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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: Thu, 13 Jun 2024 09:17:44 +0300
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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.

-- 
Mikko