Path: ...!weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Truthmaker Maximalism and undecidable decision problems --- the way truth really works
Date: Wed, 12 Jun 2024 10:13:31 +0300
Organization: -
Lines: 82
Message-ID: <v4bhqr$1hqq1$1@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> <v44suh$3m841$4@dont-email.me> <v4693h$8jv1$1@dont-email.me> <v473en$ggn5$3@dont-email.me> <v48vbe$us2b$1@dont-email.me> <v49sla$14ek5$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 12 Jun 2024 09:13:31 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="e515b1279c357cb12b13f8f2101e67a0";
	logging-data="1633089"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19px44M+XdFFaTDhn4Yj59l"
User-Agent: Unison/2.2
Cancel-Lock: sha1:jfV8xVA+7Q2O5jIdCDf2c1VIFwk=
Bytes: 4712

On 2024-06-11 16:06:02 +0000, olcott said:

> 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*

As far as is empirially known. But a formal system is not limited by
the limitations of our empirical knowledge.

-- 
Mikko