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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 23:00:51 -0400
Organization: i2pn2 (i2pn.org)
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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.
> 
>> Note, some Formal Logic system specifically DEFINE how to handle 
>> inconsistant statements (typically uses a non-binary logic system, 
>> which makes the term "inconsistant" somewhat of a poorly defined term).
>>
> 
> If they do not reject inconsistent axioms then they are wrong.
> 
>>>
>>>>>
>>>>> *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
>>>>
>>>> Nope, only for systems that accept those requirements.
>>>>
>>>> There are (typically non-binary) systems that do not include one or 
>>>> both of the first two "laws".
>>>>
>>>
>>> I personally construe those as nonsense.
>>> True, False and not a truth-bearer are the only ones
>>> that I consider correct.
>>>
>>
>>
>> So, you admit that you logic system isn't the classical binary system, 
>> and thus not applicable for most classical logic based on binary 
>> logic, and that you mind is just unimaginative enough to handle 
>> broader systems of logic.
>>
> 
> Classic logic makes sure to ignore that some expressions
> of language are not truth-bearers.

Not "ignore" but restrict out of the system.

> 
>> I guess you just admitted that your definiton of 
> 
> I defined the foundation of ALL truth, when logic diverges
> from this then logic is incorrect.

Not allowed.

You may want to, but you can't.

Logic systems have been defined without your rules, and you can't force 
them to take them. You just automatically kick yourself out of them.

> 
> 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.

But that doesn't work in some systems.

Note, "the universe" doesn't matter in formal systems, unless you define 
"the universe" to BE the formal system.

> 
>> a "Foundation of Logic" has just defined yourself out of all the 
>> fields you want to talk about, since they do NOT have the logic value 
>> of "not a truth-bearer".
>>
>>
>