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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems
Date: Sun, 9 Jun 2024 22:56:45 -0400
Organization: i2pn2 (i2pn.org)
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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 formal system that defines inconsistant axioms, is still a formal 
system, and defines inconsistent axioms.

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

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".