P= "This statement is false"
Is P a proposition? This question depends largely on how P is interpreted,
because the sentence itself does not have T/F value (it is given by its evaluator).
Now, if the T/F value of the P as shown is defined by an evaluator, a circular
argument is formed. In this regard, the sentence P should be classified as
something like undefined or undecidable. P is not a 'proper' proposition.

bool P() {
return !Evalu_TF(P);
};

This 'undefined' solution extends to several paradoxes like "Achilles and the
tortoise" and Supertask (the given problem does not contain the answer or
confusing). The verdict, including 'circular argument', also applies to a
number of foundamental math proofs. I just mention it. What involved is huge.

On Monday, 8 August 2022 at 20:37:08 UTC+8, wij wrote:
> P= "This statement is false"
> Is P a proposition? This question depends largely on how P is interpreted,
> because the sentence itself does not have T/F value (it is given by its evaluator).
> Now, if the T/F value of the P as shown is defined by an evaluator, a circular
> argument is formed. In this regard, the sentence P should be classified as
> something like undefined or undecidable. P is not a 'proper' proposition.
>
> bool P() {
> return !Evalu_TF(P);
> };
>
> This 'undefined' solution extends to several paradoxes like "Achilles and the
> tortoise" and Supertask (the given problem does not contain the answer or
> confusing). The verdict, including 'circular argument', also applies to a
> number of foundamental math proofs. I just mention it. What involved is huge.

In current "Halting Problem" atmosphere. I should add:

void P(Arg x) {
if(H(p,x)==0) return;
Infinite_Loop: goto Infinite_loop;
}

Such P is defined (if H is defined).
In reality, all random string (program) are defined to x86 CPU.
Basically, no program is "pathological" to CPU. Similar cases are like in
Godel's incompleteness proof (I did not really read it), such 'P' is defined
and does exist (if H exists).

On 8/8/22 9:20 AM, wij wrote:
> On Monday, 8 August 2022 at 20:37:08 UTC+8, wij wrote:
>> P= "This statement is false"
>> Is P a proposition? This question depends largely on how P is interpreted,
>> because the sentence itself does not have T/F value (it is given by its evaluator).
>> Now, if the T/F value of the P as shown is defined by an evaluator, a circular
>> argument is formed. In this regard, the sentence P should be classified as
>> something like undefined or undecidable. P is not a 'proper' proposition.
>>
>> bool P() {
>> return !Evalu_TF(P);
>> };
>>
>> This 'undefined' solution extends to several paradoxes like "Achilles and the
>> tortoise" and Supertask (the given problem does not contain the answer or
>> confusing). The verdict, including 'circular argument', also applies to a
>> number of foundamental math proofs. I just mention it. What involved is huge.

Right, we can show that P is not a Truth Bearer, and thus doesn't have a
truth value.

>
> In current "Halting Problem" atmosphere. I should add:
>
> void P(Arg x) {
> if(H(p,x)==0) return;
> Infinite_Loop: goto Infinite_loop;
> }
>
> Such P is defined (if H is defined).
> In reality, all random string (program) are defined to x86 CPU.
> Basically, no program is "pathological" to CPU. Similar cases are like in
> Godel's incompleteness proof (I did not really read it), such 'P' is defined
> and does exist (if H exists).

Right, P(P) is a Halting Computation DOES have a truth value for ANY H
that can be defined, thus the Halting Question is a Truth Bearer, and
thus HAS a correct answer, even if H can't give it.

The question, What can H(P,P) return to be correct, is a question that
doesn't have a Truth Value, and thus isn't a Truth Bearer, but it fails
to be a proper question even before that point, as H needs to be a
DEFINED function, and thus H(P,P) has a defined value, which could be
correct or not (in fact, we know it will not). Asking what it could do
if it was something different is an improper question.

We CAN ask, what can H1(P,P) return to be corect, as that question DOES
have an answer (at least if H can be determined to be Halting or proved
to be non-halting). H1(P,P) returns the opposite of whatever H(P,P)
return, if it returns, or non-halting if H(P,P) will be non-halting.

If we can't determine if H(P,P) is Halting or Not, then we don't know
what value to return from H1(P,P), but one of the answers WILL be correct.

On Monday, August 8, 2022 at 8:37:08 AM UTC-4, wyni...@gmail.com wrote:
> P= "This statement is false"
> Is P a proposition? This question depends largely on how P is interpreted,
> because the sentence itself does not have T/F value (it is given by its evaluator).
> Now, if the T/F value of the P as shown is defined by an evaluator, a circular
> argument is formed. In this regard, the sentence P should be classified as
> something like undefined or undecidable. P is not a 'proper' proposition.
>
> bool P() {
> return !Evalu_TF(P);
> };
>
> This 'undefined' solution extends to several paradoxes like "Achilles and the
> tortoise" and Supertask (the given problem does not contain the answer or
> confusing). The verdict, including 'circular argument', also applies to a
> number of foundamental math proofs. I just mention it. What involved is huge.
i called the olcott program a cycle detector many years ago
daniel2380++

On Tuesday, 9 August 2022 at 08:38:28 UTC+8, richar...@gmail.com wrote:
> On 8/8/22 9:20 AM, wij wrote:
> > On Monday, 8 August 2022 at 20:37:08 UTC+8, wij wrote:
> >> P= "This statement is false"
> >> Is P a proposition? This question depends largely on how P is interpreted,
> >> because the sentence itself does not have T/F value (it is given by its evaluator).
> >> Now, if the T/F value of the P as shown is defined by an evaluator, a circular
> >> argument is formed. In this regard, the sentence P should be classified as
> >> something like undefined or undecidable. P is not a 'proper' proposition.
> >>
> >> bool P() {
> >> return !Evalu_TF(P);
> >> };
> >>
> >> This 'undefined' solution extends to several paradoxes like "Achilles and the
> >> tortoise" and Supertask (the given problem does not contain the answer or
> >> confusing). The verdict, including 'circular argument', also applies to a
> >> number of foundamental math proofs. I just mention it. What involved is huge.
> Right, we can show that P is not a Truth Bearer, and thus doesn't have a
> truth value.
> >
> > In current "Halting Problem" atmosphere. I should add:
> >
> > void P(Arg x) {
> > if(H(p,x)==0) return;
> > Infinite_Loop: goto Infinite_loop;
> > }
> >
> > Such P is defined (if H is defined).
> > In reality, all random string (program) are defined to x86 CPU.
> > Basically, no program is "pathological" to CPU. Similar cases are like in
> > Godel's incompleteness proof (I did not really read it), such 'P' is defined
> > and does exist (if H exists).
> Right, P(P) is a Halting Computation DOES have a truth value for ANY H
> that can be defined, thus the Halting Question is a Truth Bearer, and
> thus HAS a correct answer, even if H can't give it.
>
>
> The question, What can H(P,P) return to be correct, is a question that
> doesn't have a Truth Value, and thus isn't a Truth Bearer, but it fails
> to be a proper question even before that point, as H needs to be a
> DEFINED function, and thus H(P,P) has a defined value, which could be
> correct or not (in fact, we know it will not). Asking what it could do
> if it was something different is an improper question.
>
> We CAN ask, what can H1(P,P) return to be corect, as that question DOES
> have an answer (at least if H can be determined to be Halting or proved
> to be non-halting). H1(P,P) returns the opposite of whatever H(P,P)
> return, if it returns, or non-halting if H(P,P) will be non-halting.
>
> If we can't determine if H(P,P) is Halting or Not, then we don't know
> what value to return from H1(P,P), but one of the answers WILL be correct.

Sorry, would you make you point clearer?

On 8/8/2022 7:37 AM, wij wrote:
> P= "This statement is false"
> Is P a proposition? This question depends largely on how P is interpreted,
> because the sentence itself does not have T/F value (it is given by its evaluator).
> Now, if the T/F value of the P as shown is defined by an evaluator, a circular
> argument is formed. In this regard, the sentence P should be classified as
> something like undefined or undecidable. P is not a 'proper' proposition.
>
> bool P() {
> return !Evalu_TF(P);
> };
>
> This 'undefined' solution extends to several paradoxes like "Achilles and the
> tortoise" and Supertask (the given problem does not contain the answer or
> confusing). The verdict, including 'circular argument', also applies to a
> number of foundamental math proofs. I just mention it. What involved is huge.

I bought LiarParadox.org to address this issue.
It used to hound a Wordpress site that had all my papers.
Now the papers are on Researchgate.org

Here is my earliest paper on the Liar Paradox:

https://www.researchgate.net/publication/307442489_Formalizing_the_logical_self-reference_error_of_the_Liar_Paradox

Here is the error in C++:

int main()
{ bool LiarPardox = (LiarParadox == true);
}

--
Copyright 2022 Pete Olcott

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

On 8/9/22 2:02 PM, olcott wrote:
> On 8/8/2022 7:37 AM, wij wrote:
>> P= "This statement is false"
>> Is P a proposition? This question depends largely on how P is
>> interpreted,
>> because the sentence itself does not have T/F value (it is given by
>> its evaluator).
>> Now, if the T/F value of the P as shown is defined by an evaluator, a
>> circular
>> argument is formed. In this regard, the sentence P should be
>> classified as
>> something like undefined or undecidable. P is not a 'proper' proposition.
>>
>> bool P() {
>>    return !Evalu_TF(P);
>> };
>>
>> This 'undefined' solution extends to several paradoxes like "Achilles
>> and the
>> tortoise" and Supertask (the given problem does not contain the answer or
>> confusing). The verdict, including 'circular argument', also applies to a
>> number of foundamental math proofs. I just mention it. What involved
>> is huge.
>
> I bought LiarParadox.org to address this issue.
> It used to hound a Wordpress site that had all my papers.
> Now the papers are on Researchgate.org
>
> Here is my earliest paper on the Liar Paradox:
>
> https://www.researchgate.net/publication/307442489_Formalizing_the_logical_self-reference_error_of_the_Liar_Paradox
>
>
> Here is the error in C++:
>
> int main()
> {
>   bool LiarPardox = (LiarParadox == true);
> }
>

Which in C++ (or C) is UNDEFINED BEHAVIOR, as you are referencing the
value of the variable LiarParadox before it is set.

You have the problem that neither C nor C++ has the capability of
expressing the statement you are trying to represent, as they can only
COMPUTE based on values given, not solve systems of equations.

You need a language which allows the expression of this level of statement.

Note, C and C++ are only Turing Complete languages, which doesn't mean
they are capable of expressing all statements of logic, as logic is more
expressive than simple computations.

On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
> ...
> int main()
> {
> bool LiarPardox = (LiarParadox == true);
> }

Yes, that is the good part of using C/C++ language to express idea.
"This statement is true" is also an 'undefined' statement in this regard.

On 8/10/2022 10:00 AM, wij wrote:
> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>> ...
>> int main()
>> {
>> bool LiarPardox = (LiarParadox == true);
>> }
>
> Yes, that is the good part of using C/C++ language to express idea.
> "This statement is true" is also an 'undefined' statement in this regard.
>

*What is the proper definition of a truth bearer*?

Expressions of language that can be resolved to a truth value are [truth
bearers]. This includes expressions of language that currently have
unknown truth values.

Expressions of language that cannot possibly be resolved to a truth
value because their type or structure are not [truth bearers].

Expressions of language that contradict their own truth value: "This
sentence is not true." cannot possibly be resolved to a truth value are
not [truth bearers].

There are only two ways that an expression of language can be resolved
to a truth value:
(1) An expression of language is assigned a truth value such as "cats
are animals" is defined to be true.
(2) Truth preserving operations are applied to expressions of language
that are known to be true. {cats are animals} and {animals are living
things} therefore {cats are living things}. Copyright 2021 PL Olcott

--
Copyright 2022 Pete Olcott

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

On Wednesday, 10 August 2022 at 19:07:04 UTC+2, olcott wrote:
> Expressions of language that can be resolved to a truth value are [truth
> bearers]. This includes expressions of language that currently have
> unknown truth values.

So then the expression 'x = x` is a truth-bearer.

In [1]: expression = 'x == x'

It has an unknown truth-value until evaluated.

It can be resolved to True;

In [2]: x = object()

In [3]: eval(expression)
Out[3]: True

Or it can be resolved to False;

In [4]: x = another_object()

In [5]: eval(expression)
Out[5]: False

Sounds like you don't understand how truth works?

On 8/10/2022 2:55 PM, Skep Dick wrote:
> On Wednesday, 10 August 2022 at 19:07:04 UTC+2, olcott wrote:
>> Expressions of language that can be resolved to a truth value are [truth
>> bearers]. This includes expressions of language that currently have
>> unknown truth values.
>
> So then the expression 'x = x` is a truth-bearer.
>
> In [1]: expression = 'x == x'
>

It is a tautology that a thing <is> itself: 'x == x'
expression = 'x == x'
merely adds one level of indirect reference.

--
Copyright 2022 Pete Olcott

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

On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> It is a tautology that a thing <is> itself: 'x == x'
> expression = 'x == x'
> merely adds one level of indirect reference.

"Tautology" means "true in ALL possible models/interpretations".

"x == x" is NOT a tautology. I literally just showed you a model in which it's false.

On 8/10/2022 3:17 PM, Skep Dick wrote:
> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
>> It is a tautology that a thing <is> itself: 'x == x'
>> expression = 'x == x'
>> merely adds one level of indirect reference.
>
> "Tautology" means "true in ALL possible models/interpretations".
>
> "x == x" is NOT a tautology.

A thing is NOT itself?

--
Copyright 2022 Pete Olcott

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

On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
> On 8/10/2022 3:17 PM, Skep Dick wrote:
> > On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> >> It is a tautology that a thing <is> itself: 'x == x'
> >> expression = 'x == x'
> >> merely adds one level of indirect reference.
> >
> > "Tautology" means "true in ALL possible models/interpretations".
> >
> > "x == x" is NOT a tautology.
> A thing is NOT itself?

What? Why are you interpreting 'x==x' as a statement?
It's a question!

Is x the same as x?

Both answers are perfectly valid in different contexts:
yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.

On 8/10/2022 4:09 PM, Skep Dick wrote:
> On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
>> On 8/10/2022 3:17 PM, Skep Dick wrote:
>>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
>>>> It is a tautology that a thing <is> itself: 'x == x'
>>>> expression = 'x == x'
>>>> merely adds one level of indirect reference.
>>>
>>> "Tautology" means "true in ALL possible models/interpretations".
>>>
>>> "x == x" is NOT a tautology.
>> A thing is NOT itself?
>
> What? Why are you interpreting 'x==x' as a statement?
> It's a question!
>
> Is x the same as x?
>
> Both answers are perfectly valid in different contexts:
> yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
> no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.

Yuu cannot correctly cross the boundary from the analytic to the synthetic.

--
Copyright 2022 Pete Olcott

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

On Wednesday, 10 August 2022 at 23:18:17 UTC+2, olcott wrote:
> On 8/10/2022 4:09 PM, Skep Dick wrote:
> > On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
> >> On 8/10/2022 3:17 PM, Skep Dick wrote:
> >>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> >>>> It is a tautology that a thing <is> itself: 'x == x'
> >>>> expression = 'x == x'
> >>>> merely adds one level of indirect reference.
> >>>
> >>> "Tautology" means "true in ALL possible models/interpretations".
> >>>
> >>> "x == x" is NOT a tautology.
> >> A thing is NOT itself?
> >
> > What? Why are you interpreting 'x==x' as a statement?
> > It's a question!
> >
> > Is x the same as x?
> >
> > Both answers are perfectly valid in different contexts:
> > yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
> > no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
> Yuu cannot correctly cross the boundary from the analytic to the synthetic.

What boundary? Everything is synthetic.

Even when you think you are being analytical you are synthesising an analysis.

On 8/10/22 1:06 PM, olcott wrote:
> On 8/10/2022 10:00 AM, wij wrote:
>> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>>>   ...
>>> int main()
>>> {
>>> bool LiarPardox = (LiarParadox == true);
>>> }
>>
>> Yes, that is the good part of using C/C++ language to express idea.
>> "This statement is true" is also an 'undefined' statement in this regard.
>>
>
> *What is the proper definition of a truth bearer*?
>
> Expressions of language that can be resolved to a truth value are [truth
> bearers]. This includes expressions of language that currently have
> unknown truth values.
>
> Expressions of language that cannot possibly be resolved to a truth
> value because their type or structure are not [truth bearers].
>
> Expressions of language that contradict their own truth value: "This
> sentence is not true." cannot possibly be resolved to a truth value are
> not [truth bearers].
>
> There are only two ways that an expression of language can be resolved
> to a truth value:
> (1) An expression of language is assigned a truth value such as "cats
> are animals" is defined to be true.
> (2) Truth preserving operations are applied to expressions of language
> that are known to be true. {cats are animals} and {animals are living
> things} therefore {cats are living things}. Copyright 2021 PL Olcott
>

Or, the Truth of the statement can be EMPIRICALLY demonstrated.

The statement "The Earth is Round" is True, not because we have assigned
the "Round Property" to the name "Earth", or because we have somehow
manipulated know true statements to prove that the Earth must be round,
but because by DIRECT OBSERVATION, we see that it meets the definition
we has assigned to "Round".

Note, that "Cats are Animals" is NOT just a matter of definition, but of
this sort of empirical proof.

First we define what we mean by an "Animal", as a certain classification
of living organisms.

Then we define what we mean by a "Cat", which while it might include a
requirment that these be animals, might not.

We can then (if not forced by the definition) determine if Cats actually
are Animals.

There have been a number of cases where something that was THOUGHT to be
a thing that was part of a category, turned out on better understanding
to not actually be actually in that category, but was something else.

The Truth value of "Halting" is this sort of property. We have a
definition of it, that it relates to a Machine reaching a final state
for a given input, but the "proof" of a given Machine Halting or Not
isn't really proof in the normal sense, but the emperical running of the
machine and seeing if we get it to halt. If it doesn't halt, we might
need to resort to some logic to prove that it won't. But the emperical
fact that if we run the machine and reach the final state says that no
matter what logic you claim to have used to show it won't halt, that
logic is proved incorrect by the emperical fact that it did.

On 8/10/22 5:09 PM, Skep Dick wrote:
> On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
>> On 8/10/2022 3:17 PM, Skep Dick wrote:
>>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
>>>> It is a tautology that a thing <is> itself: 'x == x'
>>>> expression = 'x == x'
>>>> merely adds one level of indirect reference.
>>>
>>> "Tautology" means "true in ALL possible models/interpretations".
>>>
>>> "x == x" is NOT a tautology.
>> A thing is NOT itself?
>
> What? Why are you interpreting 'x==x' as a statement?
> It's a question!
>
> Is x the same as x?
>
> Both answers are perfectly valid in different contexts:
> yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
> no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
>
>
>
>

So why does the one x bind in a different context then the other?

Of course, there IS a case where x == x can legitimately return FALSE,
because there do exists some systems with an unusual definition of equality.

If x has the value of not-a-number (NaN) then by the offical definition
of IEEE floating print logic,

x == x needs to return FALSE, and is one way to test a floating point
value to see if it is a NaN.

On 8/10/2022 7:44 PM, Richard Damon wrote:
> On 8/10/22 1:06 PM, olcott wrote:
>> On 8/10/2022 10:00 AM, wij wrote:
>>> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>>>>   ...
>>>> int main()
>>>> {
>>>> bool LiarPardox = (LiarParadox == true);
>>>> }
>>>
>>> Yes, that is the good part of using C/C++ language to express idea.
>>> "This statement is true" is also an 'undefined' statement in this
>>> regard.
>>>
>>
>> *What is the proper definition of a truth bearer*?
>>
>> Expressions of language that can be resolved to a truth value are
>> [truth bearers]. This includes expressions of language that currently
>> have unknown truth values.
>>
>> Expressions of language that cannot possibly be resolved to a truth
>> value because their type or structure are not [truth bearers].
>>
>> Expressions of language that contradict their own truth value: "This
>> sentence is not true." cannot possibly be resolved to a truth value
>> are not [truth bearers].
>>
>> There are only two ways that an expression of language can be resolved
>> to a truth value:
>> (1) An expression of language is assigned a truth value such as "cats
>> are animals" is defined to be true.
>> (2) Truth preserving operations are applied to expressions of language
>> that are known to be true. {cats are animals} and {animals are living
>> things} therefore {cats are living things}. Copyright 2021 PL Olcott
>>
>
> Or, the Truth of the statement can be EMPIRICALLY demonstrated.
>

Yes you are correct. I was only referring to analytic rather than
synthetic truth.

https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

--
Copyright 2022 Pete Olcott

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

On 8/10/22 8:59 PM, olcott wrote:
> On 8/10/2022 7:44 PM, Richard Damon wrote:
>> On 8/10/22 1:06 PM, olcott wrote:
>>> On 8/10/2022 10:00 AM, wij wrote:
>>>> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>>>>>   ...
>>>>> int main()
>>>>> {
>>>>> bool LiarPardox = (LiarParadox == true);
>>>>> }
>>>>
>>>> Yes, that is the good part of using C/C++ language to express idea.
>>>> "This statement is true" is also an 'undefined' statement in this
>>>> regard.
>>>>
>>>
>>> *What is the proper definition of a truth bearer*?
>>>
>>> Expressions of language that can be resolved to a truth value are
>>> [truth bearers]. This includes expressions of language that currently
>>> have unknown truth values.
>>>
>>> Expressions of language that cannot possibly be resolved to a truth
>>> value because their type or structure are not [truth bearers].
>>>
>>> Expressions of language that contradict their own truth value: "This
>>> sentence is not true." cannot possibly be resolved to a truth value
>>> are not [truth bearers].
>>>
>>> There are only two ways that an expression of language can be
>>> resolved to a truth value:
>>> (1) An expression of language is assigned a truth value such as "cats
>>> are animals" is defined to be true.
>>> (2) Truth preserving operations are applied to expressions of
>>> language that are known to be true. {cats are animals} and {animals
>>> are living things} therefore {cats are living things}. Copyright 2021
>>> PL Olcott
>>>
>>
>> Or, the Truth of the statement can be EMPIRICALLY demonstrated.
>>
>
> Yes you are correct. I was only referring to analytic rather than
> synthetic truth.
>
> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>

But then you keep using the wrong term. And use wrong examples.

"Cats are Animals" is NOT actually an Analytic Truth, since the terms
refer to things that actually exist, and so the ACTUAL truth relies on
Reality.

By YOUR logic, we could say "Cats are Plants" to be an analytic truth by
just defining it that way, but such a system is inconsistent with
reality, and thus not accepted.

Note, the term "Truth Beared" is NOT limited to just analytic truth. A
statement can be a truth bearer even if the only way to determine its
truth is emperical.

On 8/10/2022 8:19 PM, Richard Damon wrote:
> On 8/10/22 8:59 PM, olcott wrote:
>> On 8/10/2022 7:44 PM, Richard Damon wrote:
>>> On 8/10/22 1:06 PM, olcott wrote:
>>>> On 8/10/2022 10:00 AM, wij wrote:
>>>>> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>>>>>>   ...
>>>>>> int main()
>>>>>> {
>>>>>> bool LiarPardox = (LiarParadox == true);
>>>>>> }
>>>>>
>>>>> Yes, that is the good part of using C/C++ language to express idea.
>>>>> "This statement is true" is also an 'undefined' statement in this
>>>>> regard.
>>>>>
>>>>
>>>> *What is the proper definition of a truth bearer*?
>>>>
>>>> Expressions of language that can be resolved to a truth value are
>>>> [truth bearers]. This includes expressions of language that
>>>> currently have unknown truth values.
>>>>
>>>> Expressions of language that cannot possibly be resolved to a truth
>>>> value because their type or structure are not [truth bearers].
>>>>
>>>> Expressions of language that contradict their own truth value: "This
>>>> sentence is not true." cannot possibly be resolved to a truth value
>>>> are not [truth bearers].
>>>>
>>>> There are only two ways that an expression of language can be
>>>> resolved to a truth value:
>>>> (1) An expression of language is assigned a truth value such as
>>>> "cats are animals" is defined to be true.
>>>> (2) Truth preserving operations are applied to expressions of
>>>> language that are known to be true. {cats are animals} and {animals
>>>> are living things} therefore {cats are living things}. Copyright
>>>> 2021 PL Olcott
>>>>
>>>
>>> Or, the Truth of the statement can be EMPIRICALLY demonstrated.
>>>
>>
>> Yes you are correct. I was only referring to analytic rather than
>> synthetic truth.
>>
>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>
>
> But then you keep using the wrong term. And use wrong examples.
>
> "Cats are Animals" is NOT actually an Analytic Truth,
WRONG

“Analytic” sentences, such as “Pediatricians are doctors,” have
historically been characterized as ones that are true by virtue of the
meanings of their words alone and/or can be known to be so solely by
knowing those meanings.
https://plato.stanford.edu/entries/analytic-synthetic/

--
Copyright 2022 Pete Olcott

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

On Thursday, 11 August 2022 at 02:44:14 UTC+2, richar...@gmail.com wrote:
> On 8/10/22 1:06 PM, olcott wrote:
> > On 8/10/2022 10:00 AM, wij wrote:
> >> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
> >>> ...
> >>> int main()
> >>> {
> >>> bool LiarPardox = (LiarParadox == true);
> >>> }
> >>
> >> Yes, that is the good part of using C/C++ language to express idea.
> >> "This statement is true" is also an 'undefined' statement in this regard.
> >>
> >
> > *What is the proper definition of a truth bearer*?
> >
> > Expressions of language that can be resolved to a truth value are [truth
> > bearers]. This includes expressions of language that currently have
> > unknown truth values.
> >
> > Expressions of language that cannot possibly be resolved to a truth
> > value because their type or structure are not [truth bearers].
> >
> > Expressions of language that contradict their own truth value: "This
> > sentence is not true." cannot possibly be resolved to a truth value are
> > not [truth bearers].
> >
> > There are only two ways that an expression of language can be resolved
> > to a truth value:
> > (1) An expression of language is assigned a truth value such as "cats
> > are animals" is defined to be true.
> > (2) Truth preserving operations are applied to expressions of language
> > that are known to be true. {cats are animals} and {animals are living
> > things} therefore {cats are living things}. Copyright 2021 PL Olcott
> >
> Or, the Truth of the statement can be EMPIRICALLY demonstrated.

> The statement "The Earth is Round" is True, not because we have assigned
> the "Round Property" to the name "Earth", or because we have somehow
> manipulated know true statements to prove that the Earth must be round,
> but because by DIRECT OBSERVATION, we see that it meets the definition
> we has assigned to "Round".

The Earth meets your definition of “round”? Why? Earth is not round. We approximate it to be round, or oblate.

But that is just what we say about it colloquially. It isn’t literally true.

On Thursday, 11 August 2022 at 02:49:23 UTC+2, richar...@gmail.com wrote:
> On 8/10/22 5:09 PM, Skep Dick wrote:
> > On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
> >> On 8/10/2022 3:17 PM, Skep Dick wrote:
> >>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
> >>>> It is a tautology that a thing <is> itself: 'x == x'
> >>>> expression = 'x == x'
> >>>> merely adds one level of indirect reference.
> >>>
> >>> "Tautology" means "true in ALL possible models/interpretations".
> >>>
> >>> "x == x" is NOT a tautology.
> >> A thing is NOT itself?
> >
> > What? Why are you interpreting 'x==x' as a statement?
> > It's a question!
> >
> > Is x the same as x?
> >
> > Both answers are perfectly valid in different contexts:
> > yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
> > no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
> >
> >
> >
> >
> So why does the one x bind in a different context then the other?
It isn’t a different context.

I am binding x to two different objects.

Instances of object are equal to themselves.
Instances of another…object aren’t.

> Of course, there IS a case where x == x can legitimately return FALSE,
> because there do exists some systems with an unusual definition of equality.
>
>
> If x has the value of not-a-number (NaN) then by the offical definition
> of IEEE floating print logic,
>
> x == x needs to return FALSE, and is one way to test a floating point
> value to see if it is a NaN.

None of this matters. The point I am making is that the expression “x == x” has no value by default.
Assigning one to it is a design choice.

The value of “x=x” is a free variable. It can be anything you want it to be.

On 8/10/22 10:38 PM, Skep Dick wrote:
> On Thursday, 11 August 2022 at 02:49:23 UTC+2, richar...@gmail.com wrote:
>> On 8/10/22 5:09 PM, Skep Dick wrote:
>>> On Wednesday, 10 August 2022 at 23:02:00 UTC+2, olcott wrote:
>>>> On 8/10/2022 3:17 PM, Skep Dick wrote:
>>>>> On Wednesday, 10 August 2022 at 22:10:01 UTC+2, olcott wrote:
>>>>>> It is a tautology that a thing <is> itself: 'x == x'
>>>>>> expression = 'x == x'
>>>>>> merely adds one level of indirect reference.
>>>>>
>>>>> "Tautology" means "true in ALL possible models/interpretations".
>>>>>
>>>>> "x == x" is NOT a tautology.
>>>> A thing is NOT itself?
>>>
>>> What? Why are you interpreting 'x==x' as a statement?
>>> It's a question!
>>>
>>> Is x the same as x?
>>>
>>> Both answers are perfectly valid in different contexts:
>>> yes - x is the same as x. It remained the same from one moment into the next. Classical logic.
>>> no - x is not the same as x. it changed from one moment into the next. Schrödinger logic.
>>>
>>>
>>>
>>>
>> So why does the one x bind in a different context then the other?
> It isn’t a different context.
>
> I am binding x to two different objects.
>
> Instances of object are equal to themselves.
> Instances of another…object aren’t.
>

And how does your language know which x to bind to which object?

It seems you have an inconsisten system.

>
>> Of course, there IS a case where x == x can legitimately return FALSE,
>> because there do exists some systems with an unusual definition of equality.
>>
>>
>> If x has the value of not-a-number (NaN) then by the offical definition
>> of IEEE floating print logic,
>>
>> x == x needs to return FALSE, and is one way to test a floating point
>> value to see if it is a NaN.
>
> None of this matters. The point I am making is that the expression “x == x” has no value by default.
> Assigning one to it is a design choice.
>
> The value of “x=x” is a free variable. It can be anything you want it to be.
>

Since == is a comparison, and not a binding, nornally, two references to
the same name in a given expression will be bound to the same object.

Or, is you system just randomly changing the binding of a variable in
the middle of operations on a whim?

On 8/10/22 9:28 PM, olcott wrote:
> On 8/10/2022 8:19 PM, Richard Damon wrote:
>> On 8/10/22 8:59 PM, olcott wrote:
>>> On 8/10/2022 7:44 PM, Richard Damon wrote:
>>>> On 8/10/22 1:06 PM, olcott wrote:
>>>>> On 8/10/2022 10:00 AM, wij wrote:
>>>>>> On Wednesday, 10 August 2022 at 02:02:13 UTC+8, olcott wrote:
>>>>>>>   ...
>>>>>>> int main()
>>>>>>> {
>>>>>>> bool LiarPardox = (LiarParadox == true);
>>>>>>> }
>>>>>>
>>>>>> Yes, that is the good part of using C/C++ language to express idea.
>>>>>> "This statement is true" is also an 'undefined' statement in this
>>>>>> regard.
>>>>>>
>>>>>
>>>>> *What is the proper definition of a truth bearer*?
>>>>>
>>>>> Expressions of language that can be resolved to a truth value are
>>>>> [truth bearers]. This includes expressions of language that
>>>>> currently have unknown truth values.
>>>>>
>>>>> Expressions of language that cannot possibly be resolved to a truth
>>>>> value because their type or structure are not [truth bearers].
>>>>>
>>>>> Expressions of language that contradict their own truth value:
>>>>> "This sentence is not true." cannot possibly be resolved to a truth
>>>>> value are not [truth bearers].
>>>>>
>>>>> There are only two ways that an expression of language can be
>>>>> resolved to a truth value:
>>>>> (1) An expression of language is assigned a truth value such as
>>>>> "cats are animals" is defined to be true.
>>>>> (2) Truth preserving operations are applied to expressions of
>>>>> language that are known to be true. {cats are animals} and {animals
>>>>> are living things} therefore {cats are living things}. Copyright
>>>>> 2021 PL Olcott
>>>>>
>>>>
>>>> Or, the Truth of the statement can be EMPIRICALLY demonstrated.
>>>>
>>>
>>> Yes you are correct. I was only referring to analytic rather than
>>> synthetic truth.
>>>
>>> https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
>>>
>>
>> But then you keep using the wrong term. And use wrong examples.
>>
>> "Cats are Animals" is NOT actually an Analytic Truth,
> WRONG
>
> “Analytic” sentences, such as “Pediatricians are doctors,” have
> historically been characterized as ones that are true by virtue of the
> meanings of their words alone and/or can be known to be so solely by
> knowing those meanings.
> https://plato.stanford.edu/entries/analytic-synthetic/
>

But the definition of "Pediatrician" is that it is a TYPE of doctor that
.....

It specifically defines the label as a subclass.

"Cat" is a different sort of thing, while we conventionaally might use a
"animal" reference in describing it, that is because the sort of thing
we call a "Cat" happens to emperically be an animal.

"Cats" are a classification of a set of entities with certain
properties. It just so happens to turn out that one of them is that they
also fall within the classification we call animals.

This shows the "flaw" of trying to use too sharp of a knife to divide
the types of truth from each other.