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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: Analytic Truth-makers
Date: Tue, 23 Jul 2024 23:03:32 -0400
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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 that shows that no Natural Number 
(as both PA and MM have the same mathematics) can satisfy the 
relationship that was developed in MM using operations that exist in PA, 
so the relationship moves into PA.

So, PA has a statement that is known to be true in PA (but the knowledge 
come from outside PA, but in a way that IS transferable). This truth we 
can see can be established in PA by an infinite sequence of steps, that 
of checking each of the infinite set of Natural Numbers, and by doing a 
finite number of steps on each of them, show that that number does ot 
satisfy the relationship. From the proof in MM, we know that even in PA, 
no number can satisfy the relationship (remember, MM was defined to have 
the same mathematics as PA, so the math results transfer) due to the 
proof in MM.

So, if you really want to create your own logic, you will either need to 
prevent that sort of math from existing, or have some totally different 
form of logic, which you will need to fully define.

When you get your paper written FULLY EXPLAINING how it works, and what 
you can prove from it, you might have something.

Of course, considering you record for working out problems, it seems 
like it will have a snowflakes chance in hell to actually be written, so 
I won't hold my breath.

Of course, until you do create such a system and show what it can do, 
any comments you make about it are just baseless, and any attempt to 
apply it to other peoples work is just a LIE.

Since they didn't use your logic and your definition (how could they, 
you haven't actually fully formulated them) you can't hold them to it.

Of course, it seems you don't understand how that works, so good luck 
trying to create you own system.

> 
>> but only an infinite sequence. But a Analytic Truth MUST be a 
>> "truth-bearer", so you just blew up your whole logic system with your 
>> lies.
>>
>>>
>>> ~True(L,x) ∧ ~True(L,~x)
>>> means that x is not a truth-bearer in L.
>>> It does not mean that L is incomplete
>>>
>>
>