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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems
Date: Sun, 9 Jun 2024 22:12:57 -0500
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On 6/9/2024 9:56 PM, Richard Damon wrote:
> On 6/9/24 10:47 PM, olcott wrote:
>> On 6/9/2024 2:36 PM, Richard Damon wrote:
>>> On 6/9/24 3:08 PM, olcott wrote:
>>>> On 6/9/2024 1:54 PM, Richard Damon wrote:
>>>>> On 6/9/24 2:40 PM, olcott wrote:
>>>>>> 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.
>>>>>
>>>>> So, you admit that your definition is just inconsistant, as it says 
>>>>> FOR ALL and then you admit it isn't FOR ALL
>>>>>
>>>>> And a formal system proven inconsistant isn't necessarily 
>>>>> incorrect, just inconsistent.
>>>>>
>>>>
>>>> To the extent that they define inconsistency they
>>>> are not truth-makers.
>>>
>>>
>>> YOU hae a TYPE ERROR in your statement.
>>>
>>> That just proves that YOUR logic is incorrect.
>>>
>>> How can a SYSTEM be a propsition?
>>>
>>
>> *Stopping at your first big mistake*
>>
>> When we ask the question: What is a truthmaker? The generic answer is 
>> whatever makes an expression of language true <is> its truthmaker.
>>
>> A cat in your living room is not a proposition yet makes the
>> sentence: "there is a cat in my living room" true, thus <is> its
>> truthmaker.
>>
> 
> Which isn't a formal system.
> 

A cat in your living room <is> a truthmaker and is not
a formal system.

> A formal system that defines inconsistant axioms, is still a formal 
> system, and defines inconsistent axioms.
> 

Yes and it is wrong.

> It may well be a formal system DESIGNED to handle inconsistant 
> statements, by using multi-valued logic.
> 

That is not the way that truth really works.
Did a person invent the value of PI or discover it?

I am not inventing the notion of truthmaker I am making this notion
more clear.

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.

> It might be based on a limited form of logic that prevents the principle 
> of explosion from happening, and thus even with some inconsistancies, it 
> can be used to show some other useful results.
> 
> That doesn't make the system "not true".
> 
> YOu are just showing that you concept of logic is way too limited to be 
> "the ultimate definition of logic".
> 
> 

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