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devel / comp.theory / Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

SubjectAuthor
* Correcting logic to make it a system of correct reasoningolcott
+* Correcting logic to make it a system of correct reasoningRichard Damon
|+* Correcting logic to make it a system of correct reasoningolcott
||`* Correcting logic to make it a system of correct reasoningRichard Damon
|| `* Correcting logic to make it a system of correct reasoningolcott
||  `* Correcting logic to make it a system of correct reasoningRichard Damon
||   `* Correcting logic to make it a system of correct reasoningolcott
||    `* Correcting logic to make it a system of correct reasoningRichard Damon
||     `* Correcting logic to make it a system of correct reasoningolcott
||      `* Correcting logic to make it a system of correct reasoningRichard Damon
||       `* Correcting logic to make it a system of correct reasoningolcott
||        `* Correcting logic to make it a system of correct reasoningRichard Damon
||         `* Correcting logic to make it a system of correct reasoningolcott
||          `- Correcting logic to make it a system of correct reasoningRichard Damon
|`- Correcting logic to make it a system of correct reasoningJeff Barnett
+* Correcting logic to make it a system of correct reasoningAndré G. Isaak
|`* Correcting logic to make it a system of correct reasoningolcott
| `* Correcting logic to make it a system of correct reasoningAndré G. Isaak
|  +* Correcting logic to make it a system of correct reasoningolcott
|  |+* Correcting logic to make it a system of correct reasoningAndré G. Isaak
|  ||`* Correcting logic to make it a system of correct reasoningolcott
|  || `* Correcting logic to make it a system of correct reasoningAndré G. Isaak
|  ||  `* Correcting logic to make it a system of correct reasoningolcott
|  ||   `- Correcting logic to make it a system of correct reasoningRichard Damon
|  |`* Correcting logic to make it a system of correct reasoningRichard Damon
|  | `* Correcting logic to make it a system of correct reasoningolcott
|  |  `* Correcting logic to make it a system of correct reasoningRichard Damon
|  |   `* Correcting logic to make it a system of correct reasoningolcott
|  |    `- Correcting logic to make it a system of correct reasoningRichard Damon
|  `* Correcting logic to make it a system of correct reasoningBen
|   `- Correcting logic to make it a system of correct reasoningolcott
`* Correcting logic to make it a system of correct reasoningBen
 `* Correcting logic to make it a system of correct reasoningolcott
  +* Correcting logic to make it a system of correct reasoningDennis Bush
  |`* Correcting logic to make it a system of correct reasoningolcott
  | `* Correcting logic to make it a system of correct reasoningDennis Bush
  |  `* Correcting logic to make it a system of correct reasoningolcott
  |   +* Correcting logic to make it a system of correct reasoningDennis Bush
  |   |`* Correcting logic to make it a system of correct reasoning [ veryolcott
  |   | `* Correcting logic to make it a system of correct reasoning [ veryDennis Bush
  |   |  `* Correcting logic to make it a system of correct reasoning [ veryolcott
  |   |   `* Correcting logic to make it a system of correct reasoning [ veryDennis Bush
  |   |    `* Correcting logic to make it a system of correct reasoning [olcott
  |   |     `* Correcting logic to make it a system of correct reasoning [Dennis Bush
  |   |      `* Correcting logic to make it a system of correct reasoning [olcott
  |   |       `* Correcting logic to make it a system of correct reasoning [Dennis Bush
  |   |        +- Correcting logic to make it a system of correct reasoning [Richard Damon
  |   |        `* Correcting logic to make it a system of correct reasoning [olcott
  |   |         `* Correcting logic to make it a system of correct reasoning [Dennis Bush
  |   |          `* Correcting logic to make it a system of correct reasoning [olcott
  |   |           `- Correcting logic to make it a system of correct reasoning [Dennis Bush
  |   `- Correcting logic to make it a system of correct reasoningRichard Damon
  `* Correcting logic to make it a system of correct reasoningBen
   `* Correcting logic to make it a system of correct reasoning [olcott
    +- Correcting logic to make it a system of correct reasoning [Richard Damon
    `* Correcting logic to make it a system of correct reasoning [ previously undiscoveBen
     `* Correcting logic to make it a system of correct reasoning [olcott
      +* Correcting logic to make it a system of correct reasoning [ previously undiscoveRichard Damon
      |`* Correcting logic to make it a system of correct reasoning [olcott
      | `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |  `* Correcting logic to make it a system of correct reasoning [olcott
      |   `* Correcting logic to make it a system of correct reasoning [ philosophical underpRichard Damon
      |    `* Correcting logic to make it a system of correct reasoning [olcott
      |     `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |      `* Correcting logic to make it a system of correct reasoning [olcott
      |       `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |        `* Correcting logic to make it a system of correct reasoning [olcott
      |         `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |          `* Correcting logic to make it a system of correct reasoning [olcott
      |           `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |            `* Correcting logic to make it a system of correct reasoning [olcott
      |             `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |              `* Correcting logic to make it a system of correct reasoning [olcott
      |               `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |                `* Correcting logic to make it a system of correct reasoning [olcott
      |                 `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |                  `* Correcting logic to make it a system of correct reasoning [olcott
      |                   `* Correcting logic to make it a system of correct reasoning [Richard Damon
      |                    `* Correcting logic to make it a system of correct reasoning [olcott
      |                     `- Correcting logic to make it a system of correct reasoning [Richard Damon
      `* Correcting logic to make it a system of correct reasoning [ previously undiscoveBen
       `* Correcting logic to make it a system of correct reasoning [olcott
        +* Correcting logic to make it a system of correct reasoning [ previously undiscoveBen
        |`* Correcting logic to make it a system of correct reasoning [olcott
        | +* Correcting logic to make it a system of correct reasoning [Dennis Bush
        | |`* Correcting logic to make it a system of correct reasoning [olcott
        | | `- Correcting logic to make it a system of correct reasoning [Richard Damon
        | `* Correcting logic to make it a system of correct reasoning [ previously undiscoveBen
        |  `* Correcting logic to make it a system of correct reasoning [olcott
        |   +* Correcting logic to make it a system of correct reasoning [Richard Damon
        |   |`* Correcting logic to make it a system of correct reasoning [olcott
        |   | `* Correcting logic to make it a system of correct reasoning [Richard Damon
        |   |  `* Correcting logic to make it a system of correct reasoning [olcott
        |   |   `* Correcting logic to make it a system of correct reasoning [Richard Damon
        |   |    `* Correcting logic to make it a system of correct reasoning [olcott
        |   |     `* Correcting logic to make it a system of correct reasoning [ computer science is Richard Damon
        |   |      `* Correcting logic to make it a system of correct reasoning [olcott
        |   |       `- Correcting logic to make it a system of correct reasoning [Richard Damon
        |   `* Correcting logic to make it a system of correct reasoning [ previously undiscoveBen
        |    `* Correcting logic to make it a system of correct reasoning [olcott
        |     `* Correcting logic to make it a system of correct reasoning [ previously undiscoveBen
        `- Correcting logic to make it a system of correct reasoning [Richard Damon

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

<87lev5w47b.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben)
Newsgroups: comp.theory
Subject: Re: Correcting logic to make it a system of correct reasoning
Date: Fri, 13 May 2022 21:46:48 +0100
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 by: Ben - Fri, 13 May 2022 20:46 UTC

olcott <NoOne@NoWhere.com> writes:

> 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.

It is now dead obvious that you accept that no algorithm can do what the
world calls "decide halting". That is, in the context of C-like code
that you are more comfortable with, no D can exist such that D(X,Y) is
true if and only if X(Y) halts and is false otherwise.

Do you now accept that this is not possible? (I know, I know... I
don't really expect an answer.)

That you have code that decides something else is neither here nor
there.

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

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

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

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

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

> We know that there is a number that solves an equation, but we don't
> know that number, or how to compute that number.
>
> Can we say that it is true that such a number exists?
>

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

> This means that we can define the floor of that number, which will be an
> integer (call it N), is it true that this number exists?
>
> That interger, MUST be either even or odd, so we know that either
> iseven(N) is true or isodd(N) is true.
>
> By your logic, the 'truth value' of both of those must be 'untrue' since
> we can not prove which one it is.
>
> This is the sort of problem you run into with your system.
>
>>
>>> There is NOTHING about an analytic statement that says it can only be
>>> true if it is provable. Note, "its truth value is unknown" doesn't
>>> mean it doesn't have a truth value, just that we don't know what that
>>> value is.
>>>
>>
>> Within any formal system unprovable in the system means untrue in the
>> system.
>>
>> The entire body of analytic truth is constructed only on the basis of
>> semantic connections between expressions of language, or expressions
>> that are stipulated to have the semantic property of Boolean true.
>> Lacking both of these and the expression is untrue.
>>
>> Since axioms are provable on the basis that they are axioms then both
>> of these factors that make an expression true also make it provable.
>>
>
> You clearly are just stating words by rote and not actually
> understanding them.
>

There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1) or
the consequences of (2).

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

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

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

> You are making a Category Error in you logic system, and confusing
> Knowledge with Truth.
>
>>
>>
>>> You are confusing Knowledge with Truth.
>>>
>>> Your whole system is built on a Category Error.
>>>
>>
>>
>

--
Copyright 2022 Pete Olcott

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

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

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Subject: Re: Correcting logic to make it a system of correct reasoning
From: dbush.mo...@gmail.com (Dennis Bush)
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 by: Dennis Bush - Fri, 13 May 2022 20:57 UTC

On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
> 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.

The input, by definition, specifies P(P). P(P) halts, therefore by definition the correct answer is 1. H(P,P)==0, therefore H is wrong.

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

More projection.

Re: Correcting logic to make it a system of correct reasoning [ previously undiscovered rare cases ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [
previously undiscovered rare cases ]
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 by: olcott - Fri, 13 May 2022 21:05 UTC

On 5/13/2022 3:46 PM, Ben wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> 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.
>
> It is now dead obvious that you accept that no algorithm can do what the
> world calls "decide halting".

Tarski makes a similar mistake when he concludes that True() is not a
definable predicate entirely on the basis that he cannot prove that the
liar paradox is true. It never occurred to him that the liar paradox is
simply untrue.

That the definition of the halting problem criteria (in some rare cases)
directly contradicts the definition of a computer science decider that
requires all deciders to compute the mapping from their inputs
conclusively proves that the definition of the halting problem criteria
is incorrect in these (previously undiscovered) rare cases.

> That is, in the context of C-like code
> that you are more comfortable with, no D can exist such that D(X,Y) is
> true if and only if X(Y) halts and is false otherwise.
>
> Do you now accept that this is not possible? (I know, I know... I
> don't really expect an answer.)
>
> That you have code that decides something else is neither here nor
> there.
>

--
Copyright 2022 Pete Olcott

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

Re: Correcting logic to make it a system of correct reasoning [ very foolish ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [ very
foolish ]
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 by: olcott - Fri, 13 May 2022 21:10 UTC

On 5/13/2022 3:57 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
>> 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.
>
> The input, by definition, specifies P(P).

That is the same as defining the cat in your living room to be a dog.

It is empirically proven that H(P,P)==0 is correct on the basis of the
correct simulation of the input to H(P,P) by H.

It is proven to be correct because the execution trace derived by H
matches the behavior specified by the x86 source-code of P.

There really are no weasel words around this and any of these weasel
words that you try to use only make you look very foolish.

> P(P) halts, therefore by definition the correct answer is 1. H(P,P)==0, therefore H is wrong.
>
>>
>> That is does not specify the halt status that you expect makes your
>> expectation incorrect.
>
> More projection.

--
Copyright 2022 Pete Olcott

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

Re: Correcting logic to make it a system of correct reasoning [ very foolish ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [ very
foolish ]
From: dbush.mo...@gmail.com (Dennis Bush)
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 by: Dennis Bush - Fri, 13 May 2022 21:16 UTC

On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
> On 5/13/2022 3:57 PM, Dennis Bush wrote:
> > On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
> >> 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.
> >
> > The input, by definition, specifies P(P).
> That is the same as defining the cat in your living room to be a dog.

So you're saying the requirement can't be met? That means you agree with the conclusion of the halting problem proofs that there is no input you can give to H to correctly determine whether P(P) halts.

>
> It is empirically proven that H(P,P)==0 is correct on the basis of the
> correct simulation of the input to H(P,P) by H.
>
> It is proven to be correct because the execution trace derived by H
> matches the behavior specified by the x86 source-code of P.

You mean like how the execution trace of Ha3(N,5) matches the behavior specified by the x86 source code of N, proving by your logic that Ha3(N,5)==false is correct?

>
> There really are no weasel words around this and any of these weasel
> words that you try to use only make you look very foolish.

Yet more projection. When are you going to open that movie theater? I can't wait to see how nice the picture looks!

> > P(P) halts, therefore by definition the correct answer is 1. H(P,P)==0, therefore H is wrong.
> >
> >>
> >> That is does not specify the halt status that you expect makes your
> >> expectation incorrect.
> >
> > More projection.
> --
> Copyright 2022 Pete Olcott
>
> "Talent hits a target no one else can hit;
> Genius hits a target no one else can see."
> Arthur Schopenhauer

Re: Correcting logic to make it a system of correct reasoning [ very foolish ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [ very
foolish ]
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 by: olcott - Fri, 13 May 2022 21:17 UTC

On 5/13/2022 4:16 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
>>>> 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.
>>>
>>> The input, by definition, specifies P(P).
>> That is the same as defining the cat in your living room to be a dog.
>
> So you're saying the requirement can't be met?

I am saying that no matter how hard you try to make believe that the cat
in your living room is a dog, it is still a cat.

> That means you agree with the conclusion of the halting problem proofs that there is no input you can give to H to correctly determine whether P(P) halts.
>
>>
>> It is empirically proven that H(P,P)==0 is correct on the basis of the
>> correct simulation of the input to H(P,P) by H.
>>
>> It is proven to be correct because the execution trace derived by H
>> matches the behavior specified by the x86 source-code of P.
>
> You mean like how the execution trace of Ha3(N,5) matches the behavior specified by the x86 source code of N, proving by your logic that Ha3(N,5)==false is correct?
>
>>
>> There really are no weasel words around this and any of these weasel
>> words that you try to use only make you look very foolish.
>
> Yet more projection. When are you going to open that movie theater? I can't wait to see how nice the picture looks!
>
>
>>> P(P) halts, therefore by definition the correct answer is 1. H(P,P)==0, therefore H is wrong.
>>>
>>>>
>>>> That is does not specify the halt status that you expect makes your
>>>> expectation incorrect.
>>>
>>> More projection.
>> --
>> Copyright 2022 Pete Olcott
>>
>> "Talent hits a target no one else can hit;
>> Genius hits a target no one else can see."
>> Arthur Schopenhauer

--
Copyright 2022 Pete Olcott

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

Re: Correcting logic to make it a system of correct reasoning [ very foolish ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [ very
foolish ]
From: dbush.mo...@gmail.com (Dennis Bush)
Injection-Date: Fri, 13 May 2022 21:22:22 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Dennis Bush - Fri, 13 May 2022 21:22 UTC

On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
> On 5/13/2022 4:16 PM, Dennis Bush wrote:
> > On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
> >> On 5/13/2022 3:57 PM, Dennis Bush wrote:
> >>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
> >>>> 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.
> >>>
> >>> The input, by definition, specifies P(P).
> >> That is the same as defining the cat in your living room to be a dog.
> >
> > So you're saying the requirement can't be met?
> I am saying that no matter how hard you try to make believe that the cat
> in your living room is a dog, it is still a cat.

Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.

So how are you going to spend your time now that you're no longer working on the halting problem?

> > That means you agree with the conclusion of the halting problem proofs that there is no input you can give to H to correctly determine whether P(P) halts.
> >
> >>
> >> It is empirically proven that H(P,P)==0 is correct on the basis of the
> >> correct simulation of the input to H(P,P) by H.
> >>
> >> It is proven to be correct because the execution trace derived by H
> >> matches the behavior specified by the x86 source-code of P.
> >
> > You mean like how the execution trace of Ha3(N,5) matches the behavior specified by the x86 source code of N, proving by your logic that Ha3(N,5)==false is correct?
> >
> >>
> >> There really are no weasel words around this and any of these weasel
> >> words that you try to use only make you look very foolish.
> >
> > Yet more projection. When are you going to open that movie theater? I can't wait to see how nice the picture looks!
> >
> >
> >>> P(P) halts, therefore by definition the correct answer is 1. H(P,P)==0, therefore H is wrong.
> >>>
> >>>>
> >>>> That is does not specify the halt status that you expect makes your
> >>>> expectation incorrect.
> >>>
> >>> More projection.
> >> --
> >> Copyright 2022 Pete Olcott
> >>
> >> "Talent hits a target no one else can hit;
> >> Genius hits a target no one else can see."
> >> Arthur Schopenhauer
>
>
> --
> Copyright 2022 Pete Olcott
>
> "Talent hits a target no one else can hit;
> Genius hits a target no one else can see."
> Arthur Schopenhauer

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

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

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

Which means... ?

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

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

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

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

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

You still don't understand, do you.

You still confuse Truth with Knowledge.

Pitiful.

>
>> You are making a Category Error in you logic system, and confusing
>> Knowledge with Truth.
>>
>>>
>>>
>>>> You are confusing Knowledge with Truth.
>>>>
>>>> Your whole system is built on a Category Error.
>>>>
>>>
>>>
>>
>
>


Click here to read the complete article
Re: Correcting logic to make it a system of correct reasoning

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

On 5/13/22 4:14 PM, olcott wrote:
> On 5/13/2022 3:03 PM, Richard Damon wrote:
>> On 5/13/22 3:11 PM, olcott wrote:
>>> On 5/13/2022 2:00 PM, André G. Isaak wrote:
>>>> On 2022-05-13 12:50, olcott wrote:
>>>>> On 5/13/2022 1:28 PM, André G. Isaak wrote:
>>>>>> On 2022-05-13 11:20, olcott wrote:
>>>>>>> *Validity and Soundness*
>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>> a form that makes it impossible for the premises to be true and
>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive
>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>>>
>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>> unrelated.
>>>>>>
>>>>>> That isn't valid. Perhaps you should learn what 'valid' actually
>>>>>> means before you attempt to "correct" the definition.
>>>>>>
>>>>>> [Also, the above isn't even an argument. It is simply a
>>>>>> conditional statement. It has no conclusion].
>>>>>>
>>>>>
>>>>> (a) The Moon is made of green cheese.
>>>>> (b) Water is a kind of concrete.
>>>>> (c) Therefore all dogs are cats.
>>>>>
>>>>> Because the premises are false and the conclusion is false it is
>>>>> not a case of the conclusion is true and the premises are false,
>>>>> thus meets the above validity criteria.
>>>>
>>>> No. It isn't valid. You don't seem to grasp the concept of validity.
>>>>
>>>> Logic has no concept of whether, for example, the moon is made of
>>>> green cheese. An argument is valid if there is no truth *assignment*
>>>> under which the premises are true and the conclusion is false. The
>>>> actual truth values of these expressions don't play a role in the
>>>> definition of validity.
>>>>
>>>
>>> I reach my key insights by progressively refining very high level
>>> abstractions into their corresponding concrete examples.
>>>
>>> Clearly I have not yet translated this abstraction:
>>>
>>> A deductive argument is said to be valid if and only if it takes a
>>> form such that its conclusion is a necessary consequence of all of
>>> its premises.
>>>
>>> Into a concrete example of the issue that it corrects, quite yet.
>>>
>>>>>>> *Here is my correction to that issue*
>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>> a form such that its conclusion is a necessary consequence of all
>>>>>>> of its premises.
>>>>>>
>>>>>> And that differs from the standard definition how exactly? Unless
>>>>>> you have some special personal meaning for 'necessary consequence'
>>>>>> it would
>>>>>
>>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>>
>>>> Defined how exactly?
>>>>
>>>> André
>>>>
>>>
>>> Here is the original way that semantic relevance was defined:
>>> Semantically unrelated premises and conclusion is not possible with
>>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>
>>> Because syllogisms are comprised of
>>> https://en.wikipedia.org/wiki/Categorical_proposition
>>>
>>>
>>>
>>>
>>
>> My first thought is that if you are going to be limiting your
>> reasoning capability to simple things. You seem to be stuck in using
>> simple logic methods, which will limit what you can actually prove.
>>
>
> Not when all of natural language semantics has been fully formalized and
> directly integrated into its own formal system.

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

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

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

>
>> What you don't seem to understand is that much of what we have
>> logically proven, is based on higher order logical systems, which
>> these simple forms just can't handle.
>>
>> In particular, Computation theory, like much of mathematics, needs
>> second order (or higher) logic forms, which the simple logic just
>> can't handle.
>
> I created Minimal Type Theory to express HOL using very slightly adapted
> syntax of FOL. In an early version of MTT it translated its expressions
> into directed graphs so that pathological self-reference could be seen
> as infinite cycle in the di-graph.
>
> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>

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

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

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

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 by: Richard Damon - Fri, 13 May 2022 21:44 UTC

On 5/13/22 4:32 PM, olcott wrote:
> 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.

There is only ONE definition of the Halting Problem,

can you make a machine that answers in finite time if the Machine M
applied to input w will Halt, by giving it a representation of that
machine and input.

If it is impossible by your definition of a decider to construct such a
machine, it doesn't say that the definition are contradictory, but that
the answer is that there is no such machine.

>
>>> 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.

Except that it doesn't, since BY DEFINITION it input SPECIFIES the
computation P(P), or you formed the input incorrectly.

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

No, it means YOU were 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.
>
>

Re: Correcting logic to make it a system of correct reasoning [ previously undiscovered rare cases ]

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 by: Richard Damon - Fri, 13 May 2022 21:47 UTC

On 5/13/22 5:05 PM, olcott wrote:
> On 5/13/2022 3:46 PM, Ben wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> 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.
>>
>> It is now dead obvious that you accept that no algorithm can do what the
>> world calls "decide halting".
>
> Tarski makes a similar mistake when he concludes that True() is not a
> definable predicate entirely on the basis that he cannot prove that the
> liar paradox is true. It never occurred to him that the liar paradox is
> simply untrue.
>
> That the definition of the halting problem criteria (in some rare cases)
> directly contradicts the definition of a computer science decider that
> requires all deciders to compute the mapping from their inputs
> conclusively proves that the definition of the halting problem criteria
> is incorrect in these (previously undiscovered) rare cases.

No, it doesn't contradict that definition.

The Halting Problem is asking IF you can make a machine to do x.

If the definition of a decider means that it can't do x, then the answer
is NO, you can't make a machie to do x.

You are off by a level of logic in what is being asked.

>
>>  That is, in the context of C-like code
>> that you are more comfortable with, no D can exist such that D(X,Y) is
>> true if and only if X(Y) halts and is false otherwise.
>>
>> Do you now accept that this is not possible?  (I know, I know...  I
>> don't really expect an answer.)
>>
>> That you have code that decides something else is neither here nor
>> there.
>>
>
>

Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

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 by: olcott - Fri, 13 May 2022 21:47 UTC

On 5/13/2022 4:22 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
>> On 5/13/2022 4:16 PM, Dennis Bush wrote:
>>> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
>>>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
>>>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
>>>>>> 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.
>>>>>
>>>>> The input, by definition, specifies P(P).
>>>> That is the same as defining the cat in your living room to be a dog.
>>>
>>> So you're saying the requirement can't be met?
>> I am saying that no matter how hard you try to make believe that the cat
>> in your living room is a dog, it is still a cat.
>
> Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.

Tarski makes a similar mistake when he concludes that True() is not a
definable predicate entirely on the basis that he cannot prove that the
liar paradox is true. It never occurred to him that the liar paradox is
simply untrue.

That the definition of the halting problem criteria (in some rare cases)
directly contradicts the definition of a computer science decider that
requires all deciders to compute the mapping from their inputs
conclusively proves that the definition of the halting problem criteria
is incorrect in these (previously undiscovered) rare cases.

--
Copyright 2022 Pete Olcott

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

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

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

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

Unprovable means untrue and does not mean false in Prolog.

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


Click here to read the complete article
Re: Correcting logic to make it a system of correct reasoning

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

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

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

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

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

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

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

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

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

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

On 5/13/2022 4:39 PM, Richard Damon wrote:
> On 5/13/22 4:14 PM, olcott wrote:
>> On 5/13/2022 3:03 PM, Richard Damon wrote:
>>> On 5/13/22 3:11 PM, olcott wrote:
>>>> On 5/13/2022 2:00 PM, André G. Isaak wrote:
>>>>> On 2022-05-13 12:50, olcott wrote:
>>>>>> On 5/13/2022 1:28 PM, André G. Isaak wrote:
>>>>>>> On 2022-05-13 11:20, olcott wrote:
>>>>>>>> *Validity and Soundness*
>>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>>> a form that makes it impossible for the premises to be true and
>>>>>>>> the conclusion nevertheless to be false. Otherwise, a deductive
>>>>>>>> argument is said to be invalid. https://iep.utm.edu/val-snd/
>>>>>>>>
>>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>>> unrelated.
>>>>>>>
>>>>>>> That isn't valid. Perhaps you should learn what 'valid' actually
>>>>>>> means before you attempt to "correct" the definition.
>>>>>>>
>>>>>>> [Also, the above isn't even an argument. It is simply a
>>>>>>> conditional statement. It has no conclusion].
>>>>>>>
>>>>>>
>>>>>> (a) The Moon is made of green cheese.
>>>>>> (b) Water is a kind of concrete.
>>>>>> (c) Therefore all dogs are cats.
>>>>>>
>>>>>> Because the premises are false and the conclusion is false it is
>>>>>> not a case of the conclusion is true and the premises are false,
>>>>>> thus meets the above validity criteria.
>>>>>
>>>>> No. It isn't valid. You don't seem to grasp the concept of validity.
>>>>>
>>>>> Logic has no concept of whether, for example, the moon is made of
>>>>> green cheese. An argument is valid if there is no truth
>>>>> *assignment* under which the premises are true and the conclusion
>>>>> is false. The actual truth values of these expressions don't play a
>>>>> role in the definition of validity.
>>>>>
>>>>
>>>> I reach my key insights by progressively refining very high level
>>>> abstractions into their corresponding concrete examples.
>>>>
>>>> Clearly I have not yet translated this abstraction:
>>>>
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form such that its conclusion is a necessary consequence of all of
>>>> its premises.
>>>>
>>>> Into a concrete example of the issue that it corrects, quite yet.
>>>>
>>>>>>>> *Here is my correction to that issue*
>>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>>> a form such that its conclusion is a necessary consequence of
>>>>>>>> all of its premises.
>>>>>>>
>>>>>>> And that differs from the standard definition how exactly? Unless
>>>>>>> you have some special personal meaning for 'necessary
>>>>>>> consequence' it would
>>>>>>
>>>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>>>
>>>>> Defined how exactly?
>>>>>
>>>>> André
>>>>>
>>>>
>>>> Here is the original way that semantic relevance was defined:
>>>> Semantically unrelated premises and conclusion is not possible with
>>>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>>
>>>> Because syllogisms are comprised of
>>>> https://en.wikipedia.org/wiki/Categorical_proposition
>>>>
>>>>
>>>>
>>>>
>>>
>>> My first thought is that if you are going to be limiting your
>>> reasoning capability to simple things. You seem to be stuck in using
>>> simple logic methods, which will limit what you can actually prove.
>>>
>>
>> Not when all of natural language semantics has been fully formalized
>> and directly integrated into its own formal system.
>
> Nope doesn't work. Remember, formal system are based on a finite, or
> perhaps extended to countable, number of base axiom.
>
> I think you basis is going to hit the problem that the number of natural
> language 'facts' you are entering into your system isn't so limited.
>
> Having an uncountable number of axioms in your system breaks a lot of
> thngs. In fact, I think it breaks the definition of 'provable' or
> 'refutable'.
>
>>
>>> What you don't seem to understand is that much of what we have
>>> logically proven, is based on higher order logical systems, which
>>> these simple forms just can't handle.
>>>
>>> In particular, Computation theory, like much of mathematics, needs
>>> second order (or higher) logic forms, which the simple logic just
>>> can't handle.
>>
>> I created Minimal Type Theory to express HOL using very slightly
>> adapted syntax of FOL. In an early version of MTT it translated its
>> expressions into directed graphs so that pathological self-reference
>> could be seen as infinite cycle in the di-graph.
>>
>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>
>
> Again, the error you are going to run into is your system is now based
> on an uncountable number of inital truths, so a lot of the rules for
> reasoning break down. This makes you system VERY prone to becoming
> inconsistent (if not a certainty).
>
> There are problems when you allow uncountable infinites into your base
> logic.
>

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

--
Copyright 2022 Pete Olcott

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

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

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Fri, 13 May 2022 22:14 UTC

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


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

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

On 5/13/22 5:56 PM, olcott wrote:
> On 5/13/2022 4:39 PM, Richard Damon wrote:
>> On 5/13/22 4:14 PM, olcott wrote:
>>> On 5/13/2022 3:03 PM, Richard Damon wrote:
>>>> On 5/13/22 3:11 PM, olcott wrote:
>>>>> On 5/13/2022 2:00 PM, André G. Isaak wrote:
>>>>>> On 2022-05-13 12:50, olcott wrote:
>>>>>>> On 5/13/2022 1:28 PM, André G. Isaak wrote:
>>>>>>>> On 2022-05-13 11:20, olcott wrote:
>>>>>>>>> *Validity and Soundness*
>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>> takes a form that makes it impossible for the premises to be
>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a
>>>>>>>>> deductive argument is said to be invalid.
>>>>>>>>> https://iep.utm.edu/val-snd/
>>>>>>>>>
>>>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>>>> unrelated.
>>>>>>>>
>>>>>>>> That isn't valid. Perhaps you should learn what 'valid' actually
>>>>>>>> means before you attempt to "correct" the definition.
>>>>>>>>
>>>>>>>> [Also, the above isn't even an argument. It is simply a
>>>>>>>> conditional statement. It has no conclusion].
>>>>>>>>
>>>>>>>
>>>>>>> (a) The Moon is made of green cheese.
>>>>>>> (b) Water is a kind of concrete.
>>>>>>> (c) Therefore all dogs are cats.
>>>>>>>
>>>>>>> Because the premises are false and the conclusion is false it is
>>>>>>> not a case of the conclusion is true and the premises are false,
>>>>>>> thus meets the above validity criteria.
>>>>>>
>>>>>> No. It isn't valid. You don't seem to grasp the concept of validity.
>>>>>>
>>>>>> Logic has no concept of whether, for example, the moon is made of
>>>>>> green cheese. An argument is valid if there is no truth
>>>>>> *assignment* under which the premises are true and the conclusion
>>>>>> is false. The actual truth values of these expressions don't play
>>>>>> a role in the definition of validity.
>>>>>>
>>>>>
>>>>> I reach my key insights by progressively refining very high level
>>>>> abstractions into their corresponding concrete examples.
>>>>>
>>>>> Clearly I have not yet translated this abstraction:
>>>>>
>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>> form such that its conclusion is a necessary consequence of all of
>>>>> its premises.
>>>>>
>>>>> Into a concrete example of the issue that it corrects, quite yet.
>>>>>
>>>>>>>>> *Here is my correction to that issue*
>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>> takes a form such that its conclusion is a necessary
>>>>>>>>> consequence of all of its premises.
>>>>>>>>
>>>>>>>> And that differs from the standard definition how exactly?
>>>>>>>> Unless you have some special personal meaning for 'necessary
>>>>>>>> consequence' it would
>>>>>>>
>>>>>>> Semantic relevance is a key aspect of 'necessary consequence'.
>>>>>>
>>>>>> Defined how exactly?
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> Here is the original way that semantic relevance was defined:
>>>>> Semantically unrelated premises and conclusion is not possible with
>>>>> syllogisms. https://en.wikipedia.org/wiki/Syllogism#Basic_structure
>>>>>
>>>>> Because syllogisms are comprised of
>>>>> https://en.wikipedia.org/wiki/Categorical_proposition
>>>>>
>>>>>
>>>>>
>>>>>
>>>>
>>>> My first thought is that if you are going to be limiting your
>>>> reasoning capability to simple things. You seem to be stuck in using
>>>> simple logic methods, which will limit what you can actually prove.
>>>>
>>>
>>> Not when all of natural language semantics has been fully formalized
>>> and directly integrated into its own formal system.
>>
>> Nope doesn't work. Remember, formal system are based on a finite, or
>> perhaps extended to countable, number of base axiom.
>>
>> I think you basis is going to hit the problem that the number of
>> natural language 'facts' you are entering into your system isn't so
>> limited.
>>
>> Having an uncountable number of axioms in your system breaks a lot of
>> thngs. In fact, I think it breaks the definition of 'provable' or
>> 'refutable'.
>>
>>>
>>>> What you don't seem to understand is that much of what we have
>>>> logically proven, is based on higher order logical systems, which
>>>> these simple forms just can't handle.
>>>>
>>>> In particular, Computation theory, like much of mathematics, needs
>>>> second order (or higher) logic forms, which the simple logic just
>>>> can't handle.
>>>
>>> I created Minimal Type Theory to express HOL using very slightly
>>> adapted syntax of FOL. In an early version of MTT it translated its
>>> expressions into directed graphs so that pathological self-reference
>>> could be seen as infinite cycle in the di-graph.
>>>
>>> https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF
>>>
>>
>> Again, the error you are going to run into is your system is now based
>> on an uncountable number of inital truths, so a lot of the rules for
>> reasoning break down. This makes you system VERY prone to becoming
>> inconsistent (if not a certainty).
>>
>> There are problems when you allow uncountable infinites into your base
>> logic.
>>
>
> Uncountable truths that are entirely comprised of different combinations
> of countable constituent parts are evaluatable on the basis of these
> constituents that are later recombined back into the original expression.
>

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

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

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

Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [
Tarski made the same mistake ]
From: dbush.mo...@gmail.com (Dennis Bush)
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 by: Dennis Bush - Fri, 13 May 2022 22:21 UTC

On Friday, May 13, 2022 at 5:47:57 PM UTC-4, olcott wrote:
> On 5/13/2022 4:22 PM, Dennis Bush wrote:
> > On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
> >> On 5/13/2022 4:16 PM, Dennis Bush wrote:
> >>> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
> >>>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
> >>>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
> >>>>>> 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.
> >>>>>
> >>>>> The input, by definition, specifies P(P).
> >>>> That is the same as defining the cat in your living room to be a dog.
> >>>
> >>> So you're saying the requirement can't be met?
> >> I am saying that no matter how hard you try to make believe that the cat
> >> in your living room is a dog, it is still a cat.
> >
> > Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.
> Tarski makes a similar mistake when he concludes that True() is not a
> definable predicate entirely on the basis that he cannot prove that the
> liar paradox is true. It never occurred to him that the liar paradox is
> simply untrue.
>
> That the definition of the halting problem criteria (in some rare cases)
> directly contradicts the definition of a computer science decider that
> requires all deciders to compute the mapping from their inputs
> conclusively proves that the definition of the halting problem criteria
> is incorrect in these (previously undiscovered) rare cases.

There is no contradiction regarding the definition of a decider. From your preferred definition:

> The term decider doesn't really have a standard meaning

Even then, there's nothing that says an input can't represent something else as implementation detail of what can actually be passed.

But just for the sake of argument, let's say that a halt decider as described by the halting problem doesn't fit the definition of a decider. Then at *most* we have a terminology problem. So let's create a new term:

Determiner : A determiner maps its inputs to an accept or reject state based on the properties of non-inputs which the inputs represent as defined by a give problem statement

So the halting problem is not actually talking about a halt *decider* but a halt *determiner*, as the latter allows strings to represent turing machines. So the proofs can be corrected by changing all references of "halt decider" to "halt determiner".

So the halting problem actually states:

A halt determiner is a turing machine H such that for any <M> which is a representation of a turing machine and w which is the input to that turing machine:
H applied to <M> w reports halting if and only if M applied to w halts, and
H applied to <M> w reports non-halting if and only if M applied to w does not halt

So the problem still exists. Nothing else about the proof has changed. We've just corrected the terminology of what H is. And the proof is not refuted

This also means that your H, which is a halt *decider*, has no bearing on the halting problem, since you usefully pointed out that the halting problem deals with halt determiners and not halt deciders.

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

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 by: olcott - Fri, 13 May 2022 22:23 UTC

On 5/13/2022 5:14 PM, Richard Damon wrote:
> On 5/13/22 5:53 PM, olcott wrote:
>> On 5/13/2022 4:30 PM, Richard Damon wrote:
>>> On 5/13/22 4:56 PM, olcott wrote:
>>>> On 5/13/2022 3:43 PM, Richard Damon wrote:
>>>>> On 5/13/22 3:43 PM, olcott wrote:
>>>>>> On 5/13/2022 2:13 PM, Richard Damon wrote:
>>>>>>> On 5/13/22 2:10 PM, olcott wrote:
>>>>>>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>>>>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>>>>>>> *Validity and Soundness*
>>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>>> takes a form that makes it impossible for the premises to be
>>>>>>>>>> true and the conclusion nevertheless to be false. Otherwise, a
>>>>>>>>>> deductive argument is said to be invalid.
>>>>>>>>>> https://iep.utm.edu/val-snd/
>>>>>>>>>>
>>>>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>>>>> unrelated.
>>>>>>>>>>
>>>>>>>>>> *Here is my correction to that issue*
>>>>>>>>>> A deductive argument is said to be valid if and only if it
>>>>>>>>>> takes a form such that its conclusion is a necessary
>>>>>>>>>> consequence of all of its premises.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> And, have you done the basic investigation to find out how much
>>>>>>>>> of conventional logic you invalidate with that change?
>>>>>>>>>
>>>>>>>>
>>>>>>>> It categorically changes everything that is broken.
>>>>>>>
>>>>>>> So, you are saying we need to throw out EVERYTHING we know and
>>>>>>> start over?
>>>>>>>
>>>>>>
>>>>>> Change everything that diverges from my spec:
>>>>>> A deductive argument is said to be valid if and only if it takes a
>>>>>> form such that its conclusion is a necessary consequence of all of
>>>>>> its premises.
>>>>>>
>>>>>>> I think, especially with the comment below, people will decide
>>>>>>> that your "new" logic systm isn't worth the cost to switch to.
>>>>>>>
>>>>>>>>
>>>>>>>>> Note, that it may be hard to define "necessary consequence" in
>>>>>>>>> a formal matter.
>>>>>>>>>
>>>>>>>>
>>>>>>>> {A,B} ⊢ C only when truth preserving operations are applied to
>>>>>>>> {A,B} to derive C.
>>>>>>>
>>>>>>> And what do you define truth perserving as?
>>>>>>>
>>>>>>
>>>>>> Semantic relevance is maintained.
>>>>>>
>>>>>>> Normally the phrase means that True Premises always generate True
>>>>>>> Results (which means the statement "If the moon is made of green
>>>>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time
>>>>>>> the premise is true (never) the conclusion is true.
>>>>>>>
>>>>>>>>
>>>>>>>>> It should be noted that your example, while considered an vaild
>>>>>>>>> inference by normal logic, can never be used to actually prove
>>>>>>>>> its conclusion, so doesn't actually cause problems in normal
>>>>>>>>> logic (can you show a case where it does?)
>>>>>>>>>
>>>>>>>>
>>>>>>>> With my correction true and unprovable is impossible, unprovable
>>>>>>>> simply means untrue.
>>>>>>>>
>>>>>>>
>>>>>>> Ok, then you have just stated that your new logic system can't
>>>>>>> handle mathematics, and thus "Computer SCience" no longer exists
>>>>>>> as a logical system.
>>>>>>>
>>>>>>
>>>>>> It corrects the divergence of classical and symbolic logic from
>>>>>> correct reasoning.
>>>>>>
>>>>>>> This makes you system not much more than a toy for most people.
>>>>>>>
>>>>>>>>> Note, that at least by some meanings of your words, it could be
>>>>>>>>> construed that you only accept as a correct deductive argument,
>>>>>>>>> and arguement whose premises can at least some times be true,
>>>>>>>>> but there are some statements we don't know if they CAN be
>>>>>>>>> sometimes true, so your logic system would seem to not allow
>>>>>>>>> doing logic with that sort of statement.
>>>>>>>>>
>>>>>>>>
>>>>>>>> An analytic statement is only known to be true when it is
>>>>>>>> derived by applying only truth preserving operations to all of
>>>>>>>> its premises and all of its premises are known to be true,
>>>>>>>> otherwise its truth value is unknown.
>>>>>>>>
>>>>>>>
>>>>>>> KNOWN to be True, not IS TRUE.
>>>>>>
>>>>>> It remains unknown until it is known to be true or false.
>>>>>> My system only eliminates impossibly true or false.
>>>>>>
>>>>>
>>>>> So, you don't know what is still valid to use?
>>>>>
>>>>>
>>>>>>>
>>>>>>> Your statement even admits that truth value might be unknow,
>>>>>>> which might allow it to even be UNKNOWABLE (maybe just in that
>>>>>>> system) if it can't be proven or refuted.
>>>>>>>
>>>>>>
>>>>>> unprovable in the system means untrue in the system.
>>>>>
>>>>> And what does 'untrue' mean?
>>>>>
>>>>
>>>> Untrue means the same thing as Prolog's negation as failure.
>>>
>>> Which means... ?
>>>
>>> Prolog, as I remember, ASSUMES that anything not provable is FALSE
>>> (not 'untrue').
>>>
>>
>> Unprovable means untrue and does not mean false in Prolog.
>>
>>>>
>>>>> We know that there is a number that solves an equation, but we
>>>>> don't know that number, or how to compute that number.
>>>>>
>>>>> Can we say that it is true that such a number exists?
>>>>>
>>>>
>>>> If you defined your terms correctly, then yes because this has been
>>>> stipulated in your deinitions.
>>>>
>>>>> This means that we can define the floor of that number, which will
>>>>> be an integer (call it N), is it true that this number exists?
>>>>>
>>>>> That interger, MUST be either even or odd, so we know that either
>>>>> iseven(N) is true or isodd(N) is true.
>>>>>
>>>>> By your logic, the 'truth value' of both of those must be 'untrue'
>>>>> since we can not prove which one it is.
>>>>>
>>>>> This is the sort of problem you run into with your system.
>>>>>
>>>>>>
>>>>>>> There is NOTHING about an analytic statement that says it can
>>>>>>> only be true if it is provable. Note, "its truth value is
>>>>>>> unknown" doesn't mean it doesn't have a truth value, just that we
>>>>>>> don't know what that value is.
>>>>>>>
>>>>>>
>>>>>> Within any formal system unprovable in the system means untrue in
>>>>>> the system.
>>>>>>
>>>>>> The entire body of analytic truth is constructed only on the basis
>>>>>> of semantic connections between expressions of language, or
>>>>>> expressions that are stipulated to have the semantic property of
>>>>>> Boolean true. Lacking both of these and the expression is untrue.
>>>>>>
>>>>>> Since axioms are provable on the basis that they are axioms then
>>>>>> both of these factors that make an expression true also make it
>>>>>> provable.
>>>>>>
>>>>>
>>>>> You clearly are just stating words by rote and not actually
>>>>> understanding them.
>>>>>
>>>>
>>>> There are only two possible ways that any analytical expression of
>>>> language can possibly be true:
>>>> (1) It is stipulated to be true.
>>>> (2) It is derived by applying only truth preserving operations to
>>>> (1) or the consequences of (2).
>>>
>>> So there exists an integer number N is neither Even or Odd? (it is
>>> untrue for both tests)
>>>
>>> I don't think you actually understand what that means.
>>>
>>>>
>>>>> Analytic Truth is truth that is provable, that is correct, but it
>>>>> accepts that there is OTHER things that happen to be true but are
>>>>> not provable.
>>>>>
>>>>
>>>> Analytic truth includes every expression of language that can be
>>>> completely verified as totally true entirely on the basis of its
>>>> meaning without requiring any sense data from the sense organs.
>>>>
>>>> Empirical expressions of language also require sense data from the
>>>> sense organs to verify their truth.
>>>
>>> You still don't understand, do you.
>>>
>>> You still confuse Truth with Knowledge.
>> There are only two possible ways that any analytical expression of
>> language can possibly be true:
>> (1) It is stipulated to be true.
>> (2) It is derived by applying only truth preserving operations to (1)
>> or the consequences of (2).
>>
>> Try and provide an example of a possible truth that does not require
>> one of those two.
>>
>
> The result of applying the operation of replacing N by N/2 if  N is even
> or by 3N+1 if N is odd will eventually get you to the number 1 for all
> Natural numbers N > 0.
>
> This statement MUST be either True or False, by its nature, there is no
> other possible state.
>
> This statement seems to be true, but it has unable to be proven to be true.
>
> Yes, we can not validly USE the idea that this statement is true to
> prove something else, because we know that it is still possible that it
> won't be true. But we CAN use that it will either be true or false to
> show something.
>
> That is an analytical expression that isn't proven to be an analytical
> truth, but it may still be true,


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Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

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Tarski made the same mistake ]
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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Fri, 13 May 2022 22:29 UTC

On 5/13/2022 5:21 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 5:47:57 PM UTC-4, olcott wrote:
>> On 5/13/2022 4:22 PM, Dennis Bush wrote:
>>> On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
>>>> On 5/13/2022 4:16 PM, Dennis Bush wrote:
>>>>> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
>>>>>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
>>>>>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
>>>>>>>> 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.
>>>>>>>
>>>>>>> The input, by definition, specifies P(P).
>>>>>> That is the same as defining the cat in your living room to be a dog.
>>>>>
>>>>> So you're saying the requirement can't be met?
>>>> I am saying that no matter how hard you try to make believe that the cat
>>>> in your living room is a dog, it is still a cat.
>>>
>>> Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.
>> Tarski makes a similar mistake when he concludes that True() is not a
>> definable predicate entirely on the basis that he cannot prove that the
>> liar paradox is true. It never occurred to him that the liar paradox is
>> simply untrue.
>>
>> That the definition of the halting problem criteria (in some rare cases)
>> directly contradicts the definition of a computer science decider that
>> requires all deciders to compute the mapping from their inputs
>> conclusively proves that the definition of the halting problem criteria
>> is incorrect in these (previously undiscovered) rare cases.
>
> There is no contradiction regarding the definition of a decider. From your preferred definition:
>
>> The term decider doesn't really have a standard meaning
>

Same post same author:

How is this definition? Deciders compute the mapping from their inputs
to an accept or reject state. – Feb 19 at 17:55

This is the standard definition. – Yuval Filmus Feb 19 at 17:56

> Even then, there's nothing that says an input can't represent something else as implementation detail of what can actually be passed.

Then it is no longer a computation AKA a pure function of its inputs.

--
Copyright 2022 Pete Olcott

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

Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

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Subject: Re: Correcting logic to make it a system of correct reasoning [
Tarski made the same mistake ]
From: dbush.mo...@gmail.com (Dennis Bush)
Injection-Date: Fri, 13 May 2022 22:35:21 +0000
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 by: Dennis Bush - Fri, 13 May 2022 22:35 UTC

On Friday, May 13, 2022 at 6:30:02 PM UTC-4, olcott wrote:
> On 5/13/2022 5:21 PM, Dennis Bush wrote:
> > On Friday, May 13, 2022 at 5:47:57 PM UTC-4, olcott wrote:
> >> On 5/13/2022 4:22 PM, Dennis Bush wrote:
> >>> On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
> >>>> On 5/13/2022 4:16 PM, Dennis Bush wrote:
> >>>>> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
> >>>>>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
> >>>>>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
> >>>>>>>> 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.
> >>>>>>>
> >>>>>>> The input, by definition, specifies P(P).
> >>>>>> That is the same as defining the cat in your living room to be a dog.
> >>>>>
> >>>>> So you're saying the requirement can't be met?
> >>>> I am saying that no matter how hard you try to make believe that the cat
> >>>> in your living room is a dog, it is still a cat.
> >>>
> >>> Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.
> >> Tarski makes a similar mistake when he concludes that True() is not a
> >> definable predicate entirely on the basis that he cannot prove that the
> >> liar paradox is true. It never occurred to him that the liar paradox is
> >> simply untrue.
> >>
> >> That the definition of the halting problem criteria (in some rare cases)
> >> directly contradicts the definition of a computer science decider that
> >> requires all deciders to compute the mapping from their inputs
> >> conclusively proves that the definition of the halting problem criteria
> >> is incorrect in these (previously undiscovered) rare cases.
> >
> > There is no contradiction regarding the definition of a decider. From your preferred definition:
> >
> >> The term decider doesn't really have a standard meaning
> >
> Same post same author:
>
> How is this definition? Deciders compute the mapping from their inputs
> to an accept or reject state. – Feb 19 at 17:55
>
> This is the standard definition. – Yuval Filmus Feb 19 at 17:56
> > Even then, there's nothing that says an input can't represent something else as implementation detail of what can actually be passed.
> Then it is no longer a computation AKA a pure function of its inputs.

It absolutely is. Those string inputs map 1-to-1 with a turning machine as per the definition of a halt determiner.

I also see that you deceptively removed the definition of a halt determiner and the description of how that fixes the proofs, so let me put that back:

Determiner : A determiner maps its inputs to an accept or reject state based on the properties of non-inputs which the inputs represent as defined by a give problem statement

So the halting problem is not actually talking about a halt *decider* but a halt *determiner*, as the latter allows strings to represent turing machines. So the proofs can be corrected by changing all references of "halt decider" to "halt determiner".

So the halting problem actually states:

A halt determiner is a turing machine H such that for any <M> which is a representation of a turing machine and w which is the input to that turing machine:
H applied to <M> w reports halting if and only if M applied to w halts, and
H applied to <M> w reports non-halting if and only if M applied to w does not halt

So the problem still exists. Nothing else about the proof has changed. We've just corrected the terminology of what H is. And the proof is not refuted

This also means that your H, which is a halt *decider*, has no bearing on the halting problem, since you usefully pointed out that the halting problem deals with halt determiners and not halt deciders.

Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

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 by: Richard Damon - Fri, 13 May 2022 22:59 UTC

On 5/13/22 6:35 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 6:30:02 PM UTC-4, olcott wrote:
>> On 5/13/2022 5:21 PM, Dennis Bush wrote:
>>> On Friday, May 13, 2022 at 5:47:57 PM UTC-4, olcott wrote:
>>>> On 5/13/2022 4:22 PM, Dennis Bush wrote:
>>>>> On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
>>>>>> On 5/13/2022 4:16 PM, Dennis Bush wrote:
>>>>>>> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
>>>>>>>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
>>>>>>>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
>>>>>>>>>> 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.
>>>>>>>>>
>>>>>>>>> The input, by definition, specifies P(P).
>>>>>>>> That is the same as defining the cat in your living room to be a dog.
>>>>>>>
>>>>>>> So you're saying the requirement can't be met?
>>>>>> I am saying that no matter how hard you try to make believe that the cat
>>>>>> in your living room is a dog, it is still a cat.
>>>>>
>>>>> Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.
>>>> Tarski makes a similar mistake when he concludes that True() is not a
>>>> definable predicate entirely on the basis that he cannot prove that the
>>>> liar paradox is true. It never occurred to him that the liar paradox is
>>>> simply untrue.
>>>>
>>>> That the definition of the halting problem criteria (in some rare cases)
>>>> directly contradicts the definition of a computer science decider that
>>>> requires all deciders to compute the mapping from their inputs
>>>> conclusively proves that the definition of the halting problem criteria
>>>> is incorrect in these (previously undiscovered) rare cases.
>>>
>>> There is no contradiction regarding the definition of a decider. From your preferred definition:
>>>
>>>> The term decider doesn't really have a standard meaning
>>>
>> Same post same author:
>>
>> How is this definition? Deciders compute the mapping from their inputs
>> to an accept or reject state. – Feb 19 at 17:55
>>
>> This is the standard definition. – Yuval Filmus Feb 19 at 17:56
>>> Even then, there's nothing that says an input can't represent something else as implementation detail of what can actually be passed.
>> Then it is no longer a computation AKA a pure function of its inputs.
>
> It absolutely is. Those string inputs map 1-to-1 with a turning machine as per the definition of a halt determiner.
>
> I also see that you deceptively removed the definition of a halt determiner and the description of how that fixes the proofs, so let me put that back:
>
> Determiner : A determiner maps its inputs to an accept or reject state based on the properties of non-inputs which the inputs represent as defined by a give problem statement
>
> So the halting problem is not actually talking about a halt *decider* but a halt *determiner*, as the latter allows strings to represent turing machines. So the proofs can be corrected by changing all references of "halt decider" to "halt determiner".
>
> So the halting problem actually states:
>
> A halt determiner is a turing machine H such that for any <M> which is a representation of a turing machine and w which is the input to that turing machine:
> H applied to <M> w reports halting if and only if M applied to w halts, and
> H applied to <M> w reports non-halting if and only if M applied to w does not halt
>
> So the problem still exists. Nothing else about the proof has changed. We've just corrected the terminology of what H is. And the proof is not refuted
>
> This also means that your H, which is a halt *decider*, has no bearing on the halting problem, since you usefully pointed out that the halting problem deals with halt determiners and not halt deciders.
>

And, actually we don't need to play with this nomenclature, as the
actual statement is can we create a TURING MACHINE, that computes the
result, the problem doesn't state it needs to be 'a decider'.

Now, that machine doesn't actually need to be an actual 'Decider' as
defined in Computation Theory, as the REAL definition for a decider is a
Turing Machine that halts for all inputs (and as a consequence creates a
mapping from input tape to output tape + Halt State. The Turing Machine
looked at from the halting problem doesn't need to halt for ALL inputs,
only all input that represent a Turing Machine applied to an input, so
an input that doesn't actually represent that can generate a non-halting
result.

We use the term Halt Decider, because if we CAN find such a machine,
then it will (basically) fit the definiton of a Halt Decider, as a
machine that computes the mapping of the input tape (which represents
the computation to be decided on) to an output (which indicates if that
computation would halt or run forever). This matches the definition that
an XX decider computes the mapping of the XX function. This is an
important piece that PO omits from his definition, that to be a
SOMETHING decider, your mapping needs to match the SOMETHING function,
he is just claiming it compute SOME function, not the RIGHT function.


Click here to read the complete article
Re: Correcting logic to make it a system of correct reasoning [ previously undiscovered rare cases ]

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 by: Ben - Fri, 13 May 2022 23:01 UTC

olcott <NoOne@NoWhere.com> writes:

> On 5/13/2022 3:46 PM, Ben wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 5/13/2022 2:16 PM, Ben wrote:
>>>> 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.
>> It is now dead obvious that you accept that no algorithm can do what the
>> world calls "decide halting".
>
> Tarski makes a similar mistake...

<snip distractions>

>> That is, in the context of C-like code
>> that you are more comfortable with, no D can exist such that D(X,Y) is
>> true if and only if X(Y) halts and is false otherwise.
>> Do you now accept that this is not possible? (I know, I know... I
>> don't really expect an answer.)

As expected, no answer. You can't answer this because you know that
would be the end of you bragging about halting.

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

Re: Correcting logic to make it a system of correct reasoning [ Tarski made the same mistake ]

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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Fri, 13 May 2022 23:01 UTC

On 5/13/2022 5:35 PM, Dennis Bush wrote:
> On Friday, May 13, 2022 at 6:30:02 PM UTC-4, olcott wrote:
>> On 5/13/2022 5:21 PM, Dennis Bush wrote:
>>> On Friday, May 13, 2022 at 5:47:57 PM UTC-4, olcott wrote:
>>>> On 5/13/2022 4:22 PM, Dennis Bush wrote:
>>>>> On Friday, May 13, 2022 at 5:17:58 PM UTC-4, olcott wrote:
>>>>>> On 5/13/2022 4:16 PM, Dennis Bush wrote:
>>>>>>> On Friday, May 13, 2022 at 5:10:21 PM UTC-4, olcott wrote:
>>>>>>>> On 5/13/2022 3:57 PM, Dennis Bush wrote:
>>>>>>>>> On Friday, May 13, 2022 at 4:32:49 PM UTC-4, olcott wrote:
>>>>>>>>>> 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.
>>>>>>>>>
>>>>>>>>> The input, by definition, specifies P(P).
>>>>>>>> That is the same as defining the cat in your living room to be a dog.
>>>>>>>
>>>>>>> So you're saying the requirement can't be met?
>>>>>> I am saying that no matter how hard you try to make believe that the cat
>>>>>> in your living room is a dog, it is still a cat.
>>>>>
>>>>> Nothing but more bad analogies with no explanation, which means you're unable to explain why I'm wrong, and that you therefore implicitly agree that I'm correct.
>>>> Tarski makes a similar mistake when he concludes that True() is not a
>>>> definable predicate entirely on the basis that he cannot prove that the
>>>> liar paradox is true. It never occurred to him that the liar paradox is
>>>> simply untrue.
>>>>
>>>> That the definition of the halting problem criteria (in some rare cases)
>>>> directly contradicts the definition of a computer science decider that
>>>> requires all deciders to compute the mapping from their inputs
>>>> conclusively proves that the definition of the halting problem criteria
>>>> is incorrect in these (previously undiscovered) rare cases.
>>>
>>> There is no contradiction regarding the definition of a decider. From your preferred definition:
>>>
>>>> The term decider doesn't really have a standard meaning
>>>
>> Same post same author:
>>
>> How is this definition? Deciders compute the mapping from their inputs
>> to an accept or reject state. – Feb 19 at 17:55
>>
>> This is the standard definition. – Yuval Filmus Feb 19 at 17:56
>>> Even then, there's nothing that says an input can't represent something else as implementation detail of what can actually be passed.
>> Then it is no longer a computation AKA a pure function of its inputs.
>
> It absolutely is. Those string inputs map 1-to-1 with a turning machine as per the definition of a halt determiner.
It has been empirically proven that H(P,P)==0 is the correct halt status
for the input to H(P,P) on the basis of the empirically proven correct
simulation of the input to H(P,P) that H derives.

Not only must a halt decider compute the mapping from its inputs it must
compute the mapping only on the basis of what its inputs explicitly
specify otherwise it is not a computation (pure function of its inputs)
at all.

--
Copyright 2022 Pete Olcott

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

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