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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 12:23:26 -0400
Organization: i2pn2 (i2pn.org)
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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 ."

So, your logic only works in systems small enough to be somewhat akin to 
toys. Those that are limited enough not to be able to cause the 
problems, which means it excludes most systems that support math.

> 
>>>
>>>> olcott schrieb:
>>>>> When provable means true and false means unprovable
>>>>> then (Γ ⊢ X) means X is true in Γ.
>>>>> then (Γ ⊢ ~X) means X is conventional false  in Γ.
>>>>> the (Γ ⊬ X) ∧ (Γ ⊬ ~X) X is not a truth bearer in Γ.
>>>
>>
>