On 5/21/2023 11:54 AM, Richard Damon wrote:
> On 5/21/23 10:04 AM, olcott wrote:
>> On 5/21/2023 6:57 AM, Richard Damon wrote:
>>> On 5/21/23 12:31 AM, olcott wrote:
>>>> On 5/20/2023 8:49 AM, Richard Damon wrote:
>>>>> On 5/20/23 1:20 AM, olcott wrote:
>>>>>> On 5/19/2023 5:54 PM, Richard Damon wrote:
>>>>>>> On 5/19/23 10:05 AM, olcott wrote:
>>>>>>>> On 5/19/2023 6:31 AM, Richard Damon wrote:
>>>>>>>>> On 5/18/23 10:44 PM, olcott wrote:
>>>>>>>>>> On 5/18/2023 8:37 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/18/23 6:36 PM, olcott wrote:
>>>>>>>>>>>> On 5/18/2023 5:09 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 5/18/23 5:38 PM, olcott wrote:
>>>>>>>>>>>>>> On 5/18/2023 4:27 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>> On 2023-05-18 15:11, olcott wrote:
>>>>>>>>>>>>>>>> On 5/18/2023 4:04 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>> On 2023-05-18 14:42, olcott wrote:
>>>>>>>>>>>>>>>>>> On 5/18/2023 3:34 PM, Andy Walker wrote:
>>>>>>>>>>>>>>>>>>> On 18/05/2023 20:35, olcott wrote:
>>>>>>>>>>>>>>>>>>>> We can say that we know that it is true that the
>>>>>>>>>>>>>>>>>>>> Goldbach conjecture is
>>>>>>>>>>>>>>>>>>>> true or false, yet no one and nothing can determine
>>>>>>>>>>>>>>>>>>>> which.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>      You can /say/ whatever you like, but (a) the
>>>>>>>>>>>>>>>>>>> phrase "it is true that
>>>>>>>>>>>>>>>>>>> X" adds nothing to "X", and (b) for the specific case
>>>>>>>>>>>>>>>>>>> of the GC, your phrase
>>>>>>>>>>>>>>>>>>> "yet no one ... which" is [manifestly] unprovable, so
>>>>>>>>>>>>>>>>>>> what you say is not as
>>>>>>>>>>>>>>>>>>> interesting as you might think.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> When we defeat Tarski then Chat Bots will be able to
>>>>>>>>>>>>>>>>>> distinguish between
>>>>>>>>>>>>>>>>>> true and false and take on each and every
>>>>>>>>>>>>>>>>>> disinformation post on social
>>>>>>>>>>>>>>>>>> media and refute it every which way before the
>>>>>>>>>>>>>>>>>> disinformation has any
>>>>>>>>>>>>>>>>>> chance to take hold.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Your position here is entirely incoherent since you
>>>>>>>>>>>>>>>>> claim that your focus is solely on 'analytic knowledge'.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I define analytic knowledge as any expression of formal
>>>>>>>>>>>>>>>> or natural
>>>>>>>>>>>>>>>> language that is true by definition. A correct model of
>>>>>>>>>>>>>>>> the world has
>>>>>>>>>>>>>>>> all of the essential details of the world described and
>>>>>>>>>>>>>>>> or defined
>>>>>>>>>>>>>>>> using language.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> So in exactly what sense is a claim like "there was no
>>>>>>>>>>>>>>> widespread election fraud in 2020" true by definition?
>>>>>>>>>>>>>>> Which exact definitions do you think lead the above to be
>>>>>>>>>>>>>>> true?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> There is no evidence that has ever been presented of
>>>>>>>>>>>>>> widespread election
>>>>>>>>>>>>>> fraud that could have possibly changed the outcome of the
>>>>>>>>>>>>>> 2020
>>>>>>>>>>>>>> presidential election from any source what-so-ever.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> But that doesn't make it "True By Definition", it makes it
>>>>>>>>>>>>> True by Empirical fact.
>>>>>>>>>>>>
>>>>>>>>>>>> True by the definition of the complete model of the world
>>>>>>>>>>>> that includes
>>>>>>>>>>>> every detail of general knowledge that can be expressed
>>>>>>>>>>>> using language.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> But that make it Empirical Truth, not Analytic.
>>>>>>>>>>>
>>>>>>>>>>> You just don't seem to actually understand what that means.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> The complete and correct model of the world includes things
>>>>>>>>>> that have at
>>>>>>>>>> one time been validated by the sense organs. That rainbows
>>>>>>>>>> have more
>>>>>>>>>> than one color is analytical this is provided by the
>>>>>>>>>> definition of
>>>>>>>>>> rainbow.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> So, you are removing the analyitical / synthetic-emperical
>>>>>>>>> distinction from your logic system.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Any expression of language that requires direct and immediate
>>>>>>>> sense data
>>>>>>>> from the sense organs to verify the truth of the current
>>>>>>>> situation is
>>>>>>>> still construed as empirical.
>>>>>>>>
>>>>>>>> Analytic is every expression of language that an AI mind could
>>>>>>>> analyze.
>>>>>>>
>>>>>>> But, by your logic, once a Human uses his senses to verify that
>>>>>>> data, it becomes "Human Knowledge" and entered into the database,
>>>>>>> and becomes analytical. Maybe not about "Now", but is about 5
>>>>>>> minutes ago.
>>>>>>>
>>>>>>
>>>>>> You are correct that the vetting process has not been defined yet.
>>>>>> Because I want an honest dialogue it is best to acknowledge the
>>>>>> current
>>>>>> limitations. That provides a road map into the future.
>>>>>>
>>>>>> What are the boundary conditions and the criteria to know what you
>>>>>> know?
>>>>>> How do stipulated truths get vetted?
>>>>>>
>>>>>
>>>>> But why do you just ignore the definition of things and
>>>>> fundamentally change them. That, in effect, distroys a lot of
>>>>> "knowledge" as it no longer applies to your system.
>>>>>
>>>>
>>>> Correct reasoning must establish a new foundation to correct the
>>>> cases where logic diverges from correct reasoning.
>>>
>>> So, since you aren't using the logic of the proofs you are taliking
>>> about, you aren't using "correct reasoning" at all.
>>>
>>>>
>>>> The system that enables incompleteness and undefinability must be
>>>> corrected.
>>>
>>> So do so, which means you start at the beginning, not the end. Your
>>> current path is just showing fundamental errors in logic, as you
>>> start from positions that haven't been proven to be true in your
>>> logic system.
>>>
>>
>> When analytically true means
>> (a) Finite strings are stipulated to have the semantic property of
>> Boolean true.
>>
>> Only by stipulating relations between finite strings do finite strings
>> acquire semantic meaning otherwise they remain meaningless. All of these
>> stipulated relations are stipulated to have the semantic property of
>> Boolean true.
>>
>> (b) Finite strings are semantically deduced from the above set
>
> Which is basically how "Standard Logic" works, depending on how you are
> trying to define "semantically deduced", which is something you seem to
> be unable to do, probably because you don't understand what you are
> saying well enough.

On 5/21/23 2:24 PM, olcott wrote:
> On 5/21/2023 11:54 AM, Richard Damon wrote:
>> On 5/21/23 10:04 AM, olcott wrote:
>>> On 5/21/2023 6:57 AM, Richard Damon wrote:
>>>> On 5/21/23 12:31 AM, olcott wrote:
>>>>> On 5/20/2023 8:49 AM, Richard Damon wrote:
>>>>>> On 5/20/23 1:20 AM, olcott wrote:
>>>>>>> On 5/19/2023 5:54 PM, Richard Damon wrote:
>>>>>>>> On 5/19/23 10:05 AM, olcott wrote:
>>>>>>>>> On 5/19/2023 6:31 AM, Richard Damon wrote:
>>>>>>>>>> On 5/18/23 10:44 PM, olcott wrote:
>>>>>>>>>>> On 5/18/2023 8:37 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/18/23 6:36 PM, olcott wrote:
>>>>>>>>>>>>> On 5/18/2023 5:09 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 5/18/23 5:38 PM, olcott wrote:
>>>>>>>>>>>>>>> On 5/18/2023 4:27 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>> On 2023-05-18 15:11, olcott wrote:
>>>>>>>>>>>>>>>>> On 5/18/2023 4:04 PM, André G. Isaak wrote:
>>>>>>>>>>>>>>>>>> On 2023-05-18 14:42, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 5/18/2023 3:34 PM, Andy Walker wrote:
>>>>>>>>>>>>>>>>>>>> On 18/05/2023 20:35, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> We can say that we know that it is true that the
>>>>>>>>>>>>>>>>>>>>> Goldbach conjecture is
>>>>>>>>>>>>>>>>>>>>> true or false, yet no one and nothing can determine
>>>>>>>>>>>>>>>>>>>>> which.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>      You can /say/ whatever you like, but (a) the
>>>>>>>>>>>>>>>>>>>> phrase "it is true that
>>>>>>>>>>>>>>>>>>>> X" adds nothing to "X", and (b) for the specific
>>>>>>>>>>>>>>>>>>>> case of the GC, your phrase
>>>>>>>>>>>>>>>>>>>> "yet no one ... which" is [manifestly] unprovable,
>>>>>>>>>>>>>>>>>>>> so what you say is not as
>>>>>>>>>>>>>>>>>>>> interesting as you might think.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> When we defeat Tarski then Chat Bots will be able to
>>>>>>>>>>>>>>>>>>> distinguish between
>>>>>>>>>>>>>>>>>>> true and false and take on each and every
>>>>>>>>>>>>>>>>>>> disinformation post on social
>>>>>>>>>>>>>>>>>>> media and refute it every which way before the
>>>>>>>>>>>>>>>>>>> disinformation has any
>>>>>>>>>>>>>>>>>>> chance to take hold.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Your position here is entirely incoherent since you
>>>>>>>>>>>>>>>>>> claim that your focus is solely on 'analytic knowledge'.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I define analytic knowledge as any expression of formal
>>>>>>>>>>>>>>>>> or natural
>>>>>>>>>>>>>>>>> language that is true by definition. A correct model of
>>>>>>>>>>>>>>>>> the world has
>>>>>>>>>>>>>>>>> all of the essential details of the world described and
>>>>>>>>>>>>>>>>> or defined
>>>>>>>>>>>>>>>>> using language.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So in exactly what sense is a claim like "there was no
>>>>>>>>>>>>>>>> widespread election fraud in 2020" true by definition?
>>>>>>>>>>>>>>>> Which exact definitions do you think lead the above to
>>>>>>>>>>>>>>>> be true?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> There is no evidence that has ever been presented of
>>>>>>>>>>>>>>> widespread election
>>>>>>>>>>>>>>> fraud that could have possibly changed the outcome of the
>>>>>>>>>>>>>>> 2020
>>>>>>>>>>>>>>> presidential election from any source what-so-ever.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But that doesn't make it "True By Definition", it makes it
>>>>>>>>>>>>>> True by Empirical fact.
>>>>>>>>>>>>>
>>>>>>>>>>>>> True by the definition of the complete model of the world
>>>>>>>>>>>>> that includes
>>>>>>>>>>>>> every detail of general knowledge that can be expressed
>>>>>>>>>>>>> using language.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> But that make it Empirical Truth, not Analytic.
>>>>>>>>>>>>
>>>>>>>>>>>> You just don't seem to actually understand what that means.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> The complete and correct model of the world includes things
>>>>>>>>>>> that have at
>>>>>>>>>>> one time been validated by the sense organs. That rainbows
>>>>>>>>>>> have more
>>>>>>>>>>> than one color is analytical this is provided by the
>>>>>>>>>>> definition of
>>>>>>>>>>> rainbow.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, you are removing the analyitical / synthetic-emperical
>>>>>>>>>> distinction from your logic system.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Any expression of language that requires direct and immediate
>>>>>>>>> sense data
>>>>>>>>> from the sense organs to verify the truth of the current
>>>>>>>>> situation is
>>>>>>>>> still construed as empirical.
>>>>>>>>>
>>>>>>>>> Analytic is every expression of language that an AI mind could
>>>>>>>>> analyze.
>>>>>>>>
>>>>>>>> But, by your logic, once a Human uses his senses to verify that
>>>>>>>> data, it becomes "Human Knowledge" and entered into the
>>>>>>>> database, and becomes analytical. Maybe not about "Now", but is
>>>>>>>> about 5 minutes ago.
>>>>>>>>
>>>>>>>
>>>>>>> You are correct that the vetting process has not been defined yet.
>>>>>>> Because I want an honest dialogue it is best to acknowledge the
>>>>>>> current
>>>>>>> limitations. That provides a road map into the future.
>>>>>>>
>>>>>>> What are the boundary conditions and the criteria to know what
>>>>>>> you know?
>>>>>>> How do stipulated truths get vetted?
>>>>>>>
>>>>>>
>>>>>> But why do you just ignore the definition of things and
>>>>>> fundamentally change them. That, in effect, distroys a lot of
>>>>>> "knowledge" as it no longer applies to your system.
>>>>>>
>>>>>
>>>>> Correct reasoning must establish a new foundation to correct the
>>>>> cases where logic diverges from correct reasoning.
>>>>
>>>> So, since you aren't using the logic of the proofs you are taliking
>>>> about, you aren't using "correct reasoning" at all.
>>>>
>>>>>
>>>>> The system that enables incompleteness and undefinability must be
>>>>> corrected.
>>>>
>>>> So do so, which means you start at the beginning, not the end. Your
>>>> current path is just showing fundamental errors in logic, as you
>>>> start from positions that haven't been proven to be true in your
>>>> logic system.
>>>>
>>>
>>> When analytically true means
>>> (a) Finite strings are stipulated to have the semantic property of
>>> Boolean true.
>>>
>>> Only by stipulating relations between finite strings do finite strings
>>> acquire semantic meaning otherwise they remain meaningless. All of these
>>> stipulated relations are stipulated to have the semantic property of
>>> Boolean true.
>>>
>>> (b) Finite strings are semantically deduced from the above set
>>
>> Which is basically how "Standard Logic" works, depending on how you
>> are trying to define "semantically deduced", which is something you
>> seem to be unable to do, probably because you don't understand what
>> you are saying well enough.
>
> If standard logic was correct then we could say that because you
> contradict yourself we can know that what you are saying is true.
> https://en.wikipedia.org/wiki/Principle_of_explosion
>
>>>
>>> Undefinability and incompleteness cannot occur
>>
>> Nope, because for the ACTUAL definitions of Truth, (b) allows for an
>> infinite sequences of deductions, while "Proof" and "Knowledge"
>> require a finite sequence.
>>
>
> I did not limit semantically deduced to finite steps.
>
>> You also don't seem to understand what Tarski means by "undefinable",
>> which just seems par for the course, he means there does not exist a
>> proper "definition" of a predicate that allows for the determination
>> of the truth of a statement.
>>
>
> Yes that is exactly what he means.
> Because his proof is based on the liar paradox this is like saying that
> a baker cannot bake cakes because they cannot bake cakes using only red
> house bricks for ingredients.
>
>>>
>>> When an expression of language is neither of the above two then it is
>>> simply untrue. The Liar Paradox is simply untrue, likewise with an
>>> expression within a formal system that asserts its own unprovability
>>> within this same formal system.
>>
>> But then you are saying the Empirical Truth is "Untrue".
>>
>> Yes, a statement that MERELY asserts its own unprovability can not be
>> proven to be True (but can be proven to not be False),
>
> You are merely saying that self-contradictory expressions of language
> are not truth bearers.
>
> <snip>
>
>>>
>>> ?- LP = not(true(LP)).
>>> LP = not(true(LP)).
>>>
>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>> false.
>>>
>>> Outside the scope of pathological self-reference the same
>>> expression may become true:
>>> This sentence is not true: "This sentence is not true" is true
>>>
>>> Prolog is only detecting and rejecting the pathological
>>> self-reference the same expression could be encoded as:
>>>
>>> ?- X = foo(bar(X)).
>>> X = foo(bar(X)).
>>>
>>> ?- unify_with_occurs_check(X, foo(bar(X))).
>>> false.
>>>
>>>
>>
>> But Prolog doesn't have the power to handle the logic you are refering
>> to (unless that is all the power of your system, at which point it
>> isn't powerful enough to handle any of the proofs you are talking about).
>
> Prolog does have the power to reject the Liar Paradox along with every
> other simple expression having pathological self-reference (Olcott 2004).
>
>

On 2023-05-21 12:24, olcott wrote:

> If standard logic was correct then we could say that because you
> contradict yourself we can know that what you are saying is true.
> https://en.wikipedia.org/wiki/Principle_of_explosion

That, of course, is not even remotely what the principle of explosion says.

André

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

On 5/21/2023 2:27 PM, André G. Isaak wrote:
> On 2023-05-21 12:24, olcott wrote:
>
>> If standard logic was correct then we could say that because you
>> contradict yourself we can know that what you are saying is true.
>> https://en.wikipedia.org/wiki/Principle_of_explosion
>
> That, of course, is not even remotely what the principle of explosion says.
>
> André
>

In classical logic, intuitionistic logic and similar logical systems,
the principle of explosion (Latin: ex falso [sequitur] quodlibet, 'from
falsehood, anything [follows]'; or ex contradictione [sequitur]
quodlibet, 'from contradiction, anything [follows]'), or the principle
of Pseudo-Scotus (falsely attributed to Duns Scotus), is the law
according to which any statement can be proven from a contradiction.[1]
That is, once a contradiction has been asserted, any proposition
(including their negations) can be inferred from it; this is known as
deductive explosion.[2][3]

Thus (according to the quote above) Richard's contradictions prove that
he is telling the truth.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/21/23 3:32 PM, olcott wrote:
> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>> On 2023-05-21 12:24, olcott wrote:
>>
>>> If standard logic was correct then we could say that because you
>>> contradict yourself we can know that what you are saying is true.
>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> That, of course, is not even remotely what the principle of explosion
>> says.
>>
>> André
>>
>
> In classical logic, intuitionistic logic and similar logical systems,
> the principle of explosion (Latin: ex falso [sequitur] quodlibet, 'from
> falsehood, anything [follows]'; or ex contradictione [sequitur]
> quodlibet, 'from contradiction, anything [follows]'), or the principle
> of Pseudo-Scotus (falsely attributed to Duns Scotus), is the law
> according to which any statement can be proven from a contradiction.[1]
> That is, once a contradiction has been asserted, any proposition
> (including their negations) can be inferred from it; this is known as
> deductive explosion.[2][3]
>
> Thus (according to the quote above) Richard's contradictions prove that
> he is telling the truth.
>
>

Yes, once a logic system (of very minimal logical power) admits one
contradiction as Truth, the system can prove any statement that can be
expressed in that system, and its opposite.

You clearly don't understand this, as you say that your logic system is
immune to it, which can't happen unless your system follows those very
strict limitations.

You don't quite understand what that means, because it isn't just having
a contradition that causes the explosion, but establishing that both
sides of a contraction are true.

On 5/21/2023 2:46 PM, Richard Damon wrote:
> On 5/21/23 3:32 PM, olcott wrote:
>> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>>> On 2023-05-21 12:24, olcott wrote:
>>>
>>>> If standard logic was correct then we could say that because you
>>>> contradict yourself we can know that what you are saying is true.
>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>
>>> That, of course, is not even remotely what the principle of explosion
>>> says.
>>>
>>> André
>>>
>>
>> In classical logic, intuitionistic logic and similar logical systems,
>> the principle of explosion (Latin: ex falso [sequitur] quodlibet,
>> 'from falsehood, anything [follows]'; or ex contradictione [sequitur]
>> quodlibet, 'from contradiction, anything [follows]'), or the principle
>> of Pseudo-Scotus (falsely attributed to Duns Scotus), is the law
>> according to which any statement can be proven from a
>> contradiction.[1] That is, once a contradiction has been asserted, any
>> proposition (including their negations) can be inferred from it; this
>> is known as deductive explosion.[2][3]
>>
>> Thus (according to the quote above) Richard's contradictions prove
>> that he is telling the truth.
>>
>>
>
> Yes, once a logic system (of very minimal logical power) admits one
> contradiction as Truth, the system can prove any statement that can be
> expressed in that system, and its opposite.
>

You don't understand that admitting any contradiction as truth is a
grievous error ?

I am beginning to think that the human mind is hardwired to short-
circuit. I can't understand how this this POE nonsense wasn't put down
within two weeks of its first presentation.

> You clearly don't understand this, as you say that your logic system is
> immune to it, which can't happen unless your system follows those very
> strict limitations.
>
> You don't quite understand what that means, because it isn't just having
> a contradition that causes the explosion, but establishing that both
> sides of a contraction are true.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2023-05-21 13:32, olcott wrote:
> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>> On 2023-05-21 12:24, olcott wrote:
>>
>>> If standard logic was correct then we could say that because you
>>> contradict yourself we can know that what you are saying is true.
>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>
>> That, of course, is not even remotely what the principle of explosion
>> says.
>>
>> André
>>
>
> In classical logic, intuitionistic logic and similar logical systems,
> the principle of explosion (Latin: ex falso [sequitur] quodlibet, 'from
> falsehood, anything [follows]'; or ex contradictione [sequitur]
> quodlibet, 'from contradiction, anything [follows]'), or the principle
> of Pseudo-Scotus (falsely attributed to Duns Scotus), is the law
> according to which any statement can be proven from a contradiction.[1]
> That is, once a contradiction has been asserted, any proposition
> (including their negations) can be inferred from it; this is known as
> deductive explosion.[2][3]
>
> Thus (according to the quote above) Richard's contradictions prove that
> he is telling the truth.

I'm perfectly aware that you are capable of quoting things. But you
don't seem to understand what you are quoting.

Stating a contradiction doesn't make the contradiction true. The
principle of explosion basically asserts that if one actually COULD
establish the truth of contradictory statements then all hell would
break loose, which is why any system of logic which purports to be
useful must ensure that this cannot happen.

(A & ¬A) -> B

tells us NOTHING WHATSOEVER about the truth of B unless we can
simultaneously demonstrate that A is true AND that ¬A is true. In any
system which is not fundamentally broken, that should be impossible to do.

André

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

On 5/21/2023 4:13 PM, André G. Isaak wrote:
> On 2023-05-21 13:32, olcott wrote:
>> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>>> On 2023-05-21 12:24, olcott wrote:
>>>
>>>> If standard logic was correct then we could say that because you
>>>> contradict yourself we can know that what you are saying is true.
>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>
>>> That, of course, is not even remotely what the principle of explosion
>>> says.
>>>
>>> André
>>>
>>
>> In classical logic, intuitionistic logic and similar logical systems,
>> the principle of explosion (Latin: ex falso [sequitur] quodlibet,
>> 'from falsehood, anything [follows]'; or ex contradictione [sequitur]
>> quodlibet, 'from contradiction, anything [follows]'), or the principle
>> of Pseudo-Scotus (falsely attributed to Duns Scotus), is the law
>> according to which any statement can be proven from a
>> contradiction.[1] That is, once a contradiction has been asserted, any
>> proposition (including their negations) can be inferred from it; this
>> is known as deductive explosion.[2][3]
>>
>> Thus (according to the quote above) Richard's contradictions prove
>> that he is telling the truth.
>
> I'm perfectly aware that you are capable of quoting things. But you
> don't seem to understand what you are quoting.
>
> Stating a contradiction doesn't make the contradiction true. The
> principle of explosion basically asserts that if one actually COULD
> establish the truth of contradictory statements then all hell would
> break loose, which is why any system of logic which purports to be
> useful must ensure that this cannot happen.
>

*That is not even close to what the quote actually says*

once a contradiction has been asserted, any
proposition (including their negations) can
be inferred from it

This is a much better way to eliminate explosion.
(A ∧ ¬A) ⊢ ⊥
⊥ ⊢ ⊥

> (A & ¬A) -> B
>
> tells us NOTHING WHATSOEVER about the truth of B unless we can
> simultaneously demonstrate that A is true AND that ¬A is true. In any
> system which is not fundamentally broken, that should be impossible to do.
>
> André
>

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/21/23 4:26 PM, olcott wrote:
> You don't understand that admitting any contradiction as truth is a
> grievous error ?
>

So asserting that a computation that Halts can be declared non-halting
by a simulating halt decider is a grievous error.

Since the halting of the actual machine can be established by running it.

If it is consider proven that H saying it is non-halting is also
correct, you are just admitting to a contradiction.

On 2023-05-21 15:25, olcott wrote:
> On 5/21/2023 4:13 PM, André G. Isaak wrote:
>> On 2023-05-21 13:32, olcott wrote:
>>> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>>>> On 2023-05-21 12:24, olcott wrote:
>>>>
>>>>> If standard logic was correct then we could say that because you
>>>>> contradict yourself we can know that what you are saying is true.
>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>
>>>> That, of course, is not even remotely what the principle of
>>>> explosion says.
>>>>
>>>> André
>>>>
>>>
>>> In classical logic, intuitionistic logic and similar logical systems,
>>> the principle of explosion (Latin: ex falso [sequitur] quodlibet,
>>> 'from falsehood, anything [follows]'; or ex contradictione [sequitur]
>>> quodlibet, 'from contradiction, anything [follows]'), or the
>>> principle of Pseudo-Scotus (falsely attributed to Duns Scotus), is
>>> the law according to which any statement can be proven from a
>>> contradiction.[1] That is, once a contradiction has been asserted,
>>> any proposition (including their negations) can be inferred from it;
>>> this is known as deductive explosion.[2][3]
>>>
>>> Thus (according to the quote above) Richard's contradictions prove
>>> that he is telling the truth.
>>
>> I'm perfectly aware that you are capable of quoting things. But you
>> don't seem to understand what you are quoting.
>>
>> Stating a contradiction doesn't make the contradiction true. The
>> principle of explosion basically asserts that if one actually COULD
>> establish the truth of contradictory statements then all hell would
>> break loose, which is why any system of logic which purports to be
>> useful must ensure that this cannot happen.
>>
>
> *That is not even close to what the quote actually says*
>
>    once a contradiction has been asserted, any
>    proposition (including their negations) can
>    be inferred from it

Which contradicts nothing which I said.

> This is a much better way to eliminate explosion.
> (A ∧ ¬A) ⊢ ⊥
> ⊥ ⊢ ⊥

The principle of explosion follows directly from the truth tables
associated with AND, OR, and NOT whereas ((A ∧ ¬A) ⊢ ⊥) does not. The
latter would only hold in a system which redefines at least one of these
three operators. Which are you proposing to change?

André

--
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On 5/21/23 5:25 PM, olcott wrote:
> *That is not even close to what the quote actually says*
>
>    once a contradiction has been asserted, any
>    proposition (including their negations) can
>    be inferred from it
>
> This is a much better way to eliminate explosion.
> (A ∧ ¬A) ⊢ ⊥
> ⊥ ⊢ ⊥
>

You realize that asserting that A and not A is false doesn't actually do
anything, as rules don't "automaticaaly fire" just because they are
statisifed, so having a rule that says no contradictions allowed doesn't
actually make that happen.

In fact, the definition of NOT says that A and not A can't both be true
at once, except that rule doesn't actually work that way.

The prover gets to choose what rules he applies at each step, and gets
the result defined by the rules.

The point of the principle of explosion is that once you have added some
truthmaker that allows you to make a proof of both a statement and its
complement, the system is broken, and a natural result of this is that
everything becomes true and everything becomes false.

The system was broken as soon as the bad truthmaker was inserted, the
problem is only discovered when you can find one of the contradictions
it can produce.

On 5/21/2023 5:08 PM, André G. Isaak wrote:
> On 2023-05-21 15:25, olcott wrote:
>> On 5/21/2023 4:13 PM, André G. Isaak wrote:
>>> On 2023-05-21 13:32, olcott wrote:
>>>> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>>>>> On 2023-05-21 12:24, olcott wrote:
>>>>>
>>>>>> If standard logic was correct then we could say that because you
>>>>>> contradict yourself we can know that what you are saying is true.
>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>
>>>>> That, of course, is not even remotely what the principle of
>>>>> explosion says.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> In classical logic, intuitionistic logic and similar logical
>>>> systems, the principle of explosion (Latin: ex falso [sequitur]
>>>> quodlibet, 'from falsehood, anything [follows]'; or ex
>>>> contradictione [sequitur] quodlibet, 'from contradiction, anything
>>>> [follows]'), or the principle of Pseudo-Scotus (falsely attributed
>>>> to Duns Scotus), is the law according to which any statement can be
>>>> proven from a contradiction.[1] That is, once a contradiction has
>>>> been asserted, any proposition (including their negations) can be
>>>> inferred from it; this is known as deductive explosion.[2][3]
>>>>
>>>> Thus (according to the quote above) Richard's contradictions prove
>>>> that he is telling the truth.
>>>
>>> I'm perfectly aware that you are capable of quoting things. But you
>>> don't seem to understand what you are quoting.
>>>
>>> Stating a contradiction doesn't make the contradiction true. The
>>> principle of explosion basically asserts that if one actually COULD
>>> establish the truth of contradictory statements then all hell would
>>> break loose, which is why any system of logic which purports to be
>>> useful must ensure that this cannot happen.
>>>
>>
>> *That is not even close to what the quote actually says*
>>
>>     once a contradiction has been asserted, any
>>     proposition (including their negations) can
>>     be inferred from it
>
> Which contradicts nothing which I said.
>
>> This is a much better way to eliminate explosion.
>> (A ∧ ¬A) ⊢ ⊥
>> ⊥ ⊢ ⊥
>
> The principle of explosion follows directly from the truth tables
> associated with AND, OR, and NOT whereas ((A ∧ ¬A) ⊢ ⊥) does not.

Because ⊥ is another name for F: (A ∧ ¬A) ⊢ ⊥
A ¬A A ∧ ¬A
T F F
F T F

Thus when the text says P, ¬P ⊢ Q it forgot to resolve A ∧ ¬A ⊢ False

Step Proposition Derivation
1 P Assumption
2 ¬P Assumption
3 P ∨ Q Disjunction introduction (1)
4 Q Disjunctive syllogism (3,2)

Disjunction introduction (False ∨ Q) ⊢ Q is not the way that correct
reasoning really works. *That may be the key error*

If you know that Q is true to begin with there is no need for
Disjunction introduction.

If you don't know that Q is true to begin with then Disjunction
introduction is not a truth preserving operation it transforms an
unknown truth value into true.

> The
> latter would only hold in a system which redefines at least one of these
> three operators. Which are you proposing to change?
>
> André
>

I read further along in the article are you were correct.
P, ¬P ⊢ ⊥ For any statements P and Q, if P and not-P are both true,
then it logically follows that Q is true.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 5/21/23 6:37 PM, olcott wrote:
> On 5/21/2023 5:08 PM, André G. Isaak wrote:
>> On 2023-05-21 15:25, olcott wrote:
>>> On 5/21/2023 4:13 PM, André G. Isaak wrote:
>>>> On 2023-05-21 13:32, olcott wrote:
>>>>> On 5/21/2023 2:27 PM, André G. Isaak wrote:
>>>>>> On 2023-05-21 12:24, olcott wrote:
>>>>>>
>>>>>>> If standard logic was correct then we could say that because you
>>>>>>> contradict yourself we can know that what you are saying is true.
>>>>>>> https://en.wikipedia.org/wiki/Principle_of_explosion
>>>>>>
>>>>>> That, of course, is not even remotely what the principle of
>>>>>> explosion says.
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> In classical logic, intuitionistic logic and similar logical
>>>>> systems, the principle of explosion (Latin: ex falso [sequitur]
>>>>> quodlibet, 'from falsehood, anything [follows]'; or ex
>>>>> contradictione [sequitur] quodlibet, 'from contradiction, anything
>>>>> [follows]'), or the principle of Pseudo-Scotus (falsely attributed
>>>>> to Duns Scotus), is the law according to which any statement can be
>>>>> proven from a contradiction.[1] That is, once a contradiction has
>>>>> been asserted, any proposition (including their negations) can be
>>>>> inferred from it; this is known as deductive explosion.[2][3]
>>>>>
>>>>> Thus (according to the quote above) Richard's contradictions prove
>>>>> that he is telling the truth.
>>>>
>>>> I'm perfectly aware that you are capable of quoting things. But you
>>>> don't seem to understand what you are quoting.
>>>>
>>>> Stating a contradiction doesn't make the contradiction true. The
>>>> principle of explosion basically asserts that if one actually COULD
>>>> establish the truth of contradictory statements then all hell would
>>>> break loose, which is why any system of logic which purports to be
>>>> useful must ensure that this cannot happen.
>>>>
>>>
>>> *That is not even close to what the quote actually says*
>>>
>>>     once a contradiction has been asserted, any
>>>     proposition (including their negations) can
>>>     be inferred from it
>>
>> Which contradicts nothing which I said.
>>
>>> This is a much better way to eliminate explosion.
>>> (A ∧ ¬A) ⊢ ⊥
>>> ⊥ ⊢ ⊥
>>
>> The principle of explosion follows directly from the truth tables
>> associated with AND, OR, and NOT whereas ((A ∧ ¬A) ⊢ ⊥) does not.
>
> Because ⊥ is another name for F: (A ∧ ¬A) ⊢ ⊥
> A    ¬A    A ∧ ¬A
> T    F    F
> F    T    F
>
> Thus when the text says P, ¬P ⊢ Q it forgot to resolve A ∧ ¬A ⊢ False

There is no requirement to "resolve" all possible rules.

ANd the issue isn't some one just asseerting P and ~P, the issue is when
you can PROVE both P and ~P from your axioms.

>
> Step    Proposition    Derivation
> 1    P        Assumption
> 2    ¬P        Assumption
> 3    P ∨ Q       Disjunction introduction (1)
> 4    Q        Disjunctive syllogism (3,2)

And there's your problem, it doesn't come from "Assumptions" but by P
and ~P being PROVED from other propositions in the system.

>
> Disjunction introduction (False ∨ Q) ⊢ Q is not the way that correct
> reasoning really works. *That may be the key error*

So, if you can prove that (False ∨ Q) IS true, what other value can Q
have other than True?

You problem is you keep on thinking these thing come from ASSUMPTIONS,
but they don't, the come from previous proofs.

Maybe that shows the level of your own logic, you need to assume too
much (like everything)

>
> If you know that Q is true to begin with there is no need for
> Disjunction introduction.
>
> If you don't know that Q is true to begin with then Disjunction
> introduction is not a truth preserving operation it transforms an
> unknown truth value into true.

Only if you are working in a very limited logic system.

If we have established that A or B must be true, and then we establish
that A must be false, what value can B have other than True?

That IS considered Truth Perserving in most logic system.

Yes, there are some very restrictive systems that do not allow a premise
to be "non-atomic" (I.E, the and/or of multiple terms) but these system
become very limited and can only handle simpler logic, as even the First
Order logic operations of For All X, or there Exist an X have to be
removed as those are, in effect, non-atomic.

>
>> The latter would only hold in a system which redefines at least one of
>> these three operators. Which are you proposing to change?
>>
>> André
>>
>
> I read further along in the article are you were correct.
> P, ¬P ⊢ ⊥ For any statements P and Q, if P and not-P are both true,
> then it logically follows that Q is true.
>
>
>