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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 19:57:03 -0400
Organization: i2pn2 (i2pn.org)
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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.

YOu don't seem to be understanding the English, I think your brainwashed 
filter is just clogged.

> 
>> After all, you admitted that if the Goldbach conjecture would be an 
>> Analytic TRUTH if it was only established by an infinite sequence of 
>> truth preserving operations.
>>
> 
> If an infinite number of steps do show that Goldbach is
> provable in PA then Goldbach is true in PA.

Right, Just like they showed that G is true.

> 
>> Since you don't know the meaning of the words, you just prove yourself 
>> unqualified to talk about such things.
>>
> 
> Any proof requiring an infinite number of steps never resolved
> to a truth value thus its truth value remains unknown.

No, "Proofs" can not have an infinite number of steps, proofs are ALWAYS 
finite in conventional logic.



> 
> An alternative finite proof in MM only shows that the expression
> is true in MM.

Nope, since the rules of math are the same, it must also be true in PA.

I guess you think that just because 2+3 = 5 in one system with normal 
mathematics, in another system with the exact same rules for mathematics 
then 2 + 3 might be 6.

> 
> Truthmakers cannot cross system boundaries. --
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer
> 

But the base truthmakers for G in MM and PA are the same items, there is 
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