Correcting logic to make it a system of correct reasoning

[olcott]

*Validity and Soundness*
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion
nevertheless to be false. Otherwise, a deductive argument is said to be
invalid. https://iep.utm.edu/val-snd/

If the Moon is made of green cheese then all dogs are cats is valid and
even though premises and conclusion are semantically unrelated.

*Here is my correction to that issue*
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.




--
Copyright 2022 Pete Olcott

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

[Richard Damon]

On 5/13/22 1:20 PM, olcott wrote:
> *Validity and Soundness*
> A deductive argument is said to be valid if and only if it takes a form
> that makes it impossible for the premises to be true and the conclusion
> nevertheless to be false. Otherwise, a deductive argument is said to be
> invalid. https://iep.utm.edu/val-snd/
>
> If the Moon is made of green cheese then all dogs are cats is valid and
> even though premises and conclusion are semantically unrelated.
>
> *Here is my correction to that issue*
> A deductive argument is said to be valid if and only if it takes a form
> such that its conclusion is a necessary consequence of all of its premises.
>

And, have you done the basic investigation to find out how much of
conventional logic you invalidate with that change?

Note, that it may be hard to define "necessary consequence" in a formal
matter.

It should be noted that your example, while considered an vaild
inference by normal logic, can never be used to actually prove its
conclusion, so doesn't actually cause problems in normal logic (can you
show a case where it does?)

Note, that at least by some meanings of your words, it could be
construed that you only accept as a correct deductive argument, and
arguement whose premises can at least some times be true, but there are
some statements we don't know if they CAN be sometimes true, so your
logic system would seem to not allow doing logic with that sort of
statement.

[olcott]

On 5/13/2022 12:47 PM, Richard Damon wrote:
> On 5/13/22 1:20 PM, olcott wrote:
>> *Validity and Soundness*
>> A deductive argument is said to be valid if and only if it takes a
>> form that makes it impossible for the premises to be true and the
>> conclusion nevertheless to be false. Otherwise, a deductive argument
>> is said to be invalid. https://iep.utm.edu/val-snd/
>>
>> If the Moon is made of green cheese then all dogs are cats is valid
>> and even though premises and conclusion are semantically unrelated.
>>
>> *Here is my correction to that issue*
>> A deductive argument is said to be valid if and only if it takes a
>> form such that its conclusion is a necessary consequence of all of its
>> premises.
>>
>
> And, have you done the basic investigation to find out how much of
> conventional logic you invalidate with that change?
>

It categorically changes everything that is broken.

> Note, that it may be hard to define "necessary consequence" in a formal
> matter.
>

{A,B} ⊢ C only when truth preserving operations are applied to {A,B} to
derive C.

> It should be noted that your example, while considered an vaild
> inference by normal logic, can never be used to actually prove its
> conclusion, so doesn't actually cause problems in normal logic (can you
> show a case where it does?)
>

With my correction true and unprovable is impossible, unprovable simply
means untrue.

> Note, that at least by some meanings of your words, it could be
> construed that you only accept as a correct deductive argument, and
> arguement whose premises can at least some times be true, but there are
> some statements we don't know if they CAN be sometimes true, so your
> logic system would seem to not allow doing logic with that sort of
> statement.
>

An analytic statement is only known to be true when it is derived by
applying only truth preserving operations to all of its premises and all
of its premises are known to be true, otherwise its truth value is unknown.

[André G. Isaak]

On 2022-05-13 11:20, olcott wrote:
> *Validity and Soundness*
> A deductive argument is said to be valid if and only if it takes a form
> that makes it impossible for the premises to be true and the conclusion
> nevertheless to be false. Otherwise, a deductive argument is said to be
> invalid. https://iep.utm.edu/val-snd/
>
> If the Moon is made of green cheese then all dogs are cats is valid and
> even though premises and conclusion are semantically unrelated.

That isn't valid. Perhaps you should learn what 'valid' actually means
before you attempt to "correct" the definition.

[Also, the above isn't even an argument. It is simply a conditional
statement. It has no conclusion].

> *Here is my correction to that issue*
> A deductive argument is said to be valid if and only if it takes a form
> such that its conclusion is a necessary consequence of all of its premises.

And that differs from the standard definition how exactly? Unless you
have some special personal meaning for 'necessary consequence' it would
appear to be simply a paraphrase of the definition you cite above.

André


--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

[olcott]

On 5/13/2022 1:28 PM, André G. Isaak wrote:
> On 2022-05-13 11:20, olcott wrote:
>> *Validity and Soundness*
>> A deductive argument is said to be valid if and only if it takes a
>> form that makes it impossible for the premises to be true and the
>> conclusion nevertheless to be false. Otherwise, a deductive argument
>> is said to be invalid. https://iep.utm.edu/val-snd/
>>
>> If the Moon is made of green cheese then all dogs are cats is valid
>> and even though premises and conclusion are semantically unrelated.
>
> That isn't valid. Perhaps you should learn what 'valid' actually means
> before you attempt to "correct" the definition.
>
> [Also, the above isn't even an argument. It is simply a conditional
> statement. It has no conclusion].
>

(a) The Moon is made of green cheese.
(b) Water is a kind of concrete.
(c) Therefore all dogs are cats.

Because the premises are false and the conclusion is false it is not a
case of the conclusion is true and the premises are false, thus meets
the above validity criteria.

>> *Here is my correction to that issue*
>> A deductive argument is said to be valid if and only if it takes a
>> form such that its conclusion is a necessary consequence of all of its
>> premises.
>
> And that differs from the standard definition how exactly? Unless you
> have some special personal meaning for 'necessary consequence' it would

Semantic relevance is a key aspect of 'necessary consequence'.

> appear to be simply a paraphrase of the definition you cite above.
>
> André
>
>


--

[André G. Isaak]

On 2022-05-13 12:50, olcott wrote:
> On 5/13/2022 1:28 PM, André G. Isaak wrote:
>> On 2022-05-13 11:20, olcott wrote:
>>> *Validity and Soundness*
>>> A deductive argument is said to be valid if and only if it takes a
>>> form that makes it impossible for the premises to be true and the
>>> conclusion nevertheless to be false. Otherwise, a deductive argument
>>> is said to be invalid. https://iep.utm.edu/val-snd/
>>>
>>> If the Moon is made of green cheese then all dogs are cats is valid
>>> and even though premises and conclusion are semantically unrelated.
>>
>> That isn't valid. Perhaps you should learn what 'valid' actually means
>> before you attempt to "correct" the definition.
>>
>> [Also, the above isn't even an argument. It is simply a conditional
>> statement. It has no conclusion].
>>
>
> (a) The Moon is made of green cheese.
> (b) Water is a kind of concrete.
> (c) Therefore all dogs are cats.
>
> Because the premises are false and the conclusion is false it is not a
> case of the conclusion is true and the premises are false, thus meets
> the above validity criteria.

No. It isn't valid. You don't seem to grasp the concept of validity.

Logic has no concept of whether, for example, the moon is made of green
cheese. An argument is valid if there is no truth *assignment* under
which the premises are true and the conclusion is false. The actual
truth values of these expressions don't play a role in the definition of
validity.

>>> *Here is my correction to that issue*
>>> A deductive argument is said to be valid if and only if it takes a
>>> form such that its conclusion is a necessary consequence of all of
>>> its premises.
>>
>> And that differs from the standard definition how exactly? Unless you
>> have some special personal meaning for 'necessary consequence' it would
>
> Semantic relevance is a key aspect of 'necessary consequence'.

Defined how exactly?

[olcott]

I reach my key insights by progressively refining very high level
abstractions into their corresponding concrete examples.

Clearly I have not yet translated this abstraction:

A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.

Into a concrete example of the issue that it corrects, quite yet.

>>>> *Here is my correction to that issue*
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form such that its conclusion is a necessary consequence of all of
>>>> its premises.
>>>
>>> And that differs from the standard definition how exactly? Unless you
>>> have some special personal meaning for 'necessary consequence' it would
>>
>> Semantic relevance is a key aspect of 'necessary consequence'.
>
> Defined how exactly?
>
> André
>

Here is the original way that semantic relevance was defined:
Semantically unrelated premises and conclusion is not possible with
syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of
https://en.wikipedia.org/wiki/Categorical_proposition

[Richard Damon]

On 5/13/22 2:10 PM, olcott wrote:
> On 5/13/2022 12:47 PM, Richard Damon wrote:
>> On 5/13/22 1:20 PM, olcott wrote:
>>> *Validity and Soundness*
>>> A deductive argument is said to be valid if and only if it takes a
>>> form that makes it impossible for the premises to be true and the
>>> conclusion nevertheless to be false. Otherwise, a deductive argument
>>> is said to be invalid. https://iep.utm.edu/val-snd/
>>>
>>> If the Moon is made of green cheese then all dogs are cats is valid
>>> and even though premises and conclusion are semantically unrelated.
>>>
>>> *Here is my correction to that issue*
>>> A deductive argument is said to be valid if and only if it takes a
>>> form such that its conclusion is a necessary consequence of all of
>>> its premises.
>>>
>>
>> And, have you done the basic investigation to find out how much of
>> conventional logic you invalidate with that change?
>>
>
> It categorically changes everything that is broken.

So, you are saying we need to throw out EVERYTHING we know and start over?

I think, especially with the comment below, people will decide that your
"new" logic systm isn't worth the cost to switch to.

>
>> Note, that it may be hard to define "necessary consequence" in a
>> formal matter.
>>
>
> {A,B} ⊢ C only when truth preserving operations are applied to {A,B} to
> derive C.

And what do you define truth perserving as?

Normally the phrase means that True Premises always generate True
Results (which means the statement "If the moon is made of green cheese
then ll dogs are cats" IS Truth Preserving, since any time the premise
is true (never) the conclusion is true.

>
>> It should be noted that your example, while considered an vaild
>> inference by normal logic, can never be used to actually prove its
>> conclusion, so doesn't actually cause problems in normal logic (can
>> you show a case where it does?)
>>
>
> With my correction true and unprovable is impossible, unprovable simply
> means untrue.
>

Ok, then you have just stated that your new logic system can't handle
mathematics, and thus "Computer SCience" no longer exists as a logical
system.

This makes you system not much more than a toy for most people.

>> Note, that at least by some meanings of your words, it could be
>> construed that you only accept as a correct deductive argument, and
>> arguement whose premises can at least some times be true, but there
>> are some statements we don't know if they CAN be sometimes true, so
>> your logic system would seem to not allow doing logic with that sort
>> of statement.
>>
>
> An analytic statement is only known to be true when it is derived by
> applying only truth preserving operations to all of its premises and all
> of its premises are known to be true, otherwise its truth value is unknown.
>

KNOWN to be True, not IS TRUE.

Your statement even admits that truth value might be unknow, which might
allow it to even be UNKNOWABLE (maybe just in that system) if it can't
be proven or refuted.

There is NOTHING about an analytic statement that says it can only be
true if it is provable. Note, "its truth value is unknown" doesn't mean
it doesn't have a truth value, just that we don't know what that value is.

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

[André G. Isaak]

Abstractions are designed to cover a large number of different cases. A
concrete example cannot capture an abstraction.

> Clearly I have not yet translated this abstraction:
>
> A deductive argument is said to be valid if and only if it takes a form
> such that its conclusion is a necessary consequence of all of its premises.
>
> Into a concrete example of the issue that it corrects, quite yet.

Are you acknowledging that you haven't the foggiest idea what 'valid'
means? If you're trying to say more than this, I fail to see what it
might be.

>>>>> *Here is my correction to that issue*
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form such that its conclusion is a necessary consequence of all of
>>>>> its premises.
>>>>
>>>> And that differs from the standard definition how exactly? Unless
>>>> you have some special personal meaning for 'necessary consequence'
>>>> it would
>>>
>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>
>> Defined how exactly?
>>
>> André
>>
>
> Here is the original way that semantic relevance was defined:
> Semantically unrelated premises and conclusion is not possible with
> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>
> Because syllogisms are comprised of
> https://en.wikipedia.org/wiki/Categorical_proposition

How exactly do two wikipedia articles provide a definition of 'semantic
relevance' when neither article contains the word 'semantic' nor the
word 'relevance'?

[olcott]

On 5/13/2022 2:13 PM, Richard Damon wrote:
> On 5/13/22 2:10 PM, olcott wrote:
>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>> On 5/13/22 1:20 PM, olcott wrote:
>>>> *Validity and Soundness*
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form that makes it impossible for the premises to be true and the
>>>> conclusion nevertheless to be false. Otherwise, a deductive argument
>>>> is said to be invalid. https://iep.utm.edu/val-snd/
>>>>
>>>> If the Moon is made of green cheese then all dogs are cats is valid
>>>> and even though premises and conclusion are semantically unrelated.
>>>>
>>>> *Here is my correction to that issue*
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form such that its conclusion is a necessary consequence of all of
>>>> its premises.
>>>>
>>>
>>> And, have you done the basic investigation to find out how much of
>>> conventional logic you invalidate with that change?
>>>
>>
>> It categorically changes everything that is broken.
>
> So, you are saying we need to throw out EVERYTHING we know and start over?
>

Change everything that diverges from my spec:

A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.

> I think, especially with the comment below, people will decide that your
> "new" logic systm isn't worth the cost to switch to.
>
>>
>>> Note, that it may be hard to define "necessary consequence" in a
>>> formal matter.
>>>
>>
>> {A,B} ⊢ C only when truth preserving operations are applied to {A,B}
>> to derive C.
>
> And what do you define truth perserving as?
>

Semantic relevance is maintained.

> Normally the phrase means that True Premises always generate True
> Results (which means the statement "If the moon is made of green cheese
> then ll dogs are cats" IS Truth Preserving, since any time the premise
> is true (never) the conclusion is true.
>
>>
>>> It should be noted that your example, while considered an vaild
>>> inference by normal logic, can never be used to actually prove its
>>> conclusion, so doesn't actually cause problems in normal logic (can
>>> you show a case where it does?)
>>>
>>
>> With my correction true and unprovable is impossible, unprovable
>> simply means untrue.
>>
>
> Ok, then you have just stated that your new logic system can't handle
> mathematics, and thus "Computer SCience" no longer exists as a logical
> system.
>

It corrects the divergence of classical and symbolic logic from correct
reasoning.

> This makes you system not much more than a toy for most people.
>
>>> Note, that at least by some meanings of your words, it could be
>>> construed that you only accept as a correct deductive argument, and
>>> arguement whose premises can at least some times be true, but there
>>> are some statements we don't know if they CAN be sometimes true, so
>>> your logic system would seem to not allow doing logic with that sort
>>> of statement.
>>>
>>
>> An analytic statement is only known to be true when it is derived by
>> applying only truth preserving operations to all of its premises and
>> all of its premises are known to be true, otherwise its truth value is
>> unknown.
>>
>
> KNOWN to be True, not IS TRUE.

It remains unknown until it is known to be true or false.
My system only eliminates impossibly true or false.

>
> Your statement even admits that truth value might be unknow, which might
> allow it to even be UNKNOWABLE (maybe just in that system) if it can't
> be proven or refuted.
>

unprovable in the system means untrue in the system.

> There is NOTHING about an analytic statement that says it can only be
> true if it is provable. Note, "its truth value is unknown" doesn't mean
> it doesn't have a truth value, just that we don't know what that value is.
>

Within any formal system unprovable in the system means untrue in the
system.

The entire body of analytic truth is constructed only on the basis of
semantic connections between expressions of language, or expressions
that are stipulated to have the semantic property of Boolean true.
Lacking both of these and the expression is untrue.

Since axioms are provable on the basis that they are axioms then both of
these factors that make an expression true also make it provable.

> You are confusing Knowledge with Truth.
>
> Your whole system is built on a Category Error.
>

[olcott]

I am saying that I am redefining the concept of logical validity to
eliminate its divergence from correct reasoning.

A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.

This requires semantic relevance between the all the premises and the
conclusion to be maintained.

>>>>>> *Here is my correction to that issue*
>>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>>> form such that its conclusion is a necessary consequence of all of
>>>>>> its premises.
>>>>>
>>>>> And that differs from the standard definition how exactly? Unless
>>>>> you have some special personal meaning for 'necessary consequence'
>>>>> it would
>>>>
>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>
>>> Defined how exactly?
>>>
>>> André
>>>
>>
>> Here is the original way that semantic relevance was defined:
>> Semantically unrelated premises and conclusion is not possible with
>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>
>> Because syllogisms are comprised of
>> https://en.wikipedia.org/wiki/Categorical_proposition
>
> How exactly do two wikipedia articles provide a definition of 'semantic
> relevance' when neither article contains the word 'semantic' nor the
> word 'relevance'?
>
> André
>

https://en.wikipedia.org/wiki/Relevance_logic

Also it can be easily seen that Categorical_propositions cannot possibly
diverge from semantic relevance.

[André G. Isaak]

Except you haven't show any instances where it diverges from 'correct
reasoning'. You gave an example argument which was *not* valid, claimed
that it was valid and that this "fact" was somehow a problem. The only
problem I can see is your failure to grasp what it means for something
to be valid.

If you can't even figure out whether an argument is valid or not, you're
not in any position to claim there is something wrong with the accepted
concept of validity.

[Richard Damon]

My first thought is that if you are going to be limiting your reasoning
capability to simple things. You seem to be stuck in using simple logic
methods, which will limit what you can actually prove.

What you don't seem to understand is that much of what we have logically
proven, is based on higher order logical systems, which these simple
forms just can't handle.

In particular, Computation theory, like much of mathematics, needs
second order (or higher) logic forms, which the simple logic just can't
handle.

[olcott]

True and unprovable become impossible because Provable() is an aspect of
True().

> You gave an example argument which was *not* valid, claimed
> that it was valid and that this "fact" was somehow a problem. The only
> problem I can see is your failure to grasp what it means for something
> to be valid.
>
> If you can't even figure out whether an argument is valid or not, you're
> not in any position to claim there is something wrong with the accepted
> concept of validity.
>
> André
>


--

[olcott]

Not when all of natural language semantics has been fully formalized and
directly integrated into its own formal system.

> What you don't seem to understand is that much of what we have logically
> proven, is based on higher order logical systems, which these simple
> forms just can't handle.
>
> In particular, Computation theory, like much of mathematics, needs
> second order (or higher) logic forms, which the simple logic just can't
> handle.

I created Minimal Type Theory to express HOL using very slightly adapted
syntax of FOL. In an early version of MTT it translated its expressions
into directed graphs so that pathological self-reference could be seen
as infinite cycle in the di-graph.

https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF

[Richard Damon]

So, you don't know what is still valid to use?

>>
>> Your statement even admits that truth value might be unknow, which
>> might allow it to even be UNKNOWABLE (maybe just in that system) if it
>> can't be proven or refuted.
>>
>
> unprovable in the system means untrue in the system.

And what does 'untrue' mean?

We know that there is a number that solves an equation, but we don't
know that number, or how to compute that number.

Can we say that it is true that such a number exists?

This means that we can define the floor of that number, which will be an
integer (call it N), is it true that this number exists?

That interger, MUST be either even or odd, so we know that either
iseven(N) is true or isodd(N) is true.

By your logic, the 'truth value' of both of those must be 'untrue' since
we can not prove which one it is.

This is the sort of problem you run into with your system.

>
>> There is NOTHING about an analytic statement that says it can only be
>> true if it is provable. Note, "its truth value is unknown" doesn't
>> mean it doesn't have a truth value, just that we don't know what that
>> value is.
>>
>
> Within any formal system unprovable in the system means untrue in the
> system.
>
> The entire body of analytic truth is constructed only on the basis of
> semantic connections between expressions of language, or expressions
> that are stipulated to have the semantic property of Boolean true.
> Lacking both of these and the expression is untrue.
>
> Since axioms are provable on the basis that they are axioms then both of
> these factors that make an expression true also make it provable.
>

You clearly are just stating words by rote and not actually
understanding them.

Analytic Truth is truth that is provable, that is correct, but it
accepts that there is OTHER things that happen to be true but are not
provable.

You are making a Category Error in you logic system, and confusing
Knowledge with Truth.

[Jeff Barnett]

On 5/13/2022 11:47 AM, Richard Damon wrote:
> On 5/13/22 1:20 PM, olcott wrote:
>> *Validity and Soundness*
>> A deductive argument is said to be valid if and only if it takes a
>> form that makes it impossible for the premises to be true and the
>> conclusion nevertheless to be false. Otherwise, a deductive argument
>> is said to be invalid. https://iep.utm.edu/val-snd/
>>
>> If the Moon is made of green cheese then all dogs are cats is valid
>> and even though premises and conclusion are semantically unrelated.
>>
>> *Here is my correction to that issue*
>> A deductive argument is said to be valid if and only if it takes a
>> form such that its conclusion is a necessary consequence of all of its
>> premises.
>>
>
> And, have you done the basic investigation to find out how much of
> conventional logic you invalidate with that change?
>
> Note, that it may be hard to define "necessary consequence" in a formal
> matter.
>
> It should be noted that your example, while considered an vaild
> inference by normal logic, can never be used to actually prove its
> conclusion, so doesn't actually cause problems in normal logic (can you
> show a case where it does?)

Most "heavy duty" theorem proving programs use resolution style logic
and are beholding to the fact that "false -> anything" is valid. The
standard approach is to reform the theorem so that you assume that the
gives, axioms, whatever are true, and you assume the consequence (what
the theorem says is true) is false. The conjunction of all this stuff
(everything assumed connected with and operators) then processed. The
general idea is then to show that this implies the empty conjunction: as
we all know conjunction of an empty collection of clauses has truth
value true (as intersection over an empty collection of sets is the
universe of discourse). This in turn implies that deriving the empty
conjunction contradicts the hypothesis as well as anything else in the
domain of intercourse; and this actually means that the theorem is true
and that it was just proven, i.e., if the theorem isn't true, the logic
extended by including the theorem is inconsistent.

Note that the quibble with the PO formulation is with the word "all" in
the phrase "necessary consequence of all of its premises". In order to
check this condition (consider brute force) you must PROVE the theorem
false for every nonempty subset of the premises. This, must of course,
include all the axioms as well as theorem specific assumptions. And just
think of the consequences of that.

> Note, that at least by some meanings of your words, it could be
> construed that you only accept as a correct deductive argument, and
> arguement whose premises can at least some times be true, but there are
> some statements we don't know if they CAN be sometimes true, so your
> logic system would seem to not allow doing logic with that sort of

> statement.--
Jeff Barnett

[olcott]

Untrue means the same thing as Prolog's negation as failure.

> We know that there is a number that solves an equation, but we don't
> know that number, or how to compute that number.
>
> Can we say that it is true that such a number exists?
>

If you defined your terms correctly, then yes because this has been
stipulated in your deinitions.

> This means that we can define the floor of that number, which will be an
> integer (call it N), is it true that this number exists?
>
> That interger, MUST be either even or odd, so we know that either
> iseven(N) is true or isodd(N) is true.
>
> By your logic, the 'truth value' of both of those must be 'untrue' since
> we can not prove which one it is.
>
> This is the sort of problem you run into with your system.
>
>>
>>> There is NOTHING about an analytic statement that says it can only be
>>> true if it is provable. Note, "its truth value is unknown" doesn't
>>> mean it doesn't have a truth value, just that we don't know what that
>>> value is.
>>>
>>
>> Within any formal system unprovable in the system means untrue in the
>> system.
>>
>> The entire body of analytic truth is constructed only on the basis of
>> semantic connections between expressions of language, or expressions
>> that are stipulated to have the semantic property of Boolean true.
>> Lacking both of these and the expression is untrue.
>>
>> Since axioms are provable on the basis that they are axioms then both
>> of these factors that make an expression true also make it provable.
>>
>
> You clearly are just stating words by rote and not actually
> understanding them.
>

There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1) or
the consequences of (2).

> Analytic Truth is truth that is provable, that is correct, but it
> accepts that there is OTHER things that happen to be true but are not
> provable.
>

Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its meaning
without requiring any sense data from the sense organs.

Empirical expressions of language also require sense data from the sense
organs to verify their truth.

> You are making a Category Error in you logic system, and confusing
> Knowledge with Truth.
>
>>
>>
>>> You are confusing Knowledge with Truth.
>>>
>>> Your whole system is built on a Category Error.
>>>
>>
>>
>

[Richard Damon]

Which means... ?

Prolog, as I remember, ASSUMES that anything not provable is FALSE (not
'untrue').

So there exists an integer number N is neither Even or Odd? (it is
untrue for both tests)

I don't think you actually understand what that means.

>
>> Analytic Truth is truth that is provable, that is correct, but it
>> accepts that there is OTHER things that happen to be true but are not
>> provable.
>>
>
> Analytic truth includes every expression of language that can be
> completely verified as totally true entirely on the basis of its meaning
> without requiring any sense data from the sense organs.
>
> Empirical expressions of language also require sense data from the sense
> organs to verify their truth.

You still don't understand, do you.

You still confuse Truth with Knowledge.

Pitiful.

[Richard Damon]

Nope doesn't work. Remember, formal system are based on a finite, or
perhaps extended to countable, number of base axiom.

I think you basis is going to hit the problem that the number of natural
language 'facts' you are entering into your system isn't so limited.

Having an uncountable number of axioms in your system breaks a lot of
thngs. In fact, I think it breaks the definition of 'provable' or
'refutable'.

>
>> What you don't seem to understand is that much of what we have
>> logically proven, is based on higher order logical systems, which
>> these simple forms just can't handle.
>>
>> In particular, Computation theory, like much of mathematics, needs
>> second order (or higher) logic forms, which the simple logic just
>> can't handle.
>
> I created Minimal Type Theory to express HOL using very slightly adapted
> syntax of FOL. In an early version of MTT it translated its expressions
> into directed graphs so that pathological self-reference could be seen
> as infinite cycle in the di-graph.
>
> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>

Again, the error you are going to run into is your system is now based
on an uncountable number of inital truths, so a lot of the rules for
reasoning break down. This makes you system VERY prone to becoming
inconsistent (if not a certainty).

There are problems when you allow uncountable infinites into your base
logic.

[olcott]

Unprovable means untrue and does not mean false in Prolog.

Try and provide an example of a possible truth that does not require one
of those two.

[Richard Damon]

On 5/13/22 4:08 PM, olcott wrote:

> True and unprovable become impossible because Provable() is an aspect of
> True().
>

Can you actually PROVE that statement, if not, by its own defintion, it
isn't True.

If you resort to making it an axiom, then you run into the issue that
the accepted axioms define the system, and don't apply to systems that
don't take those axioms.

You also need to be sure that you don't make your system inconsistent,
and there exists proofs that show that such an axiom lead to
inconsistent systems once they try to take on certail levels of complexity.

In particular, no logic system can express all the properties of the
integer number system and be consistent (no provable statement can be
refuted) and complete (all truths are provable) at the same time.

Basically, you are defining youself into a corner and restricting what
you can meaningfully logically deduce.

[olcott]

Uncountable truths that are entirely comprised of different combinations
of countable constituent parts are evaluatable on the basis of these
constituents that are later recombined back into the original expression.

[Richard Damon]

The result of applying the operation of replacing N by N/2 if N is even
or by 3N+1 if N is odd will eventually get you to the number 1 for all
Natural numbers N > 0.

This statement MUST be either True or False, by its nature, there is no
other possible state.

This statement seems to be true, but it has unable to be proven to be true.

Yes, we can not validly USE the idea that this statement is true to
prove something else, because we know that it is still possible that it
won't be true. But we CAN use that it will either be true or false to
show something.

That is an analytical expression that isn't proven to be an analytical
truth, but it may still be true, and is neither stipulated true or
derived from an analytical proof.

Again. you are confusing True, with Proven/Known.

It MAY be True, or its Converse IS True, we know it must be one or the
other.

It is not KNOWN to be True, or Proven.

[Richard Damon]

Nope, if you can create an uncountable number of combinations, you CAN'T
just use the countable number of base elements.

Proving is based on creating a FINITE (or countable) sequence of steps
that combine a FINITE (or countable0 number of proven statements to show
something.

If the logic system can create an uncountable number of true statements
to work from, then there may be an sequence from an UNCOUNATBLE number
of steps fromt the countble base set, and thus beyond the reach of proving.

[olcott]

Probably an unconscious strawman error, that does not contradict my
original claim because it is a strawman error.

True(x) iff Stipulated_True(x) or Proven_True(x)
I am referring to <is> true and you are referring to <might be> true,
they are not the same.

[Richard Damon]

Then why dod you say "Possible truth", if you meant an ACTUAL truth.

How about;

x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1

True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
Proven Truth by your rules.

[olcott]

My system rejects expressions of language that are impossibly true such
as expressions that are true and unprovable.

> How about;
>
> x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1
>
> True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
> Proven Truth by your rules.
>

[olcott]

On 5/13/2022 6:22 PM, Richard Damon wrote:
> On 5/13/22 7:05 PM, olcott wrote:
>> On 5/13/2022 6:01 PM, Ben wrote:
>>> olcott <No...@NoWhere.com> writes:
>>>
>>>> On 5/13/2022 3:46 PM, Ben wrote:
>>>>> olcott <No...@NoWhere.com> writes:
>>>>>
>>>>>> On 5/13/2022 2:16 PM, Ben wrote:
>>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>>
>>>>>>>> *Validity and Soundness*
>>>>>>> Good plan.  You've run aground as far as halting is concerned, so
>>>>>>> you
>>>>>>> better find another topic you don't know about.
>>>>>>
>>>>>> It has been dead obvious that H(P,P)==0 is the correct halt status
>>>>>> for
>>>>>> the input to H(P,P) on the basis of the actual behavior that this
>>>>>> input actually specifies.
>>>>> It is now dead obvious that you accept that no algorithm can do
>>>>> what the
>>>>> world calls "decide halting".
>>>>
>>>> Tarski makes a similar mistake...
>>>
>>> <snip distractions>
>>>
>>>>>   That is, in the context of C-like code
>>>>> that you are more comfortable with, no D can exist such that D(X,Y) is
>>>>> true if and only if X(Y) halts and is false otherwise.
>>>>> Do you now accept that this is not possible?  (I know, I know...  I
>>>>> don't really expect an answer.)
>>>
>>> As expected, no answer.  You can't answer this because you know that
>>> would be the end of you bragging about halting.
>>>
>>
>> All undecidable problems always have very well hidden logical
>> incoherence, false assumptions, or very well hidden gaps in their
>> reasoning otherwise the fundamental nature of truth itself is broken.
>>
>
> No, YOUR definition of truth gets proved to be inconsistent with the
> system.
>
> If you want to insist that Truth must be Provable, then you need to
> strictly limit the capabilities of your logic system.
>
> Your failure to understand this just shows you are a century behind in
> the knowledge of how Truth and Logic actually works.

The key thing here is not my lack of extremely in depth understanding of
all of the subtle nuances of computer science.

The key thing here is my much deeper understanding of how logic systems
systems sometimes diverge from correct reasoning when examined at the
very high level abstraction of the philosophical foundation of the
notion of (analytic) truth itself.

Wittgenstein had the exact same issue with mathematicians
learned-by-rote by-the-book without the slightest inkling of any of the
key philosophical underpinnings of these things, simply taking for
granted that they are all these underpinnings are infallibly correct.

When these underpinnings are incorrect this error is totally invisible
to every learned-by-rote by-the-book mathematician.

[Richard Damon]

So, you are playing Humpty Dumpty?

It sounds like you are just insisting on the axiom that True is
Provable, which is NOT an axiom that is part of Computation Theory, and
in fact has been proven that if added to this sort of field of logic
makes the system inconssistent, and by your definition that makes it
inccorect.

That means you axiom is incorrect and thus WRONG.

You are proving that you are ignorant of how logic works because your
mind is just too smal to understand.

"Your System" is not the system in use in Formal Logic, especially not
Computation Theory as a branch of Mathematics. Until you understand
that, you are just going to continue making a FOOL of yourself as you
make claims that are just not true in the system that you claim to be
working (Remember, in an existing logic system, you don't get to change
the rules).

[Richard Damon]

> ittgensteinW had the exact same issue with mathematicians

> learned-by-rote by-the-book without the slightest inkling of any of the
> key philosophical underpinnings of these things, simply taking for
> granted that they are all these underpinnings are infallibly correct.
>
> When these underpinnings are incorrect this error is totally invisible
> to every learned-by-rote by-the-book mathematician.
>

That other people have made the same errors, doesn't make you right.

Note also, you are refering to a person who lived nearly that century
ago, to a man who admitted he didn't understand mathematics (and thought
it not valuable)

You aseem to be refering to writings published post-humously about a his
comments on a paper he hadn't yet actually read, and that he never
repeated after actually reading the paper.

Yes, that is very good basis for claiming your idea have to be right.

You have shown ZERO understanding for the rules of logic, and that your
opinions are basically worthless.

If you want to try to ACTUAL PROVE something, based on REAL ESTABLISHED
rules of logic, go ahead and give a try.

Note, this means NOT just falling back to "the meaning of the words"
except when you are actually QUOTING the accepted meaning of those words
in the field and showing how they apply.

I don't know if I have ever seen you put together a string of logic more
that one or two steps before you go off on a "this must be true" side
track, and never actually use any of the fundamental definitions. (You
may quotes some of them, but then never actually use that definition in
your nest step of the proof).

[olcott]

He refuted Godel in a single paragraph and was so far over everyone's
head that they mistook his analysis for simplistic rather than most
elegant bare essence.

> You aseem to be refering to writings published post-humously about a his
> comments on a paper he hadn't yet actually read, and that he never
> repeated after actually reading the paper.
>
> Yes, that is very good basis for claiming your idea have to be right.
>
> You have shown ZERO understanding for the rules of logic, and that your
> opinions are basically worthless.
>
> If you want to try to ACTUAL PROVE something, based on REAL ESTABLISHED
> rules of logic, go ahead and give a try.
>
> Note, this means NOT just falling back to "the meaning of the words"
> except when you are actually QUOTING the accepted meaning of those words
> in the field and showing how they apply.
>
> I don't know if I have ever seen you put together a string of logic more
> that one or two steps before you go off on a "this must be true" side
> track, and never actually use any of the fundamental definitions. (You
> may quotes some of them, but then never actually use that definition in
> your nest step of the proof).

[Richard Damon]

Nope, He made the same mistake YOU are making and not understanding what
Godel actually said (because he hadn't read the paper).

As I understand it (and I will admit this isn't a field I have intensly
studied), this statement is solely from private notes that were
published after his death. If he really believed in this statement as
was sure of it, it would seem natural that he actually would of
published it.

It seems likely that he had some nagging thought that there was an error
in his logic that he worked on and either never resolved or he found his
logic error and thus stopped believing in that statement.

This make the "appeal" to him as an authority to rebut Godel incorrect,
as he never stood as an authority to make such a claim, he just
investigated it in private notes.

Perhaps he realized that his argument to try to prove that Truth can be
proven rested on the assumption of a definition that Truth was Provable
and thus is just a circular argument.

As I have put to you, PROVE that Truth must be Provable, or by your own
logic the statement isn't true. We KNOW (if we have any intelligence)
that there are Truths that we do not know about, so it is established
that some truths are at least unknown for now. What is the basis for
saying that there can't be an aspect that happens to be true even though
we can not prove it?

[olcott]

On 5/14/2022 3:07 AM, Ben wrote:
> olcott <No...@NoWhere.com> writes:
>

>> The halting criteria that the halting problem expects is wrong because
>> it contradicts the definition of a computer science decider in some
>> rare cases that no one never noticed before.
>
> Well that's pretty clear. The halting problem, as defined by everyone
> by you (i.e. about which computations are finite and which are not) is
> indeed undecidable.
>

Not at all. We must simply correct the error of the halting problem
definition so that it does not diverge from the definition of a decider
thus causes it to diverge from the definition of a computation.

> You are even (almost) correct about the halting theorem. The two
> notions of "computation" and "halt decider", as conventionally defined,
> are contradictory.
>

*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an
input, whether the program *specified by this description* will finish
running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem

[Richard Damon]

On 5/14/22 10:00 AM, olcott wrote:
> On 5/14/2022 3:07 AM, Ben wrote:
>> olcott <No...@NoWhere.com> writes:
>>
>>> The halting criteria that the halting problem expects is wrong because
>>> it contradicts the definition of a computer science decider in some
>>> rare cases that no one never noticed before.
>>
>> Well that's pretty clear.  The halting problem, as defined by everyone
>> by you (i.e. about which computations are finite and which are not) is
>> indeed undecidable.
>>
>
> Not at all. We must simply correct the error of the halting problem
> definition so that it does not diverge from the definition of a decider
> thus causes it to diverge from the definition of a computation.
>
>> You are even (almost) correct about the halting theorem.  The two
>> notions of "computation" and "halt decider", as conventionally defined,
>> are contradictory.
>>
>
> *The corrected halting problem definition*
> In computability theory, the halting problem is the problem of
> determining, from a description of an arbitrary computer program and an
> input, whether the program *specified by this description* will finish
> running,  or continue to run forever.
> https://en.wikipedia.org/wiki/Halting_problem
>
>

WRONG, you don't get to change the definition of the Problem.

You are just proving that you don't understand the nature of logic, or
of Truth.

The Halting Problem STARTS with some arbitrary program. If that program
can't be specified to the "decider", then the decider just fails to be
an answer to the Halting Problem.

Otherwise, I can trivially write a "correct" halt decider by just
defining that it can accept a very limited set of encoded programs (like
none with backward jumps), and then I can easily decide if they will
halt or not.

This example shows the incorrectness of YOUR (false) definition.

You just continue to prove your ignorance of the field.

[olcott]

Since I wrote Wittgenstein's entire same proof myself shortly before I
ever heard of Wittgenstein I have first-hand direct knowledge that his
reasoning is correct.

His full quote is on page 6
https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel

This is the key source of our agreement that makes Wittgenstein have the
exact same view as mine:

'True in Russell's system' means, as was said: proved
in Russell's system; and 'false in Russell's system'
means:the opposite has been proved in Russell's system.-

True(x) iff Stipulated_True(x) or Proven_True(x)

There are only two possible ways that any analytical expression of
language can possibly be true:

(1) It is stipulated to be true. // like an axiom

(2) It is derived by applying only truth preserving operations to (1) or

the consequences of (2). // like sound deduction

Analytic truth includes every expression of language that can be
completely verified as totally true entirely on the basis of its meaning
without requiring any sense data from the sense organs.

Empirical expressions of language also require sense data from the sense
organs to verify their truth.

This means that if there are no connected set of semantics meanings
(sound deduction) that make an analytical expression of language true
then then it cannot possibly be true unless it was stipulated as true.

The conclusion of Wittgenstein's analysis and mind is that if G is
unprovable in F then G is simply untrue in F.
Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)).

Even though F does meet the erroneous mathematical definition of
Incomplete(F) that F was ever construed as incomplete is simply
incorrect because it does not screen out expressions of language that
are simply not truth bearers.

Tarski made this same mistake with a much simply yet comparable proof to
the Gödel 1931 incompleteness theorem:
Tarski undefinability theorem 1936
https://liarparadox.org/Tarski_275_276.pdf

"the sentence x which is undecidable in the original theory
becomes a decidable sentence in the enriched theory."

It is not that Tarski's metatheory is smarter than his theory.
It is that Tarski's x (the liar paradox) is not provable or true in his
theory because it is not a truth bearer in his theory in the same way
that Gödel's G is not a truth bearer in F.

[olcott]

On 5/14/2022 9:31 AM, Richard Damon wrote:
> On 5/14/22 10:00 AM, olcott wrote:
>> On 5/14/2022 3:07 AM, Ben wrote:
>>> olcott <No...@NoWhere.com> writes:
>>>
>>>> The halting criteria that the halting problem expects is wrong because
>>>> it contradicts the definition of a computer science decider in some
>>>> rare cases that no one never noticed before.
>>>
>>> Well that's pretty clear.  The halting problem, as defined by everyone
>>> by you (i.e. about which computations are finite and which are not) is
>>> indeed undecidable.
>>>
>>
>> Not at all. We must simply correct the error of the halting problem
>> definition so that it does not diverge from the definition of a
>> decider thus causes it to diverge from the definition of a computation.
>>
>>> You are even (almost) correct about the halting theorem.  The two
>>> notions of "computation" and "halt decider", as conventionally defined,
>>> are contradictory.
>>>
>>
>> *The corrected halting problem definition*
>> In computability theory, the halting problem is the problem of
>> determining, from a description of an arbitrary computer program and
>> an input, whether the program *specified by this description* will
>> finish running,  or continue to run forever.
>> https://en.wikipedia.org/wiki/Halting_problem
>>
>>
>
> WRONG, you don't get to change the definition of the Problem.
>

[ computer science is inconsistent ]
If two definitions within computer science contradict each other then
computer science itself is an inconsistent system thus conclusively
proving that computer science diverges from correct reasoning.

If all halt deciders must compute the mapping from their inputs to an
accept/reject state on the basis of the actual behavior that this input
actually specifies and the halting problem specifies that a halt decider
must compute the mapping from non-inputs, then one of these two must go
or computer science remains inconsistent.

learned-by-rote people that only know things by-the-book tend to take
the gospel of textbooks as holy words contradictions and all.

Like with religious people they tend to believe that the contradictions
are somehow resolved at a level higher than their current understanding.

> You are just proving that you don't understand the nature of logic, or
> of Truth.
>
> The Halting Problem STARTS with some arbitrary program. If that program
> can't be specified to the "decider", then the decider just fails to be
> an answer to the Halting Problem.
>
> Otherwise, I can trivially write a "correct" halt decider by just
> defining that it can accept a very limited set of encoded programs (like
> none with backward jumps), and then I can easily decide if they will
> halt or not.
>
> This example shows the incorrectness of YOUR (false) definition.
>
> You just continue to prove your ignorance of the field.

[Richard Damon]

No, you THINK his reasoning is correct because you agree with it,

That is NOT proof. You thinking it is shows your lack of understanding.

>
> His full quote is on page 6
> https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
>
>
> This is the key source of our agreement that makes Wittgenstein have the
> exact same view as mine:
>
>    'True in Russell's system' means, as was said: proved
>     in Russell's system; and 'false in Russell's system'
>     means:the opposite has been proved in Russell's system.-
>
> True(x) iff Stipulated_True(x) or Proven_True(x)

Which either needs to be taken as an assumption, or needs to be proved
to be true.

If needs to be taken as an assumption, it is not something that IS
unconditionally true.

>
> There are only two possible ways that any analytical expression of
> language can possibly be true:
> (1) It is stipulated to be true. // like an axiom
> (2) It is derived by applying only truth preserving operations to (1) or
> the consequences of (2).         // like sound deduction

WRONG.

There are only two possible ways that they can be ANALYTICALLY true.

>
> Analytic truth includes every expression of language that can be
> completely verified as totally true entirely on the basis of its meaning
> without requiring any sense data from the sense organs.

And there are other truths besides Analytic Truth. That is implied by
the need of the adjective.

>
> Empirical expressions of language also require sense data from the sense
> organs to verify their truth.

Nope, things can be empirically true even without the sense data.
Without the sense data they are not KNOWN to be true, but might be.

>
> This means that if there are no connected set of semantics meanings
> (sound deduction) that make an analytical expression of language true
> then then it cannot possibly be true unless it was stipulated as true.

WRONG. You are again confalating KNOWLEDGE with TRUTH.

>
> The conclusion of Wittgenstein's analysis and mind is that if G is
> unprovable in F then G is simply untrue in F.
> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)).

WRONG.

Makes the erroneous assumption that Truth requires proof, and becomes a
circular argument.

>
> Even though F does meet the erroneous mathematical definition of
> Incomplete(F) that F was ever construed as incomplete is simply
> incorrect because it does not screen out expressions of language that
> are simply not truth bearers.

Except that the expression of language WAS a Truth Bearer, as a given
statement MUST be either Provable or not. This comes because you of
course can't prove an statement that can't be true, like a non-sense
sentence.

Unless you are willing to define that Provability isn't a Truth Bearer,
which since you are then defining Truth as Provable, the Truth of a
statement isn't a Truth Bearer, you have a problem. You whole logic
system collapses as it can no longer talk about itself.

[olcott]

No, I independently verified his reasoning before I ever saw his reasoning.

> That is NOT proof. You thinking it is shows your lack of understanding.
>
>>
>> His full quote is on page 6
>> https://www.researchgate.net/publication/333907915_Proof_that_Wittgenstein_is_correct_about_Godel
>>
>>
>> This is the key source of our agreement that makes Wittgenstein have
>> the exact same view as mine:
>>
>>     'True in Russell's system' means, as was said: proved
>>      in Russell's system; and 'false in Russell's system'
>>      means:the opposite has been proved in Russell's system.-
>>
>> True(x) iff Stipulated_True(x) or Proven_True(x)
>
> Which either needs to be taken as an assumption, or needs to be proved
> to be true.
>

That no counter-examples can possibly exist is complete proof that it is
true. There are no categories of expressions of language that are both
true and neither stipulated as true or proven to be true (sound
deduction) on the basis of semantic connections to other true
expressions of language.

> If needs to be taken as an assumption, it is not something that IS
> unconditionally true.
>
>>

>> There are only two possible ways that any ANALYTICALLY expression of

>> language can possibly be true:
>> (1) It is stipulated to be true. // like an axiom
>> (2) It is derived by applying only truth preserving operations to (1)
>> or the consequences of (2).         // like sound deduction
>
> WRONG.
>
> There are only two possible ways that they can be ANALYTICALLY true.
>

Should I capitalize my use of ANALYTICALLY too so that you can see that
I already specified this? (I capitalized it, above)

>>
>> Analytic truth includes every expression of language that can be
>> completely verified as totally true entirely on the basis of its
>> meaning without requiring any sense data from the sense organs.
>
> And there are other truths besides Analytic Truth. That is implied by
> the need of the adjective.

All of math and logic is exclusively ANALYTICAL.

>>
>> Empirical expressions of language also require sense data from the
>> sense organs to verify their truth.
>
> Nope, things can be empirically true even without the sense data.
> Without the sense data they are not KNOWN to be true, but might be.
>

to verify their truth.
to verify their truth.
to verify their truth.

>>
>> This means that if there are no connected set of semantics meanings
>> (sound deduction) that make an analytical expression of language true
>> then then it cannot possibly be true unless it was stipulated as true.
>
> WRONG. You are again confalating KNOWLEDGE with TRUTH.

Counter-examples are categorically impossible because ALL ANALYTIC
expressions of language ONLY derive their truth value from semantic
connections to other ANALYTIC expressions of language that are known to
be true, AKA sound deduction.

>>
>> The conclusion of Wittgenstein's analysis and mind is that if G is
>> unprovable in F then G is simply untrue in F.
>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)).
>
> WRONG.
>
> Makes the erroneous assumption that Truth requires proof, and becomes a
> circular argument.

It is not a circle it is a tree of sound deduction.
The conclusion is linked backwards (sound deduction in reverse) to every
expression of language that derives it.

>
>>
>> Even though F does meet the erroneous mathematical definition of
>> Incomplete(F) that F was ever construed as incomplete is simply
>> incorrect because it does not screen out expressions of language that
>> are simply not truth bearers.
>
> Except that the expression of language WAS a Truth Bearer, as a given
> statement MUST be either Provable or not. This comes because you of
> course can't prove an statement that can't be true, like a non-sense
> sentence.
>

As recently as 1974, people were still clueless about the issue of the
liar paradox.It is the simplest of all self-reference paradoxes so I
bought the domain name liarparadox.org for my work.

Tarski based his whole proof on the liar paradox and proved in his
metatheory that it is not provable in his theory, same result as Godel.

> Unless you are willing to define that Provability isn't a Truth Bearer,
> which since you are then defining Truth as Provable, the Truth of a
> statement isn't a Truth Bearer, you have a problem. You whole logic
> system collapses as it can no longer talk about itself.
>

True(F, x) is implemented as Provable(F, x) through sound deduction on
the basis of premises known to be true. In a reverse sound deduction
(same thing as Prolog back-chaining inference) know truths (AKA Prolog
facts) are sought on the basis of Prolog rules.

https://www.google.com/search?q=prolog+back+chainikng&rlz=1C1GCEJ_enUS813US813&oq=prolog+back+chainikng&aqs=chrome..69i57j33i10i160.4658j0j15&sourceid=chrome&ie=UTF-8

[Richard Damon]

Except that you are ignoring that the definitions are NOT inconsistent,
unless you require that Halting be computable.

The Halting Mapping of Turing Machines is well defined, as a mapping of
a Turing Machine + finite String Input -> { Halting, Non-Halting} based
on if the Turing Machine will reach a final state in any finite number
of steps, or never reach such a final state after an unbounded number of
step.

Right? That is a very straight forward definition, and all Inputs have a
well defined and definite output. No Machine + Input can do both be
Halting and Non-Halting, or fail to be at least one of Halting or
Non-Halting. (Either then number of steps processed halts at a finite
number in a final state or counts to an unbounded number).

A Decider, always maps an input (in its domain) to an output (in its
range). The quesiton of the Halting Problem is does there exist a
Decider that its input -> output map matches the Halting Mapping.

Since a decider in this case is a Turing Machine, we know that its input
is a string in a given alphabet, so the question comes, can we alway
express a Turing Machine as a finite string representation, and the
answer to that is YES. (Maybe not in all alphabets, but there exist
alphabets that can express them).

This is because BY DEFINITON, a Turing Machine has a finite number of
states, and accepts a tape with a finite alphabet, thus we have a finite
number of states * a fintie number if symbols at the tape head giving a
finite number of cases specifying a finite state, a finite symbol, and a
binary tape motion. This is thus expressable in a finite string.

Thus we can ALWAYS convert the input to the Halting Mapping into some
input that FULLY EXPRESSES what the input is, thus there exists machines
with a range that expresses ALL possible Turing Machine + Input
possibilities. We actually knew that before from the existence of the
Universal Turing Machine, which takes as its input such a description.

Thus, if a given machine can't "understand" its input as such a machine
in some cases, the error is in that particular machine, not the
specification.

Now, yes, it is still possible that no machine can actually compute such
a mapping, but that is the question itself. Your error is you seem to be
presuming that the definition of a Halt Decider requires that such a
machine actually exist, which it doesn't.

It is the same as you idea that the Truth of a statement requires that a
Proof or Refutation exist, which it doesn't. (We are allowed to have
Unknown and even Unknowable Truths).

There is no conflict, just the fact that such a machine can not exist.

[Richard Damon]

WRONG. Again you conflate Analytic truth with truth.

The Collatz conjecture, that there exist no number N such that the
sequence of progreesing to 3N+1 for N odd, and N/2 for N even doesn't
eventually reach 1, MUST be either True of False. There is no possible
"non-answer", as math doesn't allow for such things.

Thus either the statement "Collatz is True", or "Collatz is False", must
be true, and there is no known proof or refutation for either, While
this doesn't prove that no proof exists, it does point out a flaw with
your statement, until you have actually proved or refuted a statement,
you don't even know if it could be a truth bearer.

Thus we have a, at least possible, counter-example when you claim none
exist. You can only refute this as a possible counter-example by actualy
proving that a proof or refutation actually exists.

>
>> If needs to be taken as an assumption, it is not something that IS
>> unconditionally true.
>>
>>>
>>> There are only two possible ways that any ANALYTICALLY expression of
>>> language can possibly be true:
>>> (1) It is stipulated to be true. // like an axiom
>>> (2) It is derived by applying only truth preserving operations to (1)
>>> or the consequences of (2).         // like sound deduction
>>
>> WRONG.
>>
>> There are only two possible ways that they can be ANALYTICALLY true.
>>
>
> Should I capitalize my use of ANALYTICALLY too so that you can see that
> I already specified this? (I capitalized it, above)

Except then it points out that you erroeous omit it in your other
statements.

>
>>>
>>> Analytic truth includes every expression of language that can be
>>> completely verified as totally true entirely on the basis of its
>>> meaning without requiring any sense data from the sense organs.
>>
>> And there are other truths besides Analytic Truth. That is implied by
>> the need of the adjective.
>
> All of math and logic is exclusively ANALYTICAL.

That is part of your error. Math and Logic use analytical methods to
prove its ideas, but not all Truth in math and logic is Analytical.

>
>>>
>>> Empirical expressions of language also require sense data from the
>>> sense organs to verify their truth.
>>
>> Nope, things can be empirically true even without the sense data.
>> Without the sense data they are not KNOWN to be true, but might be.
>>
>
> to verify their truth.
> to verify their truth.
> to verify their truth.

Truth doesn't need to be "Verified" to be True. It only needs to be
verified before its Truth can be used to create other Truths in a Proof.

>
>>>
>>> This means that if there are no connected set of semantics meanings
>>> (sound deduction) that make an analytical expression of language true
>>> then then it cannot possibly be true unless it was stipulated as true.
>>
>> WRONG. You are again confalating KNOWLEDGE with TRUTH.
>
> Counter-examples are categorically impossible because ALL ANALYTIC
> expressions of language ONLY derive their truth value from semantic
> connections to other ANALYTIC expressions of language that are known to
> be true, AKA sound deduction.
>

Thus, the circular definition.

You only show that ANALYTIC Truth must be proven, not Truth.

Analytics accept that not all Truth is Analytically proven. You make a
category error assuming all Truth must be Analytically True.

Note, An Analytical Statement might be True but not Analytically ture.

>
>>>
>>> The conclusion of Wittgenstein's analysis and mind is that if G is
>>> unprovable in F then G is simply untrue in F.
>>> Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)).
>>
>> WRONG.
>>
>> Makes the erroneous assumption that Truth requires proof, and becomes
>> a circular argument.
>
> It is not a circle it is a tree of sound deduction.
> The conclusion is linked backwards (sound deduction in reverse) to every
> expression of language that derives it.

Nope. Give the NON-CIRCULAR proof.

Your failure to show what you claim is evidence that you don't actually
have a real proof.

Your statement that "Something is True only if it is Provable" is itself
a contradiction unless you can ACTUALLY prove it, and until you do, you
can not use it.

Without such a proof, the statement says it can not be true, so you can
not use it.

>
>>
>>>
>>> Even though F does meet the erroneous mathematical definition of
>>> Incomplete(F) that F was ever construed as incomplete is simply
>>> incorrect because it does not screen out expressions of language that
>>> are simply not truth bearers.
>>
>> Except that the expression of language WAS a Truth Bearer, as a given
>> statement MUST be either Provable or not. This comes because you of
>> course can't prove an statement that can't be true, like a non-sense
>> sentence.
>>
>
> As recently as 1974, people were still clueless about the issue of the
> liar paradox.It is the simplest of all self-reference paradoxes so I
> bought the domain name liarparadox.org for my work.
>
> Tarski based his whole proof on the liar paradox and proved in his
> metatheory that it is not provable in his theory, same result as Godel.
>
>> Unless you are willing to define that Provability isn't a Truth
>> Bearer, which since you are then defining Truth as Provable, the Truth
>> of a statement isn't a Truth Bearer, you have a problem. You whole
>> logic system collapses as it can no longer talk about itself.
>>
>
> True(F, x) is implemented as Provable(F, x) through sound deduction on
> the basis of premises known to be true. In a reverse sound deduction
> (same thing as Prolog back-chaining inference) know truths (AKA Prolog
> facts) are sought on the basis of Prolog rules.
>
> https://www.google.com/search?q=prolog+back+chainikng&rlz=1C1GCEJ_enUS813US813&oq=prolog+back+chainikng&aqs=chrome..69i57j33i10i160.4658j0j15&sourceid=chrome&ie=UTF-8
>
>

And Prolog doesn't define logic, but is just a programming languge to
handle simple rule sets.

Note, Prolog doesn't provide a well implemented "Not" operator, in part
BECAUSE it defines a statement that is unprovable as false.

If you want to limit your logic to what Prolog can handle, be my guess,
but then stay out of things beyond its capability, like Compuation Theory.

I don't think you are smart enough to understand the limitation of
Prolog (or even simple logic) and thus make enormous errors not
understanding the limited domain of your tools.

You just don't see that you logic system has become horribly
inconsistent because you close your eyes to those errors and say that
logic must be wrong, but you can't actually define WHAT is wrong with
the logic, because it actually does follow the rules you propose.

[olcott]

Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the
corresponding output. https://en.wikipedia.org/wiki/Computable_function

The halting criteria are defined such that they diverge from the
definition of a decider and they also diverge form the definition of a
computable function in some rare cases. In these cases the halting
criteria are incorrect.

> The Halting Mapping of Turing Machines is well defined, as a mapping of
> a Turing Machine + finite String Input -> { Halting, Non-Halting} based
> on if the Turing Machine will reach a final state in any finite number
> of steps, or never reach such a final state after an unbounded number of
> step.
>

It must be the actual behavior actually specified by the inputs and
cannot be the behavior specified by non-inputs unless this behavior is
identical to the behavior of the inputs.

It has previously simply always been (incorrectly) assumed to be the
case that the behavior specified by the inputs cannot possibly diverge
from the behavior of their direct execution.

In those cases where the actual behavior of the actual input to H(P,P)
is not identical to the behavior of the direct execution of P(P) the
definition of the halting criteria directly contradicts the definition
of a decider and the definition of a computation, thus invalidating it.

[olcott]

I am ALWAYS only talking about ANALYTIC TRUTH, the only time I ever talk
about EMPIRICAL TRUTH, is to say that I am not talking about that.

> The Collatz conjecture, that there exist no number N such that the
> sequence of progreesing to 3N+1 for N odd, and N/2 for N even doesn't
> eventually reach 1, MUST be either True of False. There is no possible
> "non-answer", as math doesn't allow for such things.
>

If the answer requires an infinite search then this answer cannot be
derived in finite time. None-the-less there exists a connected set of
semantic meanings that make it true or false even if they cannot be
found in finite time.

[Richard Damon]

Then stop talking about things that aren't analytically true.

For instance, Godel's G is NOT 'Analytically True' in F, because you
can't prove it, but it IS 'True' because you can show via a meta-logical
proof in a higher system that it actually is True.

Collatz Conjecture IS either True or False, but it may not be
Analytically True or False until someone can prove or refute it.

It is possible that it is True, but totally unprovable, at least in the
systems it is definied in, so it can NEVER be "Analytically True", but
it is still True, and the conjure has ALWAYS been a Truth Bearer.

The key point is that just because something isn't Analytically True, or
Analytically refuted doesn't mean that the statement isn't a Truth Bearer.

Note also, There are true statements that are neither Analytically True
or Emperically True. Those are distinctions made in fields of KNOWLEDGE,
and only relate to catagorizing KNOWN Truths, or KNOWLEDGE.
Epistemology, as you seem to like describing what you are talking about
ISN'T about studying Truth, but KNOWLEDGE. A proper student of the field
understands the difference, but you don't seem to be able to do that.

Epistemology does NOT define what is "True", only what is "Known". A
Proper Epistemolist understand that there are things that are True that
are outside knowledge.

>
>> The Collatz conjecture, that there exist no number N such that the
>> sequence of progreesing to 3N+1 for N odd, and N/2 for N even doesn't
>> eventually reach 1, MUST be either True of False. There is no possible
>> "non-answer", as math doesn't allow for such things.
>>
>
> If the answer requires an infinite search then this answer cannot be
> derived in finite time. None-the-less there exists a connected set of
> semantic meanings that make it true or false even if they cannot be
> found in finite time.

But a non-finite chain of reasoning is NOT considered a proof, at least
by the normal definitions of a proof.

[olcott]

OK great this is a key agreement between us.

> Collatz Conjecture IS either True or False, but it may not be
> Analytically True or False until someone can prove or refute it.
>

Analytically True or False is the same as True or False, except that is
excludes expressions of language dealing with sense data from the sense
organs.

> It is possible that it is True, but totally unprovable, at least in the
> systems it is definied in, so it can NEVER be "Analytically True", but
> it is still True, and the conjure has ALWAYS been a Truth Bearer.
>

If it is true then there must be a connected set of semantic meanings
proving that it is true otherwise it is not true.

I don't think that it matters whether or not this connected set can be
found, thus is still would exists even if it took an infinite search to
find.

> The key point is that just because something isn't Analytically True, or
> Analytically refuted doesn't mean that the statement isn't a Truth Bearer.
>
> Note also, There are true statements that are neither Analytically True
> or Emperically True. Those are distinctions made in fields of KNOWLEDGE,
> and only relate to catagorizing KNOWN Truths, or KNOWLEDGE.
> Epistemology, as you seem to like describing what you are talking about
> ISN'T about studying Truth, but KNOWLEDGE. A proper student of the field
> understands the difference, but you don't seem to be able to do that.
>
> Epistemology does NOT define what is "True", only what is "Known". A
> Proper Epistemolist understand that there are things that are True that
> are outside knowledge.
>
>
>
>>
>>> The Collatz conjecture, that there exist no number N such that the
>>> sequence of progreesing to 3N+1 for N odd, and N/2 for N even doesn't
>>> eventually reach 1, MUST be either True of False. There is no
>>> possible "non-answer", as math doesn't allow for such things.
>>>
>>
>> If the answer requires an infinite search then this answer cannot be
>> derived in finite time. None-the-less there exists a connected set of
>> semantic meanings that make it true or false even if they cannot be
>> found in finite time.
>
> But a non-finite chain of reasoning is NOT considered a proof, at least
> by the normal definitions of a proof.
>

I am referring to correct reasoning that differs somewhat from logic.

[Richard Damon]

FALSE. Where is the Collatz conjecture being True in that? (If it is)

>> It is possible that it is True, but totally unprovable, at least in
>> the systems it is definied in, so it can NEVER be "Analytically True",
>> but it is still True, and the conjure has ALWAYS been a Truth Bearer.
>>
>
> If it is true then there must be a connected set of semantic meanings
> proving that it is true otherwise it is not true.
>
> I don't think that it matters whether or not this connected set can be
> found, thus is still would exists even if it took an infinite search to
> find.

Unless you make the finite sequence from axioms to the result, you don't
have a Proof.

>
>> The key point is that just because something isn't Analytically True,
>> or Analytically refuted doesn't mean that the statement isn't a Truth
>> Bearer.
>>
>> Note also, There are true statements that are neither Analytically
>> True or Emperically True. Those are distinctions made in fields of
>> KNOWLEDGE, and only relate to catagorizing KNOWN Truths, or KNOWLEDGE.
>> Epistemology, as you seem to like describing what you are talking
>> about ISN'T about studying Truth, but KNOWLEDGE. A proper student of
>> the field understands the difference, but you don't seem to be able to
>> do that.
>>
>> Epistemology does NOT define what is "True", only what is "Known". A
>> Proper Epistemolist understand that there are things that are True
>> that are outside knowledge.
>>
>>
>>
>>>
>>>> The Collatz conjecture, that there exist no number N such that the
>>>> sequence of progreesing to 3N+1 for N odd, and N/2 for N even
>>>> doesn't eventually reach 1, MUST be either True of False. There is
>>>> no possible "non-answer", as math doesn't allow for such things.
>>>>
>>>
>>> If the answer requires an infinite search then this answer cannot be
>>> derived in finite time. None-the-less there exists a connected set of
>>> semantic meanings that make it true or false even if they cannot be
>>> found in finite time.
>>
>> But a non-finite chain of reasoning is NOT considered a proof, at
>> least by the normal definitions of a proof.
>>
>
> I am referring to correct reasoning that differs somewhat from logic.
>

Then why are you talking about fields of LOGIC?

Formal Logic STARTS with its definition of what is correct reasoning in
that Formal System.

You can not change that definition without needing to restart at the
begining of that Formal System.

I have pointed this out many times.

If you want to change the ground rules of logic, you need to start at
the other end, and begin with a NEW Formal Logic with your new rules.

People HAVE looked at this idea of inserting the conditon that something
is only True if it can be proven, and it greatly limits the power of the
logic system, in particular, it can't handle much math.

I get the feeling that you haven't really looked at that area, because
it seems too much "learn by rote", and says you can't get to where you
want to get to.

In short, your ignorance of the past has doomed you to repeat the great
mistakes of the past.

[Richard Damon]

You just don't understand do you. The Halting Criteria is NOT defined as
a "Computable Function", so can't be in conflict with the definition of
a decider. In fact, the question is "Is the Halting Function
Commputable?" This means that if the definition of the Halting Criteria
is incompatible with making a computation from it, we get the simple
answer of "No, the Halting Function is not computable"

You don't seem to understnad that not all functions are computatable,
and that for those that answer to the question of can you make a Turing
Machine compute them is just "No".

>
>> The Halting Mapping of Turing Machines is well defined, as a mapping
>> of a Turing Machine + finite String Input -> { Halting, Non-Halting}
>> based on if the Turing Machine will reach a final state in any finite
>> number of steps, or never reach such a final state after an unbounded
>> number of step.
>>
>
> It must be the actual behavior actually specified by the inputs and
> cannot be the behavior specified by non-inputs unless this behavior is
> identical to the behavior of the inputs.

Right, and since the input specifies all the details of the Turing
Machine in question, the "behavior" of that input relates to that machine.

That IS the input, not a non-input. In fact, YOUR example asks about a
non-input, as P calls H which isn't provided in the input, and thus it
is invalid for your H to answer about that behavior.

>
> It has previously simply always been (incorrectly) assumed to be the
> case that the behavior specified by the inputs cannot possibly diverge
> from the behavior of their direct execution.

Because BY DEFINITION, it CAN'T, or the decider doesn't meet the
requriements.

>
> In those cases where the actual behavior of the actual input to H(P,P)
> is not identical to the behavior of the direct execution of P(P) the
> definition of the halting criteria directly contradicts the definition
> of a decider and the definition of a computation, thus invalidating it.

Nope, it proves that your H fails to meet the requriements. After all,
the input DOES specify the behavior being asked about, if it was
constructed correctly as a representation of the machine in question.

Thus any error is on the decider or the person who designed it and the
representation specification.

Note, DEFINITIONS CAN NOT BE INVALID.

There is no contradiction between the definition of a decider and the
Halting Problem, only the fact that no decider can exist that meets the
requirements

If you can't handle that, then that is YOUR problem, not the logic systems.

[olcott]

So this is where correct reasoning and logic diverge on terminology.
When I refer to a set of connected semantic meanings this seems not
exactly the same thing as a proof. If this set does not exist, then the
expression is not true. If the set exists yet is impossible to find then
it is still true.

So that I can correct its mistakes. It has mistakes (incoherence and
inconsistency) baked right into the definitions of its terms of the art.

>
> Formal Logic STARTS with its definition of what is correct reasoning in
> that Formal System.
>
> You can not change that definition without needing to restart at the
> begining of that Formal System.
>
> I have pointed this out many times.
>
> If you want to change the ground rules of logic, you need to start at
> the other end, and begin with a NEW Formal Logic with your new rules.
>

Same idea as logic, created to correct the errors of logic.

> People HAVE looked at this idea of inserting the conditon that something
> is only True if it can be proven, and it greatly limits the power of the
> logic system, in particular, it can't handle much math.
>
> I get the feeling that you haven't really looked at that area, because
> it seems too much "learn by rote", and says you can't get to where you
> want to get to.
>

Logic has mistakes (incoherence and inconsistency) baked right into the
definitions of its terms of the art. When we contrast logic with correct
reasoning then we might see that these are mistakes.

> In short, your ignorance of the past has doomed you to repeat the great
> mistakes of the past.

[olcott]

So in this same way we can make another undecidable problem in computer
science: there is no "box of oreos" in computer science that can compute
the length of a finite string in the same way that there is no
non-computation that can compute halting.

[Richard Damon]

So something can be "Provable" yet no "Proof" actually be findable or
expressable?

That means you might not know if you have Proven Something.

So, again, your are at the wrong end. If you want to change the
fundamental definitions, you need to be talking about the Core Logic
rules that you think need to be changed, not try to change them in a
derived logic system, when such a change is NOT allowed.

>
>>
>> Formal Logic STARTS with its definition of what is correct reasoning
>> in that Formal System.
>>
>> You can not change that definition without needing to restart at the
>> begining of that Formal System.
>>
>> I have pointed this out many times.
>>
>> If you want to change the ground rules of logic, you need to start at
>> the other end, and begin with a NEW Formal Logic with your new rules.
>>
>
> Same idea as logic, created to correct the errors of logic.

So start with your new logic system and see what you can get to in your
limited time left, Sounds like you have wasted decades of time by
working at the wrong end of the stick.

>
>> People HAVE looked at this idea of inserting the conditon that
>> something is only True if it can be proven, and it greatly limits the
>> power of the logic system, in particular, it can't handle much math.
>>
>> I get the feeling that you haven't really looked at that area, because
>> it seems too much "learn by rote", and says you can't get to where you
>> want to get to.
>>
>
> Logic has mistakes (incoherence and inconsistency) baked right into the
> definitions of its terms of the art. When we contrast logic with correct
> reasoning then we might see that these are mistakes.

So YOU say. Then start at the base and see how far you can get based on
your new idea.

Probably only a few decades of work for someone who knows what they are
doing.

Starting at the wrong end is like trying to stop a mile long freight
train by dragging a bucket out the back of the caboose.

[Richard Damon]

Another of your famous nonsensical diversions. Since there IS NO "box of
oreos" in Computer Science, you just committed another category error
proving you don't know what you are talking about.

[olcott]

We cannot correctly label any analytical expression of language as true
unless and until:
(1) It has been stipulated to be true.

(2) a connected set of semantic meanings back-chain to expressions of
language that have been stipulated to be true.
This is the same system that Prolog uses.

The reason that I keep referring to the Tarski proof is it essentially
the exact same proof Gödel after Gödel has been simplified 100,000-fold.
https://liarparadox.org/Tarski_275_276.pdf

Tarski simply uses the liar paradox which

Gödel says:
14 Every epistemological antinomy can likewise be used for a similar
undecidability proof

Thus making Tarski's simpler proof equivalent to Gödel's, even though
Tarski's whole proof is only two pages long.

>>
>>>
>>> Formal Logic STARTS with its definition of what is correct reasoning
>>> in that Formal System.
>>>
>>> You can not change that definition without needing to restart at the
>>> begining of that Formal System.
>>>
>>> I have pointed this out many times.
>>>
>>> If you want to change the ground rules of logic, you need to start at
>>> the other end, and begin with a NEW Formal Logic with your new rules.
>>>
>>
>> Same idea as logic, created to correct the errors of logic.
>
> So start with your new logic system and see what you can get to in your
> limited time left, Sounds like you have wasted decades of time by
> working at the wrong end of the stick.
>
>>
>>> People HAVE looked at this idea of inserting the conditon that
>>> something is only True if it can be proven, and it greatly limits the
>>> power of the logic system, in particular, it can't handle much math.
>>>
>>> I get the feeling that you haven't really looked at that area,
>>> because it seems too much "learn by rote", and says you can't get to
>>> where you want to get to.
>>>
>>
>> Logic has mistakes (incoherence and inconsistency) baked right into
>> the definitions of its terms of the art. When we contrast logic with
>> correct reasoning then we might see that these are mistakes.
>
> So YOU say. Then start at the base and see how far you can get based on
> your new idea.
>

I started this "new idea" in 1997.

> Probably only a few decades of work for someone who knows what they are
> doing.
>
> Starting at the wrong end is like trying to stop a mile long freight
> train by dragging a bucket out the back of the caboose.
>
>>
>>> In short, your ignorance of the past has doomed you to repeat the
>>> great mistakes of the past.
>>
>>
>

[olcott]

In this same way requiring a non-computation to compute is an incorrect
problem definition.

[Richard Damon]

Source for this "Claim". It can not be labeld "Analytically True", yes,
but nothing says it can not be True. (If we can't prove it True we can
not use it to actually directly prove something else, but it can be True).

You seem to be saying that the Collatz conjecture can not have a Truth
Value, because it has not been proven, even though it can be proven that
it must be either True of False?

This is where you claim of working only with "Analytic Truth" breaks
down, because you use statement that only apply to analytic truths to
apply to all truths, and thus you actually LIE.

Until you can actually PROVE that statement (that the analytic statement
can not be "True" (refering to Truth in General) then your are just
LYING in your claims and being a Hypocrit, as you claim the only Truths
you can use are Analytically True, and thus Provable, without actually
Proving your statement.

>
> The reason that I keep referring to the Tarski proof is it essentially
> the exact same proof Gödel after Gödel has been simplified 100,000-fold.
> https://liarparadox.org/Tarski_275_276.pdf
>
> Tarski simply uses the liar paradox which
>
> Gödel says:
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof
>
> Thus making Tarski's simpler proof equivalent to Gödel's, even though
> Tarski's whole proof is only two pages long.

And you again assume that True -> Provable which it does not.

Note, Tarski specific restricts himself to field that support
Arithmatic, and it has been proven that such a field does NOT support
the concept that True -> Provable without becoming inconsistent.

The fact that you ignore the incosistancies shows you lack of
understanding of logic.

So what have you done with it? What basic laws of logic have you shown
still hold and which don't?

Have you gotten anywhere near trying to support math under your system?

This is the area that you might be able to make productive work with a
paper, assuming you actually HAVE some new idea that isn't just one of
the old tired theories that either dead ended or created some know
limited logic system.

My first guess is that you haven't studied enough of the work in this
field to even know if your idea is really new, as you keep running into
the same traps that they did a century ago, so you obviously haven't
learned from them. (But of course, they Learned-By-Rote what can't work,
so aren't useful to study).

[Richard Damon]

Nope, just you making Herring in Red sauce.

You are just proving your ignorance.

[olcott]

It can only be declared as having an unknown truth value.

[Richard Damon]

Which means it HAS a truth value of True or False but we don't know which.

That is VERY difffernt then it having neither, which is what you have
been claimiing (or at least what your words meant).

This shows your confusion between Truth and Knowledge.

Truth is about what actually IS

Knowledge is about what we know about what is.

[olcott]

On 5/15/2022 7:18 AM, Ben wrote:
> olcott <No...@NoWhere.com> writes:
>

>> On 5/14/2022 6:20 PM, Ben wrote:
>>> olcott <No...@NoWhere.com> writes:
>>>
>>>> On 5/14/2022 3:07 AM, Ben wrote:
>>>>> olcott <No...@NoWhere.com> writes:
>>>>>
>>>>>> The halting criteria that the halting problem expects is wrong because
>>>>>> it contradicts the definition of a computer science decider in some
>>>>>> rare cases that no one never noticed before.
>>>>> Well that's pretty clear. The halting problem, as defined by everyone
>>>>> by you (i.e. about which computations are finite and which are not) is
>>>>> indeed undecidable.
>>>>
>>>> Not at all.

>>> So you believe it is possible for a function D to be written such that
>>> D(X,Y) == true if and only of X(Y) halts and false otherwise?
>>
>> In the same way that a TM can use a "box of oreos" to compute the
>> length of a finite string a non-computation can compute the halt
>> status of a non-input.
>>
>> The HP is defined incorrectly. It cannot be about computations, it
>> must be about the computations that inputs specify.
>
> The two pointers X and Y can be taken to specify a function call X(Y).

Not when they are correctly simulated by H.

> That's what they specify in the call D(X,Y) that you are trying so hard
> to avoid taking about. What you take them to specify in a call to your
> H is not interesting.
>
> Your H is boring because "the computations that input specify" are so
> limited. Many simple computations consisting of one pointer called with
> the other as an argument can't be specified at all (apparently) so you
> should probably stop wasting time on your H.
>
> Either there can be a function D such that D(X,Y) == false if and only
> of the computation, X(Y), specified by those "inputs" does not halt, or
> there can't be. But even after 18 years of what you call "research" you
> won't dare hazard a guess about the possible existence of such an
> important algorithm!

You continue to push the nutty idea that the halt decider is required to
"compute" on non-computation.

Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the
corresponding output. https://en.wikipedia.org/wiki/Computable_function

[olcott]

Unless and Until a (possibly unknown) connection exists between an
expression of language back-chained by sound deductive inference steps
to known truth, the expression is not true.

> This shows your confusion between Truth and Knowledge.
>
> Truth is about what actually IS
>
> Knowledge is about what we know about what is.

None-the-less the sequence of inference steps must exist, analytical
truth is parasitic.

[Richard Damon]

Absolutely NOT. There does NOT need to be proof that something is true.

IF you want to claim that, by YOUR definition, you need to actually
PROVE it.

And, you can't do that by assuming it, you need to actually PROVE it
from the accepted axioms.

Since you can't, that just shows your statement isn't TRUE.

It is a fact, that it HAS been proved that if you include such a rule in
your axioms, that you can get an inconsistent system once you allow
certain logical operations to be used, that are needed to support
mathemeatics.

So, your arguement fails.

[Richard Damon]

If H^ is not a computation, then H isn't either.

You are just proving that you don't understand what this topic is about.

It has been shown that you can convert ANY Turing Machine to a
representation, and the input to H is defined as a Representation of a
Turing Machine.

If you arguement is that you can't decide on the behavior of a Turing
Machine just from a representation of it as a computation, then you are
just agreeing that the Halting Problem IS impossible to "Compute" even
if you don't understand that is what you are saying.

[olcott]

“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/

Every analytic expression of language (including math and logic) must be
connected to it meaning showing that it is true OR IT IS NOT TRUE.

Expressions of language that are not connected to their meaning are
meaningless thus neither true nor false.

> And, you can't do that by assuming it, you need to actually PROVE it
> from the accepted axioms.
>
> Since you can't, that just shows your statement isn't TRUE.
>
> It is a fact, that it HAS been proved that if you include such a rule in
> your axioms, that you can get an inconsistent system once you allow
> certain logical operations to be used, that are needed to support
> mathemeatics.
>
> So, your arguement fails.

[Ben]

olcott <No...@NoWhere.com> writes:

> On 5/15/2022 7:18 AM, Ben wrote:
>> olcott <No...@NoWhere.com> writes:
>>
>>> On 5/14/2022 6:20 PM, Ben wrote:
>>>> olcott <No...@NoWhere.com> writes:
>>>>
>>>>> On 5/14/2022 3:07 AM, Ben wrote:
>>>>>> olcott <No...@NoWhere.com> writes:
>>>>>>
>>>>>>> The halting criteria that the halting problem expects is wrong because
>>>>>>> it contradicts the definition of a computer science decider in some
>>>>>>> rare cases that no one never noticed before.
>>>>>> Well that's pretty clear. The halting problem, as defined by everyone
>>>>>> by you (i.e. about which computations are finite and which are not) is
>>>>>> indeed undecidable.
>>>>>
>>>>> Not at all.
>>>> So you believe it is possible for a function D to be written such that
>>>> D(X,Y) == true if and only of X(Y) halts and false otherwise?
>>>
>>> In the same way that a TM can use a "box of oreos" to compute the
>>> length of a finite string a non-computation can compute the halt
>>> status of a non-input.
>>>
>>> The HP is defined incorrectly. It cannot be about computations, it
>>> must be about the computations that inputs specify.
>>
>> The two pointers X and Y can be taken to specify a function call X(Y).
>
> Not when they are correctly simulated by H.

Then H is not a halt decider:

>> That's what they specify in the call D(X,Y) that you are trying so hard
>> to avoid taking about.

> You continue to push the nutty idea that the halt decider is required to
> "compute" on non-computation.

X(Y) is a computation entirely determined by the data to be found at X
and Y (and possibly by following further links from that data). The two
"input" pointers specify, without any ambiguity, the computation that D
is supposed to tell up about (and which you now accept, albeit
implicitly, that it can't).

No one cares about anything else that can be determined by examining X
and Y other than whether the call X(Y) is finite or not. At least you
are now 100% clear that H is not deciding anything we care about.

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

[olcott]

H(P,P)==0 is a correct computation.

> You are just proving that you don't understand what this topic is about.
>
> It has been shown that you can convert ANY Turing Machine to a
> representation, and the input to H is defined as a Representation of a
> Turing Machine.
>

int sum(int x, int y)
{
return x + y;
}


H(P,P) (a dependent computation) cannot report on P(P) an independent
computation in the same way that sum(3,4) cannot report on sum(8,7).

> If you arguement is that you can't decide on the behavior of a Turing
> Machine just from a representation of it as a computation, then you are
> just agreeing that the Halting Problem IS impossible to "Compute" even
> if you don't understand that is what you are saying.

[Richard Damon]

Only if H isn't a Halting Decider.

Since P(P) halts when H(P,P) is 0, it CAN'T be correct.

DEFINITION.

>
>> You are just proving that you don't understand what this topic is about.
>>
>> It has been shown that you can convert ANY Turing Machine to a
>> representation, and the input to H is defined as a Representation of a
>> Turing Machine.
>>
>
> int sum(int x, int y)
> {
>   return x + y;
> }
>
>
> H(P,P) (a dependent computation) cannot report on P(P) an independent
> computation in the same way that sum(3,4) cannot report on sum(8,7).

So you ADMIT that there is a compuation that H can't give the answer to
the Halting Problem?

That just PROVES the Theorem you are trying to disprove.

[olcott]

Your definition of halt decider contradicts the definition of a decider
and also contradicts the definition of a computation, thus is incorrect.

When we restrict the definition of a halt decider to a computation then
H(P,P)==0 is a correct computation by a decider.

a function is computable if there exists an algorithm that can do the
job of the function, i.e. given an input of the function domain it can
return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function

> Since P(P) halts when H(P,P) is 0, it CAN'T be correct.
>
> DEFINITION.
>
>>
>>> You are just proving that you don't understand what this topic is about.
>>>
>>> It has been shown that you can convert ANY Turing Machine to a
>>> representation, and the input to H is defined as a Representation of
>>> a Turing Machine.
>>>
>>
>> int sum(int x, int y)
>> {
>>    return x + y;
>> }
>>
>>
>> H(P,P) (a dependent computation) cannot report on P(P) an independent
>> computation in the same way that sum(3,4) cannot report on sum(8,7).
>
> So you ADMIT that there is a compuation that H can't give the answer to
> the Halting Problem?
>
> That just PROVES the Theorem you are trying to disprove.
> >>
>>> If you arguement is that you can't decide on the behavior of a Turing
>>> Machine just from a representation of it as a computation, then you
>>> are just agreeing that the Halting Problem IS impossible to "Compute"
>>> even if you don't understand that is what you are saying.
>>
>>
>

[Richard Damon]

So, how do you use the meaning of the words in "The Square of the
Hypotonuse of a right triangle is equal to the sume of the squares of
the other two sides" to show it is true?

I think you will have problems.

[Richard Damon]

HOW?

A decider is a computation that halts for all inputs.

A Computation is a merely a model of calculation based on a well defined
algorithm.

>
> When we restrict the definition of a halt decider to a computation then
> H(P,P)==0 is a correct computation by a decider.

But that IS the question, can you actually make a Computation that can
decide on the Halting Function. You don't get to change the Halting
Function, you either get to make a Computation/Decider that computes it
or you admit that it isn't possible.

THAT IS the question.

>
> a function is computable if there exists an algorithm that can do the
> job of the function, i.e. given an input of the function domain it can
> return the corresponding output.
> https://en.wikipedia.org/wiki/Computable_function

Right, an the question is is that mapping of (M,w) to the Halting Status
of M applied to w computable.

If you say it can't be done because that mapping contradicts the meaning
of a decider/compuation, then the answer is NO, the Halting Function is
NOT computable.

>
>> Since P(P) halts when H(P,P) is 0, it CAN'T be correct.
>>
>> DEFINITION.
>>
>>>
>>>> You are just proving that you don't understand what this topic is
>>>> about.
>>>>
>>>> It has been shown that you can convert ANY Turing Machine to a
>>>> representation, and the input to H is defined as a Representation of
>>>> a Turing Machine.
>>>>
>>>
>>> int sum(int x, int y)
>>> {
>>>    return x + y;
>>> }
>>>
>>>
>>> H(P,P) (a dependent computation) cannot report on P(P) an independent
>>> computation in the same way that sum(3,4) cannot report on sum(8,7).
>>
>> So you ADMIT that there is a compuation that H can't give the answer
>> to the Halting Problem?
>>
>> That just PROVES the Theorem you are trying to disprove.

Yep, you are just proving that which you try to disprove by your own
arguements.

If we can't even try to define a decider to do the job, then it can't be
done.