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

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*Validity and Soundness*

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

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

*Here is my correction to that issue*

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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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

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

*Here is my correction to that issue*

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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

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On 5/13/22 1:20 PM, olcott wrote:

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

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

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

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

*Validity and Soundness*

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

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

*Here is my correction to that issue*

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

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

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

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

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

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On 5/13/2022 12:47 PM, Richard Damon wrote:

It categorically changes everything that is broken.

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

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

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.

--

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 1:20 PM, olcott wrote:

*Validity and Soundness*

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

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

*Here is my correction to that issue*

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

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

It categorically changes everything that is broken.

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

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

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

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

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

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

--

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: agis...@gm.invalid (André G. Isaak)

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

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View all headersFrom: agis...@gm.invalid (André G. Isaak)

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On 2022-05-13 11:20, olcott wrote:

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

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

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

André

--

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

*Validity and Soundness*

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

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

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

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

*Here is my correction to that issue*

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

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

André

--

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

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On 5/13/2022 1:28 PM, André G. Isaak wrote:

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

--

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 2022-05-13 11:20, olcott wrote:

*Validity and Soundness*

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

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

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

*Here is my correction to that issue*

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

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

André

--

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: agis...@gm.invalid (André G. Isaak)

Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.lang.semantics

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

Date: Fri, 13 May 2022 13:00:03 -0600

Organization: Christians and Atheists United Against Creeping Agnosticism

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View all headersFrom: agis...@gm.invalid (André G. Isaak)

Newsgroups: comp.theory,comp.ai.philosophy,sci.logic,sci.lang.semantics

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

Date: Fri, 13 May 2022 13:00:03 -0600

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On 2022-05-13 12:50, olcott wrote:

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

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

Defined how exactly?

André

--

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On 5/13/2022 1:28 PM, André G. Isaak wrote:

On 2022-05-13 11:20, olcott wrote:

*Validity and Soundness*

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

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

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

*Here is my correction to that issue*

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

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On 5/13/2022 2:00 PM, André G. Isaak wrote:

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

Clearly I have not yet translated this abstraction:

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

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

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

--

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 2022-05-13 12:50, olcott wrote:

On 5/13/2022 1:28 PM, André G. Isaak wrote:

On 2022-05-13 11:20, olcott wrote:

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

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

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

--

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 2:10 PM, olcott wrote:

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

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

And what do you define truth perserving as?

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

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

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

KNOWN to be True, not IS TRUE.

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

On 5/13/2022 12:47 PM, Richard Damon wrote:

On 5/13/22 1:20 PM, olcott wrote:

*Validity and Soundness*

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

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

*Here is my correction to that issue*

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

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

It categorically changes everything that is broken.

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

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

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

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

And what do you define truth perserving as?

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

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

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

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

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

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

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

KNOWN to be True, not IS TRUE.

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

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From: agis...@gm.invalid (André G. Isaak)

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

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View all headersFrom: agis...@gm.invalid (André G. Isaak)

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On 2022-05-13 13:11, olcott wrote:

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

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

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

André

--

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On 5/13/2022 2:00 PM, André G. Isaak wrote:

On 2022-05-13 12:50, olcott wrote:

On 5/13/2022 1:28 PM, André G. Isaak 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

André

--

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On 5/13/2022 2:13 PM, Richard Damon wrote:

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.

Semantic relevance is maintained.

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

It remains unknown until it is known to be true or false.

My system only eliminates impossibly true or false.

unprovable in the system means untrue in the 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.

--

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 2:10 PM, olcott wrote:

On 5/13/2022 12:47 PM, Richard Damon wrote:

On 5/13/22 1:20 PM, olcott 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.

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

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

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

And what do you define truth perserving as?

Semantic relevance is maintained.

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

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

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

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

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

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

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

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

KNOWN to be True, not IS TRUE.

It remains unknown until it is known to be true or false.

My system only eliminates impossibly true or false.

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

unprovable in the system means untrue in the system.

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

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

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

--

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 2:20 PM, André G. Isaak wrote:

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

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

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

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

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

--

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 2022-05-13 13:11, olcott wrote:

On 5/13/2022 2:00 PM, André G. Isaak wrote:

On 2022-05-13 12:50, olcott 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

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

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

André

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

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

--

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 2022-05-13 13:51, olcott wrote:

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

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

André

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On 5/13/2022 2:20 PM, André G. Isaak wrote:

On 2022-05-13 13:11, olcott wrote:

On 5/13/2022 2:00 PM, André G. Isaak 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

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

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

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

André

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On 5/13/22 3:11 PM, olcott wrote:

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

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

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

On 5/13/2022 2:00 PM, André G. Isaak 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

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

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

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On 5/13/2022 3:02 PM, André G. Isaak wrote:

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

--

Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;

Genius hits a target no one else can see."

Arthur Schopenhauer

On 2022-05-13 13:51, olcott wrote:

On 5/13/2022 2:20 PM, André G. Isaak wrote:

On 2022-05-13 13:11, olcott 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

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

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

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

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

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

Except you haven't show any instances where it diverges from 'correct reasoning'.

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

You gave an example argument which was *not* valid, claimed that it was valid and that this "fact" was somehow a problem. The only problem I can see is your failure to grasp what it means for something to be valid.

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

André

--

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 3:03 PM, Richard Damon wrote:

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

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

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

--

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 3:11 PM, olcott wrote:

On 5/13/2022 2:00 PM, André G. Isaak 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

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

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

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

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

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

--

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 3:43 PM, olcott wrote:

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

And what does 'untrue' mean?

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

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

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

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

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

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

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

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

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

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:

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.

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.

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

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On 5/13/2022 11:47 AM, Richard Damon wrote:

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

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

On 5/13/22 1:20 PM, olcott 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?

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

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

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

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

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

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

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

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

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

(1) It is stipulated to be true.

(2) It is derived by applying only truth preserving operations to (1) or the consequences of (2).

Analytic truth 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.

--

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 3:43 PM, olcott wrote:

On 5/13/2022 2:13 PM, Richard Damon wrote:

On 5/13/22 2:10 PM, olcott 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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

(1) It is stipulated to be true.

(2) It is derived by applying only truth preserving operations to (1) or the consequences of (2).

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

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

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

--

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 4:56 PM, olcott wrote:

Which means... ?

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

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

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

You still don't understand, do you.

You still confuse Truth with Knowledge.

Pitiful.

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:

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').

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.

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.

Pitiful.

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

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On 5/13/22 4:14 PM, olcott wrote:

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

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

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

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

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

On 5/13/2022 3:03 PM, Richard Damon wrote:

On 5/13/22 3:11 PM, olcott wrote:

On 5/13/2022 2:00 PM, André G. Isaak 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

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

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

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

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

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

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

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

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

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

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

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

Unprovable means untrue and does not mean false in Prolog.

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.

--

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 4:56 PM, olcott wrote:

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

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

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.

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.

--

Copyright 2022 Pete Olcott

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Arthur Schopenhauer

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

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

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

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

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

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

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

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

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

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

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

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

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On 5/13/2022 4:39 PM, Richard Damon wrote:

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

--

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 4:14 PM, olcott wrote:

On 5/13/2022 3:03 PM, Richard Damon wrote:

On 5/13/22 3:11 PM, olcott 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

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

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

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

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

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

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

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

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

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

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

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

--

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 5:53 PM, olcott wrote:

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

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

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

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

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

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

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

It is not KNOWN to be True, or Proven.

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:

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.

There are only two possible ways that any analytical expression of

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, and is neither stipulated true or derived from an analytical proof.

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

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

It is not KNOWN to be True, or Proven.

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

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

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

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

On 5/13/2022 4:39 PM, Richard Damon wrote:

On 5/13/22 4:14 PM, olcott wrote:

On 5/13/2022 3:03 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.

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

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

(a) The Moon is made of green cheese.

(b) Water is a kind of concrete.

(c) Therefore all dogs are cats.

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

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

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

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

Clearly I have not yet translated this abstraction:

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

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

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

And that differs from the standard definition how exactly? Unless you have some special personal meaning for 'necessary consequence' it would

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

Defined how exactly?

André

Here is the original way that semantic relevance was defined:

Semantically unrelated premises and conclusion is not possible with syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure

Because syllogisms are comprised of

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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