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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Wed, 24 Jul 2024 19:44:42 -0500
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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.

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


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