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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems --- the way truth really works
Date: Wed, 12 Jun 2024 16:41:10 +0300
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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.

-- 
Mikko