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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems
Date: Tue, 11 Jun 2024 10:45:50 +0300
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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.

> People are free to stipulate the value of PI as exactly
> 3.0 and they are simply wrong.

But they are free to use the small greek letter pi for other purposes.

-- 
Mikko