Path: ...!2.eu.feeder.erje.net!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic,comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems
Date: Sun, 9 Jun 2024 13:40:16 -0500
Organization: A noiseless patient Spider
Lines: 76
Message-ID: <v44suh$3m841$4@dont-email.me>
References: <v44i60$3jnc8$1@dont-email.me> <v44o5t$3l9t2$1@dont-email.me>
 <v44r29$3egpa$5@i2pn2.org> <v44rd0$3m841$2@dont-email.me>
 <v44sa5$3egpa$10@i2pn2.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Sun, 09 Jun 2024 20:40:17 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="f8e472f6a5ded880f3c8d2cedf42e75a";
	logging-data="3874945"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19vjNrMVK87rp9BQoQZs1z0"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:jiCHnulntVsPO7RT2tWPcW5N3+k=
In-Reply-To: <v44sa5$3egpa$10@i2pn2.org>
Content-Language: en-US
Bytes: 4083

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.

>>
>> *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.

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