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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Wed, 24 Jul 2024 21:05:10 -0400
Organization: i2pn2 (i2pn.org)
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On 7/24/24 8:44 PM, olcott wrote:
> On 7/24/2024 6:57 PM, Richard Damon wrote:
>> On 7/24/24 10:20 AM, olcott wrote:
>>> On 7/24/2024 6:28 AM, Richard Damon wrote:
>>>> On 7/24/24 12:09 AM, olcott wrote:
>>>>> On 7/23/2024 10:27 PM, Richard Damon wrote:
>>>>>> On 7/23/24 11:17 PM, olcott wrote:
>>>>>>> On 7/23/2024 10:03 PM, Richard Damon wrote:
>>>>>>>> On 7/23/24 10:45 PM, olcott wrote:
>>>>>>>>> On 7/23/2024 9:15 PM, Richard Damon wrote:
>>>>>>>>>> On 7/23/24 12:26 PM, olcott wrote:
>>>>>>>>>>> On 7/23/2024 9:51 AM, Wasell wrote:
>>>>>>>>>>>> On Mon, 22 Jul 2024 20:17:15 -0400, in article
>>>>>>>>>>>> <3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org>, 
>>>>>>>>>>>> Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 7/22/24 8:11 PM, olcott wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> [...]
>>>>>>>>>>>>
>>>>>>>>>>>>>> *No stupid I have never been saying anything like that* If 
>>>>>>>>>>>>>> g and
>>>>>>>>>>>>>> ~g is not provable in PA then g is not a truth-bearer in PA.
>>>>>>>>>>>>>
>>>>>>>>>>>>> What makes it different fron Goldbach's conjecture?
>>>>>>>>>>>>
>>>>>>>>>>>> I think a better example might be Goodstein's theorem [1].
>>>>>>>>>>>>
>>>>>>>>>>>> * It is expressible in the same language as PA.
>>>>>>>>>>>>
>>>>>>>>>>>> * It is neither provable, nor disprovable, in PA.
>>>>>>>>>>>>
>>>>>>>>>>>> * We know that it is true in the standard model of arithmetic.
>>>>>>>>>>>>
>>>>>>>>>>>> * We know that it is false in some (necessarily 
>>>>>>>>>>>> non-standard) models
>>>>>>>>>>>>    of arithmetic.
>>>>>>>>>>>>
>>>>>>>>>>>> * It was discovered and proved long before it was shown to be
>>>>>>>>>>>>    undecidable in PA.
>>>>>>>>>>>>
>>>>>>>>>>>> The only drawback is that the theorem is somewhat more 
>>>>>>>>>>>> complicated
>>>>>>>>>>>> than Goldbach's conjecture -- not a lot, but a bit.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> [1] <https://en.wikipedia.org/wiki/Goodstein%27s_theorem>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> I am establishing a new meaning for
>>>>>>>>>>> {true on the basis of meaning expressed in language}
>>>>>>>>>>> Formerly known as {analytic truth}.
>>>>>>>>>>> This makes True(L,x) computable and definable.
>>>>>>>>>>
>>>>>>>>>> You may say that, but you then refuse to do the work to 
>>>>>>>>>> actually do that.
>>>>>>>>>>
>>>>>>>>>> The problem is that if you try to redefine the foundation, you 
>>>>>>>>>> need to build the whole building all over again, but you just 
>>>>>>>>>> don't understand what you need to do that.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> L is the language of a formal mathematical system.
>>>>>>>>>>> x is an expression of that language.
>>>>>>>>>>>
>>>>>>>>>>> When we understand that True(L,x) means that there is a finite
>>>>>>>>>>> sequence of truth preserving operations in L from the semantic
>>>>>>>>>>> meaning of x to x in L, then mathematical incompleteness is 
>>>>>>>>>>> abolished.
>>>>>>>>>>
>>>>>>>>>> Except you just defined that this isn't true, as you admit 
>>>>>>>>>> that the Goldbach conjecgture COULD be an analytic truth even 
>>>>>>>>>> if it doesn't have a finte sequence of truth perserving 
>>>>>>>>>> operations, 
>>>>>>>>>
>>>>>>>>> I redefined analytic truth to account for that. Things
>>>>>>>>> like the Goldbach conjecture are in the different class
>>>>>>>>> of currently unknowable.
>>>>>>>>
>>>>>>>> In other words, NOTHING you are talking about apply to the logic 
>>>>>>>> that anyone else is using.
>>>>>>>>
>>>>>>>> Note, Godel's G can't be put into that category, as it is KNOWN 
>>>>>>>> to be true in PA, because of a proof in MM 
>>>>>>>
>>>>>>> You ONLY construe it to be true in PA because that is
>>>>>>> the answer that you memorized.
>>>>>>
>>>>>> No, it is True in PA, because it is LITERALLY True by the words it 
>>>>>> uses.
>>>>>>
>>>>>>>
>>>>>>> When you understand that true requires a sequence of
>>>>>>> truth preserving operations and they do not exist in
>>>>>>> PA then it is not true in PA.
>>>>>>
>>>>>> But they DO exist in PA, I guess you just don't understand how 
>>>>>> math works.
>>>>>>
>>>>>> The sequence of steps is:
>>>>>>
>>>>>> Check the number 0 to see if it satisfies the PRR. Answer = No.
>>>>>> Check the number 1 to see if it satisfies the PRR. Answer = No.
>>>>>> Check the number 2 to see if it satisfies the PRR. Answer = No.
>>>>>>
>>>>>> keep repeating counting up through all the Natural Numbers.
>>>>>>  From the trick in MM, we can see that the math in PA will say no 
>>>>>> to all of them.
>>>>>>
>>>>>> Thus, after an infinite number of steps of truth preserving 
>>>>>> operations, we reach the conclusion that NO natural numbers 
>>>>>> actually exist that meet that PRR, just like G claimed, so it is 
>>>>>> correct.
>>>>>>
>>>>>
>>>>> The lack of a proof means untruth.
>>>>
>>>> Nope, lack of a proof means unknown, as you have agreed. 
>>>
>>> If an infinite number of steps fail to show that G is
>>> provable in PA then G is untrue in PA.
>>
>> But the infinte number of steps DO show that G is true in PA, because 
>> is shows that EVERY Natural Number fails to meet the requirment.
>>
> 
> No stupid it does not shown this.
> An infinite number of steps fail to meet the requirement
> of showing that G is true.

Then how does that same sort of infinite sequence make Goldbach's 
conjecture true.

> 
> "This sentence is not true" is indeed not true and that
> *does not make it true* even though its assertion is satisfied.
> 

So? That isn't the chain that G uses. The fact that you are just showing 
your STUPIDITY doesn't make other people wrong for using concepts thhat 
are just too complicated for yolu.

I'm sorry, but it seems that you are just incapable of understanding the 
simple principles that are needed, but that seems to be because you have 
just gaslit yourself into your stupid state, as you are just proving to 
the world.

If you don't think so, you are just deluding yourself, and you may die 
"happy", but still stupidly wrong.