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devel / comp.theory / Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

SubjectAuthor
* Proof that H(P,P)==0 is correct [ refuting the halting problem proofsolcott
+* Proof that H(P,P)==0 is correct [ refuting the halting problemMr Flibble
|`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
| +- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
| +* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Mr Flibble
| |`- Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
| `* Proof that H(P,P)==0 is correct [ refuting the halting problemMr Flibble
|  `* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   +* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Mr Flibble
|   |`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   | +* Proof that H(P,P)==0 is correct [ refuting the halting problemMr Flibble
|   | |`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   | | +- Proof that H(P,P)==0 is correct [ refuting the halting problemMr Flibble
|   | | +* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|   | | |`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   | | | +* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|   | | | |`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   | | | | +* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|   | | | | |`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   | | | | | +- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
|   | | | | | `- Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|   | | | | `- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
|   | | | `- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
|   | | `- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
|   | `- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
|   `- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
+- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
+* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|`* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
| +- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
| `* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|  `* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|   +- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
|   `* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|    `* Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|     +* Proof that H(P,P)==0 is correct [ refuting the halting problemMr Flibble
|     |`- Proof that H(P,P)==0 is correct [ refuting the halting problemolcott
|     +* Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Ben
|     |`* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | +- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | +* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Ben
|     | |`* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | | `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Ben
|     | |  `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   +* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |`* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   | +* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Dennis Bush
|     | |   | |`* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   | | `- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Mr Flibble
|     | |   | +- Proof that H(P,P)==0 is correct [ foundation of truth itself ]wij
|     | |   | `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |  `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   |   `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |    `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   |     `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |      `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   |       `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |        `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   |         `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |          `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   |           +- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |           `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]André G. Isaak
|     | |   |            +- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |   |            `- Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |   `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Ben
|     | |    `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |     +* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |     |`* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |     | `- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Richard Damon
|     | |     +* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Ben
|     | |     |`* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |     | `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Ben
|     | |     |  `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |     |   `- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Ben
|     | |     `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Mikko
|     | |      `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |       `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Mikko
|     | |        `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     | |         `- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Mikko
|     | `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]Mikko
|     |  `* Proof that H(P,P)==0 is correct [ foundation of truth itself ]olcott
|     |   `- Proof that H(P,P)==0 is correct [ foundation of truth itself ]Mikko
|     `- Proof that H(P,P)==0 is correct [ refuting the halting problemRichard Damon
+- Proof that H(P,P)==0 is correct [ refuting the halting problem proofs ](V2)Mikko
`- Proof that H(P,P)==0 is correct [ refuting the halting problemwij

Pages:1234
Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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Subject: Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]
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From: Rich...@Damon-Family.org (Richard Damon)
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Date: Fri, 13 May 2022 20:41:25 -0400
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 by: Richard Damon - Sat, 14 May 2022 00:41 UTC

On 5/13/22 8:20 PM, olcott wrote:
> On 5/13/2022 7:04 PM, Richard Damon wrote:
>> On 5/13/22 7:26 PM, olcott wrote:
>>> On 5/13/2022 6:20 PM, Richard Damon wrote:
>>>> On 5/13/22 7:09 PM, olcott wrote:
>>>>> On 5/13/2022 6:07 PM, Richard Damon wrote:
>>>>>> On 5/13/22 6:06 PM, olcott wrote:
>>>>>>> On 5/13/2022 5:04 PM, Richard Damon wrote:
>>>>>>>> On 5/13/22 5:48 PM, olcott wrote:
>>>>>>>>> On 5/13/2022 4:22 PM, Richard Damon wrote:
>>>>>>>>>> On 5/13/22 4:22 PM, olcott wrote:
>>>>>>>>>>> On 5/13/2022 3:11 PM, Richard Damon wrote:
>>>>>>>>>>>> On 5/13/22 3:24 PM, olcott wrote:
>>>>>>>>>>>>> On 5/13/2022 2:06 PM, Ben wrote:
>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 5/13/2022 6:05 AM, Ben wrote:
>>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> All of my studies of Gödel 1931, Tarski 1936, the HP
>>>>>>>>>>>>>>>>> and the Liar
>>>>>>>>>>>>>>>>> Paradox have been concrete proxies for my study of the
>>>>>>>>>>>>>>>>> philosophical
>>>>>>>>>>>>>>>>> foundation of analytical truth.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Why have you not had anything published?  Everyone here
>>>>>>>>>>>>>>>> knows why, but
>>>>>>>>>>>>>>>> what's your opinion?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I have to conclusively prove my point concretely such the
>>>>>>>>>>>>>>> every single
>>>>>>>>>>>>>>> detail of my reasoning can be verified as factually
>>>>>>>>>>>>>>> correct before
>>>>>>>>>>>>>>> people will understand that I have corrected errors in
>>>>>>>>>>>>>>> some of the
>>>>>>>>>>>>>>> aspects of the basic foundations of logic.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hmm.. but it's "dead obvious", isn't it?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> It has been dead obvious that H(P,P)==0 is the correct halt
>>>>>>>>>>>>> status for the input to H(P,P) on the basis of the actual
>>>>>>>>>>>>> behavior that this input actually specifies.
>>>>>>>>>>>>>
>>>>>>>>>>>>> This has been dead obvious on this basis for at least six
>>>>>>>>>>>>> months, yet people very persistently insisted on simply
>>>>>>>>>>>>> ignoring the easily verifiable facts for this whole six
>>>>>>>>>>>>> month period.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Nope, since BY THE PROBLEM STATEMENT of the Halting Problem,
>>>>>>>>>>>> the "actual behavior" of the input to H applied to <H^> <H^>
>>>>>>>>>>>> is DEFINED to be the behavior of H^ applied to <H^>.
>>>>>>>>>>>>
>>>>>>>>>>> The ultimate measure superseding and overruling every other
>>>>>>>>>>> measure is the actual behavior of the actual input as
>>>>>>>>>>> demonstrated by a correct simulation of this input by the
>>>>>>>>>>> simulating halt decider.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> THen H is PROVEN to not be a Halt Decider, because the Halting
>>>>>>>>>> Mapping is defined differently.
>>>>>>>>>>
>>>>>>>>>> If the definition of H doesn't match the requirements of the
>>>>>>>>>> problem, then it just fails to be an aswer to the problem.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> 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.
>>>>>>>>>
>>>>>>>>
>>>>>>>> You are just proving that you don't know what you are talking
>>>>>>>> about. Definitions can not be 'incorrect', as they are DEFINITIONS.
>>>>>>>
>>>>>>> That is a naive thing to say.
>>>>>>> This means that a pair of contradictory defininitions within the
>>>>>>> same system would both be correct. This is simply not the way
>>>>>>> that truth actually works.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Right, they both ARE correct, and make the system inconsistent.
>>>>>
>>>>> Inconsistent is another word for incorrect, thus in any system of
>>>>> correct reasoning there can be no contradictory definitions.
>>>>
>>>> Nopw, not the same definitions by the normal definitions.
>>>>
>>>
>>> I am referring to a system of correct reasoning and showing how
>>> symbolic logic diverges from this.
>>
>> IF you aren't talking about Formal Logic and the rules for it, then
>> you are talking in the wrong place. Note, you don't get to change the
>> rules.
>
> When the rules of logic prove to be inconsistent then that proves that
> they do not correspond to correct reasoning, thus making them incorrect.

The rules of logic ARE the rules of logic. PERIOD.

If you disagree with what the logic says, fine, you reject those fields
of logic as useful. Others disagree.

Most others will say that YOU are incorrect.

>
>>
>> If you really want to try to turn the whole field of logic on its
>> head, you really need to be working in the fields that deal with the
>> core basics of how logic works.
>>
>
> This issue is the philosophical foundation of logic is inconsistent.

But it IS the foundation of logic.

If you want to try to come up with something better, go ahead, work on it.

>
>> Comutation Theory and the Halting Problem is NOT where to try to
>> change those things. The fact that you even think it is tends to be a
>> pretty good sign that you don't really understand what you are talking
>> about.
>>
>> My guess is that if you actually had an idea of that level, you needed
>> to start decades ago in the right places for THAT sort of discussion.
>>
>
> I started in 1997. The HP is the only concrete example where all of the
> details of the error in the philosophical foundation of logic can be
> shown in all of its complete detail as actually fully operational code.


Click here to read the complete article
Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

<t5mv57$8lc$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=32442&group=comp.theory#32442

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]
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 by: André G. Isaak - Sat, 14 May 2022 01:03 UTC

On 2022-05-13 18:20, olcott wrote:

> When the rules of logic prove to be inconsistent then that proves that
> they do not correspond to correct reasoning, thus making them incorrect.

But you haven't identified any rules of logic which are inconsistent.

André

--
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service.

Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sat, 14 May 2022 01:21 UTC

On 5/13/22 9:03 PM, André G. Isaak wrote:
> On 2022-05-13 18:20, olcott wrote:
>
>> When the rules of logic prove to be inconsistent then that proves that
>> they do not correspond to correct reasoning, thus making them incorrect.
>
> But you haven't identified any rules of logic which are inconsistent.
>
> André
>
>

They are inconsistent with HIS idea that Truth must be provable, Which
can't be Proved so isn't True in a system that wants to use it.

It can only be an Axiom, but it has been proved inconsistent with most
logic system that are complicated enough, so adding it distroys the
logic system.

This shows that it is HIS idea that is inconsistent and must be rejected
for not being correct reasoning.

Of course, that logc will just blow the circuit breakers in his head.

Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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 by: olcott - Sat, 14 May 2022 03:37 UTC

On 5/13/2022 8:03 PM, André G. Isaak wrote:
> On 2022-05-13 18:20, olcott wrote:
>
>> When the rules of logic prove to be inconsistent then that proves that
>> they do not correspond to correct reasoning, thus making them incorrect.
>
> But you haven't identified any rules of logic which are inconsistent.
>
> André

I have not articulated this clearly enough yet.

--
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: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

<t5np3l$li6$1@dont-email.me>

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From: mikko.le...@iki.fi (Mikko)
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Subject: Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]
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 by: Mikko - Sat, 14 May 2022 08:26 UTC

On 2022-05-13 16:15:35 +0000, olcott said:

> On 5/13/2022 8:11 AM, Mikko wrote:
>> On 2022-05-13 01:25:37 +0000, olcott said:
>>
>>> Taking a form such as this: Provide a natural number N such that N > 7
>>> and N < 3, the answer must be a natural number.
>>
>> Or a proof that no such natural number exists.
>>
>
> The answer is restricted to elements of the set of natural numbers
> hence making the problem undecidable through Flibble's category error.

Undecidable does not apply as the question is not about a claim but
about a number. But no number satisfies all requirements. A common
convention with problems of this type is that the clause "or prove
that no solution exists" is omitted but understood to be a part of
the problem.

Mikko

Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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 by: Mikko - Sat, 14 May 2022 08:45 UTC

On 2022-05-13 22:57:47 +0000, olcott said:

> 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.

There is a category error in that statement. Mathematical truths do not
refer to empirical facts so they cannot be empirically proven. Whether
H(P,P) == 0 is true or false is a mathematical question so it cannot be
determined empirically.

Mikko

Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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 by: olcott - Sat, 14 May 2022 09:28 UTC

On 5/14/2022 3:45 AM, Mikko wrote:
> On 2022-05-13 22:57:47 +0000, olcott said:
>
>> 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.
>
> There is a category error in that statement. Mathematical truths do not
> refer to empirical facts so they cannot be empirically proven. Whether
> H(P,P) == 0 is true or false is a mathematical question so it cannot be
> determined empirically.
>
> Mikko
>

In programming language theory and proof theory, the Curry–Howard
correspondence (also known as the Curry–Howard isomorphism or
equivalence, or the proofs-as-programs and propositions- or
formulae-as-types interpretation) is the direct relationship between
computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

--
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: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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Subject: Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]
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 by: Mikko - Sat, 14 May 2022 12:55 UTC

On 2022-05-14 09:28:20 +0000, olcott said:

> On 5/14/2022 3:45 AM, Mikko wrote:
>> On 2022-05-13 22:57:47 +0000, olcott said:
>>
>>> 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.
>>
>> There is a category error in that statement. Mathematical truths do not
>> refer to empirical facts so they cannot be empirically proven. Whether
>> H(P,P) == 0 is true or false is a mathematical question so it cannot be
>> determined empirically.
>>
>> Mikko
>>
>
> In programming language theory and proof theory, the Curry–Howard
> correspondence (also known as the Curry–Howard isomorphism or
> equivalence, or the proofs-as-programs and propositions- or
> formulae-as-types interpretation) is the direct relationship between
> computer programs and mathematical proofs.
> https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

That is a mathematical equivalence between mathematical structures.
Nothing empirical there.

Mikko

Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

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 by: olcott - Sat, 14 May 2022 13:53 UTC

On 5/14/2022 7:55 AM, Mikko wrote:
> On 2022-05-14 09:28:20 +0000, olcott said:
>
>> On 5/14/2022 3:45 AM, Mikko wrote:
>>> On 2022-05-13 22:57:47 +0000, olcott said:
>>>
>>>> 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.
>>>
>>> There is a category error in that statement. Mathematical truths do not
>>> refer to empirical facts so they cannot be empirically proven. Whether
>>> H(P,P) == 0 is true or false is a mathematical question so it cannot be
>>> determined empirically.
>>>
>>> Mikko
>>>
>>
>> In programming language theory and proof theory, the Curry–Howard
>> correspondence (also known as the Curry–Howard isomorphism or
>> equivalence, or the proofs-as-programs and propositions- or
>> formulae-as-types interpretation) is the direct relationship between
>> computer programs and mathematical proofs.
>> https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
>
> That is a mathematical equivalence between mathematical structures.
> Nothing empirical there.
>
> Mikko
>

proofs-as-programs and programs do run, thus the mapping between the
math and empirical validation of this math. C is a formal language of a
formal system.

--
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: Proof that H(P,P)==0 is correct [ foundation of truth itself ]

<t5qfor$oek$1@dont-email.me>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=32532&group=comp.theory#32532

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: mikko.le...@iki.fi (Mikko)
Newsgroups: comp.theory
Subject: Re: Proof that H(P,P)==0 is correct [ foundation of truth itself ]
Date: Sun, 15 May 2022 12:05:31 +0300
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 by: Mikko - Sun, 15 May 2022 09:05 UTC

On 2022-05-14 13:53:29 +0000, olcott said:

> On 5/14/2022 7:55 AM, Mikko wrote:
>> On 2022-05-14 09:28:20 +0000, olcott said:
>>
>>> On 5/14/2022 3:45 AM, Mikko wrote:
>>>> On 2022-05-13 22:57:47 +0000, olcott said:
>>>>
>>>>> 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.
>>>>
>>>> There is a category error in that statement. Mathematical truths do not
>>>> refer to empirical facts so they cannot be empirically proven. Whether
>>>> H(P,P) == 0 is true or false is a mathematical question so it cannot be
>>>> determined empirically.
>>>>
>>>> Mikko
>>>>
>>>
>>> In programming language theory and proof theory, the Curry–Howard
>>> correspondence (also known as the Curry–Howard isomorphism or
>>> equivalence, or the proofs-as-programs and propositions- or
>>> formulae-as-types interpretation) is the direct relationship between
>>> computer programs and mathematical proofs.
>>> https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
>>
>> That is a mathematical equivalence between mathematical structures.
>> Nothing empirical there.
>>
>> Mikko
>>
>
> proofs-as-programs and programs do run, thus the mapping between the
> math and empirical validation of this math.

Even when the same text can be interpreted as a proof or as a program,
those interpretaions involve different semantics. Therefore the execution
does not validate anything beyond the syntax.

> C is a formal language of a formal system.

No, it is not. The definition C leaves much unspecified and allows
unspecified extensions. Conseqently, one confoming C implementation
may accept a program that another conforming implementation rejects,
and the same conforming C program may produce different results when
run in tow different cocforming implementations.

Mikko

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