*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

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.

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

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.

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

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.

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

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

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

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

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

And what do you define truth perserving as?

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

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

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

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

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

KNOWN to be True, not IS TRUE.

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

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

You are confusing Knowledge with Truth.

Your whole system is built on a Category Error.

André G. Isaak <agisaak@gm.invalid> writes:

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

>> Semantic relevance is a key aspect of 'necessary consequence'.
>
> Defined how exactly?

If ever a question demonstrated the power of hope over experience, this
is it!

--
Ben.

olcott <NoOne@NoWhere.com> writes:

> *Validity and Soundness*

Good plan. You've run aground as far as halting is concerned, so you
better find another topic you don't know about.

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

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.

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

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

On 5/13/2022 2:15 PM, Ben wrote:
> André G. Isaak <agisaak@gm.invalid> writes:
>
>> On 2022-05-13 12:50, olcott wrote:
>
>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>
>> Defined how exactly?
>
> If ever a question demonstrated the power of hope over experience, this
> is it!
>

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

--
Copyright 2022 Pete Olcott

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

On 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.

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.

On 5/13/2022 2:16 PM, Ben wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> *Validity and Soundness*
>
> Good plan. You've run aground as far as halting is concerned, so you
> better find another topic you don't know about.
>

It has been dead obvious that H(P,P)==0 is the correct halt status for
the input to H(P,P) on the basis of the actual behavior that this input
actually specifies.

This has been dead obvious on this basis for at least six months, yet my
reviewers very persistently insisted on simply ignoring the easily
verifiable facts for this whole six month period.

Now my reviewers are playing a "hail Mary" claiming that even though the
actual behavior of the actual input to H(P,P) actually factually is
non-halting it is incorrect for H to report that is input is non-halting.

--
Copyright 2022 Pete Olcott

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

On 5/13/2022 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

On Friday, May 13, 2022 at 4:04:48 PM UTC-4, olcott wrote:
> On 5/13/2022 2:16 PM, Ben wrote:
> > olcott <No...@NoWhere.com> writes:
> >
> >> *Validity and Soundness*
> >
> > Good plan. You've run aground as far as halting is concerned, so you
> > better find another topic you don't know about.
> >
> It has been dead obvious that H(P,P)==0 is the correct halt status for
> the input to H(P,P) on the basis of the actual behavior that this input
> actually specifies.

It is dead obvious to everyone (except you) that H(P,P) == 0 is incorrect because the actual behavior that the input actually specifies is, by the definition of the problem, P(P).

>
> This has been dead obvious on this basis for at least six months, yet my
> reviewers very persistently insisted on simply ignoring the easily
> verifiable facts for this whole six month period.

Projecting. Again. You're the one ignoring verifiable facts, not to mention detailed reasons why you are wrong.

>
> Now my reviewers are playing a "hail Mary" claiming that even though the
> actual behavior of the actual input to H(P,P) actually factually is
> non-halting it is incorrect for H to report that is input is non-halting.

We recognize that you're H isn't mapping the halting function but some other function that you've defined.

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

On 5/13/2022 3:08 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 4:04:48 PM UTC-4, olcott wrote:
>> On 5/13/2022 2:16 PM, Ben wrote:
>>> olcott <No...@NoWhere.com> writes:
>>>
>>>> *Validity and Soundness*
>>>
>>> Good plan. You've run aground as far as halting is concerned, so you
>>> better find another topic you don't know about.
>>>
>> It has been dead obvious that H(P,P)==0 is the correct halt status for
>> the input to H(P,P) on the basis of the actual behavior that this input
>> actually specifies.
>
> It is dead obvious to everyone (except you) that H(P,P) == 0 is incorrect because the actual behavior that the input actually specifies is, by the definition of the problem, P(P).

That is easily shown to be factually incorrect on the basis of the
correct simulation of the input to H(P,P) compared to the direct
execution of P(P). They have empirically proven entirely different
sequences of configurations.

I have no time for people that very persistently insist on ignoring the
easily verifiable facts.

--
Copyright 2022 Pete Olcott

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

On Friday, May 13, 2022 at 4:19:26 PM UTC-4, olcott wrote:
> On 5/13/2022 3:08 PM, Dennis Bush wrote:
> > On Friday, May 13, 2022 at 4:04:48 PM UTC-4, olcott wrote:
> >> On 5/13/2022 2:16 PM, Ben wrote:
> >>> olcott <No...@NoWhere.com> writes:
> >>>
> >>>> *Validity and Soundness*
> >>>
> >>> Good plan. You've run aground as far as halting is concerned, so you
> >>> better find another topic you don't know about.
> >>>
> >> It has been dead obvious that H(P,P)==0 is the correct halt status for
> >> the input to H(P,P) on the basis of the actual behavior that this input
> >> actually specifies.
> >
> > It is dead obvious to everyone (except you) that H(P,P) == 0 is incorrect because the actual behavior that the input actually specifies is, by the definition of the problem, P(P).
> That is easily shown to be factually incorrect

Definitions can't be incorrect. They just "are".

> on the basis of the
> correct simulation of the input to H(P,P) compared to the direct
> execution of P(P).

False, as has been explained many times.

> They have empirically proven entirely different
> sequences of configurations.

Which is just a fancy way of describing how H manages to get the wrong answer.

>
> I have no time for people that very persistently insist on ignoring the
> easily verifiable facts.

So no time for yourself?

On 5/13/2022 3:23 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 4:19:26 PM UTC-4, olcott wrote:
>> On 5/13/2022 3:08 PM, Dennis Bush wrote:
>>> On Friday, May 13, 2022 at 4:04:48 PM UTC-4, olcott wrote:
>>>> On 5/13/2022 2:16 PM, Ben wrote:
>>>>> olcott <No...@NoWhere.com> writes:
>>>>>
>>>>>> *Validity and Soundness*
>>>>>
>>>>> Good plan. You've run aground as far as halting is concerned, so you
>>>>> better find another topic you don't know about.
>>>>>
>>>> It has been dead obvious that H(P,P)==0 is the correct halt status for
>>>> the input to H(P,P) on the basis of the actual behavior that this input
>>>> actually specifies.
>>>
>>> It is dead obvious to everyone (except you) that H(P,P) == 0 is incorrect because the actual behavior that the input actually specifies is, by the definition of the problem, P(P).
>> That is easily shown to be factually incorrect
>
> Definitions can't be incorrect. They just "are".

No two contradictory definitions in the same system can both be correct.

>> on the basis of the
>> correct simulation of the input to H(P,P) compared to the direct
>> execution of P(P).
>
> False, as has been explained many times.
>
>> They have empirically proven entirely different
>> sequences of configurations.
>
> Which is just a fancy way of describing how H manages to get the wrong answer.

That H(P,P) does correctly decide the halt status that its input
specifies make H(P,P)== 0 necessarily correct.

That is does not specify the halt status that you expect makes your
expectation incorrect.

>>
>> I have no time for people that very persistently insist on ignoring the
>> easily verifiable facts.
>
> So no time for yourself?

H(P,P)==0 is proven to be correct empirically in that it does correctly
decide the halt status that its input specifies.

That is does not specify the halt status that you expect makes your
expectation incorrect.

--
Copyright 2022 Pete Olcott

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

On 5/13/22 3:43 PM, olcott wrote:
> On 5/13/2022 2:13 PM, Richard Damon wrote:
>> On 5/13/22 2:10 PM, olcott wrote:
>>> 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.
>>
>
>

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