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On 5/13/2022 5:14 PM, Richard Damon wrote:

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/13/22 5:53 PM, olcott wrote:

On 5/13/2022 4:30 PM, Richard Damon wrote:

On 5/13/22 4:56 PM, olcott wrote:

On 5/13/2022 3:43 PM, Richard Damon wrote:

On 5/13/22 3:43 PM, olcott wrote:

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.

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?

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

Which means... ?

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

Unprovable means untrue and does not mean false in Prolog.

There are only two possible ways that any analytical expression of

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).

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.

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).

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

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,

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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On 5/13/22 6:23 PM, olcott wrote:

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.

On 5/13/2022 5:14 PM, Richard Damon wrote:

On 5/13/22 5:53 PM, olcott wrote:

On 5/13/2022 4:30 PM, Richard Damon wrote:

On 5/13/22 4:56 PM, olcott wrote:

On 5/13/2022 3:43 PM, Richard Damon wrote:

On 5/13/22 3:43 PM, olcott wrote:

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.

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?

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

Which means... ?

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

Unprovable means untrue and does not mean false in Prolog.

There are only two possible ways that any analytical expression of

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).

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.

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).

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

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,

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.

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.

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From: NoO...@NoWhere.com (olcott)

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On 5/13/2022 6:14 PM, Richard Damon wrote:

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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/13/22 6:23 PM, olcott wrote:

On 5/13/2022 5:14 PM, Richard Damon wrote:

On 5/13/22 5:53 PM, olcott wrote:

On 5/13/2022 4:30 PM, Richard Damon wrote:

On 5/13/22 4:56 PM, olcott wrote:

On 5/13/2022 3:43 PM, Richard Damon wrote:

On 5/13/22 3:43 PM, olcott wrote:

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.

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?

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

Which means... ?

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

Unprovable means untrue and does not mean false in Prolog.

There are only two possible ways that any analytical expression of

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).

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.

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).

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

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,

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.

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

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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On 5/13/2022 6:22 PM, Richard Damon wrote:

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/13/22 7:05 PM, olcott wrote:

On 5/13/2022 6:01 PM, Ben wrote:

olcott <NoOne@NoWhere.com> writes:

On 5/13/2022 3:46 PM, Ben wrote:

olcott <NoOne@NoWhere.com> writes:

On 5/13/2022 2:16 PM, Ben wrote:It is now dead obvious that you accept that no algorithm can do what the

olcott <NoOne@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.

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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From: Rich...@Damon-Family.org (Richard Damon)

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On 5/13/22 7:20 PM, olcott wrote:

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).

On 5/13/2022 6:14 PM, Richard Damon wrote:

On 5/13/22 6:23 PM, olcott wrote:

On 5/13/2022 5:14 PM, Richard Damon wrote:

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.

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.

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.

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.

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?

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

Which means... ?

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

Unprovable means untrue and does not mean false in Prolog.

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.

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.

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).

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 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.

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).

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

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,

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.

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

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

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).

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.

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On 5/13/22 7:35 PM, olcott wrote:

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).

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 <NoOne@NoWhere.com> writes:

On 5/13/2022 3:46 PM, Ben wrote:

olcott <NoOne@NoWhere.com> writes:

On 5/13/2022 2:16 PM, Ben wrote:It is now dead obvious that you accept that no algorithm can do what the

olcott <NoOne@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.

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.

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).

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On 5/13/2022 7:27 PM, Richard Damon wrote:

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/13/22 7:35 PM, olcott wrote:

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 <NoOne@NoWhere.com> writes:

On 5/13/2022 3:46 PM, Ben wrote:

olcott <NoOne@NoWhere.com> writes:

On 5/13/2022 2:16 PM, Ben wrote:It is now dead obvious that you accept that no algorithm can do what the

olcott <NoOne@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.

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.

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)

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).

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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On 5/14/22 12:01 AM, olcott wrote:

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?

On 5/13/2022 7:27 PM, Richard Damon wrote:

On 5/13/22 7:35 PM, olcott wrote:

On 5/13/2022 6:22 PM, Richard Damon wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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?

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).

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On 5/14/2022 3:07 AM, Ben wrote:

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.

*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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

olcott <NoOne@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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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On 5/14/22 10:00 AM, olcott wrote:

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.

On 5/14/2022 3:07 AM, Ben wrote:

olcott <NoOne@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.

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]

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Wittgenstein and I ]

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On 5/14/2022 8:42 AM, Richard Damon wrote:

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/14/22 12:01 AM, olcott wrote:

On 5/13/2022 7:27 PM, Richard Damon wrote:

On 5/13/22 7:35 PM, olcott wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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?

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).

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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computer science is inconsistent ]

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computer science is inconsistent ]

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On 5/14/2022 9:31 AM, Richard Damon wrote:

[ 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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/14/22 10:00 AM, olcott wrote:

On 5/14/2022 3:07 AM, Ben wrote:

olcott <NoOne@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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]

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On 5/14/22 10:42 AM, olcott wrote:

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.

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.

WRONG.

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

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

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.

WRONG. You are again confalating KNOWLEDGE with TRUTH.

WRONG.

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

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.

On 5/14/2022 8:42 AM, Richard Damon wrote:

On 5/14/22 12:01 AM, olcott wrote:

On 5/13/2022 7:27 PM, Richard Damon wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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.

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.

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?

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).

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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On 5/14/2022 9:59 AM, Richard Damon wrote:

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

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.

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

All of math and logic is exclusively ANALYTICAL.

to verify their truth.

to verify their truth.

to verify their 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.

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.

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.

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

On 5/14/22 10:42 AM, olcott wrote:

On 5/14/2022 8:42 AM, Richard Damon wrote:

On 5/14/22 12:01 AM, olcott wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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

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.

Click here to read the complete article

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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From: Rich...@Damon-Family.org (Richard Damon)

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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On 5/14/22 10:53 AM, olcott wrote:

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.

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:

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.

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.

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.

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.

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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On 5/14/22 11:32 AM, olcott wrote:

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.

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

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.

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.

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.

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.

On 5/14/2022 9:59 AM, Richard Damon wrote:

On 5/14/22 10:42 AM, olcott wrote:

On 5/14/2022 8:42 AM, Richard Damon wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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.

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.

Click here to read the complete article

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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On 5/14/2022 10:33 AM, Richard Damon wrote:

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.

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/14/22 10:53 AM, olcott wrote:

On 5/14/2022 9:31 AM, Richard Damon wrote:

On 5/14/22 10:00 AM, olcott wrote:

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.

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.

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

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.

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.

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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On 5/14/2022 11:42 AM, Richard Damon wrote:

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.

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.

On 5/14/22 11:32 AM, olcott wrote:

On 5/14/2022 9:59 AM, Richard Damon wrote:

On 5/14/22 10:42 AM, olcott wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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.

WRONG. Again you conflate Analytic truth with truth.

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.

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.

Click here to read the complete article

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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Wittgenstein and I ]( Prolog backchaining )

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On 5/14/22 1:25 PM, olcott wrote:

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.

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

On 5/14/2022 11:42 AM, Richard Damon wrote:

On 5/14/22 11:32 AM, olcott wrote:

On 5/14/2022 9:59 AM, Richard Damon wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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

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.

WRONG. Again you conflate Analytic truth with truth.

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.

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.

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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On 5/14/2022 3:18 PM, Richard Damon wrote:

OK great this is a key agreement between us.

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.

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.

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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/14/22 1:25 PM, olcott wrote:

On 5/14/2022 11:42 AM, Richard Damon wrote:

On 5/14/22 11:32 AM, olcott wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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

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.

WRONG. Again you conflate Analytic truth with truth.

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.

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.

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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From: Rich...@Damon-Family.org (Richard Damon)

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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From: Rich...@Damon-Family.org (Richard Damon)

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On 5/14/22 5:02 PM, olcott wrote:

On 5/14/2022 3:18 PM, Richard Damon wrote:

On 5/14/22 1:25 PM, olcott wrote:

On 5/14/2022 11:42 AM, Richard Damon wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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

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.

WRONG. Again you conflate Analytic truth with truth.

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.

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.

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.

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.

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.

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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From: Rich...@Damon-Family.org (Richard Damon)

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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On 5/14/22 12:52 PM, olcott wrote:

On 5/14/2022 10:33 AM, Richard Damon wrote:

On 5/14/22 10:53 AM, olcott wrote:

On 5/14/2022 9:31 AM, Richard Damon wrote:

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.

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.

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

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.

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.

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Wittgenstein and I ]( Prolog backchaining )

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On 5/14/2022 4:15 PM, Richard Damon wrote:

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.

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

On 5/14/22 5:02 PM, olcott wrote:

On 5/14/2022 3:18 PM, Richard Damon wrote:

On 5/14/22 1:25 PM, olcott wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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

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.

WRONG. Again you conflate Analytic truth with truth.

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.

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.

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.

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.

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.

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.

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?

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.

Click here to read the complete article

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [

computer science is inconsistent ]

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On 5/14/2022 4:28 PM, Richard Damon wrote:

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 5/14/22 12:52 PM, olcott wrote:

On 5/14/2022 10:33 AM, Richard Damon wrote:

On 5/14/22 10:53 AM, olcott wrote:

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.

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.

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

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.

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.

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.

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.

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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Subject: Re: Correcting logic to make it a system of correct reasoning [

Wittgenstein and I ]( Prolog backchaining )

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On 5/14/22 5:48 PM, olcott wrote:

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.

On 5/14/2022 4:15 PM, Richard Damon wrote:

On 5/14/22 5:02 PM, olcott wrote:

On 5/14/2022 3:18 PM, Richard Damon wrote:

*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.

world calls "decide halting".

Tarski makes a similar mistake...

<snip distractions>

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.

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)

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.

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.

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.

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

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

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.

WRONG. Again you conflate Analytic truth with truth.

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.

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.

OK great this is a key agreement between us.

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.

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

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.

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

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

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.

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?

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

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.

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