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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems --- the
 way truth really works
Date: Wed, 12 Jun 2024 12:00:44 -0500
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On 6/12/2024 11:45 AM, Mikko wrote:
> On 2024-06-12 14:08:43 +0000, olcott said:
> 
>> On 6/12/2024 8:41 AM, Mikko wrote:
>>> On 2024-06-12 12:44:55 +0000, olcott said:
>>>
>>>> On 6/12/2024 2:13 AM, Mikko wrote:
>>>>> On 2024-06-11 16:06:02 +0000, olcott said:
>>>>>
>>>>>> On 6/11/2024 2:45 AM, Mikko wrote:
>>>>>>> On 2024-06-10 14:43:34 +0000, olcott said:
>>>>>>>
>>>>>>>> On 6/10/2024 2:13 AM, Mikko wrote:
>>>>>>>>> On 2024-06-09 18:40:16 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 6/9/2024 1:29 PM, Richard Damon wrote:
>>>>>>>>>>> On 6/9/24 2:13 PM, olcott wrote:
>>>>>>>>>>>> On 6/9/2024 1:08 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 6/9/24 1:18 PM, olcott wrote:
>>>>>>>>>>>>>> On 6/9/2024 10:36 AM, olcott wrote:
>>>>>>>>>>>>>>> *This has direct application to undecidable decision 
>>>>>>>>>>>>>>> problems*
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> When we ask the question: What is a truthmaker? The 
>>>>>>>>>>>>>>> generic answer is
>>>>>>>>>>>>>>> whatever makes an expression of language true <is> its 
>>>>>>>>>>>>>>> truthmaker. This
>>>>>>>>>>>>>>> entails that if there is nothing in the universe that 
>>>>>>>>>>>>>>> makes expression X
>>>>>>>>>>>>>>> true then X lacks a truthmaker and is untrue.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> X may be untrue because X is false. In that case ~X has a 
>>>>>>>>>>>>>>> truthmaker.
>>>>>>>>>>>>>>> Now we have the means to unequivocally define 
>>>>>>>>>>>>>>> truth-bearer. X is a
>>>>>>>>>>>>>>> truth-bearer iff (if and only if) X or ~X has a truthmaker.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I have been working in this same area as a 
>>>>>>>>>>>>>>> non-academician for a few
>>>>>>>>>>>>>>> years. I have only focused on expressions of language 
>>>>>>>>>>>>>>> that are {true on
>>>>>>>>>>>>>>> the basis of their meaning}.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Now that truthmaker and truthbearer are fully anchored it 
>>>>>>>>>>>>>> is easy to see
>>>>>>>>>>>>>> that self-contradictory expressions are simply not 
>>>>>>>>>>>>>> truthbearers.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> “This sentence is not true” can't be true because that 
>>>>>>>>>>>>>> would make it
>>>>>>>>>>>>>> untrue and it can't be false because that would make it true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Within the the definition of truthmaker specified above: 
>>>>>>>>>>>>>> “this sentence
>>>>>>>>>>>>>> has no truthmaker” is simply not a truthbearer. It can't 
>>>>>>>>>>>>>> be true within
>>>>>>>>>>>>>> the above specified definition of truthmaker because this 
>>>>>>>>>>>>>> would make it
>>>>>>>>>>>>>> false. It can't be false because that makes
>>>>>>>>>>>>>> it true.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Unless the system is inconsistent, in which case they can be.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Note,
>>>>>>>>>>>>
>>>>>>>>>>>> When I specify the ultimate foundation of all truth then this
>>>>>>>>>>>> does apply to truth in logic, truth in math and truth in 
>>>>>>>>>>>> science.
>>>>>>>>>>>
>>>>>>>>>>> Nope. Not for Formal system, which have a specific definition 
>>>>>>>>>>> of its truth-makers, unless you let your definition become 
>>>>>>>>>>> trivial for Formal logic where a "truth-makers" is what has 
>>>>>>>>>>> been defined to be the "truth-makers" for the system.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Formal systems are free to define their own truthmakers.
>>>>>>>>>> When these definitions result in inconsistency they are
>>>>>>>>>> proved to be incorrect.
>>>>>>>>>
>>>>>>>>> A formal system can be inconsistent without being incorrect.
>>>>>>>>
>>>>>>>> *Three laws of logic apply to all propositions*
>>>>>>>> ¬(p ∧ ¬p) Law of non-contradiction
>>>>>>>>   (p ∨ ¬p) Law of excluded middle
>>>>>>>>    p = p   Law of identity
>>>>>>>> *No it cannot*
>>>>>>>
>>>>>>> Those laws do not constrain formal systems. Each formal system 
>>>>>>> specifies
>>>>>>> its own laws, which include all or some or none of those. 
>>>>>>> Besides, a the
>>>>>>> word "proposition" need not be and often is not used in the 
>>>>>>> specification
>>>>>>> of a formal system.
>>>>>>>
>>>>>>
>>>>>> *This is the way that truth actually works*
>>>>>
>>>>> As far as is empirially known. But a formal system is not limited by
>>>>> the limitations of our empirical knowledge.
>>>>
>>>> If there really is nothing anywhere that makes expression
>>>> of language X true then X is untrue.
>>>
>>> That does not restrict what a formal system can say.
>>
>> If a formal system says:
>> "cats <are> fifteen story office buildings"
>> this formal system is wrong.
> 
> No, it is not. If you inteprete a sentence of that language 

*Correct interpretation is hardwired into the formal language*
{cats} and {office buildings} are specified by 128-bit GUIDs.

> to aååly
> to cats in the real world then you are wrong. A formal system cannot
> be wrong just like the liar's paradox cannot be true.
> 

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer