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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Thu, 25 Jul 2024 19:35:16 -0400
Organization: i2pn2 (i2pn.org)
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On 7/25/24 10:12 AM, olcott wrote:
> 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.
> 


No, I said that No Natural Number satisfied the PRR, just as G said they 
wouldn't

You clearly just don't understand English, because of the blinders you 
have built into yourself by your self-brainwashing.

That has just made you into the ignrorant pathological lying idiot wthh 
a reckless disregard for the truth that you have proven yourself to be.