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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Truthmaker Maximalism and undecidable decision problems --- the
 way truth really works
Date: Tue, 11 Jun 2024 11:06:02 -0500
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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*
*People are free to disagree and simply be wrong*

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 truthbearer. X is a
truthbearer iff (if and only if) X or ~X has a truthmaker.


>> 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.
> 

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer