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computers / comp.ai.philosophy / Re: Correcting logic to make it a system of correct reasoning

SubjectAuthor
* Correcting logic to make it a system of correct reasoningolcott
+* Re: Correcting logic to make it a system of correct reasoningRichard Damon
|+* Re: Correcting logic to make it a system of correct reasoningolcott
||`* Re: Correcting logic to make it a system of correct reasoningRichard Damon
|| `* Re: Correcting logic to make it a system of correct reasoningolcott
||  `* Re: Correcting logic to make it a system of correct reasoningRichard Damon
||   `* Re: Correcting logic to make it a system of correct reasoningolcott
||    `* Re: Correcting logic to make it a system of correct reasoningRichard Damon
||     `* Re: Correcting logic to make it a system of correct reasoningolcott
||      `* Re: Correcting logic to make it a system of correct reasoningRichard Damon
||       `* Re: Correcting logic to make it a system of correct reasoningolcott
||        `* Re: Correcting logic to make it a system of correct reasoningRichard Damon
||         `* Re: Correcting logic to make it a system of correct reasoningolcott
||          `- Re: Correcting logic to make it a system of correct reasoningRichard Damon
|`- Re: Correcting logic to make it a system of correct reasoningJeff Barnett
+* Re: Correcting logic to make it a system of correct reasoningAndré G. Isaak
|`* Re: Correcting logic to make it a system of correct reasoningolcott
| `* Re: Correcting logic to make it a system of correct reasoningAndré G. Isaak
|  `* Re: Correcting logic to make it a system of correct reasoningolcott
|   +* Re: Correcting logic to make it a system of correct reasoningAndré G. Isaak
|   |`* Re: Correcting logic to make it a system of correct reasoningolcott
|   | `* Re: Correcting logic to make it a system of correct reasoningAndré G. Isaak
|   |  `* Re: Correcting logic to make it a system of correct reasoningolcott
|   |   `- Re: Correcting logic to make it a system of correct reasoningRichard Damon
|   `* Re: Correcting logic to make it a system of correct reasoningRichard Damon
|    `* Re: Correcting logic to make it a system of correct reasoningolcott
|     `* Re: Correcting logic to make it a system of correct reasoningRichard Damon
|      `* Re: Correcting logic to make it a system of correct reasoningolcott
|       `- Re: Correcting logic to make it a system of correct reasoningRichard Damon
+* Re: Correcting logic to make it a system of correct reasoning [olcott
|`* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
| `* Re: Correcting logic to make it a system of correct reasoning [olcott
|  `* Re: Correcting logic to make it a system of correct reasoning [ philosophical unRichard Damon
|   `* Re: Correcting logic to make it a system of correct reasoning [olcott
|    `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|     `* Re: Correcting logic to make it a system of correct reasoning [olcott
|      `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|       `* Re: Correcting logic to make it a system of correct reasoning [olcott
|        `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|         `* Re: Correcting logic to make it a system of correct reasoning [olcott
|          `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|           `* Re: Correcting logic to make it a system of correct reasoning [olcott
|            `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|             `* Re: Correcting logic to make it a system of correct reasoning [olcott
|              `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|               `* Re: Correcting logic to make it a system of correct reasoning [olcott
|                `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|                 `* Re: Correcting logic to make it a system of correct reasoning [olcott
|                  `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
|                   `* Re: Correcting logic to make it a system of correct reasoning [olcott
|                    `- Re: Correcting logic to make it a system of correct reasoning [Richard Damon
`* Re: Correcting logic to make it a system of correct reasoning [olcott
 +* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
 |`* Re: Correcting logic to make it a system of correct reasoning [olcott
 | `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
 |  `* Re: Correcting logic to make it a system of correct reasoning [olcott
 |   `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
 |    `* Re: Correcting logic to make it a system of correct reasoning [olcott
 |     `* Re: Correcting logic to make it a system of correct reasoning [ computer scienceRichard Damon
 |      `* Re: Correcting logic to make it a system of correct reasoning [olcott
 |       `- Re: Correcting logic to make it a system of correct reasoning [Richard Damon
 `* Re: Correcting logic to make it a system of correct reasoning [olcott
  +* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
  |`* Re: Correcting logic to make it a system of correct reasoning [olcott
  | `* Re: Correcting logic to make it a system of correct reasoning [Richard Damon
  |  `* Re: Correcting logic to make it a system of correct reasoning [olcott
  |   `- Re: Correcting logic to make it a system of correct reasoning [Richard Damon
  `- Re: Correcting logic to make it a system of correct reasoning [ previously undisBen

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Correcting logic to make it a system of correct reasoning

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 by: olcott - Fri, 13 May 2022 17:20 UTC

*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

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

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 by: Richard Damon - Fri, 13 May 2022 17:47 UTC

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

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

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

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

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

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

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 by: olcott - Fri, 13 May 2022 18:10 UTC

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

It categorically changes everything that is broken.

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

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

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

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

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

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

--
Copyright 2022 Pete Olcott

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

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

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 by: André G. Isaak - Fri, 13 May 2022 18:28 UTC

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

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

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

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

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

André

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

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

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 by: olcott - Fri, 13 May 2022 18:50 UTC

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

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

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

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

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

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

--
Copyright 2022 Pete Olcott

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

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

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From: agis...@gm.invalid (André G. Isaak)
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 by: André G. Isaak - Fri, 13 May 2022 19:00 UTC

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

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

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

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

Defined how exactly?

André

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

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

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 by: olcott - Fri, 13 May 2022 19:11 UTC

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:
>>> 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.
>

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

Clearly I have not yet translated this abstraction:

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

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

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

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

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

--
Copyright 2022 Pete Olcott

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

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

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 by: Richard Damon - Fri, 13 May 2022 19:13 UTC

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

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

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

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

And what do you define truth perserving as?

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

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

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

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

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

KNOWN to be True, not IS TRUE.

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

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

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 by: André G. Isaak - Fri, 13 May 2022 19:20 UTC

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:
>>> 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.
>>
>
> 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.

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

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

André

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

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

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 by: olcott - Fri, 13 May 2022 19:43 UTC

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

Change everything that diverges from my spec:
A deductive argument is said to be valid if and only if it takes a form
such that its conclusion is a necessary consequence of all of its premises.

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

Semantic relevance is maintained.

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

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

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

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

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

unprovable in the system means untrue in the system.

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

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

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

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

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

--
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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 by: olcott - Fri, 13 May 2022 19:51 UTC

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

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

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

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

--
Copyright 2022 Pete Olcott

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

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

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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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 by: André G. Isaak - Fri, 13 May 2022 20:02 UTC

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:
>>> 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:
>>>>>> 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.
>>>>
>>>
>>> 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

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

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

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 by: Richard Damon - Fri, 13 May 2022 20:03 UTC

On 5/13/22 3:11 PM, olcott wrote:
> 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:
>>>> 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.
>>
>
> I reach my key insights by progressively refining very high level
> abstractions into their corresponding concrete examples.
>
> Clearly I have not yet translated this abstraction:
>
> A deductive argument is said to be valid if and only if it takes a form
> such that its conclusion is a necessary consequence of all of its premises.
>
> Into a concrete example of the issue that it corrects, quite yet.
>
>>>>> *Here is my correction to that issue*
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form such that its conclusion is a necessary consequence of all of
>>>>> its premises.
>>>>
>>>> And that differs from the standard definition how exactly? Unless
>>>> you have some special personal meaning for 'necessary consequence'
>>>> it would
>>>
>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>
>> Defined how exactly?
>>
>> André
>>
>
> Here is the original way that semantic relevance was defined:
> Semantically unrelated premises and conclusion is not possible with
> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>
> Because syllogisms are comprised of
> https://en.wikipedia.org/wiki/Categorical_proposition
>
>
>
>

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.

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

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 by: olcott - Fri, 13 May 2022 20:08 UTC

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

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

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

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 by: olcott - Fri, 13 May 2022 20:14 UTC

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:
>>> On 2022-05-13 12:50, olcott wrote:
>>>> On 5/13/2022 1:28 PM, André G. Isaak wrote:
>>>>> On 2022-05-13 11:20, olcott wrote:
>>>>>> *Validity and Soundness*
>>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>>> form that makes it impossible for the premises to be true and the
>>>>>> conclusion nevertheless to be false. Otherwise, a deductive
>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>>
>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>> valid and even though premises and conclusion are semantically
>>>>>> unrelated.
>>>>>
>>>>> That isn't valid. Perhaps you should learn what 'valid' actually
>>>>> means before you attempt to "correct" the definition.
>>>>>
>>>>> [Also, the above isn't even an argument. It is simply a conditional
>>>>> statement. It has no conclusion].
>>>>>
>>>>
>>>> (a) The Moon is made of green cheese.
>>>> (b) Water is a kind of concrete.
>>>> (c) Therefore all dogs are cats.
>>>>
>>>> Because the premises are false and the conclusion is false it is not
>>>> a case of the conclusion is true and the premises are false, thus
>>>> meets the above validity criteria.
>>>
>>> No. It isn't valid. You don't seem to grasp the concept of validity.
>>>
>>> Logic has no concept of whether, for example, the moon is made of
>>> green cheese. An argument is valid if there is no truth *assignment*
>>> under which the premises are true and the conclusion is false. The
>>> actual truth values of these expressions don't play a role in the
>>> definition of validity.
>>>
>>
>> I reach my key insights by progressively refining very high level
>> abstractions into their corresponding concrete examples.
>>
>> Clearly I have not yet translated this abstraction:
>>
>> A deductive argument is said to be valid if and only if it takes a
>> form such that its conclusion is a necessary consequence of all of its
>> premises.
>>
>> Into a concrete example of the issue that it corrects, quite yet.
>>
>>>>>> *Here is my correction to that issue*
>>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>>> form such that its conclusion is a necessary consequence of all of
>>>>>> its premises.
>>>>>
>>>>> And that differs from the standard definition how exactly? Unless
>>>>> you have some special personal meaning for 'necessary consequence'
>>>>> it would
>>>>
>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>
>>> Defined how exactly?
>>>
>>> André
>>>
>>
>> Here is the original way that semantic relevance was defined:
>> Semantically unrelated premises and conclusion is not possible with
>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>
>> Because syllogisms are comprised of
>> https://en.wikipedia.org/wiki/Categorical_proposition
>>
>>
>>
>>
>
> 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

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

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 by: Richard Damon - Fri, 13 May 2022 20:43 UTC

On 5/13/22 3:43 PM, olcott wrote:
> On 5/13/2022 2:13 PM, Richard Damon wrote:
>> On 5/13/22 2:10 PM, olcott wrote:
>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>> *Validity and Soundness*
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form that makes it impossible for the premises to be true and the
>>>>> conclusion nevertheless to be false. Otherwise, a deductive
>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>
>>>>> If the Moon is made of green cheese then all dogs are cats is valid
>>>>> and even though premises and conclusion are semantically unrelated.
>>>>>
>>>>> *Here is my correction to that issue*
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form such that its conclusion is a necessary consequence of all of
>>>>> its premises.
>>>>>
>>>>
>>>> And, have you done the basic investigation to find out how much of
>>>> conventional logic you invalidate with that change?
>>>>
>>>
>>> It categorically changes everything that is broken.
>>
>> So, you are saying we need to throw out EVERYTHING we know and start
>> over?
>>
>
> Change everything that diverges from my spec:
> A deductive argument is said to be valid if and only if it takes a form
> such that its conclusion is a necessary consequence of all of its premises.
>
>> I think, especially with the comment below, people will decide that
>> your "new" logic systm isn't worth the cost to switch to.
>>
>>>
>>>> Note, that it may be hard to define "necessary consequence" in a
>>>> formal matter.
>>>>
>>>
>>> {A,B} ⊢ C only when truth preserving operations are applied to {A,B}
>>> to derive C.
>>
>> And what do you define truth perserving as?
>>
>
> Semantic relevance is maintained.
>
>> Normally the phrase means that True Premises always generate True
>> Results (which means the statement "If the moon is made of green
>> cheese then ll dogs are cats" IS Truth Preserving, since any time the
>> premise is true (never) the conclusion is true.
>>
>>>
>>>> It should be noted that your example, while considered an vaild
>>>> inference by normal logic, can never be used to actually prove its
>>>> conclusion, so doesn't actually cause problems in normal logic (can
>>>> you show a case where it does?)
>>>>
>>>
>>> With my correction true and unprovable is impossible, unprovable
>>> simply means untrue.
>>>
>>
>> Ok, then you have just stated that your new logic system can't handle
>> mathematics, and thus "Computer SCience" no longer exists as a logical
>> system.
>>
>
> It corrects the divergence of classical and symbolic logic from correct
> reasoning.
>
>> This makes you system not much more than a toy for most people.
>>
>>>> Note, that at least by some meanings of your words, it could be
>>>> construed that you only accept as a correct deductive argument, and
>>>> arguement whose premises can at least some times be true, but there
>>>> are some statements we don't know if they CAN be sometimes true, so
>>>> your logic system would seem to not allow doing logic with that sort
>>>> of statement.
>>>>
>>>
>>> An analytic statement is only known to be true when it is derived by
>>> applying only truth preserving operations to all of its premises and
>>> all of its premises are known to be true, otherwise its truth value
>>> is unknown.
>>>
>>
>> KNOWN to be True, not IS TRUE.
>
> It remains unknown until it is known to be true or false.
> My system only eliminates impossibly true or false.
>

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

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

And what does 'untrue' mean?

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.
>>
>
>

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

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Subject: Re: Correcting logic to make it a system of correct reasoning
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 by: Jeff Barnett - Fri, 13 May 2022 20:44 UTC

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

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

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

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

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

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 by: olcott - Fri, 13 May 2022 20:56 UTC

On 5/13/2022 3:43 PM, Richard Damon wrote:
> On 5/13/22 3:43 PM, olcott wrote:
>> On 5/13/2022 2:13 PM, Richard Damon wrote:
>>> On 5/13/22 2:10 PM, olcott wrote:
>>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>>> *Validity and Soundness*
>>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>>> form that makes it impossible for the premises to be true and the
>>>>>> conclusion nevertheless to be false. Otherwise, a deductive
>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>>
>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>> valid and even though premises and conclusion are semantically
>>>>>> unrelated.
>>>>>>
>>>>>> *Here is my correction to that issue*
>>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>>> form such that its conclusion is a necessary consequence of all of
>>>>>> its premises.
>>>>>>
>>>>>
>>>>> And, have you done the basic investigation to find out how much of
>>>>> conventional logic you invalidate with that change?
>>>>>
>>>>
>>>> It categorically changes everything that is broken.
>>>
>>> So, you are saying we need to throw out EVERYTHING we know and start
>>> over?
>>>
>>
>> Change everything that diverges from my spec:
>> A deductive argument is said to be valid if and only if it takes a
>> form such that its conclusion is a necessary consequence of all of its
>> premises.
>>
>>> I think, especially with the comment below, people will decide that
>>> your "new" logic systm isn't worth the cost to switch to.
>>>
>>>>
>>>>> Note, that it may be hard to define "necessary consequence" in a
>>>>> formal matter.
>>>>>
>>>>
>>>> {A,B} ⊢ C only when truth preserving operations are applied to {A,B}
>>>> to derive C.
>>>
>>> And what do you define truth perserving as?
>>>
>>
>> Semantic relevance is maintained.
>>
>>> Normally the phrase means that True Premises always generate True
>>> Results (which means the statement "If the moon is made of green
>>> cheese then ll dogs are cats" IS Truth Preserving, since any time the
>>> premise is true (never) the conclusion is true.
>>>
>>>>
>>>>> It should be noted that your example, while considered an vaild
>>>>> inference by normal logic, can never be used to actually prove its
>>>>> conclusion, so doesn't actually cause problems in normal logic (can
>>>>> you show a case where it does?)
>>>>>
>>>>
>>>> With my correction true and unprovable is impossible, unprovable
>>>> simply means untrue.
>>>>
>>>
>>> Ok, then you have just stated that your new logic system can't handle
>>> mathematics, and thus "Computer SCience" no longer exists as a
>>> logical system.
>>>
>>
>> It corrects the divergence of classical and symbolic logic from
>> correct reasoning.
>>
>>> This makes you system not much more than a toy for most people.
>>>
>>>>> Note, that at least by some meanings of your words, it could be
>>>>> construed that you only accept as a correct deductive argument, and
>>>>> arguement whose premises can at least some times be true, but there
>>>>> are some statements we don't know if they CAN be sometimes true, so
>>>>> your logic system would seem to not allow doing logic with that
>>>>> sort of statement.
>>>>>
>>>>
>>>> An analytic statement is only known to be true when it is derived by
>>>> applying only truth preserving operations to all of its premises and
>>>> all of its premises are known to be true, otherwise its truth value
>>>> is unknown.
>>>>
>>>
>>> KNOWN to be True, not IS TRUE.
>>
>> It remains unknown until it is known to be true or false.
>> My system only eliminates impossibly true or false.
>>
>
> So, you don't know what is still valid to use?
>
>
>>>
>>> Your statement even admits that truth value might be unknow, which
>>> might allow it to even be UNKNOWABLE (maybe just in that system) if
>>> it can't be proven or refuted.
>>>
>>
>> unprovable in the system means untrue in the system.
>
> And what does 'untrue' mean?
>

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

> 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

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

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 by: Richard Damon - Fri, 13 May 2022 21:30 UTC

On 5/13/22 4:56 PM, olcott wrote:
> On 5/13/2022 3:43 PM, Richard Damon wrote:
>> On 5/13/22 3:43 PM, olcott wrote:
>>> On 5/13/2022 2:13 PM, Richard Damon wrote:
>>>> On 5/13/22 2:10 PM, olcott wrote:
>>>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>>>> *Validity and Soundness*
>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>> a form that makes it impossible for the premises to be true and
>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive
>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>>>
>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>> unrelated.
>>>>>>>
>>>>>>> *Here is my correction to that issue*
>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>> a form such that its conclusion is a necessary consequence of all
>>>>>>> of its premises.
>>>>>>>
>>>>>>
>>>>>> And, have you done the basic investigation to find out how much of
>>>>>> conventional logic you invalidate with that change?
>>>>>>
>>>>>
>>>>> It categorically changes everything that is broken.
>>>>
>>>> So, you are saying we need to throw out EVERYTHING we know and start
>>>> over?
>>>>
>>>
>>> Change everything that diverges from my spec:
>>> A deductive argument is said to be valid if and only if it takes a
>>> form such that its conclusion is a necessary consequence of all of
>>> its premises.
>>>
>>>> I think, especially with the comment below, people will decide that
>>>> your "new" logic systm isn't worth the cost to switch to.
>>>>
>>>>>
>>>>>> Note, that it may be hard to define "necessary consequence" in a
>>>>>> formal matter.
>>>>>>
>>>>>
>>>>> {A,B} ⊢ C only when truth preserving operations are applied to
>>>>> {A,B} to derive C.
>>>>
>>>> And what do you define truth perserving as?
>>>>
>>>
>>> Semantic relevance is maintained.
>>>
>>>> Normally the phrase means that True Premises always generate True
>>>> Results (which means the statement "If the moon is made of green
>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time
>>>> the premise is true (never) the conclusion is true.
>>>>
>>>>>
>>>>>> It should be noted that your example, while considered an vaild
>>>>>> inference by normal logic, can never be used to actually prove its
>>>>>> conclusion, so doesn't actually cause problems in normal logic
>>>>>> (can you show a case where it does?)
>>>>>>
>>>>>
>>>>> With my correction true and unprovable is impossible, unprovable
>>>>> simply means untrue.
>>>>>
>>>>
>>>> Ok, then you have just stated that your new logic system can't
>>>> handle mathematics, and thus "Computer SCience" no longer exists as
>>>> a logical system.
>>>>
>>>
>>> It corrects the divergence of classical and symbolic logic from
>>> correct reasoning.
>>>
>>>> This makes you system not much more than a toy for most people.
>>>>
>>>>>> Note, that at least by some meanings of your words, it could be
>>>>>> construed that you only accept as a correct deductive argument,
>>>>>> and arguement whose premises can at least some times be true, but
>>>>>> there are some statements we don't know if they CAN be sometimes
>>>>>> true, so your logic system would seem to not allow doing logic
>>>>>> with that sort of statement.
>>>>>>
>>>>>
>>>>> An analytic statement is only known to be true when it is derived
>>>>> by applying only truth preserving operations to all of its premises
>>>>> and all of its premises are known to be true, otherwise its truth
>>>>> value is unknown.
>>>>>
>>>>
>>>> KNOWN to be True, not IS TRUE.
>>>
>>> It remains unknown until it is known to be true or false.
>>> My system only eliminates impossibly true or false.
>>>
>>
>> So, you don't know what is still valid to use?
>>
>>
>>>>
>>>> Your statement even admits that truth value might be unknow, which
>>>> might allow it to even be UNKNOWABLE (maybe just in that system) if
>>>> it can't be proven or refuted.
>>>>
>>>
>>> unprovable in the system means untrue in the system.
>>
>> And what does 'untrue' mean?
>>
>
> Untrue means the same thing as Prolog's negation as failure.

Which means... ?

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

>
>> We know that there is a number that solves an equation, but we don't
>> know that number, or how to compute that number.
>>
>> Can we say that it is true that such a number exists?
>>
>
> If you defined your terms correctly, then yes because this has been
> stipulated in your deinitions.
>
>> This means that we can define the floor of that number, which will be
>> an integer (call it N), is it true that this number exists?
>>
>> That interger, MUST be either even or odd, so we know that either
>> iseven(N) is true or isodd(N) is true.
>>
>> By your logic, the 'truth value' of both of those must be 'untrue'
>> since we can not prove which one it is.
>>
>> This is the sort of problem you run into with your system.
>>
>>>
>>>> There is NOTHING about an analytic statement that says it can only
>>>> be true if it is provable. Note, "its truth value is unknown"
>>>> doesn't mean it doesn't have a truth value, just that we don't know
>>>> what that value is.
>>>>
>>>
>>> Within any formal system unprovable in the system means untrue in the
>>> system.
>>>
>>> The entire body of analytic truth is constructed only on the basis of
>>> semantic connections between expressions of language, or expressions
>>> that are stipulated to have the semantic property of Boolean true.
>>> Lacking both of these and the expression is untrue.
>>>
>>> Since axioms are provable on the basis that they are axioms then both
>>> of these factors that make an expression true also make it provable.
>>>
>>
>> You clearly are just stating words by rote and not actually
>> understanding them.
>>
>
> There are only two possible ways that any analytical expression of
> language can possibly be true:
> (1) It is stipulated to be true.
> (2) It is derived by applying only truth preserving operations to (1) or
> the consequences of (2).

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

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

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

You still don't understand, do you.

You still confuse Truth with Knowledge.

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

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 by: Richard Damon - Fri, 13 May 2022 21:39 UTC

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:
>>> 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:
>>>>>> 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.
>>>>
>>>
>>> I reach my key insights by progressively refining very high level
>>> abstractions into their corresponding concrete examples.
>>>
>>> Clearly I have not yet translated this abstraction:
>>>
>>> A deductive argument is said to be valid if and only if it takes a
>>> form such that its conclusion is a necessary consequence of all of
>>> its premises.
>>>
>>> Into a concrete example of the issue that it corrects, quite yet.
>>>
>>>>>>> *Here is my correction to that issue*
>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>> a form such that its conclusion is a necessary consequence of all
>>>>>>> of its premises.
>>>>>>
>>>>>> And that differs from the standard definition how exactly? Unless
>>>>>> you have some special personal meaning for 'necessary consequence'
>>>>>> it would
>>>>>
>>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>>
>>>> Defined how exactly?
>>>>
>>>> André
>>>>
>>>
>>> Here is the original way that semantic relevance was defined:
>>> Semantically unrelated premises and conclusion is not possible with
>>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>
>>> Because syllogisms are comprised of
>>> https://en.wikipedia.org/wiki/Categorical_proposition
>>>
>>>
>>>
>>>
>>
>> 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.

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

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 by: olcott - Fri, 13 May 2022 21:53 UTC

On 5/13/2022 4:30 PM, Richard Damon wrote:
> On 5/13/22 4:56 PM, olcott wrote:
>> On 5/13/2022 3:43 PM, Richard Damon wrote:
>>> On 5/13/22 3:43 PM, olcott wrote:
>>>> On 5/13/2022 2:13 PM, Richard Damon wrote:
>>>>> On 5/13/22 2:10 PM, olcott wrote:
>>>>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>>>>> *Validity and Soundness*
>>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>>> a form that makes it impossible for the premises to be true and
>>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive
>>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>>>>
>>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>>> unrelated.
>>>>>>>>
>>>>>>>> *Here is my correction to that issue*
>>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>>> a form such that its conclusion is a necessary consequence of
>>>>>>>> all of its premises.
>>>>>>>>
>>>>>>>
>>>>>>> And, have you done the basic investigation to find out how much
>>>>>>> of conventional logic you invalidate with that change?
>>>>>>>
>>>>>>
>>>>>> It categorically changes everything that is broken.
>>>>>
>>>>> So, you are saying we need to throw out EVERYTHING we know and
>>>>> start over?
>>>>>
>>>>
>>>> Change everything that diverges from my spec:
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form such that its conclusion is a necessary consequence of all of
>>>> its premises.
>>>>
>>>>> I think, especially with the comment below, people will decide that
>>>>> your "new" logic systm isn't worth the cost to switch to.
>>>>>
>>>>>>
>>>>>>> Note, that it may be hard to define "necessary consequence" in a
>>>>>>> formal matter.
>>>>>>>
>>>>>>
>>>>>> {A,B} ⊢ C only when truth preserving operations are applied to
>>>>>> {A,B} to derive C.
>>>>>
>>>>> And what do you define truth perserving as?
>>>>>
>>>>
>>>> Semantic relevance is maintained.
>>>>
>>>>> Normally the phrase means that True Premises always generate True
>>>>> Results (which means the statement "If the moon is made of green
>>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time
>>>>> the premise is true (never) the conclusion is true.
>>>>>
>>>>>>
>>>>>>> It should be noted that your example, while considered an vaild
>>>>>>> inference by normal logic, can never be used to actually prove
>>>>>>> its conclusion, so doesn't actually cause problems in normal
>>>>>>> logic (can you show a case where it does?)
>>>>>>>
>>>>>>
>>>>>> With my correction true and unprovable is impossible, unprovable
>>>>>> simply means untrue.
>>>>>>
>>>>>
>>>>> Ok, then you have just stated that your new logic system can't
>>>>> handle mathematics, and thus "Computer SCience" no longer exists as
>>>>> a logical system.
>>>>>
>>>>
>>>> It corrects the divergence of classical and symbolic logic from
>>>> correct reasoning.
>>>>
>>>>> This makes you system not much more than a toy for most people.
>>>>>
>>>>>>> Note, that at least by some meanings of your words, it could be
>>>>>>> construed that you only accept as a correct deductive argument,
>>>>>>> and arguement whose premises can at least some times be true, but
>>>>>>> there are some statements we don't know if they CAN be sometimes
>>>>>>> true, so your logic system would seem to not allow doing logic
>>>>>>> with that sort of statement.
>>>>>>>
>>>>>>
>>>>>> An analytic statement is only known to be true when it is derived
>>>>>> by applying only truth preserving operations to all of its
>>>>>> premises and all of its premises are known to be true, otherwise
>>>>>> its truth value is unknown.
>>>>>>
>>>>>
>>>>> KNOWN to be True, not IS TRUE.
>>>>
>>>> It remains unknown until it is known to be true or false.
>>>> My system only eliminates impossibly true or false.
>>>>
>>>
>>> So, you don't know what is still valid to use?
>>>
>>>
>>>>>
>>>>> Your statement even admits that truth value might be unknow, which
>>>>> might allow it to even be UNKNOWABLE (maybe just in that system) if
>>>>> it can't be proven or refuted.
>>>>>
>>>>
>>>> unprovable in the system means untrue in the system.
>>>
>>> And what does 'untrue' mean?
>>>
>>
>> Untrue means the same thing as Prolog's negation as failure.
>
> Which means... ?
>
> Prolog, as I remember, ASSUMES that anything not provable is FALSE (not
> 'untrue').
>

Unprovable means untrue and does not mean false in Prolog.

>>
>>> We know that there is a number that solves an equation, but we don't
>>> know that number, or how to compute that number.
>>>
>>> Can we say that it is true that such a number exists?
>>>
>>
>> If you defined your terms correctly, then yes because this has been
>> stipulated in your deinitions.
>>
>>> This means that we can define the floor of that number, which will be
>>> an integer (call it N), is it true that this number exists?
>>>
>>> That interger, MUST be either even or odd, so we know that either
>>> iseven(N) is true or isodd(N) is true.
>>>
>>> By your logic, the 'truth value' of both of those must be 'untrue'
>>> since we can not prove which one it is.
>>>
>>> This is the sort of problem you run into with your system.
>>>
>>>>
>>>>> There is NOTHING about an analytic statement that says it can only
>>>>> be true if it is provable. Note, "its truth value is unknown"
>>>>> doesn't mean it doesn't have a truth value, just that we don't know
>>>>> what that value is.
>>>>>
>>>>
>>>> Within any formal system unprovable in the system means untrue in
>>>> the system.
>>>>
>>>> The entire body of analytic truth is constructed only on the basis
>>>> of semantic connections between expressions of language, or
>>>> expressions that are stipulated to have the semantic property of
>>>> Boolean true. Lacking both of these and the expression is untrue.
>>>>
>>>> Since axioms are provable on the basis that they are axioms then
>>>> both of these factors that make an expression true also make it
>>>> provable.
>>>>
>>>
>>> You clearly are just stating words by rote and not actually
>>> understanding them.
>>>
>>
>> There are only two possible ways that any analytical expression of
>> language can possibly be true:
>> (1) It is stipulated to be true.
>> (2) It is derived by applying only truth preserving operations to (1)
>> or the consequences of (2).
>
> So there exists an integer number N is neither Even or Odd? (it is
> untrue for both tests)
>
> I don't think you actually understand what that means.
>
>>
>>> Analytic Truth is truth that is provable, that is correct, but it
>>> accepts that there is OTHER things that happen to be true but are not
>>> provable.
>>>
>>
>> Analytic truth includes every expression of language that can be
>> completely verified as totally true entirely on the basis of its
>> meaning without requiring any sense data from the sense organs.
>>
>> Empirical expressions of language also require sense data from the
>> sense organs to verify their truth.
>
> You still don't understand, do you.
>
> You still confuse Truth with Knowledge.
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).


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 by: Richard Damon - Fri, 13 May 2022 21:56 UTC

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

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

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

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

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

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

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

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

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 by: olcott - Fri, 13 May 2022 21:56 UTC

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:
>>> On 5/13/22 3:11 PM, olcott wrote:
>>>> 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:
>>>>>>> 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.
>>>>>
>>>>
>>>> I reach my key insights by progressively refining very high level
>>>> abstractions into their corresponding concrete examples.
>>>>
>>>> Clearly I have not yet translated this abstraction:
>>>>
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form such that its conclusion is a necessary consequence of all of
>>>> its premises.
>>>>
>>>> Into a concrete example of the issue that it corrects, quite yet.
>>>>
>>>>>>>> *Here is my correction to that issue*
>>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>>> a form such that its conclusion is a necessary consequence of
>>>>>>>> all of its premises.
>>>>>>>
>>>>>>> And that differs from the standard definition how exactly? Unless
>>>>>>> you have some special personal meaning for 'necessary
>>>>>>> consequence' it would
>>>>>>
>>>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>>>
>>>>> Defined how exactly?
>>>>>
>>>>> André
>>>>>
>>>>
>>>> Here is the original way that semantic relevance was defined:
>>>> Semantically unrelated premises and conclusion is not possible with
>>>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>>
>>>> Because syllogisms are comprised of
>>>> https://en.wikipedia.org/wiki/Categorical_proposition
>>>>
>>>>
>>>>
>>>>
>>>
>>> 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

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

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 by: Richard Damon - Fri, 13 May 2022 22:14 UTC

On 5/13/22 5:53 PM, olcott wrote:
> On 5/13/2022 4:30 PM, Richard Damon wrote:
>> On 5/13/22 4:56 PM, olcott wrote:
>>> On 5/13/2022 3:43 PM, Richard Damon wrote:
>>>> On 5/13/22 3:43 PM, olcott wrote:
>>>>> On 5/13/2022 2:13 PM, Richard Damon wrote:
>>>>>> On 5/13/22 2:10 PM, olcott wrote:
>>>>>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>>>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>>>>>> *Validity and Soundness*
>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>> takes a form that makes it impossible for the premises to be
>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a
>>>>>>>>> deductive argument is said to be invalid.
>>>>>>>>> https://iep.utm.edu/val-snd/
>>>>>>>>>
>>>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>>>> unrelated.
>>>>>>>>>
>>>>>>>>> *Here is my correction to that issue*
>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>> takes a form such that its conclusion is a necessary
>>>>>>>>> consequence of all of its premises.
>>>>>>>>>
>>>>>>>>
>>>>>>>> And, have you done the basic investigation to find out how much
>>>>>>>> of conventional logic you invalidate with that change?
>>>>>>>>
>>>>>>>
>>>>>>> It categorically changes everything that is broken.
>>>>>>
>>>>>> So, you are saying we need to throw out EVERYTHING we know and
>>>>>> start over?
>>>>>>
>>>>>
>>>>> Change everything that diverges from my spec:
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form such that its conclusion is a necessary consequence of all of
>>>>> its premises.
>>>>>
>>>>>> I think, especially with the comment below, people will decide
>>>>>> that your "new" logic systm isn't worth the cost to switch to.
>>>>>>
>>>>>>>
>>>>>>>> Note, that it may be hard to define "necessary consequence" in a
>>>>>>>> formal matter.
>>>>>>>>
>>>>>>>
>>>>>>> {A,B} ⊢ C only when truth preserving operations are applied to
>>>>>>> {A,B} to derive C.
>>>>>>
>>>>>> And what do you define truth perserving as?
>>>>>>
>>>>>
>>>>> Semantic relevance is maintained.
>>>>>
>>>>>> Normally the phrase means that True Premises always generate True
>>>>>> Results (which means the statement "If the moon is made of green
>>>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time
>>>>>> the premise is true (never) the conclusion is true.
>>>>>>
>>>>>>>
>>>>>>>> It should be noted that your example, while considered an vaild
>>>>>>>> inference by normal logic, can never be used to actually prove
>>>>>>>> its conclusion, so doesn't actually cause problems in normal
>>>>>>>> logic (can you show a case where it does?)
>>>>>>>>
>>>>>>>
>>>>>>> With my correction true and unprovable is impossible, unprovable
>>>>>>> simply means untrue.
>>>>>>>
>>>>>>
>>>>>> Ok, then you have just stated that your new logic system can't
>>>>>> handle mathematics, and thus "Computer SCience" no longer exists
>>>>>> as a logical system.
>>>>>>
>>>>>
>>>>> It corrects the divergence of classical and symbolic logic from
>>>>> correct reasoning.
>>>>>
>>>>>> This makes you system not much more than a toy for most people.
>>>>>>
>>>>>>>> Note, that at least by some meanings of your words, it could be
>>>>>>>> construed that you only accept as a correct deductive argument,
>>>>>>>> and arguement whose premises can at least some times be true,
>>>>>>>> but there are some statements we don't know if they CAN be
>>>>>>>> sometimes true, so your logic system would seem to not allow
>>>>>>>> doing logic with that sort of statement.
>>>>>>>>
>>>>>>>
>>>>>>> An analytic statement is only known to be true when it is derived
>>>>>>> by applying only truth preserving operations to all of its
>>>>>>> premises and all of its premises are known to be true, otherwise
>>>>>>> its truth value is unknown.
>>>>>>>
>>>>>>
>>>>>> KNOWN to be True, not IS TRUE.
>>>>>
>>>>> It remains unknown until it is known to be true or false.
>>>>> My system only eliminates impossibly true or false.
>>>>>
>>>>
>>>> So, you don't know what is still valid to use?
>>>>
>>>>
>>>>>>
>>>>>> Your statement even admits that truth value might be unknow, which
>>>>>> might allow it to even be UNKNOWABLE (maybe just in that system)
>>>>>> if it can't be proven or refuted.
>>>>>>
>>>>>
>>>>> unprovable in the system means untrue in the system.
>>>>
>>>> And what does 'untrue' mean?
>>>>
>>>
>>> Untrue means the same thing as Prolog's negation as failure.
>>
>> Which means... ?
>>
>> Prolog, as I remember, ASSUMES that anything not provable is FALSE
>> (not 'untrue').
>>
>
> Unprovable means untrue and does not mean false in Prolog.
>
>>>
>>>> We know that there is a number that solves an equation, but we don't
>>>> know that number, or how to compute that number.
>>>>
>>>> Can we say that it is true that such a number exists?
>>>>
>>>
>>> If you defined your terms correctly, then yes because this has been
>>> stipulated in your deinitions.
>>>
>>>> This means that we can define the floor of that number, which will
>>>> be an integer (call it N), is it true that this number exists?
>>>>
>>>> That interger, MUST be either even or odd, so we know that either
>>>> iseven(N) is true or isodd(N) is true.
>>>>
>>>> By your logic, the 'truth value' of both of those must be 'untrue'
>>>> since we can not prove which one it is.
>>>>
>>>> This is the sort of problem you run into with your system.
>>>>
>>>>>
>>>>>> There is NOTHING about an analytic statement that says it can only
>>>>>> be true if it is provable. Note, "its truth value is unknown"
>>>>>> doesn't mean it doesn't have a truth value, just that we don't
>>>>>> know what that value is.
>>>>>>
>>>>>
>>>>> Within any formal system unprovable in the system means untrue in
>>>>> the system.
>>>>>
>>>>> The entire body of analytic truth is constructed only on the basis
>>>>> of semantic connections between expressions of language, or
>>>>> expressions that are stipulated to have the semantic property of
>>>>> Boolean true. Lacking both of these and the expression is untrue.
>>>>>
>>>>> Since axioms are provable on the basis that they are axioms then
>>>>> both of these factors that make an expression true also make it
>>>>> provable.
>>>>>
>>>>
>>>> You clearly are just stating words by rote and not actually
>>>> understanding them.
>>>>
>>>
>>> There are only two possible ways that any analytical expression of
>>> language can possibly be true:
>>> (1) It is stipulated to be true.
>>> (2) It is derived by applying only truth preserving operations to (1)
>>> or the consequences of (2).
>>
>> So there exists an integer number N is neither Even or Odd? (it is
>> untrue for both tests)
>>
>> I don't think you actually understand what that means.
>>
>>>
>>>> Analytic Truth is truth that is provable, that is correct, but it
>>>> accepts that there is OTHER things that happen to be true but are
>>>> not provable.
>>>>
>>>
>>> Analytic truth includes every expression of language that can be
>>> completely verified as totally true entirely on the basis of its
>>> meaning without requiring any sense data from the sense organs.
>>>
>>> Empirical expressions of language also require sense data from the
>>> sense organs to verify their truth.
>>
>> You still don't understand, do you.
>>
>> You still confuse Truth with Knowledge.
> 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).
>
> Try and provide an example of a possible truth that does not require one
> of those two.
>


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 by: Richard Damon - Fri, 13 May 2022 22:19 UTC

On 5/13/22 5:56 PM, olcott wrote:
> 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:
>>>> On 5/13/22 3:11 PM, olcott wrote:
>>>>> 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:
>>>>>>>> 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.
>>>>>>
>>>>>
>>>>> I reach my key insights by progressively refining very high level
>>>>> abstractions into their corresponding concrete examples.
>>>>>
>>>>> Clearly I have not yet translated this abstraction:
>>>>>
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form such that its conclusion is a necessary consequence of all of
>>>>> its premises.
>>>>>
>>>>> Into a concrete example of the issue that it corrects, quite yet.
>>>>>
>>>>>>>>> *Here is my correction to that issue*
>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>> takes a form such that its conclusion is a necessary
>>>>>>>>> consequence of all of its premises.
>>>>>>>>
>>>>>>>> And that differs from the standard definition how exactly?
>>>>>>>> Unless you have some special personal meaning for 'necessary
>>>>>>>> consequence' it would
>>>>>>>
>>>>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>>>>
>>>>>> Defined how exactly?
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> Here is the original way that semantic relevance was defined:
>>>>> Semantically unrelated premises and conclusion is not possible with
>>>>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>>>
>>>>> Because syllogisms are comprised of
>>>>> https://en.wikipedia.org/wiki/Categorical_proposition
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>> 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.
>

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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