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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise
Date: Fri, 5 Jul 2024 17:18:07 -0400
Organization: i2pn2 (i2pn.org)
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On 7/5/24 4:12 PM, olcott wrote:
> On 7/5/2024 2:54 PM, Richard Damon wrote:
>> On 7/5/24 1:38 PM, olcott wrote:
>>> On 7/5/2024 11:23 AM, Richard Damon wrote:
>>>> On 7/4/24 11:19 PM, olcott wrote:
>>>>> On 7/4/2024 10:00 PM, Richard Damon wrote:
>>>>>> On 7/4/24 10:38 PM, olcott wrote:
>>>>>>> On 7/4/2024 8:58 PM, Mild Shock wrote:
>>>>>>>>
>>>>>>>> When red means blue, and yellow means
>>>>>>>> green, then black is white. Thanks for your hint!
>>>>>>>>
>>>>>>>> If my Grandmother had wheels she would have been a bike
>>>>>>>> https://www.youtube.com/watch?v=OplyHCIBmfE
>>>>>>>>
>>>>>>>
>>>>>>> *Here is the same thing more clearly*
>>>>>>> Every expression of language that is {true on the basis of
>>>>>>> its verbal meaning} is only made true by a sequence of truth
>>>>>>> preserving operations to this {verbal meaning}.
>>>>>>>
>>>>>>> The only way that we know that puppies are not fifteen
>>>>>>> story office buildings is that the accurate verbal model
>>>>>>> of the actual world tells use so.
>>>>>>
>>>>>> But, even if we can't find that sequence of truth perserving 
>>>>>> operations, but one exists (which might be infinite) makes the 
>>>>>> statement true, but not known.
>>>>>>
>>>>>> This is one of your confusions, You confuse a statment being True, 
>>>>>> with the statement being KNOWN to be True.
>>>>>>
>>>>>> There are a number of great problems and conjectures that seem to 
>>>>>> be true, but we can not prove them. They MUST be either True or 
>>>>>> False, as by their nature, there is no middle ground (something 
>>>>>> either exsits or it doesn't, or the count of something is either 
>>>>>> finite or infinite).
>>>>>>
>>>>>> The ACTUAL TRUTH  (or falsehood) of such a statement is thus 
>>>>>> firmly established by the system in which the conjeture is 
>>>>>> embedded, even if our knowledge of the value of the truth of the 
>>>>>> statement is not known, or possible even knowable.
>>>>>>
>>>>>> The concept of "incompleteness" for a logical system is a 
>>>>>> recognition that the system has grown powerful enough that there 
>>>>>> exist some truths in the system that no finite proof of those 
>>>>>> statements exist, and only infinite chains of inference in the 
>>>>>> system can establish it.
>>>>>>
>>>>>> Mathematics is one source for these sorts of truths, as the 
>>>>>> possiblity of problems having NO number that satisfy them, or an 
>>>>>> infinite number that satisfy them show paths that can use in 
>>>>>> infinite number of steps to prove them, and might only be provable 
>>>>>> if some "inductive" shortcut can be found.
>>>>>>
>>>>>
>>>>> Yet my system screens out pathological expressions that
>>>>> are incorrectly determined to be incompleteness of the
>>>>> formal system. When we do that then True(L,x) can be defined
>>>>> for every expression not requiring an infinite sequence
>>>>> of steps. True(L,x) or True(L,~x) or not a truth bearer in L.
>>>>
>>>> No, it dies in self-inconsistency.
>>>>
>>>> Note "Every expression BUT ..."  isn't "Every expresion ."
>>>>
>>>
>>> Every expression such that neither X nor ~X is provable in L
>>> is simply not a truth bearer in L. This does correctly reject
>>> self-contradictory expressions that wold otherwise be interpreted
>>> as the incompleteness of L.
>>
>> FALSE STATEMENT.
>>
> 
> Can't be false it is stipulated.

Can't stipulate that something is true.

Also, stipulating a definition contrary to the system puts you out of 
the system.

> 
>> Some statements are true due to an infinite number of steps to ther 
>> truth-makers of the system.
>>
> 
> Already covered that.

Nope. That is just stipulating that you system is contradictory.

> 
>> You will lead your logic system into contradictions by your definition 
>> (or you just need to treat it as a worthless phrase that doesn't 
>> actually tell you anything, particually what you call 
>> non-truth-bearers, which might actuall be statement that are true or 
>> false).
>>
> 
> Not at all. Such a system does detect and reject self-contradictory
> expressions thus does not use this as any basis for incompleteness.

Nope, it just puts your logic outside of most logic systems, and unable 
to hamdle most of the problems people really care about.

> 
>>>
>>> This works correctly for every element of the accurate verbal
>>> model of the actual world. Since we can see that things like
>>> the Goldbach conjecture can be proven *OR REFUTED* in an infinite
>>> sequence then an algorithm can see this too. For everything
>>> else it is an infallibly correct system of reasoning.
>>>
>>
>> So, you ADMIT that you definition doesn't work for some statements, 
>> and thus is not correct.
>>
> 
> It detects expressions that require infinite steps as out
> of scope and correctly determines all of the rest.

Nope, it defines your system as self-contradictory, as things like tht 
GoldBach conjecture are defined as BOTH non-truth-bearers, and as 
truth-bearers.

That seems to be the lie for your logic, that you just allow yourself to 
be wrong at times, which makes your logic worthless.

> 
>> Note, the algorithm can not tell wether the statement like to Goldback 
>> conjecture is true or not, or even if it takes an infinite number of 
>> steps to come to that answer. Thus, you statement is just a FALSEHOOD.
>>
> Not at all. Because it is dead obvious to humans that Goldbach
> can be proved or refuted in an infinite number of steps an
> algorithm can see this too.

But it might not need an infinite number of steps to refute it.

And that second definition contradicts your first, as the first defines 
Goldmach (if true) to be a non-truth-bearer, while the second tries to 
contradict that to say it is.

You can't do that in two different statements.

> 
>> You just don't understand logic well enough to understand that can't 
>> have definitions that just don't work as the basis of a system.
>>
>> By your definition, the Goldbach conjecture must currently be consider 
>> a non-truth-bearer, but we KNOW that it must be either true or false, we 
> 
> It would be construed as out-of-scope.
> Whether or not there was evidence of:
> (a) Election fraud that could have possibly changed
> the outcome of the 2020 presidential election or
> (b) Very harmful climate change caused by humans
> would be in scope.

Since both of those statements are based on EMPERICAL evidence, they are 
outside the scope of analytical logic.

> 
>> just don't know which, so you definition of a truth-bearer is just a lie.
>>
>> What you are defining are KNOWLEDGE bearers, statements that there 
>> truth can be known. 
> 
> The key problem that it solves is that it makes True(L,x)
> computable for all of the most important things that really
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