ZFC was able to reject epistemological antinomies by screening
out the pathological self-reference derived by sets as members
of themselves. Russell's Paradox was eliminated be defining set
theory differently.

In the same way that Russell's Paradox was eliminated we can
get rid of other epistemological antinomies. It is pretty
obvious that epistemological antinomies are simply semantically
unsound.

When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.

Since we have already fixed the undecidability issue of Russell's
Paradox by redefining set theory the precedent has already been
set that we can correct these issues by redefining the meaning
of their terms.

Because the undecidability of Russell's Paradox was fixed by changing
the meaning of the term {set theory} we can eliminate incompleteness
and undecidability by redefining meaning of the term {formal system}
as detailed above.

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

On 11/18/23 11:32 AM, olcott wrote:
> ZFC was able to reject epistemological antinomies by screening
> out the pathological self-reference derived by sets as members
> of themselves. Russell's Paradox was eliminated be defining set
> theory differently.
>
> In the same way that Russell's Paradox was eliminated we can
> get rid of other epistemological antinomies. It is pretty
> obvious that epistemological antinomies are simply semantically
> unsound.
>
> When we define True(L, x) as (L ⊢ x) provable from the axioms
> of L, then epistemological antinomies become simply untrue and
> no longer show incompleteness or undecidability.
>
> Since we have already fixed the undecidability issue of Russell's
> Paradox by redefining set theory the precedent has already been
> set that we can correct these issues by redefining the meaning
> of their terms.
>
> Because the undecidability of Russell's Paradox was fixed by changing
> the meaning of the term {set theory} we can eliminate incompleteness
> and undecidability by redefining meaning of the term {formal system}
> as detailed above.
>

But that doesn't abolish ALL "undecideable" decision problems.

Halting is still "Undecidable" by the meaning of the word, and the
actual problem doesn't have the "pathological self-reference" that you
are trying to refer to.

Your problem is that you don't seem to understand what a "reference"
actually is, and thus what a "self-reference" actually means.

Asking H to decide on a program that happens to be built on a copy of
the algorithm that H uses, is NOT a "reference". You only try to show
one, by creating a environment what isn't actually an "equivalent" to
the environment of a Turing Machine deciding on the representation of
another machine, and as such, your "H" isn't actually the equivalent of
any Turing Machine that meets the definition of a Halt Decider.

Yes, if you define that True means Provable, you can get a system that
dosn't have incompleteness, you also can't get the full set of
properties of the Natural Numbers in such a system.

Godel proves that by showing that from the established properties of the
Natural Numbers, you can construct a statement that IS TRUE, but
UNPROVABLE in that system.

Thus, he proves that you your system, must either not be able to show
the needed properties of the Natural Numbers, or it is inconsistant.

If you want to try to prove him wrong, you just need to start from your
logical basis, and then show that you actually CAN derive those
properties, and then prove that you system is still consistant.

This has been pointed out to you many times in the past, but it seems
that you understand that the task is just too great for your little
mind. This just points out that you ideas are actually worthless, as you
are postulating a fundamental change in the nature of logic, but then
are unable to show what that actually does.

Also, you don't understand that this idea isn't actually "new", but is
very similar to ideas that other have come up with, its just they
understand that their ideas are of limited use in restricted fields of
logic, while you don't understand that fact.

On 11/18/2023 10:32 AM, olcott wrote:
> ZFC was able to reject epistemological antinomies by screening
> out the pathological self-reference derived by sets as members
> of themselves. Russell's Paradox was eliminated be defining set
> theory differently.
>
> In the same way that Russell's Paradox was eliminated we can
> get rid of other epistemological antinomies. It is pretty
> obvious that epistemological antinomies are simply semantically
> unsound.
>
> When we define True(L, x) as (L ⊢ x) provable from the axioms
> of L, then epistemological antinomies become simply untrue and
> no longer show incompleteness or undecidability.
>
> Since we have already fixed the undecidability issue of Russell's
> Paradox by redefining set theory the precedent has already been
> set that we can correct these issues by redefining the meaning
> of their terms.
>
> Because the undecidability of Russell's Paradox was fixed by changing
> the meaning of the term {set theory} we can eliminate incompleteness
> and undecidability by redefining meaning of the term {formal system}
> as detailed above.

We can eliminate incompleteness and undecidability derived by
epistemological antinomies by redefining meaning of the term
{formal system} as detailed above.

For the halting problem H(D,D) simply screens out and rejects
input D that is defined to do the opposite of whatever Boolean
value that H returns.

Pathological self-reference {AKA epistemological antinomies}
cannot possibly create incompleteness or undecidability when it
is simply screened out as erroneous.

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

On 11/18/23 1:16 PM, olcott wrote:
> On 11/18/2023 10:32 AM, olcott wrote:
>> ZFC was able to reject epistemological antinomies by screening
>> out the pathological self-reference derived by sets as members
>> of themselves. Russell's Paradox was eliminated be defining set
>> theory differently.
>>
>> In the same way that Russell's Paradox was eliminated we can
>> get rid of other epistemological antinomies. It is pretty
>> obvious that epistemological antinomies are simply semantically
>> unsound.
>>
>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>> of L, then epistemological antinomies become simply untrue and
>> no longer show incompleteness or undecidability.
>>
>> Since we have already fixed the undecidability issue of Russell's
>> Paradox by redefining set theory the precedent has already been
>> set that we can correct these issues by redefining the meaning
>> of their terms.
>>
>> Because the undecidability of Russell's Paradox was fixed by changing
>> the meaning of the term {set theory} we can eliminate incompleteness
>> and undecidability by redefining meaning of the term {formal system}
>> as detailed above.
>
> We can eliminate incompleteness and undecidability derived by
> epistemological antinomies by redefining meaning of the term
> {formal system} as detailed above.
>
> For the halting problem H(D,D) simply screens out and rejects
> input D that is defined to do the opposite of whatever Boolean
> value that H returns.
>
> Pathological self-reference {AKA epistemological antinomies}
> cannot possibly create incompleteness or undecidability when it
> is simply screened out as erroneous.
>

Yes, you CAN try to redefine them, but then you end up with a very weak
logic system.

Note, The "Halting Problem" doesn't have a Pathological Self-Reference
in its definition, so that isn't the problem. All you doing is limiting
yourself to non-Turing complete computation systems, just like you are
limiting yourself to system that can't actually handle the full
properties of the natural numbers.

You are just showing how little you understand what you are talking about.

On 11/18/2023 12:16 PM, olcott wrote:
> On 11/18/2023 10:32 AM, olcott wrote:
>> ZFC was able to reject epistemological antinomies by screening
>> out the pathological self-reference derived by sets as members
>> of themselves. Russell's Paradox was eliminated be defining set
>> theory differently.
>>
>> In the same way that Russell's Paradox was eliminated we can
>> get rid of other epistemological antinomies. It is pretty
>> obvious that epistemological antinomies are simply semantically
>> unsound.
>>
>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>> of L, then epistemological antinomies become simply untrue and
>> no longer show incompleteness or undecidability.
>>
>> Since we have already fixed the undecidability issue of Russell's
>> Paradox by redefining set theory the precedent has already been
>> set that we can correct these issues by redefining the meaning
>> of their terms.
>>
>> Because the undecidability of Russell's Paradox was fixed by changing
>> the meaning of the term {set theory} we can eliminate incompleteness
>> and undecidability by redefining meaning of the term {formal system}
>> as detailed above.
>
> We can eliminate incompleteness and undecidability derived by
> epistemological antinomies by redefining meaning of the term
> {formal system} as detailed above.
>
> For the halting problem H(D,D) simply screens out and rejects
> input D that is defined to do the opposite of whatever Boolean
> value that H returns.
>
> Pathological self-reference {AKA epistemological antinomies}
> cannot possibly create incompleteness or undecidability when it
> is simply screened out as erroneous.
>

When we imagine that every detail of the body of human
knowledge has been formalized as higher order logic then
the only incompleteness are unknowns.

This is the way that human knowledge actually works:

True(L,x) is defined as (L ⊢ x)
False(L,x) is defined as (L ⊢ ~x)

then
epistemological antinomies are simply rejected as not truth
bearers and do not derive incompleteness or undecidability.

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

On 11/18/23 1:48 PM, olcott wrote:
> On 11/18/2023 12:16 PM, olcott wrote:
>> On 11/18/2023 10:32 AM, olcott wrote:
>>> ZFC was able to reject epistemological antinomies by screening
>>> out the pathological self-reference derived by sets as members
>>> of themselves. Russell's Paradox was eliminated be defining set
>>> theory differently.
>>>
>>> In the same way that Russell's Paradox was eliminated we can
>>> get rid of other epistemological antinomies. It is pretty
>>> obvious that epistemological antinomies are simply semantically
>>> unsound.
>>>
>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>> of L, then epistemological antinomies become simply untrue and
>>> no longer show incompleteness or undecidability.
>>>
>>> Since we have already fixed the undecidability issue of Russell's
>>> Paradox by redefining set theory the precedent has already been
>>> set that we can correct these issues by redefining the meaning
>>> of their terms.
>>>
>>> Because the undecidability of Russell's Paradox was fixed by changing
>>> the meaning of the term {set theory} we can eliminate incompleteness
>>> and undecidability by redefining meaning of the term {formal system}
>>> as detailed above.
>>
>> We can eliminate incompleteness and undecidability derived by
>> epistemological antinomies by redefining meaning of the term
>> {formal system} as detailed above.
>>
>> For the halting problem H(D,D) simply screens out and rejects
>> input D that is defined to do the opposite of whatever Boolean
>> value that H returns.
>>
>> Pathological self-reference {AKA epistemological antinomies}
>> cannot possibly create incompleteness or undecidability when it
>> is simply screened out as erroneous.
>>
>
> When we imagine that every detail of the body of human
> knowledge has been formalized as higher order logic then
> the only incompleteness are unknowns.
>

And you can't do that in a system that defined True to be provabl.

> This is the way that human knowledge actually works:
>
> True(L,x) is defined as (L ⊢ x)
> False(L,x) is defined as (L ⊢ ~x)

Nope, FALSE statement.

We know there are things that are true that we can not actually prove.

Maybe you don't understand that fact, because your mind is too limited.

>
> then
> epistemological antinomies are simply rejected as not truth
> bearers and do not derive incompleteness or undecidability.
>
>

But that doesn't get rid of "undecidable" cases, as not all of them are
based on epistemological antinomies.

In fact, (almost) no one in classical logic think that epistemolgocial
antinomies are anything other than not a truth bearer. You are just
showing that you don't really understand how those work.

On 11/18/2023 12:48 PM, olcott wrote:
> On 11/18/2023 12:16 PM, olcott wrote:
>> On 11/18/2023 10:32 AM, olcott wrote:
>>> ZFC was able to reject epistemological antinomies by screening
>>> out the pathological self-reference derived by sets as members
>>> of themselves. Russell's Paradox was eliminated be defining set
>>> theory differently.
>>>
>>> In the same way that Russell's Paradox was eliminated we can
>>> get rid of other epistemological antinomies. It is pretty
>>> obvious that epistemological antinomies are simply semantically
>>> unsound.
>>>
>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>> of L, then epistemological antinomies become simply untrue and
>>> no longer show incompleteness or undecidability.
>>>
>>> Since we have already fixed the undecidability issue of Russell's
>>> Paradox by redefining set theory the precedent has already been
>>> set that we can correct these issues by redefining the meaning
>>> of their terms.
>>>
>>> Because the undecidability of Russell's Paradox was fixed by changing
>>> the meaning of the term {set theory} we can eliminate incompleteness
>>> and undecidability by redefining meaning of the term {formal system}
>>> as detailed above.
>>
>> We can eliminate incompleteness and undecidability derived by
>> epistemological antinomies by redefining meaning of the term
>> {formal system} as detailed above.
>>
>> For the halting problem H(D,D) simply screens out and rejects
>> input D that is defined to do the opposite of whatever Boolean
>> value that H returns.
>>
>> Pathological self-reference {AKA epistemological antinomies}
>> cannot possibly create incompleteness or undecidability when it
>> is simply screened out as erroneous.
>>
>
> When we imagine that every detail of the body of human
> knowledge has been formalized as higher order logic then
> the only incompleteness are unknowns.
>
> This is the way that human knowledge actually works:
>
> True(L,x) is defined as (L ⊢ x)
> False(L,x) is defined as (L ⊢ ~x)
>
> then
> epistemological antinomies are simply rejected as not truth
> bearers and do not derive incompleteness or undecidability.

Rebutting things that I did not actually say might seem like a rebuttal
to gullible fools.

People that are paying 100% complete attention will see that such
rebuttals are the strawman error even if unintentional.

People that physically don't have the capacity to pay close attention
may commit the strawman error much of the time and not even know it.

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

On 11/18/23 9:40 PM, olcott wrote:
> On 11/18/2023 12:48 PM, olcott wrote:
>> On 11/18/2023 12:16 PM, olcott wrote:
>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>> ZFC was able to reject epistemological antinomies by screening
>>>> out the pathological self-reference derived by sets as members
>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>> theory differently.
>>>>
>>>> In the same way that Russell's Paradox was eliminated we can
>>>> get rid of other epistemological antinomies. It is pretty
>>>> obvious that epistemological antinomies are simply semantically
>>>> unsound.
>>>>
>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>> of L, then epistemological antinomies become simply untrue and
>>>> no longer show incompleteness or undecidability.
>>>>
>>>> Since we have already fixed the undecidability issue of Russell's
>>>> Paradox by redefining set theory the precedent has already been
>>>> set that we can correct these issues by redefining the meaning
>>>> of their terms.
>>>>
>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>> and undecidability by redefining meaning of the term {formal system}
>>>> as detailed above.
>>>
>>> We can eliminate incompleteness and undecidability derived by
>>> epistemological antinomies by redefining meaning of the term
>>> {formal system} as detailed above.
>>>
>>> For the halting problem H(D,D) simply screens out and rejects
>>> input D that is defined to do the opposite of whatever Boolean
>>> value that H returns.
>>>
>>> Pathological self-reference {AKA epistemological antinomies}
>>> cannot possibly create incompleteness or undecidability when it
>>> is simply screened out as erroneous.
>>>
>>
>> When we imagine that every detail of the body of human
>> knowledge has been formalized as higher order logic then
>> the only incompleteness are unknowns.
>>
>> This is the way that human knowledge actually works:
>>
>> True(L,x) is defined as (L ⊢ x)
>> False(L,x) is defined as (L ⊢ ~x)
>>
>> then
>> epistemological antinomies are simply rejected as not truth
>> bearers and do not derive incompleteness or undecidability.
>
> Rebutting things that I did not actually say might seem like a rebuttal
> to gullible fools.

And what did I rebut that you didn't say?

Making false claims is evidence of deceit. This seems to be your basic
method of arguement, claim that someone says something different then
what they actually said by miss-using their words, and building a
strawman argument from it.

>
> People that are paying 100% complete attention will see that such
> rebuttals are the strawman error even if unintentional.
>
> People that physically don't have the capacity to pay close attention
> may commit the strawman error much of the time and not even know it.
>

Yep, which describes yourself. You don't understand what people are
telling you, perhaps because you don't understand that core concepts of
formal logic, so you just presume they are talking non-sense.

That is like how you claim there is a "pathological self-reference" in
the Halting Problem, when you can't even point out where there is an
actual "Reference" (as defined in the field) in the first place.

Look, youi don't even understand the basic rules of argument, that you
respond TO the counter-point and show what is wrong with it.

By just replying to yourself, and just mentioning what you are trying to
"refute", you are just highlighting that your logic can't actually
handle the case, but you need to create a strawman in you description
and fight that,

Maybe I should just start pointing out your errors in ogical argument
form to point out your utter incapability of actually showing what you
claim.

It does seem ironic that someone who wants to claim that Truth only
comes out of proofs, can't actually form a correctly formed proof, but
seems to think that a verbal argument is the same thing.

Maybe that works in the fuzzy field of abstract philosophy, but it
doesn't cut it in actual formal logic, which is why you seem to fall so
flat. Some how you have a blind spot that the rules of logic ARE actual
rules to follow, not merely suggestions.

On 11/18/2023 12:48 PM, olcott wrote:
> On 11/18/2023 12:16 PM, olcott wrote:
>> On 11/18/2023 10:32 AM, olcott wrote:
>>> ZFC was able to reject epistemological antinomies by screening
>>> out the pathological self-reference derived by sets as members
>>> of themselves. Russell's Paradox was eliminated be defining set
>>> theory differently.
>>>
>>> In the same way that Russell's Paradox was eliminated we can
>>> get rid of other epistemological antinomies. It is pretty
>>> obvious that epistemological antinomies are simply semantically
>>> unsound.
>>>
>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>> of L, then epistemological antinomies become simply untrue and
>>> no longer show incompleteness or undecidability.
>>>
>>> Since we have already fixed the undecidability issue of Russell's
>>> Paradox by redefining set theory the precedent has already been
>>> set that we can correct these issues by redefining the meaning
>>> of their terms.
>>>
>>> Because the undecidability of Russell's Paradox was fixed by changing
>>> the meaning of the term {set theory} we can eliminate incompleteness
>>> and undecidability by redefining meaning of the term {formal system}
>>> as detailed above.
>>
>> We can eliminate incompleteness and undecidability derived by
>> epistemological antinomies by redefining meaning of the term
>> {formal system} as detailed above.
>>
>> For the halting problem H(D,D) simply screens out and rejects
>> input D that is defined to do the opposite of whatever Boolean
>> value that H returns.
>>
>> Pathological self-reference {AKA epistemological antinomies}
>> cannot possibly create incompleteness or undecidability when it
>> is simply screened out as erroneous.
>>
>
> When we imagine that every detail of the body of human
> knowledge has been formalized as higher order logic then
> the only incompleteness are unknowns.
>
> This is the way that human knowledge actually works:
>
> True(L,x) is defined as (L ⊢ x)
> False(L,x) is defined as (L ⊢ ~x)
>

This includes all human knowledge and excludes unknowns.
Your prior reply only glanced at a few of my words and thus did not
bother to notice that I was talking about the set of human knowledge.

> then
> epistemological antinomies are simply rejected as not truth
> bearers and do not derive incompleteness or undecidability.

Every expression that is neither provable nor refutable is rejected as
not a truth bearer, (within this formal system) thus epistemological
antinomies are excluded and unknowns are excluded and there is nothing
else left over.

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

On 11/19/23 11:19 AM, olcott wrote:
> On 11/18/2023 12:48 PM, olcott wrote:
>> On 11/18/2023 12:16 PM, olcott wrote:
>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>> ZFC was able to reject epistemological antinomies by screening
>>>> out the pathological self-reference derived by sets as members
>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>> theory differently.
>>>>
>>>> In the same way that Russell's Paradox was eliminated we can
>>>> get rid of other epistemological antinomies. It is pretty
>>>> obvious that epistemological antinomies are simply semantically
>>>> unsound.
>>>>
>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>> of L, then epistemological antinomies become simply untrue and
>>>> no longer show incompleteness or undecidability.
>>>>
>>>> Since we have already fixed the undecidability issue of Russell's
>>>> Paradox by redefining set theory the precedent has already been
>>>> set that we can correct these issues by redefining the meaning
>>>> of their terms.
>>>>
>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>> and undecidability by redefining meaning of the term {formal system}
>>>> as detailed above.
>>>
>>> We can eliminate incompleteness and undecidability derived by
>>> epistemological antinomies by redefining meaning of the term
>>> {formal system} as detailed above.
>>>
>>> For the halting problem H(D,D) simply screens out and rejects
>>> input D that is defined to do the opposite of whatever Boolean
>>> value that H returns.
>>>
>>> Pathological self-reference {AKA epistemological antinomies}
>>> cannot possibly create incompleteness or undecidability when it
>>> is simply screened out as erroneous.
>>>
>>
>> When we imagine that every detail of the body of human
>> knowledge has been formalized as higher order logic then
>> the only incompleteness are unknowns.
>>
>> This is the way that human knowledge actually works:
>>
>> True(L,x) is defined as (L ⊢ x)
>> False(L,x) is defined as (L ⊢ ~x)
>>
>
> This includes all human knowledge and excludes unknowns.
> Your prior reply only glanced at a few of my words and thus did not
> bother to notice that I was talking about the set of human knowledge.

But you confuse "Human Knowledge" with actual "Truth", so is just a LIE,

This means that the logic system you are trying to work in is either
inconstant or very weak., as there are statements that can be proven
that they must be either True or False, but we don't (yet) know which it
is, and even understand that it might be actually IMPOSSIBLE to prove
within the system, but your FLAWED systen says they can NOT be true
until proven, and in fact, the statment L ⊢ x needs the proof to be
know, since we need the existance of the proof to be proven for the
statement to be true.

So, either the domain of logic it can handle must be limited to just
that which works under that definition, which excludes many properties
of even the simple Natural Numbers, or it become inconsistant as
statements that can be show must be truth bearers, as they must be True
or False, because they don't allow a middle ground (like the existance
of a number with a computable property) but also, they might not be
either True or False, as we can't actually prove that existance.

>
>> then
>> epistemological antinomies are simply rejected as not truth
>> bearers and do not derive incompleteness or undecidability.
>
> Every expression that is neither provable nor refutable is rejected as
> not a truth bearer, (within this formal system) thus epistemological
> antinomies are excluded and unknowns are excluded and there is nothing
> else left over.
>

So, you INCORRECTLY reject as a "Truth Bearer" statements that ACTUALLY
HAVE A TRUTH VALUE, but that value is just not known.

In other words, you don't understand what TRUTH actually is because of
your own stupidity.

This shows that your mind is just a few sizes too small and doesn't (and
perhaps can't) understand the complexity that simple logic can generate.

On 11/19/2023 10:19 AM, olcott wrote:
> On 11/18/2023 12:48 PM, olcott wrote:
>> On 11/18/2023 12:16 PM, olcott wrote:
>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>> ZFC was able to reject epistemological antinomies by screening
>>>> out the pathological self-reference derived by sets as members
>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>> theory differently.
>>>>
>>>> In the same way that Russell's Paradox was eliminated we can
>>>> get rid of other epistemological antinomies. It is pretty
>>>> obvious that epistemological antinomies are simply semantically
>>>> unsound.
>>>>
>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>> of L, then epistemological antinomies become simply untrue and
>>>> no longer show incompleteness or undecidability.
>>>>
>>>> Since we have already fixed the undecidability issue of Russell's
>>>> Paradox by redefining set theory the precedent has already been
>>>> set that we can correct these issues by redefining the meaning
>>>> of their terms.
>>>>
>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>> and undecidability by redefining meaning of the term {formal system}
>>>> as detailed above.
>>>
>>> We can eliminate incompleteness and undecidability derived by
>>> epistemological antinomies by redefining meaning of the term
>>> {formal system} as detailed above.
>>>
>>> For the halting problem H(D,D) simply screens out and rejects
>>> input D that is defined to do the opposite of whatever Boolean
>>> value that H returns.
>>>
>>> Pathological self-reference {AKA epistemological antinomies}
>>> cannot possibly create incompleteness or undecidability when it
>>> is simply screened out as erroneous.
>>>
>>
>> When we imagine that every detail of the body of human
>> knowledge has been formalized as higher order logic then
>> the only incompleteness are unknowns.
>>
>> This is the way that human knowledge actually works:
>>
>> True(L,x) is defined as (L ⊢ x)
>> False(L,x) is defined as (L ⊢ ~x)
>>
>
> This includes all human knowledge and excludes unknowns.
> Your prior reply only glanced at a few of my words and thus did not
> bother to notice that I was talking about the set of human knowledge.
>
>> then
>> epistemological antinomies are simply rejected as not truth
>> bearers and do not derive incompleteness or undecidability.
>
> Every expression that is neither provable nor refutable is rejected as
> not a truth bearer, (within this formal system) thus epistemological
> antinomies are excluded and unknowns are excluded and there is nothing
> else left over.
>

Reviewers that don't give a rat's ass about truth and only want to stay
in rebuttal mode even if must lie to do it will refuse to acknowledge
that expressions that require infinite proofs to resolve their true
value are necessarily not truth bearers in formal systems that do not
allow infinite proofs.

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

On 11/19/23 1:08 PM, olcott wrote:
> On 11/19/2023 10:19 AM, olcott wrote:
>> On 11/18/2023 12:48 PM, olcott wrote:
>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>> out the pathological self-reference derived by sets as members
>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>> theory differently.
>>>>>
>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>> get rid of other epistemological antinomies. It is pretty
>>>>> obvious that epistemological antinomies are simply semantically
>>>>> unsound.
>>>>>
>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>> of L, then epistemological antinomies become simply untrue and
>>>>> no longer show incompleteness or undecidability.
>>>>>
>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>> Paradox by redefining set theory the precedent has already been
>>>>> set that we can correct these issues by redefining the meaning
>>>>> of their terms.
>>>>>
>>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>> as detailed above.
>>>>
>>>> We can eliminate incompleteness and undecidability derived by
>>>> epistemological antinomies by redefining meaning of the term
>>>> {formal system} as detailed above.
>>>>
>>>> For the halting problem H(D,D) simply screens out and rejects
>>>> input D that is defined to do the opposite of whatever Boolean
>>>> value that H returns.
>>>>
>>>> Pathological self-reference {AKA epistemological antinomies}
>>>> cannot possibly create incompleteness or undecidability when it
>>>> is simply screened out as erroneous.
>>>>
>>>
>>> When we imagine that every detail of the body of human
>>> knowledge has been formalized as higher order logic then
>>> the only incompleteness are unknowns.
>>>
>>> This is the way that human knowledge actually works:
>>>
>>> True(L,x) is defined as (L ⊢ x)
>>> False(L,x) is defined as (L ⊢ ~x)
>>>
>>
>> This includes all human knowledge and excludes unknowns.
>> Your prior reply only glanced at a few of my words and thus did not
>> bother to notice that I was talking about the set of human knowledge.
>>
>>> then
>>> epistemological antinomies are simply rejected as not truth
>>> bearers and do not derive incompleteness or undecidability.
>>
>> Every expression that is neither provable nor refutable is rejected as
>> not a truth bearer, (within this formal system) thus epistemological
>> antinomies are excluded and unknowns are excluded and there is nothing
>> else left over.
>>
>
> Reviewers that don't give a rat's ass about truth and only want to stay
> in rebuttal mode even if must lie to do it will refuse to acknowledge
> that expressions that require infinite proofs to resolve their true
> value are necessarily not truth bearers in formal systems that do not
> allow infinite proofs.
>
>

Is this comment directed at YOURSELF? since that is who you are replying
to. I guess you are admitting you don't give a rat's ass about what
actually is Truth, but just want to stay in your unsubstantiated
"rebuttal" mode, leaving all the errors pointed out in your logic as
accepted.

Note, since your definition of "Truth" isn't actually a definition of
Truth but of Knowledge, YOU are the one making the lies.

Also, your claim that "that expressions that require infinite proofs to
resolve their true value are necessarily not truth bearers in formal
systems that do not allow infinite proofs." is just an INCORRECT STATEMENT.

"Standard" Logic allows statements to establish there truth with
infinite chains even though proofs, being related to knowledge, needs to
be finite.

If you can find any "official" support for your claim, give it or you
are admitting that you are just a stupid liar.

Then, if you want to establish that changed rule as part of your logic,
show what you logic can do. As I have pointed out many times, you are
free to build a new logic system under the rules of formal logic, with
what ever definitions you want, it then just get put on you to establish
what that logic system can do, and you can't just borrow proofs based on
system with a different set of rules. This will mean you will need to
learn enough of "primative logic" to understand what rules get impacted
by this change. My first guess is this is far above your ability.

On 11/19/23 1:08 PM, olcott wrote:
>
> Reviewers that don't give a rat's ass about truth and only want to stay
> in rebuttal mode even if must lie to do it will refuse to acknowledge
> that expressions that require infinite proofs to resolve their true
> value are necessarily not truth bearers in formal systems that do not
> allow infinite proofs.

Simple thought experiment for you on that claim.

Question, does a number exist which satisifies some particular
computable property?

Such a question must be True or False, as either such a number exists or
it doesn't, and thus either assertion is a "Truth Bearer" by definition.

It is at least conceivably possible, that the only proof that such a
number doesn't exist is to test every possible number, and thus require
an "infinite proof" to establish this fact, so either the non-existance
of a number that satisfies some property might not actually be a "Truth
Bearer" by your definition, even though we KNOW, by the form of the
question, that it must be true or false, and thus be a Truth Bearer by
definition.

Also, by your definition, the question of the question about if that
statement was a Truth Bearer might not be a Truth Bearer, as to show
that there does not exist a finite proof of that property might not be
actually provable in a finite number of steps.

In fact, if you COULD actually prove in a finite number of steps that
you can't prove the statement in a finite number of steps, that could be
used as a proof of the statement that such a number doesn't exist (since
the existance of such a number, if one exists, is provable in a finite
number of steps by starting from that number and computing the answer,
showing it has the property.

This means you logic system sometimes can't actually ask questions until
it knows the answer.

On 11/19/2023 10:19 AM, olcott wrote:
> On 11/18/2023 12:48 PM, olcott wrote:
>> On 11/18/2023 12:16 PM, olcott wrote:
>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>> ZFC was able to reject epistemological antinomies by screening
>>>> out the pathological self-reference derived by sets as members
>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>> theory differently.
>>>>
>>>> In the same way that Russell's Paradox was eliminated we can
>>>> get rid of other epistemological antinomies. It is pretty
>>>> obvious that epistemological antinomies are simply semantically
>>>> unsound.
>>>>
>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>> of L, then epistemological antinomies become simply untrue and
>>>> no longer show incompleteness or undecidability.
>>>>
>>>> Since we have already fixed the undecidability issue of Russell's
>>>> Paradox by redefining set theory the precedent has already been
>>>> set that we can correct these issues by redefining the meaning
>>>> of their terms.
>>>>
>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>> and undecidability by redefining meaning of the term {formal system}
>>>> as detailed above.
>>>
>>> We can eliminate incompleteness and undecidability derived by
>>> epistemological antinomies by redefining meaning of the term
>>> {formal system} as detailed above.
>>>
>>> For the halting problem H(D,D) simply screens out and rejects
>>> input D that is defined to do the opposite of whatever Boolean
>>> value that H returns.
>>>
>>> Pathological self-reference {AKA epistemological antinomies}
>>> cannot possibly create incompleteness or undecidability when it
>>> is simply screened out as erroneous.
>>>
>>
>> When we imagine that every detail of the body of human
>> knowledge has been formalized as higher order logic then
>> the only incompleteness are unknowns.
>>
>> This is the way that human knowledge actually works:
>>
>> True(L,x) is defined as (L ⊢ x)
>> False(L,x) is defined as (L ⊢ ~x)
>>
>
> This includes all human knowledge and excludes unknowns.
> Your prior reply only glanced at a few of my words and thus did not
> bother to notice that I was talking about the set of human knowledge.
>
>> then
>> epistemological antinomies are simply rejected as not truth
>> bearers and do not derive incompleteness or undecidability.
>
> Every expression that is neither provable nor refutable is rejected as
> not a truth bearer, (within this formal system) thus epistemological
> antinomies are excluded and unknowns are excluded and there is nothing
> else left over.
>

When we stipulate that a truthmaker is what-so-ever makes an expression
of language true then we can know by tautology that every truth has a
truthmaker.

When we arbitrarily limit the set of truthmakers then this arbitrarily
limit screws everything up.

To define a proof as a finite set of inference steps creates the
artificial notion of unprovable truths.

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

On 11/19/23 4:49 PM, olcott wrote:
> On 11/19/2023 10:19 AM, olcott wrote:
>> On 11/18/2023 12:48 PM, olcott wrote:
>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>> out the pathological self-reference derived by sets as members
>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>> theory differently.
>>>>>
>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>> get rid of other epistemological antinomies. It is pretty
>>>>> obvious that epistemological antinomies are simply semantically
>>>>> unsound.
>>>>>
>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>> of L, then epistemological antinomies become simply untrue and
>>>>> no longer show incompleteness or undecidability.
>>>>>
>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>> Paradox by redefining set theory the precedent has already been
>>>>> set that we can correct these issues by redefining the meaning
>>>>> of their terms.
>>>>>
>>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>> as detailed above.
>>>>
>>>> We can eliminate incompleteness and undecidability derived by
>>>> epistemological antinomies by redefining meaning of the term
>>>> {formal system} as detailed above.
>>>>
>>>> For the halting problem H(D,D) simply screens out and rejects
>>>> input D that is defined to do the opposite of whatever Boolean
>>>> value that H returns.
>>>>
>>>> Pathological self-reference {AKA epistemological antinomies}
>>>> cannot possibly create incompleteness or undecidability when it
>>>> is simply screened out as erroneous.
>>>>
>>>
>>> When we imagine that every detail of the body of human
>>> knowledge has been formalized as higher order logic then
>>> the only incompleteness are unknowns.
>>>
>>> This is the way that human knowledge actually works:
>>>
>>> True(L,x) is defined as (L ⊢ x)
>>> False(L,x) is defined as (L ⊢ ~x)
>>>
>>
>> This includes all human knowledge and excludes unknowns.
>> Your prior reply only glanced at a few of my words and thus did not
>> bother to notice that I was talking about the set of human knowledge.
>>
>>> then
>>> epistemological antinomies are simply rejected as not truth
>>> bearers and do not derive incompleteness or undecidability.
>>
>> Every expression that is neither provable nor refutable is rejected as
>> not a truth bearer, (within this formal system) thus epistemological
>> antinomies are excluded and unknowns are excluded and there is nothing
>> else left over.
>>
>
> When we stipulate that a truthmaker is what-so-ever makes an expression
> of language true then we can know by tautology that every truth has a
> truthmaker.

So, just because we can't prove the statement true, doesn't mean it
isn't true.

>
> When we arbitrarily limit the set of truthmakers then this arbitrarily
> limit screws everything up.

Right, so you limiting Truthmakership to only things that are provable
is your failing.

>
> To define a proof as a finite set of inference steps creates the
> artificial notion of unprovable truths.
>

So?

Proof is in the domain of knowledge, and since we can only know things
that we can establish by our own finite capabilities, means that proofs
are normally limited to finite operations.

In the same way that "Computable", means we can get the answer in a
finite number of steps, "Provable" means we can demonstrate the truth of
the statement in a finite number of steps.

I guess this goes back to your silly idea that you are a divine being
not bound by the finiteness of mortals, but on the other hand, you
actually are bound by the finiteness of yourself, thus showing that you
can't be divine.

You still don't understand the difference between Knowledge and Truth,
it seems, in part, due to not understanding the properties of the
infinite (or even the unbounded).

Yes, I believe there are logic system that allow for something called a
"Proof" to be unbounded in length, but such systems will have issues
with defining knowledge.

If you want to work in such fields, just say so, and confine yourself to
them, and not assume that you can just transfer information between
fields that have different logical basis. That leads to the same sort of
problems as presuming that trans-finite mathematics holds the same
properties as the mathematics of finite numbers (like the Reals). They
don't.

On 11/19/2023 3:49 PM, olcott wrote:
> On 11/19/2023 10:19 AM, olcott wrote:
>> On 11/18/2023 12:48 PM, olcott wrote:
>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>> out the pathological self-reference derived by sets as members
>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>> theory differently.
>>>>>
>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>> get rid of other epistemological antinomies. It is pretty
>>>>> obvious that epistemological antinomies are simply semantically
>>>>> unsound.
>>>>>
>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>> of L, then epistemological antinomies become simply untrue and
>>>>> no longer show incompleteness or undecidability.
>>>>>
>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>> Paradox by redefining set theory the precedent has already been
>>>>> set that we can correct these issues by redefining the meaning
>>>>> of their terms.
>>>>>
>>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>> as detailed above.
>>>>
>>>> We can eliminate incompleteness and undecidability derived by
>>>> epistemological antinomies by redefining meaning of the term
>>>> {formal system} as detailed above.
>>>>
>>>> For the halting problem H(D,D) simply screens out and rejects
>>>> input D that is defined to do the opposite of whatever Boolean
>>>> value that H returns.
>>>>
>>>> Pathological self-reference {AKA epistemological antinomies}
>>>> cannot possibly create incompleteness or undecidability when it
>>>> is simply screened out as erroneous.
>>>>
>>>
>>> When we imagine that every detail of the body of human
>>> knowledge has been formalized as higher order logic then
>>> the only incompleteness are unknowns.
>>>
>>> This is the way that human knowledge actually works:
>>>
>>> True(L,x) is defined as (L ⊢ x)
>>> False(L,x) is defined as (L ⊢ ~x)
>>>
>>
>> This includes all human knowledge and excludes unknowns.
>> Your prior reply only glanced at a few of my words and thus did not
>> bother to notice that I was talking about the set of human knowledge.
>>
>>> then
>>> epistemological antinomies are simply rejected as not truth
>>> bearers and do not derive incompleteness or undecidability.
>>
>> Every expression that is neither provable nor refutable is rejected as
>> not a truth bearer, (within this formal system) thus epistemological
>> antinomies are excluded and unknowns are excluded and there is nothing
>> else left over.
>>
>
> When we stipulate that a truthmaker is what-so-ever makes an expression
> of language true then we can know by tautology that every truth has a
> truthmaker.
>
> When we arbitrarily limit the set of truthmakers then this arbitrarily
> limit screws everything up.
>
> To define a proof as a finite set of inference steps creates the
> artificial notion of unprovable truths.
>

My most important point of all this is that epistemological antinomies
are finally understood to simply be semantic nonsense that do not
actually prove incompleteness, undecidability or undefinability.

....14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)

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

On 11/19/23 6:32 PM, olcott wrote:
> On 11/19/2023 3:49 PM, olcott wrote:
>> On 11/19/2023 10:19 AM, olcott wrote:
>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>> out the pathological self-reference derived by sets as members
>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>> theory differently.
>>>>>>
>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>> unsound.
>>>>>>
>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>> no longer show incompleteness or undecidability.
>>>>>>
>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>> set that we can correct these issues by redefining the meaning
>>>>>> of their terms.
>>>>>>
>>>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>>> as detailed above.
>>>>>
>>>>> We can eliminate incompleteness and undecidability derived by
>>>>> epistemological antinomies by redefining meaning of the term
>>>>> {formal system} as detailed above.
>>>>>
>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>> value that H returns.
>>>>>
>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>> cannot possibly create incompleteness or undecidability when it
>>>>> is simply screened out as erroneous.
>>>>>
>>>>
>>>> When we imagine that every detail of the body of human
>>>> knowledge has been formalized as higher order logic then
>>>> the only incompleteness are unknowns.
>>>>
>>>> This is the way that human knowledge actually works:
>>>>
>>>> True(L,x) is defined as (L ⊢ x)
>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>
>>>
>>> This includes all human knowledge and excludes unknowns.
>>> Your prior reply only glanced at a few of my words and thus did not
>>> bother to notice that I was talking about the set of human knowledge.
>>>
>>>> then
>>>> epistemological antinomies are simply rejected as not truth
>>>> bearers and do not derive incompleteness or undecidability.
>>>
>>> Every expression that is neither provable nor refutable is rejected as
>>> not a truth bearer, (within this formal system) thus epistemological
>>> antinomies are excluded and unknowns are excluded and there is nothing
>>> else left over.
>>>
>>
>> When we stipulate that a truthmaker is what-so-ever makes an expression
>> of language true then we can know by tautology that every truth has a
>> truthmaker.
>>
>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>> limit screws everything up.
>>
>> To define a proof as a finite set of inference steps creates the
>> artificial notion of unprovable truths.
>>
>
>
> My most important point of all this is that epistemological antinomies
> are finally understood to simply be semantic nonsense that do not
> actually prove incompleteness, undecidability or undefinability.
>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)
>
>
>

No, you are just proving that you don't understand what you are talking
about.

Please try to show where Godel actually used an epistemological antinomy
in manner that required it to be anything other than a statement that
could not be logically resolved, and thus not a "Truth Bearer".

Not just this quote, which shows no such thing, but the step in the
proof that used it in a way that invalidates the proof.

The problem seems to be that you read non-technical descriptions of
things and think you understand what is actually being done in the proof.

All your words are just proving how ignorant you are of anything you
talk about.

Yes, Godel used a statement that was a epistemolgical antinomy,
something like "Statement X asserts that Statement X is not True", which
is, and most people understand it, to be such a statement that doesn't
not have a truth value.

He then converted it with a syntatic transformation that totally changes
its meaning into: "Statement X asserts that Statement X is not Provable
in F". Note, this transformed sentence is NOT an epistemological
antinomy in classic logic, as there is a truth value assignment that can
make the statement have a valid truth value, namely that X is a true
statement that is not provable.

Since the final statement that he gets, is one that MUST be a Truth
Beared, a question about the existance of a number that satisfies a
strictly computable property.

Yes, this proof does not work in a system that restricts truth to only
things that are provable, but that is not the logic system that Godel is
working in.

Your problem is that if you want to try to talk about such a logic
system with that limitation, your first step is to show that such a
system can meet the other requirements of the proof, that it supports
those need properties of the Natural Numbers. That is the problem you
are going to run into, the inevitable result of the limits to logic you
propose is that the logic system can not expand to the point of
generating those properties without falling into inconsistency.

On 11/19/2023 5:32 PM, olcott wrote:
> On 11/19/2023 3:49 PM, olcott wrote:
>> On 11/19/2023 10:19 AM, olcott wrote:
>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>> out the pathological self-reference derived by sets as members
>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>> theory differently.
>>>>>>
>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>> unsound.
>>>>>>
>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>> no longer show incompleteness or undecidability.
>>>>>>
>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>> set that we can correct these issues by redefining the meaning
>>>>>> of their terms.
>>>>>>
>>>>>> Because the undecidability of Russell's Paradox was fixed by changing
>>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>>> as detailed above.
>>>>>
>>>>> We can eliminate incompleteness and undecidability derived by
>>>>> epistemological antinomies by redefining meaning of the term
>>>>> {formal system} as detailed above.
>>>>>
>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>> value that H returns.
>>>>>
>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>> cannot possibly create incompleteness or undecidability when it
>>>>> is simply screened out as erroneous.
>>>>>
>>>>
>>>> When we imagine that every detail of the body of human
>>>> knowledge has been formalized as higher order logic then
>>>> the only incompleteness are unknowns.
>>>>
>>>> This is the way that human knowledge actually works:
>>>>
>>>> True(L,x) is defined as (L ⊢ x)
>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>
>>>
>>> This includes all human knowledge and excludes unknowns.
>>> Your prior reply only glanced at a few of my words and thus did not
>>> bother to notice that I was talking about the set of human knowledge.
>>>
>>>> then
>>>> epistemological antinomies are simply rejected as not truth
>>>> bearers and do not derive incompleteness or undecidability.
>>>
>>> Every expression that is neither provable nor refutable is rejected as
>>> not a truth bearer, (within this formal system) thus epistemological
>>> antinomies are excluded and unknowns are excluded and there is nothing
>>> else left over.
>>>
>>
>> When we stipulate that a truthmaker is what-so-ever makes an expression
>> of language true then we can know by tautology that every truth has a
>> truthmaker.
>>
>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>> limit screws everything up.
>>
>> To define a proof as a finite set of inference steps creates the
>> artificial notion of unprovable truths.
>>
>
>
> My most important point of all this is that epistemological antinomies
> are finally understood to simply be semantic nonsense that do not
> actually prove incompleteness, undecidability or undefinability.
>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)

Antinomy
....term often used in logic and epistemology, when describing a paradox
or unresolvable contradiction.
https://www.newworldencyclopedia.org/entry/Antinomy

epistemological antinomies are unprovable because they are semantic
nonsense.

"If a formal system cannot prove gibberish nonsense then the formal
system is incomplete" is itself gibberish nonsense.

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

On 11/19/23 7:15 PM, olcott wrote:
> On 11/19/2023 5:32 PM, olcott wrote:
>> On 11/19/2023 3:49 PM, olcott wrote:
>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>> theory differently.
>>>>>>>
>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>> unsound.
>>>>>>>
>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>
>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>> of their terms.
>>>>>>>
>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>> changing
>>>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>>>> as detailed above.
>>>>>>
>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>> {formal system} as detailed above.
>>>>>>
>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>> value that H returns.
>>>>>>
>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>> is simply screened out as erroneous.
>>>>>>
>>>>>
>>>>> When we imagine that every detail of the body of human
>>>>> knowledge has been formalized as higher order logic then
>>>>> the only incompleteness are unknowns.
>>>>>
>>>>> This is the way that human knowledge actually works:
>>>>>
>>>>> True(L,x) is defined as (L ⊢ x)
>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>
>>>>
>>>> This includes all human knowledge and excludes unknowns.
>>>> Your prior reply only glanced at a few of my words and thus did not
>>>> bother to notice that I was talking about the set of human knowledge.
>>>>
>>>>> then
>>>>> epistemological antinomies are simply rejected as not truth
>>>>> bearers and do not derive incompleteness or undecidability.
>>>>
>>>> Every expression that is neither provable nor refutable is rejected as
>>>> not a truth bearer, (within this formal system) thus epistemological
>>>> antinomies are excluded and unknowns are excluded and there is nothing
>>>> else left over.
>>>>
>>>
>>> When we stipulate that a truthmaker is what-so-ever makes an expression
>>> of language true then we can know by tautology that every truth has a
>>> truthmaker.
>>>
>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>> limit screws everything up.
>>>
>>> To define a proof as a finite set of inference steps creates the
>>> artificial notion of unprovable truths.
>>>
>>
>>
>> My most important point of all this is that epistemological antinomies
>> are finally understood to simply be semantic nonsense that do not
>> actually prove incompleteness, undecidability or undefinability.
>>
>> ...14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof...(Gödel 1931:43-44)
>
> Antinomy
> ...term often used in logic and epistemology, when describing a paradox
> or unresolvable contradiction.
> https://www.newworldencyclopedia.org/entry/Antinomy
>
> epistemological antinomies are unprovable because they are semantic
> nonsense.
>
> "If a formal system cannot prove gibberish nonsense then the formal
> system is incomplete" is itself gibberish nonsense.
>
>

But that isn't what Godel was doing.

You are just proving you are talking out of ignorance and YOU are the
one speaking "gibberish".

The statement "G" that is shown to be True and unprovable is NOT an
epistemological antinomy, but a statement that most definitely has a
Truth Value, and thus CAN'T be an epistemoligical antinomy.

Again, you seem to like arguing with yourself and not actually answering
the errors pointed out in your arguments, meaning you are accepting the
errors as actual errors, and thus you are accepting that you statements
are in error, and that you are just repeating the errors to show your
ignorance.

Go ahead, keep digging the grave for your reputation. You are just
burying it deeper.

On 11/19/2023 6:15 PM, olcott wrote:
> On 11/19/2023 5:32 PM, olcott wrote:
>> On 11/19/2023 3:49 PM, olcott wrote:
>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>> theory differently.
>>>>>>>
>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>> unsound.
>>>>>>>
>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>
>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>> of their terms.
>>>>>>>
>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>> changing
>>>>>>> the meaning of the term {set theory} we can eliminate incompleteness
>>>>>>> and undecidability by redefining meaning of the term {formal system}
>>>>>>> as detailed above.
>>>>>>
>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>> {formal system} as detailed above.
>>>>>>
>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>> value that H returns.
>>>>>>
>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>> is simply screened out as erroneous.
>>>>>>
>>>>>
>>>>> When we imagine that every detail of the body of human
>>>>> knowledge has been formalized as higher order logic then
>>>>> the only incompleteness are unknowns.
>>>>>
>>>>> This is the way that human knowledge actually works:
>>>>>
>>>>> True(L,x) is defined as (L ⊢ x)
>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>
>>>>
>>>> This includes all human knowledge and excludes unknowns.
>>>> Your prior reply only glanced at a few of my words and thus did not
>>>> bother to notice that I was talking about the set of human knowledge.
>>>>
>>>>> then
>>>>> epistemological antinomies are simply rejected as not truth
>>>>> bearers and do not derive incompleteness or undecidability.
>>>>
>>>> Every expression that is neither provable nor refutable is rejected as
>>>> not a truth bearer, (within this formal system) thus epistemological
>>>> antinomies are excluded and unknowns are excluded and there is nothing
>>>> else left over.
>>>>
>>>
>>> When we stipulate that a truthmaker is what-so-ever makes an expression
>>> of language true then we can know by tautology that every truth has a
>>> truthmaker.
>>>
>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>> limit screws everything up.
>>>
>>> To define a proof as a finite set of inference steps creates the
>>> artificial notion of unprovable truths.
>>>
>>
>>
>> My most important point of all this is that epistemological antinomies
>> are finally understood to simply be semantic nonsense that do not
>> actually prove incompleteness, undecidability or undefinability.
>>
>> ...14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof...(Gödel 1931:43-44)
>
> Antinomy
> ...term often used in logic and epistemology, when describing a paradox
> or unresolvable contradiction.
> https://www.newworldencyclopedia.org/entry/Antinomy
>
> epistemological antinomies are unprovable because they are semantic
> nonsense.
>
> "If a formal system cannot prove gibberish nonsense then the formal
> system is incomplete" is itself gibberish nonsense.

....14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)

The only fake deceptive rebuttal to the fact that Gödel was definitely
wrong about that is changing the subject to something else.

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

On 11/19/23 8:03 PM, olcott wrote:
> On 11/19/2023 6:15 PM, olcott wrote:
>> On 11/19/2023 5:32 PM, olcott wrote:
>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>> theory differently.
>>>>>>>>
>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>> unsound.
>>>>>>>>
>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>
>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>> of their terms.
>>>>>>>>
>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>> changing
>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>> incompleteness
>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>> system}
>>>>>>>> as detailed above.
>>>>>>>
>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>> {formal system} as detailed above.
>>>>>>>
>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>> value that H returns.
>>>>>>>
>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>> is simply screened out as erroneous.
>>>>>>>
>>>>>>
>>>>>> When we imagine that every detail of the body of human
>>>>>> knowledge has been formalized as higher order logic then
>>>>>> the only incompleteness are unknowns.
>>>>>>
>>>>>> This is the way that human knowledge actually works:
>>>>>>
>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>
>>>>>
>>>>> This includes all human knowledge and excludes unknowns.
>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>> bother to notice that I was talking about the set of human knowledge.
>>>>>
>>>>>> then
>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>
>>>>> Every expression that is neither provable nor refutable is rejected as
>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>> antinomies are excluded and unknowns are excluded and there is nothing
>>>>> else left over.
>>>>>
>>>>
>>>> When we stipulate that a truthmaker is what-so-ever makes an expression
>>>> of language true then we can know by tautology that every truth has a
>>>> truthmaker.
>>>>
>>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>>> limit screws everything up.
>>>>
>>>> To define a proof as a finite set of inference steps creates the
>>>> artificial notion of unprovable truths.
>>>>
>>>
>>>
>>> My most important point of all this is that epistemological antinomies
>>> are finally understood to simply be semantic nonsense that do not
>>> actually prove incompleteness, undecidability or undefinability.
>>>
>>> ...14 Every epistemological antinomy can likewise be used for a
>>> similar undecidability proof...(Gödel 1931:43-44)
>>
>> Antinomy
>> ...term often used in logic and epistemology, when describing a
>> paradox or unresolvable contradiction.
>> https://www.newworldencyclopedia.org/entry/Antinomy
>>
>> epistemological antinomies are unprovable because they are semantic
>> nonsense.
>>
>> "If a formal system cannot prove gibberish nonsense then the formal
>> system is incomplete" is itself gibberish nonsense.
>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)
>
> The only fake deceptive rebuttal to the fact that Gödel was definitely
> wrong about that is changing the subject to something else.
>
>
>

Which just PROVES you don't understand what you are talking about.

Your failure to answer the question I asked before proves this.

That shows that YOURS is the "fake deceptive rebuttal".

By your own logic, your statement is garbage because you mentioned using
epistemological antinomies.

So again, WHERE did he actually do this in his proof? Show the step
where he did it.

I bet your problem is you can't actually read any of the proof to see
what he is doing.

You are just too stupid to understand that you don't understand what you
are talking about.

On 11/19/2023 7:03 PM, olcott wrote:
> On 11/19/2023 6:15 PM, olcott wrote:
>> On 11/19/2023 5:32 PM, olcott wrote:
>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>> theory differently.
>>>>>>>>
>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>> unsound.
>>>>>>>>
>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>
>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>> of their terms.
>>>>>>>>
>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>> changing
>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>> incompleteness
>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>> system}
>>>>>>>> as detailed above.
>>>>>>>
>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>> {formal system} as detailed above.
>>>>>>>
>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>> value that H returns.
>>>>>>>
>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>> is simply screened out as erroneous.
>>>>>>>
>>>>>>
>>>>>> When we imagine that every detail of the body of human
>>>>>> knowledge has been formalized as higher order logic then
>>>>>> the only incompleteness are unknowns.
>>>>>>
>>>>>> This is the way that human knowledge actually works:
>>>>>>
>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>
>>>>>
>>>>> This includes all human knowledge and excludes unknowns.
>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>> bother to notice that I was talking about the set of human knowledge.
>>>>>
>>>>>> then
>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>
>>>>> Every expression that is neither provable nor refutable is rejected as
>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>> antinomies are excluded and unknowns are excluded and there is nothing
>>>>> else left over.
>>>>>
>>>>
>>>> When we stipulate that a truthmaker is what-so-ever makes an expression
>>>> of language true then we can know by tautology that every truth has a
>>>> truthmaker.
>>>>
>>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>>> limit screws everything up.
>>>>
>>>> To define a proof as a finite set of inference steps creates the
>>>> artificial notion of unprovable truths.
>>>>
>>>
>>>
>>> My most important point of all this is that epistemological antinomies
>>> are finally understood to simply be semantic nonsense that do not
>>> actually prove incompleteness, undecidability or undefinability.
>>>
>>> ...14 Every epistemological antinomy can likewise be used for a
>>> similar undecidability proof...(Gödel 1931:43-44)
>>
>> Antinomy
>> ...term often used in logic and epistemology, when describing a
>> paradox or unresolvable contradiction.
>> https://www.newworldencyclopedia.org/entry/Antinomy
>>
>> epistemological antinomies are unprovable because they are semantic
>> nonsense.
>>
>> "If a formal system cannot prove gibberish nonsense then the formal
>> system is incomplete" is itself gibberish nonsense.
>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)
>

The only fake deceptive rebuttal to the fact that Gödel was definitely
wrong about that is changing the subject to something else.

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

On 11/19/23 9:27 PM, olcott wrote:
> On 11/19/2023 7:03 PM, olcott wrote:
>> On 11/19/2023 6:15 PM, olcott wrote:
>>> On 11/19/2023 5:32 PM, olcott wrote:
>>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>>> theory differently.
>>>>>>>>>
>>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>>> unsound.
>>>>>>>>>
>>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>>
>>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>>> of their terms.
>>>>>>>>>
>>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>>> changing
>>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>>> incompleteness
>>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>>> system}
>>>>>>>>> as detailed above.
>>>>>>>>
>>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>>> {formal system} as detailed above.
>>>>>>>>
>>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>>> value that H returns.
>>>>>>>>
>>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>>> is simply screened out as erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> When we imagine that every detail of the body of human
>>>>>>> knowledge has been formalized as higher order logic then
>>>>>>> the only incompleteness are unknowns.
>>>>>>>
>>>>>>> This is the way that human knowledge actually works:
>>>>>>>
>>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>>
>>>>>>
>>>>>> This includes all human knowledge and excludes unknowns.
>>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>>> bother to notice that I was talking about the set of human knowledge.
>>>>>>
>>>>>>> then
>>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>>
>>>>>> Every expression that is neither provable nor refutable is
>>>>>> rejected as
>>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>>> antinomies are excluded and unknowns are excluded and there is
>>>>>> nothing
>>>>>> else left over.
>>>>>>
>>>>>
>>>>> When we stipulate that a truthmaker is what-so-ever makes an
>>>>> expression
>>>>> of language true then we can know by tautology that every truth has a
>>>>> truthmaker.
>>>>>
>>>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>>>> limit screws everything up.
>>>>>
>>>>> To define a proof as a finite set of inference steps creates the
>>>>> artificial notion of unprovable truths.
>>>>>
>>>>
>>>>
>>>> My most important point of all this is that epistemological antinomies
>>>> are finally understood to simply be semantic nonsense that do not
>>>> actually prove incompleteness, undecidability or undefinability.
>>>>
>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>> similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> Antinomy
>>> ...term often used in logic and epistemology, when describing a
>>> paradox or unresolvable contradiction.
>>> https://www.newworldencyclopedia.org/entry/Antinomy
>>>
>>> epistemological antinomies are unprovable because they are semantic
>>> nonsense.
>>>
>>> "If a formal system cannot prove gibberish nonsense then the formal
>>> system is incomplete" is itself gibberish nonsense.
>>
>> ...14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof...(Gödel 1931:43-44)
>>
>
> The only fake deceptive rebuttal to the fact that Gödel was definitely
> wrong about that is changing the subject to something else.
>

Again, talking to yourself showing who you actually think is doing the
"fake deceptive rebuttal".

And, you can't answer the question? You are just admitting that you are
just a stupid liar.

If he was actually wrong, you could show the point in the proof where he
did a wrong thing.

That fact you can't do that show that you are just being a stupid
ignorant liar.

As I said, by your logic, you just proved that your own proof must be
incorrect, as you also mention using epistemological antinomies.

On 11/19/2023 7:03 PM, olcott wrote:
> On 11/19/2023 6:15 PM, olcott wrote:
>> On 11/19/2023 5:32 PM, olcott wrote:
>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>> theory differently.
>>>>>>>>
>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>> unsound.
>>>>>>>>
>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>
>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>> of their terms.
>>>>>>>>
>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>> changing
>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>> incompleteness
>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>> system}
>>>>>>>> as detailed above.
>>>>>>>
>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>> {formal system} as detailed above.
>>>>>>>
>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>> value that H returns.
>>>>>>>
>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>> is simply screened out as erroneous.
>>>>>>>
>>>>>>
>>>>>> When we imagine that every detail of the body of human
>>>>>> knowledge has been formalized as higher order logic then
>>>>>> the only incompleteness are unknowns.
>>>>>>
>>>>>> This is the way that human knowledge actually works:
>>>>>>
>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>
>>>>>
>>>>> This includes all human knowledge and excludes unknowns.
>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>> bother to notice that I was talking about the set of human knowledge.
>>>>>
>>>>>> then
>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>
>>>>> Every expression that is neither provable nor refutable is rejected as
>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>> antinomies are excluded and unknowns are excluded and there is nothing
>>>>> else left over.
>>>>>
>>>>
>>>> When we stipulate that a truthmaker is what-so-ever makes an expression
>>>> of language true then we can know by tautology that every truth has a
>>>> truthmaker.
>>>>
>>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>>> limit screws everything up.
>>>>
>>>> To define a proof as a finite set of inference steps creates the
>>>> artificial notion of unprovable truths.
>>>>
>>>
>>>
>>> My most important point of all this is that epistemological antinomies
>>> are finally understood to simply be semantic nonsense that do not
>>> actually prove incompleteness, undecidability or undefinability.
>>>
>>> ...14 Every epistemological antinomy can likewise be used for a
>>> similar undecidability proof...(Gödel 1931:43-44)
>>
>> Antinomy
>> ...term often used in logic and epistemology, when describing a
>> paradox or unresolvable contradiction.
>> https://www.newworldencyclopedia.org/entry/Antinomy
>>
>> epistemological antinomies are unprovable because they are semantic
>> nonsense.
>>
>> "If a formal system cannot prove gibberish nonsense then the formal
>> system is incomplete" is itself gibberish nonsense.
>
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43-44)
>

The only fake deceptive rebuttal to the fact that Gödel was definitely
wrong about that is changing the subject to something else.

On the other hand honest reviewers would say of course you are right
about this. Expecting a formal system to prove an epistemological
antinomy is ridiculous. How could Gödel make such a huge mistake?

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

On 11/19/23 10:06 PM, olcott wrote:
> On 11/19/2023 7:03 PM, olcott wrote:
>> On 11/19/2023 6:15 PM, olcott wrote:
>>> On 11/19/2023 5:32 PM, olcott wrote:
>>>> On 11/19/2023 3:49 PM, olcott wrote:
>>>>> On 11/19/2023 10:19 AM, olcott wrote:
>>>>>> On 11/18/2023 12:48 PM, olcott wrote:
>>>>>>> On 11/18/2023 12:16 PM, olcott wrote:
>>>>>>>> On 11/18/2023 10:32 AM, olcott wrote:
>>>>>>>>> ZFC was able to reject epistemological antinomies by screening
>>>>>>>>> out the pathological self-reference derived by sets as members
>>>>>>>>> of themselves. Russell's Paradox was eliminated be defining set
>>>>>>>>> theory differently.
>>>>>>>>>
>>>>>>>>> In the same way that Russell's Paradox was eliminated we can
>>>>>>>>> get rid of other epistemological antinomies. It is pretty
>>>>>>>>> obvious that epistemological antinomies are simply semantically
>>>>>>>>> unsound.
>>>>>>>>>
>>>>>>>>> When we define True(L, x) as (L ⊢ x) provable from the axioms
>>>>>>>>> of L, then epistemological antinomies become simply untrue and
>>>>>>>>> no longer show incompleteness or undecidability.
>>>>>>>>>
>>>>>>>>> Since we have already fixed the undecidability issue of Russell's
>>>>>>>>> Paradox by redefining set theory the precedent has already been
>>>>>>>>> set that we can correct these issues by redefining the meaning
>>>>>>>>> of their terms.
>>>>>>>>>
>>>>>>>>> Because the undecidability of Russell's Paradox was fixed by
>>>>>>>>> changing
>>>>>>>>> the meaning of the term {set theory} we can eliminate
>>>>>>>>> incompleteness
>>>>>>>>> and undecidability by redefining meaning of the term {formal
>>>>>>>>> system}
>>>>>>>>> as detailed above.
>>>>>>>>
>>>>>>>> We can eliminate incompleteness and undecidability derived by
>>>>>>>> epistemological antinomies by redefining meaning of the term
>>>>>>>> {formal system} as detailed above.
>>>>>>>>
>>>>>>>> For the halting problem H(D,D) simply screens out and rejects
>>>>>>>> input D that is defined to do the opposite of whatever Boolean
>>>>>>>> value that H returns.
>>>>>>>>
>>>>>>>> Pathological self-reference {AKA epistemological antinomies}
>>>>>>>> cannot possibly create incompleteness or undecidability when it
>>>>>>>> is simply screened out as erroneous.
>>>>>>>>
>>>>>>>
>>>>>>> When we imagine that every detail of the body of human
>>>>>>> knowledge has been formalized as higher order logic then
>>>>>>> the only incompleteness are unknowns.
>>>>>>>
>>>>>>> This is the way that human knowledge actually works:
>>>>>>>
>>>>>>> True(L,x) is defined as (L ⊢ x)
>>>>>>> False(L,x) is defined as (L ⊢ ~x)
>>>>>>>
>>>>>>
>>>>>> This includes all human knowledge and excludes unknowns.
>>>>>> Your prior reply only glanced at a few of my words and thus did not
>>>>>> bother to notice that I was talking about the set of human knowledge.
>>>>>>
>>>>>>> then
>>>>>>> epistemological antinomies are simply rejected as not truth
>>>>>>> bearers and do not derive incompleteness or undecidability.
>>>>>>
>>>>>> Every expression that is neither provable nor refutable is
>>>>>> rejected as
>>>>>> not a truth bearer, (within this formal system) thus epistemological
>>>>>> antinomies are excluded and unknowns are excluded and there is
>>>>>> nothing
>>>>>> else left over.
>>>>>>
>>>>>
>>>>> When we stipulate that a truthmaker is what-so-ever makes an
>>>>> expression
>>>>> of language true then we can know by tautology that every truth has a
>>>>> truthmaker.
>>>>>
>>>>> When we arbitrarily limit the set of truthmakers then this arbitrarily
>>>>> limit screws everything up.
>>>>>
>>>>> To define a proof as a finite set of inference steps creates the
>>>>> artificial notion of unprovable truths.
>>>>>
>>>>
>>>>
>>>> My most important point of all this is that epistemological antinomies
>>>> are finally understood to simply be semantic nonsense that do not
>>>> actually prove incompleteness, undecidability or undefinability.
>>>>
>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>> similar undecidability proof...(Gödel 1931:43-44)
>>>
>>> Antinomy
>>> ...term often used in logic and epistemology, when describing a
>>> paradox or unresolvable contradiction.
>>> https://www.newworldencyclopedia.org/entry/Antinomy
>>>
>>> epistemological antinomies are unprovable because they are semantic
>>> nonsense.
>>>
>>> "If a formal system cannot prove gibberish nonsense then the formal
>>> system is incomplete" is itself gibberish nonsense.
>>
>> ...14 Every epistemological antinomy can likewise be used for a
>> similar undecidability proof...(Gödel 1931:43-44)
>>
>
> The only fake deceptive rebuttal to the fact that Gödel was definitely
> wrong about that is changing the subject to something else.

So, again, where in the proof did he do this wrong thing?

You can't show it, because he didn't do what you are claiming.

Your problem is you don't understand how the logic actually works.

>
> On the other hand honest reviewers would say of course you are right
> about this. Expecting a formal system to prove an epistemological
> antinomy is ridiculous. How could Gödel make such a huge mistake?
>

Except he didn't expect a formal system to prove an epistemological
antinomy, and the fact you imply that he claimed he did shows your
stupidity.

Yes, a real "Honest Reviewer" would see what Godel wrote, and see that
your claim that he was asking the system to prove an epistemological
antinomy is just a stupid lie on your part.

You can't even state the actual proposition that Godel put forward as
the true but unprovable statement in the system, you only see the
statements, in the meta-system, that can be derived from it.

You are just showing you fundamentally don't understand how logic or
truth or proof actually works.

You are just a LYING DISHONEST STUPID CHARLATAN that has been caught in
your lies and trying to fast talk out of your errors.

You have yet to present ANY actual proof of your claims, and have ducked
every request to provide something to actually back your claims,

Of course, since you actually know nothing about what you talk, you
can't do that, but only bluster.

Of course, you are so stupid, you think you are making your point, but
in truth, you are just proving to the world how utterly stupid you are.

If there was something to your ideas, you have buried it in your disgrace.