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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Thu, 25 Jul 2024 09:12:12 -0500
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On 7/24/2024 8:05 PM, Richard Damon wrote:
> 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. 

You already admitted that after an infinite sequence of operations
G is not satisfied in PA.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer