On 7/8/2023 8:29 PM, André G. Isaak wrote:
> On 2023-07-07 20:14, olcott wrote:
>
>> *I must use a stipulative definitions because there are no*
>> *conventional terms for the meanings that I must refer to*
>
> The problem is that you haven't offered any definitions at all,
> stipulative or otherwise. You have simply 'stipulated' "facts" that are
> contrary to reality.
>

Here is a slightly better way of saying it, it is still only a mere
sketch and possibly not much better than a high school level of quality.
When we integrate model theory with formal systems then we can obtain
True(L,x) as satisfiability. This leaves unsatisfiability as simply
meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).

I will have to refresh my memory of model theory to make sure that I did
not use conventional terms in an unconventional way.

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

On 7/9/23 2:18 PM, olcott wrote:
> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>> On 2023-07-07 20:14, olcott wrote:
>>
>>> *I must use a stipulative definitions because there are no*
>>> *conventional terms for the meanings that I must refer to*
>>
>> The problem is that you haven't offered any definitions at all,
>> stipulative or otherwise. You have simply 'stipulated' "facts" that
>> are contrary to reality.
>>
>
> Here is a slightly better way of saying it, it is still only a mere
> sketch and possibly not much better than a high school level of quality.
> When we integrate model theory with formal systems then we can obtain
> True(L,x) as satisfiability. This leaves unsatisfiability as simply
> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>
> I will have to refresh my memory of model theory to make sure that I did
> not use conventional terms in an unconventional way.
>

In other words, you ADMIT that you haven't ACTUALLY solved the problem.

Or even figured out a proper set of definitions, which after a
"lifetime" of work that needs to be done after they are defined might
show what you claim.

In other words, you have NOTHING.

There have been untold numbers of people starting with similar types of
ideas thinking they have found a way to solve the issues you claim to
have solved, who made similar starts, but then realized they have
actually failed.

The broad ideas seem to work, as you think you see in your system, but
when you get down to the details that you skim over in the overview, the
problems arise.

Note, just redefinining "Completeness" and "Satisfiability" doesn't
actually solve the problem, as those terms were defined the way they
were for a reason, which seem totally beyond your comprehesion.

On 7/9/2023 2:29 PM, Richard Damon wrote:
> On 7/9/23 2:18 PM, olcott wrote:
>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>> On 2023-07-07 20:14, olcott wrote:
>>>
>>>> *I must use a stipulative definitions because there are no*
>>>> *conventional terms for the meanings that I must refer to*
>>>
>>> The problem is that you haven't offered any definitions at all,
>>> stipulative or otherwise. You have simply 'stipulated' "facts" that
>>> are contrary to reality.
>>>
>>
>> Here is a slightly better way of saying it, it is still only a mere
>> sketch and possibly not much better than a high school level of quality.
>> When we integrate model theory with formal systems then we can obtain
>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>
>> I will have to refresh my memory of model theory to make sure that I did
>> not use conventional terms in an unconventional way.
>>
>
>
> In other words, you ADMIT that you haven't ACTUALLY solved the problem.
>
> Or even figured out a proper set of definitions, which after a
> "lifetime" of work that needs to be done after they are defined might
> show what you claim.
>
> In other words, you have NOTHING.
>
> There have been untold numbers of people starting with similar types of
> ideas thinking they have found a way to solve the issues you claim to
> have solved, who made similar starts, but then realized they have
> actually failed.
>
> The broad ideas seem to work, as you think you see in your system, but
> when you get down to the details that you skim over in the overview, the
> problems arise.
>
> Note, just redefinining "Completeness" and "Satisfiability" doesn't
> actually solve the problem, as those terms were defined the way they
> were for a reason, which seem totally beyond your comprehesion.

LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
Mathematical "incompleteness" is merely an idiomatic expression that
claims that for any language that is expressive enough to encode self-
contradictory expressions any formal system that cannot prove or
refute these semantically incorrect expressions is construed as
incomplete.

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

On 7/9/23 7:37 PM, olcott wrote:
> On 7/9/2023 2:29 PM, Richard Damon wrote:
>> On 7/9/23 2:18 PM, olcott wrote:
>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>> On 2023-07-07 20:14, olcott wrote:
>>>>
>>>>> *I must use a stipulative definitions because there are no*
>>>>> *conventional terms for the meanings that I must refer to*
>>>>
>>>> The problem is that you haven't offered any definitions at all,
>>>> stipulative or otherwise. You have simply 'stipulated' "facts" that
>>>> are contrary to reality.
>>>>
>>>
>>> Here is a slightly better way of saying it, it is still only a mere
>>> sketch and possibly not much better than a high school level of quality.
>>> When we integrate model theory with formal systems then we can obtain
>>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>>
>>> I will have to refresh my memory of model theory to make sure that I did
>>> not use conventional terms in an unconventional way.
>>>
>>
>>
>> In other words, you ADMIT that you haven't ACTUALLY solved the problem.
>>
>> Or even figured out a proper set of definitions, which after a
>> "lifetime" of work that needs to be done after they are defined might
>> show what you claim.
>>
>> In other words, you have NOTHING.
>>
>> There have been untold numbers of people starting with similar types
>> of ideas thinking they have found a way to solve the issues you claim
>> to have solved, who made similar starts, but then realized they have
>> actually failed.
>>
>> The broad ideas seem to work, as you think you see in your system, but
>> when you get down to the details that you skim over in the overview,
>> the problems arise.
>>
>> Note, just redefinining "Completeness" and "Satisfiability" doesn't
>> actually solve the problem, as those terms were defined the way they
>> were for a reason, which seem totally beyond your comprehesion.
>
> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
> Mathematical "incompleteness" is merely an idiomatic expression that
> claims that for any language that is expressive enough to encode self-
> contradictory expressions any formal system that cannot prove or
> refute these semantically incorrect expressions is construed as
> incomplete.
>

Talking about somthing you NEVER LEARNED make you make mistakes, because
you speak about things your are IGNORANT ofl.

"Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic (by
FORMALLY DEFINING "Completeness" of a Formal system).

The fact that you don't understand that, just means you are making the
mistake you accusse everyone else of making, of not looking at the
context, but here, the contexgt DOES matter.

It doesn't matter that you don't think it is a defintion that makes
sense, it IS the definition in formal system, and to disagree about that
just makes you into a LIAR.

Note, you also make the mistake of thinking the expressions are
"self-contradictor" when they are not, at least not by the actual
definition in the system. There is NOTHING "Self-Contradictory" about a
statement being True, but Unprovable, as Truth has weaker requirements
on it than Provable (Something being Provable but not True WOULD be
contradictory, which is actual a fact used in Godel's proof).

You are just PROVING that you are IGNORANT of the rules of logic, a
PATHOLOGICAL LIAR about what you claim you can actual "Prove" in logic,
and a total IDIOT and MORON when dealing with logic, because you
actually seem to think it is ok to just ignore rules because you don't
like them.

That seemn par for you, after all, isn't that what you claimed in the
child porn case, that it was "Ok" because those rules didn't apply to
you, because you were "God".

On 7/9/2023 7:22 PM, Richard Damon wrote:
> On 7/9/23 7:37 PM, olcott wrote:
>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>> On 7/9/23 2:18 PM, olcott wrote:
>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>
>>>>>> *I must use a stipulative definitions because there are no*
>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>
>>>>> The problem is that you haven't offered any definitions at all,
>>>>> stipulative or otherwise. You have simply 'stipulated' "facts" that
>>>>> are contrary to reality.
>>>>>
>>>>
>>>> Here is a slightly better way of saying it, it is still only a mere
>>>> sketch and possibly not much better than a high school level of
>>>> quality.
>>>> When we integrate model theory with formal systems then we can obtain
>>>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>>>
>>>> I will have to refresh my memory of model theory to make sure that I
>>>> did
>>>> not use conventional terms in an unconventional way.
>>>>
>>>
>>>
>>> In other words, you ADMIT that you haven't ACTUALLY solved the problem.
>>>
>>> Or even figured out a proper set of definitions, which after a
>>> "lifetime" of work that needs to be done after they are defined might
>>> show what you claim.
>>>
>>> In other words, you have NOTHING.
>>>
>>> There have been untold numbers of people starting with similar types
>>> of ideas thinking they have found a way to solve the issues you claim
>>> to have solved, who made similar starts, but then realized they have
>>> actually failed.
>>>
>>> The broad ideas seem to work, as you think you see in your system,
>>> but when you get down to the details that you skim over in the
>>> overview, the problems arise.
>>>
>>> Note, just redefinining "Completeness" and "Satisfiability" doesn't
>>> actually solve the problem, as those terms were defined the way they
>>> were for a reason, which seem totally beyond your comprehesion.
>>
>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>> Mathematical "incompleteness" is merely an idiomatic expression that
>> claims that for any language that is expressive enough to encode self-
>> contradictory expressions any formal system that cannot prove or
>> refute these semantically incorrect expressions is construed as
>> incomplete.
>>
>
> Talking about somthing you NEVER LEARNED make you make mistakes, because
> you speak about things your are IGNORANT ofl.
>
> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic (by
> FORMALLY DEFINING "Completeness" of a Formal system).
>
> The fact that you don't understand that, just means you are making the
> mistake you accusse everyone else of making, of not looking at the
> context, but here, the contexgt DOES matter.
>
> It doesn't matter that you don't think it is a defintion that makes
> sense, it IS the definition in formal system, and to disagree about that
> just makes you into a LIAR.
>

*This is satisfied by contradictory expression: φ*
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))

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

On 7/9/23 8:28 PM, olcott wrote:
> On 7/9/2023 7:22 PM, Richard Damon wrote:
>> On 7/9/23 7:37 PM, olcott wrote:
>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>
>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>
>>>>>> The problem is that you haven't offered any definitions at all,
>>>>>> stipulative or otherwise. You have simply 'stipulated' "facts"
>>>>>> that are contrary to reality.
>>>>>>
>>>>>
>>>>> Here is a slightly better way of saying it, it is still only a mere
>>>>> sketch and possibly not much better than a high school level of
>>>>> quality.
>>>>> When we integrate model theory with formal systems then we can obtain
>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>>>>
>>>>> I will have to refresh my memory of model theory to make sure that
>>>>> I did
>>>>> not use conventional terms in an unconventional way.
>>>>>
>>>>
>>>>
>>>> In other words, you ADMIT that you haven't ACTUALLY solved the problem.
>>>>
>>>> Or even figured out a proper set of definitions, which after a
>>>> "lifetime" of work that needs to be done after they are defined
>>>> might show what you claim.
>>>>
>>>> In other words, you have NOTHING.
>>>>
>>>> There have been untold numbers of people starting with similar types
>>>> of ideas thinking they have found a way to solve the issues you
>>>> claim to have solved, who made similar starts, but then realized
>>>> they have actually failed.
>>>>
>>>> The broad ideas seem to work, as you think you see in your system,
>>>> but when you get down to the details that you skim over in the
>>>> overview, the problems arise.
>>>>
>>>> Note, just redefinining "Completeness" and "Satisfiability" doesn't
>>>> actually solve the problem, as those terms were defined the way they
>>>> were for a reason, which seem totally beyond your comprehesion.
>>>
>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>> Mathematical "incompleteness" is merely an idiomatic expression that
>>> claims that for any language that is expressive enough to encode self-
>>> contradictory expressions any formal system that cannot prove or
>>> refute these semantically incorrect expressions is construed as
>>> incomplete.
>>>
>>
>> Talking about somthing you NEVER LEARNED make you make mistakes,
>> because you speak about things your are IGNORANT ofl.
>>
>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic (by
>> FORMALLY DEFINING "Completeness" of a Formal system).
>>
>> The fact that you don't understand that, just means you are making the
>> mistake you accusse everyone else of making, of not looking at the
>> context, but here, the contexgt DOES matter.
>>
>> It doesn't matter that you don't think it is a defintion that makes
>> sense, it IS the definition in formal system, and to disagree about
>> that just makes you into a LIAR.
>>
>
> *This is satisfied by contradictory expression: φ*
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>

Except that isn't a "Contradiction".

A Contradiction is the existance of a sentance that is both True and
False, that is

∃φ where φ ∧ ¬φ

Your terms (T ⊬ φ) and (T ⊬ ¬φ) aren't related by the negation symbol in
the right way.

¬(T ⊬ φ) isn't (T ⊬ ¬φ) but (T ⊢ φ)

You aren't performing your logic correctly, probably because you didn't
learn it.

So, you are just proven to be a LIAR.

On 7/9/2023 8:12 PM, Richard Damon wrote:
> On 7/9/23 8:28 PM, olcott wrote:
>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>> On 7/9/23 7:37 PM, olcott wrote:
>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>
>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>
>>>>>>> The problem is that you haven't offered any definitions at all,
>>>>>>> stipulative or otherwise. You have simply 'stipulated' "facts"
>>>>>>> that are contrary to reality.
>>>>>>>
>>>>>>
>>>>>> Here is a slightly better way of saying it, it is still only a mere
>>>>>> sketch and possibly not much better than a high school level of
>>>>>> quality.
>>>>>> When we integrate model theory with formal systems then we can obtain
>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>>>>>
>>>>>> I will have to refresh my memory of model theory to make sure that
>>>>>> I did
>>>>>> not use conventional terms in an unconventional way.
>>>>>>
>>>>>
>>>>>
>>>>> In other words, you ADMIT that you haven't ACTUALLY solved the
>>>>> problem.
>>>>>
>>>>> Or even figured out a proper set of definitions, which after a
>>>>> "lifetime" of work that needs to be done after they are defined
>>>>> might show what you claim.
>>>>>
>>>>> In other words, you have NOTHING.
>>>>>
>>>>> There have been untold numbers of people starting with similar
>>>>> types of ideas thinking they have found a way to solve the issues
>>>>> you claim to have solved, who made similar starts, but then
>>>>> realized they have actually failed.
>>>>>
>>>>> The broad ideas seem to work, as you think you see in your system,
>>>>> but when you get down to the details that you skim over in the
>>>>> overview, the problems arise.
>>>>>
>>>>> Note, just redefinining "Completeness" and "Satisfiability" doesn't
>>>>> actually solve the problem, as those terms were defined the way
>>>>> they were for a reason, which seem totally beyond your comprehesion.
>>>>
>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>> Mathematical "incompleteness" is merely an idiomatic expression that
>>>> claims that for any language that is expressive enough to encode self-
>>>> contradictory expressions any formal system that cannot prove or
>>>> refute these semantically incorrect expressions is construed as
>>>> incomplete.
>>>>
>>>
>>> Talking about somthing you NEVER LEARNED make you make mistakes,
>>> because you speak about things your are IGNORANT ofl.
>>>
>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic (by
>>> FORMALLY DEFINING "Completeness" of a Formal system).
>>>
>>> The fact that you don't understand that, just means you are making
>>> the mistake you accusse everyone else of making, of not looking at
>>> the context, but here, the contexgt DOES matter.
>>>
>>> It doesn't matter that you don't think it is a defintion that makes
>>> sense, it IS the definition in formal system, and to disagree about
>>> that just makes you into a LIAR.
>>>
>>
>> *This is satisfied by contradictory expression: φ*
>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>
>
> Except that isn't a "Contradiction".
>
> A Contradiction is the existance of a sentance that is both True and
> False, that is
>
> ∃φ where φ ∧ ¬φ
>

A self contradictory expression such as the formalized Liar Paradox
is satisfied by the above formula thus incorrectly proving that T is
incomplete.

>
> Your terms (T ⊬ φ) and (T ⊬ ¬φ) aren't related by the negation symbol in
> the right way.
>

My expression says that when φ is neither provable nor refutable in T
then T is incomplete. I have no idea how you can misconstrue this.

> ¬(T ⊬ φ) isn't (T ⊬ ¬φ) but (T ⊢ φ)
>
> You aren't performing your logic correctly, probably because you didn't
> learn it.
>
> So, you are just proven to be a LIAR.

Ad hominem makes you look quite foolish.

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

On 7/9/23 9:34 PM, olcott wrote:
> On 7/9/2023 8:12 PM, Richard Damon wrote:
>> On 7/9/23 8:28 PM, olcott wrote:
>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>
>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>
>>>>>>>> The problem is that you haven't offered any definitions at all,
>>>>>>>> stipulative or otherwise. You have simply 'stipulated' "facts"
>>>>>>>> that are contrary to reality.
>>>>>>>>
>>>>>>>
>>>>>>> Here is a slightly better way of saying it, it is still only a mere
>>>>>>> sketch and possibly not much better than a high school level of
>>>>>>> quality.
>>>>>>> When we integrate model theory with formal systems then we can
>>>>>>> obtain
>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>>>>>>
>>>>>>> I will have to refresh my memory of model theory to make sure
>>>>>>> that I did
>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>
>>>>>>
>>>>>>
>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved the
>>>>>> problem.
>>>>>>
>>>>>> Or even figured out a proper set of definitions, which after a
>>>>>> "lifetime" of work that needs to be done after they are defined
>>>>>> might show what you claim.
>>>>>>
>>>>>> In other words, you have NOTHING.
>>>>>>
>>>>>> There have been untold numbers of people starting with similar
>>>>>> types of ideas thinking they have found a way to solve the issues
>>>>>> you claim to have solved, who made similar starts, but then
>>>>>> realized they have actually failed.
>>>>>>
>>>>>> The broad ideas seem to work, as you think you see in your system,
>>>>>> but when you get down to the details that you skim over in the
>>>>>> overview, the problems arise.
>>>>>>
>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>> doesn't actually solve the problem, as those terms were defined
>>>>>> the way they were for a reason, which seem totally beyond your
>>>>>> comprehesion.
>>>>>
>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>> Mathematical "incompleteness" is merely an idiomatic expression that
>>>>> claims that for any language that is expressive enough to encode self-
>>>>> contradictory expressions any formal system that cannot prove or
>>>>> refute these semantically incorrect expressions is construed as
>>>>> incomplete.
>>>>>
>>>>
>>>> Talking about somthing you NEVER LEARNED make you make mistakes,
>>>> because you speak about things your are IGNORANT ofl.
>>>>
>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic
>>>> (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>
>>>> The fact that you don't understand that, just means you are making
>>>> the mistake you accusse everyone else of making, of not looking at
>>>> the context, but here, the contexgt DOES matter.
>>>>
>>>> It doesn't matter that you don't think it is a defintion that makes
>>>> sense, it IS the definition in formal system, and to disagree about
>>>> that just makes you into a LIAR.
>>>>
>>>
>>> *This is satisfied by contradictory expression: φ*
>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>
>>
>> Except that isn't a "Contradiction".
>>
>> A Contradiction is the existance of a sentance that is both True and
>> False, that is
>>
>> ∃φ where φ ∧ ¬φ
>>
>
> A self contradictory expression such as the formalized Liar Paradox
> is satisfied by the above formula thus incorrectly proving that T is
> incomplete.

But you have the wrong definition of incompleteness. The version using
(T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T, which means it
has a Truth Value in T.

Since the Liar's Paradox IS a Paradox, it doesn't actually HAVE a truth
value, and thus isn't in the system.

>
>>
>> Your terms (T ⊬ φ) and (T ⊬ ¬φ) aren't related by the negation symbol
>> in the right way.
>>
>
> My expression says that when φ is neither provable nor refutable in T
> then T is incomplete. I have no idea how you can misconstrue this.

But you are omitting the restriction on φ in the statement, φ must be a
statement in T.

You seem to have a blind spot to "Requirements" as you seem to often
omit them. Maybe because you goal is a unversal system for all
statements, which ISN'T the goal of standard logic, you just forget
about them.

>
>> ¬(T ⊬ φ) isn't (T ⊬ ¬φ) but (T ⊢ φ)
>>
>> You aren't performing your logic correctly, probably because you
>> didn't learn it.
>>
>> So, you are just proven to be a LIAR.
>
> Ad hominem makes you look quite foolish.
>

So, you don't understand the meaning of the term, thus showing the
statement was actually true.

You are just proving your stupidity.

On 7/9/2023 9:21 PM, Richard Damon wrote:
> On 7/9/23 9:34 PM, olcott wrote:
>> On 7/9/2023 8:12 PM, Richard Damon wrote:
>>> On 7/9/23 8:28 PM, olcott wrote:
>>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>>
>>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>>
>>>>>>>>> The problem is that you haven't offered any definitions at all,
>>>>>>>>> stipulative or otherwise. You have simply 'stipulated' "facts"
>>>>>>>>> that are contrary to reality.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Here is a slightly better way of saying it, it is still only a mere
>>>>>>>> sketch and possibly not much better than a high school level of
>>>>>>>> quality.
>>>>>>>> When we integrate model theory with formal systems then we can
>>>>>>>> obtain
>>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as simply
>>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable True(L,~x).
>>>>>>>>
>>>>>>>> I will have to refresh my memory of model theory to make sure
>>>>>>>> that I did
>>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved the
>>>>>>> problem.
>>>>>>>
>>>>>>> Or even figured out a proper set of definitions, which after a
>>>>>>> "lifetime" of work that needs to be done after they are defined
>>>>>>> might show what you claim.
>>>>>>>
>>>>>>> In other words, you have NOTHING.
>>>>>>>
>>>>>>> There have been untold numbers of people starting with similar
>>>>>>> types of ideas thinking they have found a way to solve the issues
>>>>>>> you claim to have solved, who made similar starts, but then
>>>>>>> realized they have actually failed.
>>>>>>>
>>>>>>> The broad ideas seem to work, as you think you see in your
>>>>>>> system, but when you get down to the details that you skim over
>>>>>>> in the overview, the problems arise.
>>>>>>>
>>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>>> doesn't actually solve the problem, as those terms were defined
>>>>>>> the way they were for a reason, which seem totally beyond your
>>>>>>> comprehesion.
>>>>>>
>>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>>> Mathematical "incompleteness" is merely an idiomatic expression that
>>>>>> claims that for any language that is expressive enough to encode
>>>>>> self-
>>>>>> contradictory expressions any formal system that cannot prove or
>>>>>> refute these semantically incorrect expressions is construed as
>>>>>> incomplete.
>>>>>>
>>>>>
>>>>> Talking about somthing you NEVER LEARNED make you make mistakes,
>>>>> because you speak about things your are IGNORANT ofl.
>>>>>
>>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic
>>>>> (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>>
>>>>> The fact that you don't understand that, just means you are making
>>>>> the mistake you accusse everyone else of making, of not looking at
>>>>> the context, but here, the contexgt DOES matter.
>>>>>
>>>>> It doesn't matter that you don't think it is a defintion that makes
>>>>> sense, it IS the definition in formal system, and to disagree about
>>>>> that just makes you into a LIAR.
>>>>>
>>>>
>>>> *This is satisfied by contradictory expression: φ*
>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>
>>>
>>> Except that isn't a "Contradiction".
>>>
>>> A Contradiction is the existance of a sentance that is both True and
>>> False, that is
>>>
>>> ∃φ where φ ∧ ¬φ
>>>
>>
>> A self contradictory expression such as the formalized Liar Paradox
>> is satisfied by the above formula thus incorrectly proving that T is
>> incomplete.
>
> But you have the wrong definition of incompleteness. The version using
> (T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T, which means it
> has a Truth Value in T.
>

You are confused

"A formula φ is independent of T if T ⊬ φ and T ⊬ ¬φ. A
theory T is incomplete if there is a sentence φ in L(T)
such that φ is independent of T; otherwise, T is complete."
https://arxiv.org/pdf/1902.06658.pdf

Every self-contradictory expression that can be expressed in L(T)
(the formal language of T) satisfies the above formula.

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

On 7/9/23 10:50 PM, olcott wrote:
> On 7/9/2023 9:21 PM, Richard Damon wrote:
>> On 7/9/23 9:34 PM, olcott wrote:
>>> On 7/9/2023 8:12 PM, Richard Damon wrote:
>>>> On 7/9/23 8:28 PM, olcott wrote:
>>>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>>>
>>>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>>>
>>>>>>>>>> The problem is that you haven't offered any definitions at
>>>>>>>>>> all, stipulative or otherwise. You have simply 'stipulated'
>>>>>>>>>> "facts" that are contrary to reality.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Here is a slightly better way of saying it, it is still only a
>>>>>>>>> mere
>>>>>>>>> sketch and possibly not much better than a high school level of
>>>>>>>>> quality.
>>>>>>>>> When we integrate model theory with formal systems then we can
>>>>>>>>> obtain
>>>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as
>>>>>>>>> simply
>>>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable
>>>>>>>>> True(L,~x).
>>>>>>>>>
>>>>>>>>> I will have to refresh my memory of model theory to make sure
>>>>>>>>> that I did
>>>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved the
>>>>>>>> problem.
>>>>>>>>
>>>>>>>> Or even figured out a proper set of definitions, which after a
>>>>>>>> "lifetime" of work that needs to be done after they are defined
>>>>>>>> might show what you claim.
>>>>>>>>
>>>>>>>> In other words, you have NOTHING.
>>>>>>>>
>>>>>>>> There have been untold numbers of people starting with similar
>>>>>>>> types of ideas thinking they have found a way to solve the
>>>>>>>> issues you claim to have solved, who made similar starts, but
>>>>>>>> then realized they have actually failed.
>>>>>>>>
>>>>>>>> The broad ideas seem to work, as you think you see in your
>>>>>>>> system, but when you get down to the details that you skim over
>>>>>>>> in the overview, the problems arise.
>>>>>>>>
>>>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>>>> doesn't actually solve the problem, as those terms were defined
>>>>>>>> the way they were for a reason, which seem totally beyond your
>>>>>>>> comprehesion.
>>>>>>>
>>>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>>>> Mathematical "incompleteness" is merely an idiomatic expression that
>>>>>>> claims that for any language that is expressive enough to encode
>>>>>>> self-
>>>>>>> contradictory expressions any formal system that cannot prove or
>>>>>>> refute these semantically incorrect expressions is construed as
>>>>>>> incomplete.
>>>>>>>
>>>>>>
>>>>>> Talking about somthing you NEVER LEARNED make you make mistakes,
>>>>>> because you speak about things your are IGNORANT ofl.
>>>>>>
>>>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic
>>>>>> (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>>>
>>>>>> The fact that you don't understand that, just means you are making
>>>>>> the mistake you accusse everyone else of making, of not looking at
>>>>>> the context, but here, the contexgt DOES matter.
>>>>>>
>>>>>> It doesn't matter that you don't think it is a defintion that
>>>>>> makes sense, it IS the definition in formal system, and to
>>>>>> disagree about that just makes you into a LIAR.
>>>>>>
>>>>>
>>>>> *This is satisfied by contradictory expression: φ*
>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>
>>>>
>>>> Except that isn't a "Contradiction".
>>>>
>>>> A Contradiction is the existance of a sentance that is both True and
>>>> False, that is
>>>>
>>>> ∃φ where φ ∧ ¬φ
>>>>
>>>
>>> A self contradictory expression such as the formalized Liar Paradox
>>> is satisfied by the above formula thus incorrectly proving that T is
>>> incomplete.
>>
>> But you have the wrong definition of incompleteness. The version using
>> (T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T, which means it
>> has a Truth Value in T.
>>
>
> You are confused
>
>    "A formula φ is independent of T if T ⊬ φ and T ⊬ ¬φ. A
>     theory T is incomplete if there is a sentence φ in L(T)
>     such that φ is independent of T; otherwise, T is complete."
>     https://arxiv.org/pdf/1902.06658.pdf
>
> Every self-contradictory expression that can be expressed in L(T)
> (the formal language of T) satisfies the above formula.

And what self-contradictiory expression can be expressed in L(T)?

Or are you just assuming that such an expression exists? (Your common flaw).

Do you even know what they are talking about, as it is a TECHNICAL term
with specific meaning so trying to apply some generic "Natuaral
Language" meaning is going to get you a wrong answer.

On 7/9/2023 10:54 PM, Richard Damon wrote:
> On 7/9/23 10:50 PM, olcott wrote:
>> On 7/9/2023 9:21 PM, Richard Damon wrote:
>>> On 7/9/23 9:34 PM, olcott wrote:
>>>> On 7/9/2023 8:12 PM, Richard Damon wrote:
>>>>> On 7/9/23 8:28 PM, olcott wrote:
>>>>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>>>>
>>>>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>>>>
>>>>>>>>>>> The problem is that you haven't offered any definitions at
>>>>>>>>>>> all, stipulative or otherwise. You have simply 'stipulated'
>>>>>>>>>>> "facts" that are contrary to reality.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Here is a slightly better way of saying it, it is still only a
>>>>>>>>>> mere
>>>>>>>>>> sketch and possibly not much better than a high school level
>>>>>>>>>> of quality.
>>>>>>>>>> When we integrate model theory with formal systems then we can
>>>>>>>>>> obtain
>>>>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as
>>>>>>>>>> simply
>>>>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable
>>>>>>>>>> True(L,~x).
>>>>>>>>>>
>>>>>>>>>> I will have to refresh my memory of model theory to make sure
>>>>>>>>>> that I did
>>>>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved the
>>>>>>>>> problem.
>>>>>>>>>
>>>>>>>>> Or even figured out a proper set of definitions, which after a
>>>>>>>>> "lifetime" of work that needs to be done after they are defined
>>>>>>>>> might show what you claim.
>>>>>>>>>
>>>>>>>>> In other words, you have NOTHING.
>>>>>>>>>
>>>>>>>>> There have been untold numbers of people starting with similar
>>>>>>>>> types of ideas thinking they have found a way to solve the
>>>>>>>>> issues you claim to have solved, who made similar starts, but
>>>>>>>>> then realized they have actually failed.
>>>>>>>>>
>>>>>>>>> The broad ideas seem to work, as you think you see in your
>>>>>>>>> system, but when you get down to the details that you skim over
>>>>>>>>> in the overview, the problems arise.
>>>>>>>>>
>>>>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>>>>> doesn't actually solve the problem, as those terms were defined
>>>>>>>>> the way they were for a reason, which seem totally beyond your
>>>>>>>>> comprehesion.
>>>>>>>>
>>>>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>>>>> Mathematical "incompleteness" is merely an idiomatic expression
>>>>>>>> that
>>>>>>>> claims that for any language that is expressive enough to encode
>>>>>>>> self-
>>>>>>>> contradictory expressions any formal system that cannot prove or
>>>>>>>> refute these semantically incorrect expressions is construed as
>>>>>>>> incomplete.
>>>>>>>>
>>>>>>>
>>>>>>> Talking about somthing you NEVER LEARNED make you make mistakes,
>>>>>>> because you speak about things your are IGNORANT ofl.
>>>>>>>
>>>>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in logic
>>>>>>> (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>>>>
>>>>>>> The fact that you don't understand that, just means you are
>>>>>>> making the mistake you accusse everyone else of making, of not
>>>>>>> looking at the context, but here, the contexgt DOES matter.
>>>>>>>
>>>>>>> It doesn't matter that you don't think it is a defintion that
>>>>>>> makes sense, it IS the definition in formal system, and to
>>>>>>> disagree about that just makes you into a LIAR.
>>>>>>>
>>>>>>
>>>>>> *This is satisfied by contradictory expression: φ*
>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>
>>>>>
>>>>> Except that isn't a "Contradiction".
>>>>>
>>>>> A Contradiction is the existance of a sentance that is both True
>>>>> and False, that is
>>>>>
>>>>> ∃φ where φ ∧ ¬φ
>>>>>
>>>>
>>>> A self contradictory expression such as the formalized Liar Paradox
>>>> is satisfied by the above formula thus incorrectly proving that T is
>>>> incomplete.
>>>
>>> But you have the wrong definition of incompleteness. The version
>>> using (T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T, which
>>> means it has a Truth Value in T.
>>>
>>
>> You are confused
>>
>>     "A formula φ is independent of T if T ⊬ φ and T ⊬ ¬φ. A
>>      theory T is incomplete if there is a sentence φ in L(T)
>>      such that φ is independent of T; otherwise, T is complete."
>>      https://arxiv.org/pdf/1902.06658.pdf
>>
>> Every self-contradictory expression that can be expressed in L(T)
>> (the formal language of T) satisfies the above formula.
>
>
> And what self-contradictiory expression can be expressed in L(T)?

First agree that when a self-contradictory expression would match the
formula that to call T "incomplete" on this basis would be idiomatic
and not have anything to do with any capabilities that T is missing.

>
> Or are you just assuming that such an expression exists? (Your common
> flaw).
>
> Do you even know what they are talking about, as it is a TECHNICAL term
> with specific meaning so trying to apply some generic "Natuaral
> Language" meaning is going to get you a wrong answer.
>

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

On 7/10/23 1:32 AM, olcott wrote:
> On 7/9/2023 10:54 PM, Richard Damon wrote:
>> On 7/9/23 10:50 PM, olcott wrote:
>>> On 7/9/2023 9:21 PM, Richard Damon wrote:
>>>> On 7/9/23 9:34 PM, olcott wrote:
>>>>> On 7/9/2023 8:12 PM, Richard Damon wrote:
>>>>>> On 7/9/23 8:28 PM, olcott wrote:
>>>>>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>>>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>>>>>
>>>>>>>>>>>> The problem is that you haven't offered any definitions at
>>>>>>>>>>>> all, stipulative or otherwise. You have simply 'stipulated'
>>>>>>>>>>>> "facts" that are contrary to reality.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Here is a slightly better way of saying it, it is still only
>>>>>>>>>>> a mere
>>>>>>>>>>> sketch and possibly not much better than a high school level
>>>>>>>>>>> of quality.
>>>>>>>>>>> When we integrate model theory with formal systems then we
>>>>>>>>>>> can obtain
>>>>>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as
>>>>>>>>>>> simply
>>>>>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable
>>>>>>>>>>> True(L,~x).
>>>>>>>>>>>
>>>>>>>>>>> I will have to refresh my memory of model theory to make sure
>>>>>>>>>>> that I did
>>>>>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved the
>>>>>>>>>> problem.
>>>>>>>>>>
>>>>>>>>>> Or even figured out a proper set of definitions, which after a
>>>>>>>>>> "lifetime" of work that needs to be done after they are
>>>>>>>>>> defined might show what you claim.
>>>>>>>>>>
>>>>>>>>>> In other words, you have NOTHING.
>>>>>>>>>>
>>>>>>>>>> There have been untold numbers of people starting with similar
>>>>>>>>>> types of ideas thinking they have found a way to solve the
>>>>>>>>>> issues you claim to have solved, who made similar starts, but
>>>>>>>>>> then realized they have actually failed.
>>>>>>>>>>
>>>>>>>>>> The broad ideas seem to work, as you think you see in your
>>>>>>>>>> system, but when you get down to the details that you skim
>>>>>>>>>> over in the overview, the problems arise.
>>>>>>>>>>
>>>>>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>>>>>> doesn't actually solve the problem, as those terms were
>>>>>>>>>> defined the way they were for a reason, which seem totally
>>>>>>>>>> beyond your comprehesion.
>>>>>>>>>
>>>>>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>>>>>> Mathematical "incompleteness" is merely an idiomatic expression
>>>>>>>>> that
>>>>>>>>> claims that for any language that is expressive enough to
>>>>>>>>> encode self-
>>>>>>>>> contradictory expressions any formal system that cannot prove or
>>>>>>>>> refute these semantically incorrect expressions is construed as
>>>>>>>>> incomplete.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Talking about somthing you NEVER LEARNED make you make mistakes,
>>>>>>>> because you speak about things your are IGNORANT ofl.
>>>>>>>>
>>>>>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in
>>>>>>>> logic (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>>>>>
>>>>>>>> The fact that you don't understand that, just means you are
>>>>>>>> making the mistake you accusse everyone else of making, of not
>>>>>>>> looking at the context, but here, the contexgt DOES matter.
>>>>>>>>
>>>>>>>> It doesn't matter that you don't think it is a defintion that
>>>>>>>> makes sense, it IS the definition in formal system, and to
>>>>>>>> disagree about that just makes you into a LIAR.
>>>>>>>>
>>>>>>>
>>>>>>> *This is satisfied by contradictory expression: φ*
>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>
>>>>>>
>>>>>> Except that isn't a "Contradiction".
>>>>>>
>>>>>> A Contradiction is the existance of a sentance that is both True
>>>>>> and False, that is
>>>>>>
>>>>>> ∃φ where φ ∧ ¬φ
>>>>>>
>>>>>
>>>>> A self contradictory expression such as the formalized Liar Paradox
>>>>> is satisfied by the above formula thus incorrectly proving that T is
>>>>> incomplete.
>>>>
>>>> But you have the wrong definition of incompleteness. The version
>>>> using (T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T, which
>>>> means it has a Truth Value in T.
>>>>
>>>
>>> You are confused
>>>
>>>     "A formula φ is independent of T if T ⊬ φ and T ⊬ ¬φ. A
>>>      theory T is incomplete if there is a sentence φ in L(T)
>>>      such that φ is independent of T; otherwise, T is complete."
>>>      https://arxiv.org/pdf/1902.06658.pdf
>>>
>>> Every self-contradictory expression that can be expressed in L(T)
>>> (the formal language of T) satisfies the above formula.
>>
>>
>> And what self-contradictiory expression can be expressed in L(T)?
>
> First agree that when a self-contradictory expression would match the
> formula that to call T "incomplete" on this basis would be idiomatic
> and not have anything to do with any capabilities that T is missing.

Why? You are arguing about impossible hypothetical, which is illogical.

That has always been one of your major problems, you don't understand
that some things are just impossible, because you don't understand what
Truth actually is.

>
>>
>> Or are you just assuming that such an expression exists? (Your common
>> flaw).
>>
>> Do you even know what they are talking about, as it is a TECHNICAL
>> term with specific meaning so trying to apply some generic "Natuaral
>> Language" meaning is going to get you a wrong answer.
>>
>

On 7/10/2023 6:25 AM, Richard Damon wrote:
> On 7/10/23 1:32 AM, olcott wrote:
>> On 7/9/2023 10:54 PM, Richard Damon wrote:
>>> On 7/9/23 10:50 PM, olcott wrote:
>>>> On 7/9/2023 9:21 PM, Richard Damon wrote:
>>>>> On 7/9/23 9:34 PM, olcott wrote:
>>>>>> On 7/9/2023 8:12 PM, Richard Damon wrote:
>>>>>>> On 7/9/23 8:28 PM, olcott wrote:
>>>>>>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>>>>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>>>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>>>>>>
>>>>>>>>>>>>> The problem is that you haven't offered any definitions at
>>>>>>>>>>>>> all, stipulative or otherwise. You have simply 'stipulated'
>>>>>>>>>>>>> "facts" that are contrary to reality.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Here is a slightly better way of saying it, it is still only
>>>>>>>>>>>> a mere
>>>>>>>>>>>> sketch and possibly not much better than a high school level
>>>>>>>>>>>> of quality.
>>>>>>>>>>>> When we integrate model theory with formal systems then we
>>>>>>>>>>>> can obtain
>>>>>>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability as
>>>>>>>>>>>> simply
>>>>>>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable
>>>>>>>>>>>> True(L,~x).
>>>>>>>>>>>>
>>>>>>>>>>>> I will have to refresh my memory of model theory to make
>>>>>>>>>>>> sure that I did
>>>>>>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved
>>>>>>>>>>> the problem.
>>>>>>>>>>>
>>>>>>>>>>> Or even figured out a proper set of definitions, which after
>>>>>>>>>>> a "lifetime" of work that needs to be done after they are
>>>>>>>>>>> defined might show what you claim.
>>>>>>>>>>>
>>>>>>>>>>> In other words, you have NOTHING.
>>>>>>>>>>>
>>>>>>>>>>> There have been untold numbers of people starting with
>>>>>>>>>>> similar types of ideas thinking they have found a way to
>>>>>>>>>>> solve the issues you claim to have solved, who made similar
>>>>>>>>>>> starts, but then realized they have actually failed.
>>>>>>>>>>>
>>>>>>>>>>> The broad ideas seem to work, as you think you see in your
>>>>>>>>>>> system, but when you get down to the details that you skim
>>>>>>>>>>> over in the overview, the problems arise.
>>>>>>>>>>>
>>>>>>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>>>>>>> doesn't actually solve the problem, as those terms were
>>>>>>>>>>> defined the way they were for a reason, which seem totally
>>>>>>>>>>> beyond your comprehesion.
>>>>>>>>>>
>>>>>>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>>>>>>> Mathematical "incompleteness" is merely an idiomatic
>>>>>>>>>> expression that
>>>>>>>>>> claims that for any language that is expressive enough to
>>>>>>>>>> encode self-
>>>>>>>>>> contradictory expressions any formal system that cannot prove or
>>>>>>>>>> refute these semantically incorrect expressions is construed as
>>>>>>>>>> incomplete.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Talking about somthing you NEVER LEARNED make you make
>>>>>>>>> mistakes, because you speak about things your are IGNORANT ofl.
>>>>>>>>>
>>>>>>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in
>>>>>>>>> logic (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>>>>>>
>>>>>>>>> The fact that you don't understand that, just means you are
>>>>>>>>> making the mistake you accusse everyone else of making, of not
>>>>>>>>> looking at the context, but here, the contexgt DOES matter.
>>>>>>>>>
>>>>>>>>> It doesn't matter that you don't think it is a defintion that
>>>>>>>>> makes sense, it IS the definition in formal system, and to
>>>>>>>>> disagree about that just makes you into a LIAR.
>>>>>>>>>
>>>>>>>>
>>>>>>>> *This is satisfied by contradictory expression: φ*
>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>
>>>>>>>
>>>>>>> Except that isn't a "Contradiction".
>>>>>>>
>>>>>>> A Contradiction is the existance of a sentance that is both True
>>>>>>> and False, that is
>>>>>>>
>>>>>>> ∃φ where φ ∧ ¬φ
>>>>>>>
>>>>>>
>>>>>> A self contradictory expression such as the formalized Liar Paradox
>>>>>> is satisfied by the above formula thus incorrectly proving that T is
>>>>>> incomplete.
>>>>>
>>>>> But you have the wrong definition of incompleteness. The version
>>>>> using (T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T, which
>>>>> means it has a Truth Value in T.
>>>>>
>>>>
>>>> You are confused
>>>>
>>>>     "A formula φ is independent of T if T ⊬ φ and T ⊬ ¬φ. A
>>>>      theory T is incomplete if there is a sentence φ in L(T)
>>>>      such that φ is independent of T; otherwise, T is complete."
>>>>      https://arxiv.org/pdf/1902.06658.pdf
>>>>
>>>> Every self-contradictory expression that can be expressed in L(T)
>>>> (the formal language of T) satisfies the above formula.
>>>
>>>
>>> And what self-contradictiory expression can be expressed in L(T)?
>>
>> First agree that when a self-contradictory expression would match the
>> formula that to call T "incomplete" on this basis would be idiomatic
>> and not have anything to do with any capabilities that T is missing.
>
> Why? You are arguing about impossible hypothetical, which is illogical.
>

This is a test to see if you are invested in an honest dialogue.
It really seems that you are not. It seems that you are only
interested in rebuttal.

That you say that formalizing the Liar Paradox is impossible
or that the formalized Liar Paradox would not match the above
formula really seems to show that you flunk this test.

On 7/10/23 8:49 AM, olcott wrote:
> On 7/10/2023 6:25 AM, Richard Damon wrote:
>> On 7/10/23 1:32 AM, olcott wrote:
>>> On 7/9/2023 10:54 PM, Richard Damon wrote:
>>>> On 7/9/23 10:50 PM, olcott wrote:
>>>>> On 7/9/2023 9:21 PM, Richard Damon wrote:
>>>>>> On 7/9/23 9:34 PM, olcott wrote:
>>>>>>> On 7/9/2023 8:12 PM, Richard Damon wrote:
>>>>>>>> On 7/9/23 8:28 PM, olcott wrote:
>>>>>>>>> On 7/9/2023 7:22 PM, Richard Damon wrote:
>>>>>>>>>> On 7/9/23 7:37 PM, olcott wrote:
>>>>>>>>>>> On 7/9/2023 2:29 PM, Richard Damon wrote:
>>>>>>>>>>>> On 7/9/23 2:18 PM, olcott wrote:
>>>>>>>>>>>>> On 7/8/2023 8:29 PM, André G. Isaak wrote:
>>>>>>>>>>>>>> On 2023-07-07 20:14, olcott wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> *I must use a stipulative definitions because there are no*
>>>>>>>>>>>>>>> *conventional terms for the meanings that I must refer to*
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The problem is that you haven't offered any definitions at
>>>>>>>>>>>>>> all, stipulative or otherwise. You have simply
>>>>>>>>>>>>>> 'stipulated' "facts" that are contrary to reality.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Here is a slightly better way of saying it, it is still
>>>>>>>>>>>>> only a mere
>>>>>>>>>>>>> sketch and possibly not much better than a high school
>>>>>>>>>>>>> level of quality.
>>>>>>>>>>>>> When we integrate model theory with formal systems then we
>>>>>>>>>>>>> can obtain
>>>>>>>>>>>>> True(L,x) as satisfiability. This leaves unsatisfiability
>>>>>>>>>>>>> as simply
>>>>>>>>>>>>> meaning Untrue(L,x) with False(L,x) meaning satisfiable
>>>>>>>>>>>>> True(L,~x).
>>>>>>>>>>>>>
>>>>>>>>>>>>> I will have to refresh my memory of model theory to make
>>>>>>>>>>>>> sure that I did
>>>>>>>>>>>>> not use conventional terms in an unconventional way.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> In other words, you ADMIT that you haven't ACTUALLY solved
>>>>>>>>>>>> the problem.
>>>>>>>>>>>>
>>>>>>>>>>>> Or even figured out a proper set of definitions, which after
>>>>>>>>>>>> a "lifetime" of work that needs to be done after they are
>>>>>>>>>>>> defined might show what you claim.
>>>>>>>>>>>>
>>>>>>>>>>>> In other words, you have NOTHING.
>>>>>>>>>>>>
>>>>>>>>>>>> There have been untold numbers of people starting with
>>>>>>>>>>>> similar types of ideas thinking they have found a way to
>>>>>>>>>>>> solve the issues you claim to have solved, who made similar
>>>>>>>>>>>> starts, but then realized they have actually failed.
>>>>>>>>>>>>
>>>>>>>>>>>> The broad ideas seem to work, as you think you see in your
>>>>>>>>>>>> system, but when you get down to the details that you skim
>>>>>>>>>>>> over in the overview, the problems arise.
>>>>>>>>>>>>
>>>>>>>>>>>> Note, just redefinining "Completeness" and "Satisfiability"
>>>>>>>>>>>> doesn't actually solve the problem, as those terms were
>>>>>>>>>>>> defined the way they were for a reason, which seem totally
>>>>>>>>>>>> beyond your comprehesion.
>>>>>>>>>>>
>>>>>>>>>>> LEARNED-BY-ROTE-PEOPLE WILL-INCORRECTLY-REJECT-THIS
>>>>>>>>>>> Mathematical "incompleteness" is merely an idiomatic
>>>>>>>>>>> expression that
>>>>>>>>>>> claims that for any language that is expressive enough to
>>>>>>>>>>> encode self-
>>>>>>>>>>> contradictory expressions any formal system that cannot prove or
>>>>>>>>>>> refute these semantically incorrect expressions is construed as
>>>>>>>>>>> incomplete.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Talking about somthing you NEVER LEARNED make you make
>>>>>>>>>> mistakes, because you speak about things your are IGNORANT ofl.
>>>>>>>>>>
>>>>>>>>>> "Incompletness" is not "Idiomatic", but FROMALLY DEFINED in
>>>>>>>>>> logic (by FORMALLY DEFINING "Completeness" of a Formal system).
>>>>>>>>>>
>>>>>>>>>> The fact that you don't understand that, just means you are
>>>>>>>>>> making the mistake you accusse everyone else of making, of not
>>>>>>>>>> looking at the context, but here, the contexgt DOES matter.
>>>>>>>>>>
>>>>>>>>>> It doesn't matter that you don't think it is a defintion that
>>>>>>>>>> makes sense, it IS the definition in formal system, and to
>>>>>>>>>> disagree about that just makes you into a LIAR.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> *This is satisfied by contradictory expression: φ*
>>>>>>>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ))
>>>>>>>>>
>>>>>>>>
>>>>>>>> Except that isn't a "Contradiction".
>>>>>>>>
>>>>>>>> A Contradiction is the existance of a sentance that is both True
>>>>>>>> and False, that is
>>>>>>>>
>>>>>>>> ∃φ where φ ∧ ¬φ
>>>>>>>>
>>>>>>>
>>>>>>> A self contradictory expression such as the formalized Liar Paradox
>>>>>>> is satisfied by the above formula thus incorrectly proving that T is
>>>>>>> incomplete.
>>>>>>
>>>>>> But you have the wrong definition of incompleteness. The version
>>>>>> using (T ⊬ φ) ∧ (T ⊬ ¬φ) requires that φ be a statement in T,
>>>>>> which means it has a Truth Value in T.
>>>>>>
>>>>>
>>>>> You are confused
>>>>>
>>>>>     "A formula φ is independent of T if T ⊬ φ and T ⊬ ¬φ. A
>>>>>      theory T is incomplete if there is a sentence φ in L(T)
>>>>>      such that φ is independent of T; otherwise, T is complete."
>>>>>      https://arxiv.org/pdf/1902.06658.pdf
>>>>>
>>>>> Every self-contradictory expression that can be expressed in L(T)
>>>>> (the formal language of T) satisfies the above formula.
>>>>
>>>>
>>>> And what self-contradictiory expression can be expressed in L(T)?
>>>
>>> First agree that when a self-contradictory expression would match the
>>> formula that to call T "incomplete" on this basis would be idiomatic
>>> and not have anything to do with any capabilities that T is missing.
>>
>> Why? You are arguing about impossible hypothetical, which is illogical.
>>
>
> This is a test to see if you are invested in an honest dialogue.
> It really seems that you are not. It seems that you are only
> interested in rebuttal.