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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Wed, 24 Jul 2024 09:20:47 -0500
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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.

> 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.

> 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.

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

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