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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: The error of the halting problem --- G is untrue in PA
Date: Tue, 4 Jun 2024 21:48:02 -0400
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On 6/4/24 1:45 PM, olcott wrote:
> On 6/4/2024 3:29 AM, joes wrote:
>> Am Mon, 03 Jun 2024 21:58:06 -0500 schrieb olcott:
>>> On 6/3/2024 9:47 PM, Richard Damon wrote:
>>>> On 6/3/24 10:32 PM, olcott wrote:
>>>>> On 6/3/2024 9:26 PM, Richard Damon wrote:
>>>>>> On 6/3/24 10:14 PM, olcott wrote:
>>>>>>> On 6/3/2024 8:58 PM, Richard Damon wrote:
>>>>>>>> On 6/3/24 9:51 PM, olcott wrote:
>>>>>>>>>
>>>>>>>>> When H is asked a yes/no question where both answers are
>>>>>>>>> contradicted by its input *IT IS A FREAKING RIGGED GAME*
>>>>>>>>
>>>>>>>> But both answers aren't wrong. Remember, the question is built to
>>>>>>>> make a SPECIFIC decider wrong, and by its algorithm, it will give a
>>>>>>>> SPECIFIC answer to each SPECIFIC question.
>>>>>>>>
>>>>>>> You can't get away with that head game by pretending to not
>>>>>>> understand what infinite an set of H/D pairs is.
>>>>>>
>>>>>> But it doesn't matter.
>>>>>>
>>>>> It matters enormously. Once we fully understand that the limits of
>>>>> computation were always a ruse then we can give computation the
>>>>> priority that it truly deserves. It might be the life on earth is
>>>>> killed off because we did not build a semantic lie detector quickly
>>>>> enough.
>>>>
>>>> But you are working on it wrong, because you just don't understand the
>>>> actual nature of truth.
>>>
>>> Every expression X that is true on the basis of its meaning can be
>>> proven untrue by a lack of a connection to the meaning that makes it
>>> true. *You have understood this better than anyone else*
>> No. "true expressions can be proven untrue"? There are true but 
>> unprovable
>> sentences (see Gödel).
>>
> 
> G cannot be linked by truth preserving operations to expressions of 
> language in PA that show that G is true in PA.

But it CAN.

Each natural number can be checked in a finite time against the 
primative recursive relationship, to see that it does not satisfy that 
relationship.

We can check EVERY SINGLE NUMBER, in a countable infinite number of 
steps, and thus establish that G, the statement that no natural number 
satisfies that relationship, is in fact true.

Your problem is you just don't understand what the statement G in PA 
actually is, because the math is just beyond you, so you replace it with 
something that isn't the same thing but can be shown to express things 
about the nature and implications of G.

So, your arguement is just proved to be a LIE, as most of your assertions.

> 
> G can be linked by truth preserving operations to expressions of 
> language in meta-math that show that G is true in meta-math.

Yes, and in the meta-math, we have a short cut, that actually allows us 
to PROVE the statement, not just have it established by an infinite 
number of steps.

> 
>>> When D is defined to contradict both values that H returns then D is not
>>> a truth bearer in H in the same way that the Liar Paradox "This sentence
>>> is not true" is not a truth bearer in English.
>>
>