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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 19:45:18 +0300
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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 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.

-- 
Mikko