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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: Thu, 13 Jun 2024 11:17:42 -0500
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On 6/13/2024 10:40 AM, Mikko wrote:
> On 2024-06-13 12:21:27 +0000, olcott said:
> 
>> On 6/13/2024 1:17 AM, Mikko wrote:
>>> On 2024-06-12 17:00:44 +0000, olcott said:
>>>
>>>> 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.
>>>
>>> Both of those claims are false about typical formal systems.
>>>
>>
>> When we define formal systems this way all ambiguity and vagueness is
>> eliminated. This is best exemplified in formalized English.
> 
> Typical formal system avoid ambiguity with different methods.
> Nothing mentioned above restritcs what a formal system can say.
> 

When we ask the question: What is a truthmaker?
The generic answer is whatever makes an expression of language true <is> 
its truthmaker.

If of everything there is nothing that makes expression of language X 
true then X is untrue.

The above establishes a key basis of ALL truth, truth within formal
systems is a tiny subset of this.

>> When I say I am going to drive my {cat}. this could mean
>> Transport(pet, veterinarian) operate(earth_moving_equipment).
>> When each sense meaning of every term has its own GUID then we
>> don't have to "interpret" what is mean this is fully specified.
> 
> 

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