> then this sequence never resolves to true or false.
>>>>
>>>> But it can.
>>>>
>>>> For instance, if it requires the testing of all natural numbers,
>>>> each one taking a finite number of steps, that that DOES resolve in
>>>> an infinite number of steps, and thus IS established in the logic
>>>> system.
>>>>
>>>
>>> Count to infinity is not computable.
>>
>> Didn't say it was, but not all things that are True are Computable.
>>
>>>
>>>> If there is no positive number that when put into the divide by 2 or
>>>> 3x + 1 steps that never reaches 1, then the Collatz conjecture is
>>>> true, even if it can only be verifies by testing EVERY number (that
>>>> is an infinite number of them). Things like the Collatz conjecture
>>>> MUST be Truth Beares, as either a number with the property exists or
>>>> it doesn't, so if no such number exists, we can say it is true that
>>>> no such number exists (or all numbers do the opposite) even if we
>>>> can't formally prove that result.
>>>>
>>>
>>> Maybe for these kind of things there are truths that can never be
>>> verified.
>>
>> Right, which means can't be proven.
>>
>> That shows your definition, where all truth must be provable, is
>> INCORRECT.
>>
>>>
>>>> The fact that you tiny brain can't handle how infinity works doesn't
>>>> keep infinite steps, that actually arrive at the connection, from
>>>> establishing a statement as True.
>>>>
>>>>>
>>>>> This sentence is not true.
>>>>> It is not true about what?
>>>>> It is not true about being not true.
>>>>> It is not true about being not true about what?
>>>>> It is not true about being not true about being not true...
>>>>>
>>>>
>>>> First, you are not working from the Truth Makers, so isn't even a
>>>> proper sequence of steps (You have shown this previous error in
>>>> understanding the definition of a semantic connection).
>>>>
>>>
>>> Self-contradictory expressions are not truth bearers you can either
>>> comprehend that or fail to comprehend that.
>>
>> Right, But saying you aren't provable isn't being "Self-Contradictory".
>>
>> You just are showing you don't understand that actual meaning of that
>> word.
>>
>>>
>>>> Second, this shows why Non-Truth-Bearers don't ever connect, even in
>>>> an infinite number of steps, between the truth makers and the
>>>> statement.
>>>>
>>>
>>> OK so we agree on this.
>>>
>>>> Thirdly, this statement NEVER gets to the end, not even after an
>>>> infinite number of steps, so does't connect in an infinite number of
>>>> steps. There is a difference between ACTUALLY connecting, but
>>>> needing an infinite number of steps, and never connecting.
>>>>
>>>
>>> OK so we agree on this too.
>>>
>>> You still do not acknowledge that you understand that when G asserts
>>> its own unprovability in F proving G requires a sequence of inference
>>> steps in F that prove that they themselves do not exist.
>>
>> You are still stuck on your lie that you can assert as true something
>> which can not be proven in that system.
>>
>> You just agreed that some true statements can not be "verified"
>>
>>>
>>> *x := y means x is defined to be another name for y*
>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>> This seem to be the only way that we get actual self-reference
>>> all of the textbooks merely approximate self-reference with ↔
>>
>> So, you REALLY don't understand logic. "↔" doesn't mean anything like
>> self-reference, it means always has the same truth value, even if just
>
> None-the-less

On 5/9/2023 5:38 PM, Richard Damon wrote:
> On 5/9/23 12:08 PM, olcott wrote:
>> On 5/9/2023 6:44 AM, Richard Damon wrote:
>>> On 5/8/23 10:40 PM, olcott wrote:
>>>> On 5/8/2023 6:20 PM, Richard Damon wrote:
>>>>> On 5/8/23 11:53 AM, olcott wrote:
>>>>>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>>>>>> On 5/7/23 11:40 PM, olcott wrote:
>>>>>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>>>>>> Gödel's proof it relies upon a definition of incompleteness
>>>>>>>>>> that requires formal systems to be able to prove
>>>>>>>>>> self-contradictory expressions of language.
>>>>>>>>>>
>>>>>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that
>>>>>>>>>> mathematics
>>>>>>>>>>  > contains true statements that cannot be proved. His proof
>>>>>>>>>> achieves
>>>>>>>>>>  > this by constructing paradoxical mathematical statements.
>>>>>>>>>> To see how
>>>>>>>>>>  > the proof works, begin by considering the liar's paradox:
>>>>>>>>>> "This
>>>>>>>>>>  > statement is false." This statement is true if and only if
>>>>>>>>>> it is
>>>>>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>>>>>  >
>>>>>>>>>>  > Now let's consider "This statement is unprovable." If it is
>>>>>>>>>> provable,
>>>>>>>>>>  > then we are proving a falsehood, which is extremely
>>>>>>>>>> unpleasant and is
>>>>>>>>>>  > generally assumed to be impossible. The only alternative
>>>>>>>>>> left is that
>>>>>>>>>>  > this statement is unprovable. Therefore, it is in fact both
>>>>>>>>>> true and
>>>>>>>>>>  > unprovable. Our system of reasoning is incomplete, because
>>>>>>>>>> some truths
>>>>>>>>>>  > are unprovable.
>>>>>>>>>>  >
>>>>>>>>>>  >
>>>>>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>>>>>
>>>>>>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>>>>>>
>>>>>>>>>> Does it make sense that formal systems are required to prove
>>>>>>>>>> epistemological antinomies (AKA self-contradictory
>>>>>>>>>> expressions) or should these expressions be rejected as non
>>>>>>>>>> sequitur?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Note, Consistant Formal Systems will reject actual
>>>>>>>>> epistemological antinomies as non-Truth Bearing, and thus your
>>>>>>>>> premise is incorrect.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Its definitional. In a formal system, a statement is only a
>>>>>>> member of that system if it is either True or False. A statement
>>>>>>> is only part of a formal system if it is established true or
>>>>>>> false in that system.
>>>>>>>
>>>>>>
>>>>>> Thus when we hypothesize that a formal system is powerful enough
>>>>>> to have
>>>>>> its own provability predicate in F then when G asserts its own
>>>>>> unprovability in F we understand that this would require a
>>>>>> sequence of
>>>>>> inference steps in F that prove that they themselves do not exist.
>>>>>>
>>>>>>> Since Truth is based on having a (possibly infinite) series of
>>>>>>> valid and sound inferences from the Truth Makers of a system to
>>>>>>> the Statement (or to its complement for falsehood), and a
>>>>>>> self-referential statement can NEVER have all of its premises
>>>>>>> established, since it is one of them, that can never happen.
>>>>>>
>>>>>> Alternatively if an expression involves an infinite sequence of steps
>>>>>> then this sequence never resolves to true or false.
>>>>>
>>>>> But it can.
>>>>>
>>>>> For instance, if it requires the testing of all natural numbers,
>>>>> each one taking a finite number of steps, that that DOES resolve in
>>>>> an infinite number of steps, and thus IS established in the logic
>>>>> system.
>>>>>
>>>>
>>>> Count to infinity is not computable.
>>>
>>> Didn't say it was, but not all things that are True are Computable.
>>>
>>>>
>>>>> If there is no positive number that when put into the divide by 2
>>>>> or 3x + 1 steps that never reaches 1, then the Collatz conjecture
>>>>> is true, even if it can only be verifies by testing EVERY number
>>>>> (that is an infinite number of them). Things like the Collatz
>>>>> conjecture MUST be Truth Beares, as either a number with the
>>>>> property exists or it doesn't, so if no such number exists, we can
>>>>> say it is true that no such number exists (or all numbers do the
>>>>> opposite) even if we can't formally prove that result.
>>>>>
>>>>
>>>> Maybe for these kind of things there are truths that can never be
>>>> verified.
>>>
>>> Right, which means can't be proven.
>>>
>>> That shows your definition, where all truth must be provable, is
>>> INCORRECT.
>>>
>>>>
>>>>> The fact that you tiny brain can't handle how infinity works
>>>>> doesn't keep infinite steps, that actually arrive at the
>>>>> connection, from establishing a statement as True.
>>>>>
>>>>>>
>>>>>> This sentence is not true.
>>>>>> It is not true about what?
>>>>>> It is not true about being not true.
>>>>>> It is not true about being not true about what?
>>>>>> It is not true about being not true about being not true...
>>>>>>
>>>>>
>>>>> First, you are not working from the Truth Makers, so isn't even a
>>>>> proper sequence of steps (You have shown this previous error in
>>>>> understanding the definition of a semantic connection).
>>>>>
>>>>
>>>> Self-contradictory expressions are not truth bearers you can either
>>>> comprehend that or fail to comprehend that.
>>>
>>> Right, But saying you aren't provable isn't being "Self-Contradictory".
>>>
>>> You just are showing you don't understand that actual meaning of that
>>> word.
>>>
>>>>
>>>>> Second, this shows why Non-Truth-Bearers don't ever connect, even
>>>>> in an infinite number of steps, between the truth makers and the
>>>>> statement.
>>>>>
>>>>
>>>> OK so we agree on this.
>>>>
>>>>> Thirdly, this statement NEVER gets to the end, not even after an
>>>>> infinite number of steps, so does't connect in an infinite number
>>>>> of steps. There is a difference between ACTUALLY connecting, but
>>>>> needing an infinite number of steps, and never connecting.
>>>>>
>>>>
>>>> OK so we agree on this too.
>>>>
>>>> You still do not acknowledge that you understand that when G asserts
>>>> its own unprovability in F proving G requires a sequence of
>>>> inference steps in F that prove that they themselves do not exist.
>>>
>>> You are still stuck on your lie that you can assert as true something
>>> which can not be proven in that system.
>>>
>>> You just agreed that some true statements can not be "verified"
>>>
>>>>
>>>> *x := y means x is defined to be another name for y*
>>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>> This seem to be the only way that we get actual self-reference
>>>> all of the textbooks merely approximate self-reference with ↔
>>>
>>> So, you REALLY don't understand logic. "↔" doesn't mean anything like
>>> self-reference, it means always has the same truth value, even if just
>>
>> None-the-less
>
> IF there isn't an actual self-reference, you can't claim it to be
> self-contradictory.
>

On 5/9/23 8:18 PM, olcott wrote:
> On 5/9/2023 5:38 PM, Richard Damon wrote:
>> On 5/9/23 12:08 PM, olcott wrote:
>>> On 5/9/2023 6:44 AM, Richard Damon wrote:
>>>> On 5/8/23 10:40 PM, olcott wrote:
>>>>> On 5/8/2023 6:20 PM, Richard Damon wrote:
>>>>>> On 5/8/23 11:53 AM, olcott wrote:
>>>>>>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>>>>>>> On 5/7/23 11:40 PM, olcott wrote:
>>>>>>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>>>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>>>>>>> Gödel's proof it relies upon a definition of incompleteness
>>>>>>>>>>> that requires formal systems to be able to prove
>>>>>>>>>>> self-contradictory expressions of language.
>>>>>>>>>>>
>>>>>>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that
>>>>>>>>>>> mathematics
>>>>>>>>>>>  > contains true statements that cannot be proved. His proof
>>>>>>>>>>> achieves
>>>>>>>>>>>  > this by constructing paradoxical mathematical statements.
>>>>>>>>>>> To see how
>>>>>>>>>>>  > the proof works, begin by considering the liar's paradox:
>>>>>>>>>>> "This
>>>>>>>>>>>  > statement is false." This statement is true if and only if
>>>>>>>>>>> it is
>>>>>>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>>>>>>  >
>>>>>>>>>>>  > Now let's consider "This statement is unprovable." If it
>>>>>>>>>>> is provable,
>>>>>>>>>>>  > then we are proving a falsehood, which is extremely
>>>>>>>>>>> unpleasant and is
>>>>>>>>>>>  > generally assumed to be impossible. The only alternative
>>>>>>>>>>> left is that
>>>>>>>>>>>  > this statement is unprovable. Therefore, it is in fact
>>>>>>>>>>> both true and
>>>>>>>>>>>  > unprovable. Our system of reasoning is incomplete, because
>>>>>>>>>>> some truths
>>>>>>>>>>>  > are unprovable.
>>>>>>>>>>>  >
>>>>>>>>>>>  >
>>>>>>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>>>>>>
>>>>>>>>>>> "14 Every epistemological antinomy can likewise be used for a
>>>>>>>>>>> similar undecidability proof." (Gödel 1931:40)
>>>>>>>>>>>
>>>>>>>>>>> Does it make sense that formal systems are required to prove
>>>>>>>>>>> epistemological antinomies (AKA self-contradictory
>>>>>>>>>>> expressions) or should these expressions be rejected as non
>>>>>>>>>>> sequitur?
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Note, Consistant Formal Systems will reject actual
>>>>>>>>>> epistemological antinomies as non-Truth Bearing, and thus your
>>>>>>>>>> premise is incorrect.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Its definitional. In a formal system, a statement is only a
>>>>>>>> member of that system if it is either True or False. A statement
>>>>>>>> is only part of a formal system if it is established true or
>>>>>>>> false in that system.
>>>>>>>>
>>>>>>>
>>>>>>> Thus when we hypothesize that a formal system is powerful enough
>>>>>>> to have
>>>>>>> its own provability predicate in F then when G asserts its own
>>>>>>> unprovability in F we understand that this would require a
>>>>>>> sequence of
>>>>>>> inference steps in F that prove that they themselves do not exist.
>>>>>>>
>>>>>>>> Since Truth is based on having a (possibly infinite) series of
>>>>>>>> valid and sound inferences from the Truth Makers of a system to
>>>>>>>> the Statement (or to its complement for falsehood), and a
>>>>>>>> self-referential statement can NEVER have all of its premises
>>>>>>>> established, since it is one of them, that can never happen.
>>>>>>>
>>>>>>> Alternatively if an expression involves an infinite sequence of
>>>>>>> steps
>>>>>>> then this sequence never resolves to true or false.
>>>>>>
>>>>>> But it can.
>>>>>>
>>>>>> For instance, if it requires the testing of all natural numbers,
>>>>>> each one taking a finite number of steps, that that DOES resolve
>>>>>> in an infinite number of steps, and thus IS established in the
>>>>>> logic system.
>>>>>>
>>>>>
>>>>> Count to infinity is not computable.
>>>>
>>>> Didn't say it was, but not all things that are True are Computable.
>>>>
>>>>>
>>>>>> If there is no positive number that when put into the divide by 2
>>>>>> or 3x + 1 steps that never reaches 1, then the Collatz conjecture
>>>>>> is true, even if it can only be verifies by testing EVERY number
>>>>>> (that is an infinite number of them). Things like the Collatz
>>>>>> conjecture MUST be Truth Beares, as either a number with the
>>>>>> property exists or it doesn't, so if no such number exists, we can
>>>>>> say it is true that no such number exists (or all numbers do the
>>>>>> opposite) even if we can't formally prove that result.
>>>>>>
>>>>>
>>>>> Maybe for these kind of things there are truths that can never be
>>>>> verified.
>>>>
>>>> Right, which means can't be proven.
>>>>
>>>> That shows your definition, where all truth must be provable, is
>>>> INCORRECT.
>>>>
>>>>>
>>>>>> The fact that you tiny brain can't handle how infinity works
>>>>>> doesn't keep infinite steps, that actually arrive at the
>>>>>> connection, from establishing a statement as True.
>>>>>>
>>>>>>>
>>>>>>> This sentence is not true.
>>>>>>> It is not true about what?
>>>>>>> It is not true about being not true.
>>>>>>> It is not true about being not true about what?
>>>>>>> It is not true about being not true about being not true...
>>>>>>>
>>>>>>
>>>>>> First, you are not working from the Truth Makers, so isn't even a
>>>>>> proper sequence of steps (You have shown this previous error in
>>>>>> understanding the definition of a semantic connection).
>>>>>>
>>>>>
>>>>> Self-contradictory expressions are not truth bearers you can either
>>>>> comprehend that or fail to comprehend that.
>>>>
>>>> Right, But saying you aren't provable isn't being "Self-Contradictory".
>>>>
>>>> You just are showing you don't understand that actual meaning of
>>>> that word.
>>>>
>>>>>
>>>>>> Second, this shows why Non-Truth-Bearers don't ever connect, even
>>>>>> in an infinite number of steps, between the truth makers and the
>>>>>> statement.
>>>>>>
>>>>>
>>>>> OK so we agree on this.
>>>>>
>>>>>> Thirdly, this statement NEVER gets to the end, not even after an
>>>>>> infinite number of steps, so does't connect in an infinite number
>>>>>> of steps. There is a difference between ACTUALLY connecting, but
>>>>>> needing an infinite number of steps, and never connecting.
>>>>>>
>>>>>
>>>>> OK so we agree on this too.
>>>>>
>>>>> You still do not acknowledge that you understand that when G
>>>>> asserts its own unprovability in F proving G requires a sequence of
>>>>> inference steps in F that prove that they themselves do not exist.
>>>>
>>>> You are still stuck on your lie that you can assert as true
>>>> something which can not be proven in that system.
>>>>
>>>> You just agreed that some true statements can not be "verified"
>>>>
>>>>>
>>>>> *x := y means x is defined to be another name for y*
>>>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>>> This seem to be the only way that we get actual self-reference
>>>>> all of the textbooks merely approximate self-reference with ↔
>>>>
>>>> So, you REALLY don't understand logic. "↔" doesn't mean anything
>>>> like self-reference, it means always has the same truth value, even
>>>> if just
>>>
>>> None-the-less
>>
>> IF there isn't an actual self-reference, you can't claim it to be
>> self-contradictory.
>>
>
> *Stanford Encyclopedia of Philosophy Self-Reference*
>
>    Diagonal lemma.
>    Let S be a theory extending first-order arithmetic. For every formula
>    ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩.
>
> Here the notation S ⊢ α means that α is provable in the theory S, and
> ϕ⟨ψ⟩ is short for ϕ(⟨ψ⟩). Assume a formula ϕ(x) is given that is intended
> to express some property of sentences – truth, for instance. Then the
> diagonal lemma gives the existence of a sentence ψ satisfying the
> biimplication ψ ↔ ϕ⟨ψ⟩. The sentence ϕ⟨ψ⟩ can be thought of as
> expressing that the sentence ψ has the property expressed by ϕ(x). The
> biimplication thus expresses that ψ is equivalent to the sentence
> expressing that ψ has property ϕ. One can therefore think of ψ as a
> sentence expressing of itself that it has property ϕ. In the case of
> truth, it would be a sentence expressing of itself that it is true. The
> sentence ψ is of course not self-referential in a strict sense, but
> mathematically it behaves like one.
> https://plato.stanford.edu/entries/self-reference/
>
> No one in math ever directly expresses actual self-reference, they only
> approximate it not because actual-self-reference cannot be expressed
> merely because it is unconventional to express actual self-reference.
>
> *Here is actual self-reference*
> x := y means x is defined to be another name for y
> https://en.wikipedia.org/wiki/List_of_logic_symbols
>
> ∃G ∈ WFF(F) (G := ¬(F ⊢ G))
> There exists G a WFF of F that states it is unprovable in F.
>
> ...We are therefore confronted with a proposition which asserts its own
> unprovability. 15 ... (Gödel 1931:39-41)
>
> Gödel intended his actual G to be isomorphic to the above self-
> referential expression.
>
>
>>>
>>>> as a coencident, or because the two sides derive from a common
>>>> source (but aren't the same statement).
>>>>
>>>>>
>>>>> ∃G ∈ F (G := (F ⊬ G))
>>>>> There exists a G in F that proves its own unprovabilty in F
>>>>> Maybe you have a more accurate way to translate the symbols.
>>>>
>>>> No, the statements says that there exists a G in F that STATES that
>>>> G in not provable in F.
>>>
>>> That sounds about right.
>>
>> So you argee?
>>
>
> I was struggling to find the best wording and yours is better.
>
>>>
>>>>
>>>> Where is the "Proves" operator in that statement?
>>>>
>>>> G isn't "Proving" that it is unprovable, it is just asserting it.
>>>>
>>>
>>> States is a better word that proves or asserts.
>>>
>>>> Note also, this isn't Godel's G, so mostly irrelevant. In Godel's
>>>> proof, G (in F) is just a statement about there not existing a
>>>> natural number that satisfies a particular relationship. It is only
>>>> in Meta-F that we get any of the meaning about "proving" statements,
>>>>
>>>
>>> It matches this
>>> ...We are therefore confronted with a proposition which asserts its
>>> own unprovability. 15 ...(Gödel 1931:39-41)
>>
>> Right, we have a statement, IN META-F, that shows that G in F implies,
>> through logic in meta-F, that G is not provable in F.
>>
>
> ...We are therefore confronted with a proposition which asserts its own
> unprovability. 15 ... (Gödel 1931:39-41)

On 5/9/2023 8:30 PM, Richard Damon wrote:
> On 5/9/23 8:18 PM, olcott wrote:
>> On 5/9/2023 5:38 PM, Richard Damon wrote:
>>> On 5/9/23 12:08 PM, olcott wrote:
>>>> On 5/9/2023 6:44 AM, Richard Damon wrote:
>>>>> On 5/8/23 10:40 PM, olcott wrote:
>>>>>> On 5/8/2023 6:20 PM, Richard Damon wrote:
>>>>>>> On 5/8/23 11:53 AM, olcott wrote:
>>>>>>>> On 5/8/2023 6:56 AM, Richard Damon wrote:
>>>>>>>>> On 5/7/23 11:40 PM, olcott wrote:
>>>>>>>>>> On 5/7/2023 3:00 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/7/23 1:43 PM, olcott wrote:
>>>>>>>>>>>> Gödel's proof it relies upon a definition of incompleteness
>>>>>>>>>>>> that requires formal systems to be able to prove
>>>>>>>>>>>> self-contradictory expressions of language.
>>>>>>>>>>>>
>>>>>>>>>>>>  > Kurt Gödel's incompleteness theorem demonstrates that
>>>>>>>>>>>> mathematics
>>>>>>>>>>>>  > contains true statements that cannot be proved. His proof
>>>>>>>>>>>> achieves
>>>>>>>>>>>>  > this by constructing paradoxical mathematical statements.
>>>>>>>>>>>> To see how
>>>>>>>>>>>>  > the proof works, begin by considering the liar's paradox:
>>>>>>>>>>>> "This
>>>>>>>>>>>>  > statement is false." This statement is true if and only
>>>>>>>>>>>> if it is
>>>>>>>>>>>>  > false, and therefore it is neither true nor false.
>>>>>>>>>>>>  >
>>>>>>>>>>>>  > Now let's consider "This statement is unprovable." If it
>>>>>>>>>>>> is provable,
>>>>>>>>>>>>  > then we are proving a falsehood, which is extremely
>>>>>>>>>>>> unpleasant and is
>>>>>>>>>>>>  > generally assumed to be impossible. The only alternative
>>>>>>>>>>>> left is that
>>>>>>>>>>>>  > this statement is unprovable. Therefore, it is in fact
>>>>>>>>>>>> both true and
>>>>>>>>>>>>  > unprovable. Our system of reasoning is incomplete,
>>>>>>>>>>>> because some truths
>>>>>>>>>>>>  > are unprovable.
>>>>>>>>>>>>  >
>>>>>>>>>>>>  >
>>>>>>>>>>>> https://www.scientificamerican.com/article/what-is-goumldels-proof/
>>>>>>>>>>>>
>>>>>>>>>>>> "14 Every epistemological antinomy can likewise be used for
>>>>>>>>>>>> a similar undecidability proof." (Gödel 1931:40)
>>>>>>>>>>>>
>>>>>>>>>>>> Does it make sense that formal systems are required to prove
>>>>>>>>>>>> epistemological antinomies (AKA self-contradictory
>>>>>>>>>>>> expressions) or should these expressions be rejected as non
>>>>>>>>>>>> sequitur?
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Note, Consistant Formal Systems will reject actual
>>>>>>>>>>> epistemological antinomies as non-Truth Bearing, and thus
>>>>>>>>>>> your premise is incorrect.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Try and find an example of this. (I pasted it in the wrong place)
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Its definitional. In a formal system, a statement is only a
>>>>>>>>> member of that system if it is either True or False. A
>>>>>>>>> statement is only part of a formal system if it is established
>>>>>>>>> true or false in that system.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Thus when we hypothesize that a formal system is powerful enough
>>>>>>>> to have
>>>>>>>> its own provability predicate in F then when G asserts its own
>>>>>>>> unprovability in F we understand that this would require a
>>>>>>>> sequence of
>>>>>>>> inference steps in F that prove that they themselves do not exist.
>>>>>>>>
>>>>>>>>> Since Truth is based on having a (possibly infinite) series of
>>>>>>>>> valid and sound inferences from the Truth Makers of a system to
>>>>>>>>> the Statement (or to its complement for falsehood), and a
>>>>>>>>> self-referential statement can NEVER have all of its premises
>>>>>>>>> established, since it is one of them, that can never happen.
>>>>>>>>
>>>>>>>> Alternatively if an expression involves an infinite sequence of
>>>>>>>> steps
>>>>>>>> then this sequence never resolves to true or false.
>>>>>>>
>>>>>>> But it can.
>>>>>>>
>>>>>>> For instance, if it requires the testing of all natural numbers,
>>>>>>> each one taking a finite number of steps, that that DOES resolve
>>>>>>> in an infinite number of steps, and thus IS established in the
>>>>>>> logic system.
>>>>>>>
>>>>>>
>>>>>> Count to infinity is not computable.
>>>>>
>>>>> Didn't say it was, but not all things that are True are Computable.
>>>>>
>>>>>>
>>>>>>> If there is no positive number that when put into the divide by 2
>>>>>>> or 3x + 1 steps that never reaches 1, then the Collatz conjecture
>>>>>>> is true, even if it can only be verifies by testing EVERY number
>>>>>>> (that is an infinite number of them). Things like the Collatz
>>>>>>> conjecture MUST be Truth Beares, as either a number with the
>>>>>>> property exists or it doesn't, so if no such number exists, we
>>>>>>> can say it is true that no such number exists (or all numbers do
>>>>>>> the opposite) even if we can't formally prove that result.
>>>>>>>
>>>>>>
>>>>>> Maybe for these kind of things there are truths that can never be
>>>>>> verified.
>>>>>
>>>>> Right, which means can't be proven.
>>>>>
>>>>> That shows your definition, where all truth must be provable, is
>>>>> INCORRECT.
>>>>>
>>>>>>
>>>>>>> The fact that you tiny brain can't handle how infinity works
>>>>>>> doesn't keep infinite steps, that actually arrive at the
>>>>>>> connection, from establishing a statement as True.
>>>>>>>
>>>>>>>>
>>>>>>>> This sentence is not true.
>>>>>>>> It is not true about what?
>>>>>>>> It is not true about being not true.
>>>>>>>> It is not true about being not true about what?
>>>>>>>> It is not true about being not true about being not true...
>>>>>>>>
>>>>>>>
>>>>>>> First, you are not working from the Truth Makers, so isn't even a
>>>>>>> proper sequence of steps (You have shown this previous error in
>>>>>>> understanding the definition of a semantic connection).
>>>>>>>
>>>>>>
>>>>>> Self-contradictory expressions are not truth bearers you can either
>>>>>> comprehend that or fail to comprehend that.
>>>>>
>>>>> Right, But saying you aren't provable isn't being
>>>>> "Self-Contradictory".
>>>>>
>>>>> You just are showing you don't understand that actual meaning of
>>>>> that word.
>>>>>
>>>>>>
>>>>>>> Second, this shows why Non-Truth-Bearers don't ever connect, even
>>>>>>> in an infinite number of steps, between the truth makers and the
>>>>>>> statement.
>>>>>>>
>>>>>>
>>>>>> OK so we agree on this.
>>>>>>
>>>>>>> Thirdly, this statement NEVER gets to the end, not even after an
>>>>>>> infinite number of steps, so does't connect in an infinite number
>>>>>>> of steps. There is a difference between ACTUALLY connecting, but
>>>>>>> needing an infinite number of steps, and never connecting.
>>>>>>>
>>>>>>
>>>>>> OK so we agree on this too.
>>>>>>
>>>>>> You still do not acknowledge that you understand that when G
>>>>>> asserts its own unprovability in F proving G requires a sequence
>>>>>> of inference steps in F that prove that they themselves do not exist.
>>>>>
>>>>> You are still stuck on your lie that you can assert as true
>>>>> something which can not be proven in that system.
>>>>>
>>>>> You just agreed that some true statements can not be "verified"
>>>>>
>>>>>>
>>>>>> *x := y means x is defined to be another name for y*
>>>>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>>>> This seem to be the only way that we get actual self-reference
>>>>>> all of the textbooks merely approximate self-reference with ↔
>>>>>
>>>>> So, you REALLY don't understand logic. "↔" doesn't mean anything
>>>>> like self-reference, it means always has the same truth value, even
>>>>> if just
>>>>
>>>> None-the-less
>>>
>>> IF there isn't an actual self-reference, you can't claim it to be
>>> self-contradictory.
>>>
>>
>> *Stanford Encyclopedia of Philosophy Self-Reference*
>>
>>     Diagonal lemma.
>>     Let S be a theory extending first-order arithmetic. For every formula
>>     ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩.
>>
>> Here the notation S ⊢ α means that α is provable in the theory S, and
>> ϕ⟨ψ⟩ is short for ϕ(⟨ψ⟩). Assume a formula ϕ(x) is given that is intended
>> to express some property of sentences – truth, for instance. Then the
>> diagonal lemma gives the existence of a sentence ψ satisfying the
>> biimplication ψ ↔ ϕ⟨ψ⟩. The sentence ϕ⟨ψ⟩ can be thought of as
>> expressing that the sentence ψ has the property expressed by ϕ(x). The
>> biimplication thus expresses that ψ is equivalent to the sentence
>> expressing that ψ has property ϕ. One can therefore think of ψ as a
>> sentence expressing of itself that it has property ϕ. In the case of
>> truth, it would be a sentence expressing of itself that it is true. The
>> sentence ψ is of course not self-referential in a strict sense, but
>> mathematically it behaves like one.
>> https://plato.stanford.edu/entries/self-reference/
>>
>> No one in math ever directly expresses actual self-reference, they only
>> approximate it not because actual-self-reference cannot be expressed
>> merely because it is unconventional to express actual self-reference.
>>
>> *Here is actual self-reference*
>> x := y means x is defined to be another name for y
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>
>> ∃G ∈ WFF(F) (G := ¬(F ⊢ G))
>> There exists G a WFF of F that states it is unprovable in F.
>>
>> ...We are therefore confronted with a proposition which asserts its
>> own unprovability. 15 ... (Gödel 1931:39-41)
>>
>> Gödel intended his actual G to be isomorphic to the above self-
>> referential expression.
>>
>>
>>>>
>>>>> as a coencident, or because the two sides derive from a common
>>>>> source (but aren't the same statement).
>>>>>
>>>>>>
>>>>>> ∃G ∈ F (G := (F ⊬ G))
>>>>>> There exists a G in F that proves its own unprovabilty in F
>>>>>> Maybe you have a more accurate way to translate the symbols.
>>>>>
>>>>> No, the statements says that there exists a G in F that STATES that
>>>>> G in not provable in F.
>>>>
>>>> That sounds about right.
>>>
>>> So you argee?
>>>
>>
>> I was struggling to find the best wording and yours is better.
>>
>>>>
>>>>>
>>>>> Where is the "Proves" operator in that statement?
>>>>>
>>>>> G isn't "Proving" that it is unprovable, it is just asserting it.
>>>>>
>>>>
>>>> States is a better word that proves or asserts.
>>>>
>>>>> Note also, this isn't Godel's G, so mostly irrelevant. In Godel's
>>>>> proof, G (in F) is just a statement about there not existing a
>>>>> natural number that satisfies a particular relationship. It is only
>>>>> in Meta-F that we get any of the meaning about "proving" statements,
>>>>>
>>>>
>>>> It matches this
>>>> ...We are therefore confronted with a proposition which asserts its
>>>> own unprovability. 15 ...(Gödel 1931:39-41)
>>>
>>> Right, we have a statement, IN META-F, that shows that G in F
>>> implies, through logic in meta-F, that G is not provable in F.
>>>
>>
>> ...We are therefore confronted with a proposition which asserts its
>> own unprovability. 15 ... (Gödel 1931:39-41)
>
> Right, we discover IN THE META that from the statement G we can prove
> that a CONSEQUENCE of G (only demonstratable in the Meta) is that G has
> the same truth value as its unprovability.
>>
>> Gödel intended his actual G to be isomorphic to the above self-
>> referential expression.
>
> Nope, you are over-simplifying things.

On 5/9/23 10:46 PM, olcott wrote:
> On 5/9/2023 8:30 PM, Richard Damon wrote:
>> On 5/9/23 8:18 PM, olcott wrote:
>
>>> Gödel intended his actual G to be isomorphic to the above self-
>>> referential expression.
>>
>> Nope, you are over-simplifying things.
>
> Not at all. I boiled them down to their barest essence. Gödel's G was
> intended to be and is isomorphic to a self-contradictory expression.
>
> This is dead obvious in Tarski's comparable proof where he flat out
> states that he is anchoring his proof in the actual Liar Paradox.
>
>

So, you are just PROVING that you don't understand how logic actually
works and are falling for your own Straw man Error.

The error has been pointed out to you many times, but it seems you are
too Stupid AND Ignorant to be able to understand why you are wrong.

It is clear that you don't even understand the meaning of "Isomorphic",
as you are misusing it.

Also, as has been pointed out, you don't understand what Tarski is
saying, again likely because you have brainwashed yourself so much with
your rote learning of your own errors, that you refuse to see what is
actaully there.

All you are doing is cementing you place as a laughing stock of the
logical community. Your ideas are DEAD, as you will also be soon.

On 5/10/2023 6:24 AM, Richard Damon wrote:
> On 5/9/23 10:46 PM, olcott wrote:
>> On 5/9/2023 8:30 PM, Richard Damon wrote:
>>> On 5/9/23 8:18 PM, olcott wrote:
>>
>>>> Gödel intended his actual G to be isomorphic to the above self-
>>>> referential expression.
>>>
>>> Nope, you are over-simplifying things.
>>
>> Not at all. I boiled them down to their barest essence. Gödel's G was
>> intended to be and is isomorphic to a self-contradictory expression.
>>
>> This is dead obvious in Tarski's comparable proof where he flat out
>> states that he is anchoring his proof in the actual Liar Paradox.
>>
>>
>
> So, you are just PROVING that you don't understand how logic actually
> works and are falling for your own Straw man Error.
>

No I am proving to have a deeper understanding of these things than most
others have.

When we understand that he sums up his own proof as
...We are therefore confronted with a proposition which asserts its
own unprovability. 15 ... (Gödel 1931:39-41)

Then we can see that he intended his G to be isomorphic to a G that
....which asserts its own unprovability. 15 ... (Gödel 1931:39-41)

and he intended this be self contradictory
....14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:39-41)

Here is how G asserts its own unprovability in F is self-contradictory:
Proving G requires a sequence of inference steps in F that prove that
they themselves do not exist.

That you continue to fail to understand this is not my mistake it is
your mistake.

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Since Tarski directly stated that he is anchoring his comparable proof
in the actual Liar Paradox I have provided sufficient support for my
position.

Ever since 1936 the world has been convinced that the notion of Truth
is not formally definable entirely on the basis that Tarski could not
prove that the non-truth bearer of the Liar Paradox is true.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/10/23 10:27 AM, olcott wrote:
> On 5/10/2023 6:24 AM, Richard Damon wrote:
>> On 5/9/23 10:46 PM, olcott wrote:
>>> On 5/9/2023 8:30 PM, Richard Damon wrote:
>>>> On 5/9/23 8:18 PM, olcott wrote:
>>>
>>>>> Gödel intended his actual G to be isomorphic to the above self-
>>>>> referential expression.
>>>>
>>>> Nope, you are over-simplifying things.
>>>
>>> Not at all. I boiled them down to their barest essence. Gödel's G was
>>> intended to be and is isomorphic to a self-contradictory expression.
>>>
>>> This is dead obvious in Tarski's comparable proof where he flat out
>>> states that he is anchoring his proof in the actual Liar Paradox.
>>>
>>>
>>
>> So, you are just PROVING that you don't understand how logic actually
>> works and are falling for your own Straw man Error.
>>
>
> No I am proving to have a deeper understanding of these things than most
> others have.

Nope, just that you are so dumb you don't know what you don't understand.

>
> When we understand that he sums up his own proof as
>    ...We are therefore confronted with a proposition which asserts its
>    own unprovability. 15 ... (Gödel 1931:39-41)

No, that isn't a "summary" of his proof, but a STEP in the proof.

From G in F, we can prove in Meta-F, that G

>
> Then we can see that he intended his G to be isomorphic to a G that
> ...which asserts its own unprovability. 15 ... (Gödel 1931:39-41)

Nope, you don't seem to understand what a chain of logic is.

>
> and he intended this be self contradictory
> ...14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof...(Gödel 1931:39-41)

No, it just shows that you have no idea what he is talking about, or the
meaning of the words are that you are using.

YOU are the one guilt of trying to put words in other peoples mouthes,
to then try to disprove those altered words.

In other words, your whole arguement is bassed on asserting a Strawman
Falacy.

>
> Here is how G asserts its own unprovability in F is self-contradictory:
> Proving G requires a sequence of inference steps in F that prove that
> they themselves do not exist.

Except that the ACTUAL statement of G isn't in any way
"Self-Contradictiory", so your "Isomorphism" / "Equivalence" is just
your pathologica lie.

>
> That you continue to fail to understand this is not my mistake it is
> your mistake.

Nope, You are the one making the mistake.

It is a demonstarted principle, that if EVERYONE disagrees with you, you
are likely wrong. Even the greatest who came up with new ideas, were
able to get at least a FEW of the smartest to understand what they were
talking about.

You have only gotten agreement from a couple at the bottom, and people
you have "tricked" by the misuse of words, and who don't actually agree
with your ideas.

>
> Gödel, Kurt 1931.
> On Formally Undecidable Propositions of Principia Mathematica And
> Related Systems
>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>
> Since Tarski directly stated that he is anchoring his comparable proof
> in the actual Liar Paradox I have provided sufficient support for my
> position.
>

Nope, In fact, he is using the non-truth bearing of the Liars Paradox
for his proof,

You are again showing your stupiity.

> Ever since 1936 the world has been convinced that the notion of Truth
> is not formally definable entirely on the basis that Tarski could not
> prove that the non-truth bearer of the Liar Paradox is true.
>

Nope, and you are just proving that YOU have no idea what Truth actually
is, or what Logic actually is.

You are just proving your utter ignorance and stupidity with your
pathological lying about these things.

Your eternal destiny is to be known (for as long as you are remembered)
as the ignorant pathologica liar who totally misunderstands how logic works.

YOU FAIL.

On 5/10/2023 6:29 PM, Richard Damon wrote:
> On 5/10/23 10:27 AM, olcott wrote:
>> On 5/10/2023 6:24 AM, Richard Damon wrote:
>>> On 5/9/23 10:46 PM, olcott wrote:
>>>> On 5/9/2023 8:30 PM, Richard Damon wrote:
>>>>> On 5/9/23 8:18 PM, olcott wrote:
>>>>
>>>>>> Gödel intended his actual G to be isomorphic to the above self-
>>>>>> referential expression.
>>>>>
>>>>> Nope, you are over-simplifying things.
>>>>
>>>> Not at all. I boiled them down to their barest essence. Gödel's G was
>>>> intended to be and is isomorphic to a self-contradictory expression.
>>>>
>>>> This is dead obvious in Tarski's comparable proof where he flat out
>>>> states that he is anchoring his proof in the actual Liar Paradox.
>>>>
>>>>
>>>
>>> So, you are just PROVING that you don't understand how logic actually
>>> works and are falling for your own Straw man Error.
>>>
>>
>> No I am proving to have a deeper understanding of these things than most
>> others have.
>
> Nope, just that you are so dumb you don't know what you don't understand.
>
>>
>> When we understand that he sums up his own proof as
>>     ...We are therefore confronted with a proposition which asserts its
>>     own unprovability. 15 ... (Gödel 1931:39-41)
>
> No, that isn't a "summary" of his proof, but a STEP in the proof.
>
> From G in F, we can prove in Meta-F, that G
>
>>
>> Then we can see that he intended his G to be isomorphic to a G that
>> ...which asserts its own unprovability. 15 ... (Gödel 1931:39-41)
>
> Nope, you don't seem to understand what a chain of logic is.
>
>>
>> and he intended this be self contradictory
>> ...14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof...(Gödel 1931:39-41)
>
> No, it just shows that you have no idea what he is talking about, or the
> meaning of the words are that you are using.
>
> YOU are the one guilt of trying to put words in other peoples mouthes,
> to then try to disprove those altered words.
>
> In other words, your whole arguement is bassed on asserting a Strawman
> Falacy.
>
>>
>> Here is how G asserts its own unprovability in F is self-contradictory:
>> Proving G requires a sequence of inference steps in F that prove that
>> they themselves do not exist.
>
> Except that the ACTUAL statement of G isn't in any way
> "Self-Contradictiory", so your "Isomorphism" / "Equivalence" is just
> your pathologica lie.
>
>>
>> That you continue to fail to understand this is not my mistake it is
>> your mistake.
>
> Nope, You are the one making the mistake.
>
> It is a demonstarted principle, that if EVERYONE disagrees with you, you
> are likely wrong. Even the greatest who came up with new ideas, were
> able to get at least a FEW of the smartest to understand what they were
> talking about.
>
> You have only gotten agreement from a couple at the bottom, and people
> you have "tricked" by the misuse of words, and who don't actually agree
> with your ideas.
>
>>
>> Gödel, Kurt 1931.
>> On Formally Undecidable Propositions of Principia Mathematica And
>> Related Systems
>>
>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>
>> Since Tarski directly stated that he is anchoring his comparable proof
>> in the actual Liar Paradox I have provided sufficient support for my
>> position.
>>
>
> Nope, In fact, he is using the non-truth bearing of the Liars Paradox
> for his proof,
>

I say that Tarski is using the Liar Paradox as the basis of his proof
and you say no I am wrong the truth is that Tarski is using the Liar
Paradox as the basis of his proof?

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/10/2023 6:29 PM, Richard Damon wrote:
> On 5/10/23 10:27 AM, olcott wrote:
>> On 5/10/2023 6:24 AM, Richard Damon wrote:
>>> On 5/9/23 10:46 PM, olcott wrote:
>>>> On 5/9/2023 8:30 PM, Richard Damon wrote:
>>>>> On 5/9/23 8:18 PM, olcott wrote:
>>>>
>>>>>> Gödel intended his actual G to be isomorphic to the above self-
>>>>>> referential expression.
>>>>>
>>>>> Nope, you are over-simplifying things.
>>>>
>>>> Not at all. I boiled them down to their barest essence. Gödel's G was
>>>> intended to be and is isomorphic to a self-contradictory expression.
>>>>
>>>> This is dead obvious in Tarski's comparable proof where he flat out
>>>> states that he is anchoring his proof in the actual Liar Paradox.
>>>>
>>>>
>>>
>>> So, you are just PROVING that you don't understand how logic actually
>>> works and are falling for your own Straw man Error.
>>>
>>
>> No I am proving to have a deeper understanding of these things than most
>> others have.
>
> Nope, just that you are so dumb you don't know what you don't understand.
>
I say that incorrectly. I have a deeper understanding OF THE ESSENCE OF
HIS PROOF. It is commonly understood that Gödel's actual proof is
isomorphic to {a proposition which asserts its own unprovability}. It is
also commonly understood that this is self-contradictory.

What is not commonly understood is that formal systems that cannot prove
self-contradictory expressions are not in any way deficient.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/10/23 11:01 PM, olcott wrote:
> On 5/10/2023 6:29 PM, Richard Damon wrote:

>>>
>>> Gödel, Kurt 1931.
>>> On Formally Undecidable Propositions of Principia Mathematica And
>>> Related Systems
>>>
>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>
>>> Since Tarski directly stated that he is anchoring his comparable proof
>>> in the actual Liar Paradox I have provided sufficient support for my
>>> position.
>>>
>>
>> Nope, In fact, he is using the non-truth bearing of the Liars Paradox
>> for his proof,
>>
>
> I say that Tarski is using the Liar Paradox as the basis of his proof
> and you say no I am wrong the truth is that Tarski is using the Liar
> Paradox as the basis of his proof?
>

YOU have been saying that because Tarski, erroneosly, finds that logic
can't prove the liar's paradox, his proof must be wrong, i.e there is
no definition of Truth.

I say that his proof shows that if a Definition of Truth (meaning a
determinate procedure to determine if any statement is true or false)
existed, then it would be possible to prove that the liar's paradox is a
true statement, which is NOT correct, thus there can not exist a
definition of truth.

You words are implying that we call systems incomplete or truth
undefinable because they can't resolve the Liar's Paradox.

The actual fact is that truth is undefinable, because such a definition
of truth creates the INCORRECT determination of a resolution of the
Liar's Paradox.

You are just showing you lack of understanding of what people are
saying, and a refusal to listen, (because you are afraid to learn you
are wrong) which leads to your stupidity.

On 5/10/23 11:08 PM, olcott wrote:
> On 5/10/2023 6:29 PM, Richard Damon wrote:
>> On 5/10/23 10:27 AM, olcott wrote:
>>> On 5/10/2023 6:24 AM, Richard Damon wrote:
>>>> On 5/9/23 10:46 PM, olcott wrote:
>>>>> On 5/9/2023 8:30 PM, Richard Damon wrote:
>>>>>> On 5/9/23 8:18 PM, olcott wrote:
>>>>>
>>>>>>> Gödel intended his actual G to be isomorphic to the above self-
>>>>>>> referential expression.
>>>>>>
>>>>>> Nope, you are over-simplifying things.
>>>>>
>>>>> Not at all. I boiled them down to their barest essence. Gödel's G was
>>>>> intended to be and is isomorphic to a self-contradictory expression.
>>>>>
>>>>> This is dead obvious in Tarski's comparable proof where he flat out
>>>>> states that he is anchoring his proof in the actual Liar Paradox.
>>>>>
>>>>>
>>>>
>>>> So, you are just PROVING that you don't understand how logic
>>>> actually works and are falling for your own Straw man Error.
>>>>
>>>
>>> No I am proving to have a deeper understanding of these things than most
>>> others have.
>>
>> Nope, just that you are so dumb you don't know what you don't understand.
>>
> I say that incorrectly. I have a deeper understanding OF THE ESSENCE OF
> HIS PROOF. It is commonly understood that Gödel's actual proof is
> isomorphic to {a proposition which asserts its own unprovability}. It is
> also commonly understood that this is self-contradictory.
>
> What is not commonly understood is that formal systems that cannot prove
> self-contradictory expressions are not in any way deficient.
>

But that isn't what his proof is about,

You just have a deeper MISunderstanding of what he is saying because you
don't understand what he is saying at all, but are just trying to
understand the altered strawman arguement that you think you can understand,

YOU FAIL.

None of thes proofs are about a system being deficient for not being
able to resolve a self-contradictory statement or a non-truth-bearer.
The fact you think they are just shows that you are misunderstanding the
proofs.

Godel shows a statement, THAT IS TRUE, (and thus CAN'T be
self-contradictory) that can not be proven in that system. This meets
the DEFINTION of "Incompleteness" in Logic.

Tarski shows that there are some statements, that have a truth value,
that we can not know that truth value, because the mere existance of a
"Definition" (deterministic method) to test them with leads to the
contradiction that the Liar's Paradox must be True..

The problem isn't that he expects that a system should be able to
resolve the Liar's Paradox, but that a "Definition of Truth" leads to a
claimed resolution, namely that the Liar's Paradox IS True (which means
it also must be False). He shows that a "Definition of Truth" turns the
Liar's Paradox from a non-truth-bearer into a Truth Bearer that is True
(and thus also False).

Your failure to understand this just shows your stupidity.