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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 07:21:27 -0500
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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.

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