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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: The key undecidable instance that I know about === Exclude
 Non-Truth-bearers Knucklehead !!!
Date: Sat, 15 Mar 2025 13:59:22 -0500
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On 3/15/2025 6:16 AM, joes wrote:
> Am Fri, 14 Mar 2025 22:54:51 -0500 schrieb olcott:
>> On 3/14/2025 8:57 PM, Richard Damon wrote:
>>> On 3/14/25 3:01 PM, olcott wrote:
>>>> On 3/14/2025 1:42 PM, Richard Damon wrote:
>>>>> On 3/14/25 10:27 AM, olcott wrote:
>>>>>> On 3/13/2025 6:08 AM, Mikko wrote:
>>>>>>> On 2025-03-11 23:26:28 +0000, olcott said:
>>>>>>>> On 3/11/2025 6:15 AM, Mikko wrote:
>>>>>>>>> On 2025-03-10 15:36:28 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> I created Minimal Type Theory such that self-reference can be
>>>>>>>>>> expressed concisely and correctly.
>>>>>>>>> Have you pbulished that "Minimal Type Theory" or put it to a web
>>>>>>>>> page?
>>>>>>>>> Without a pointer to it there is no point to mention it. Of
>>>>>>>>> course one can create a language that can express a self
>>>>>>>>> reference but why would one?
>>>>>>>>
>>>>>>>> https://www.researchgate.net/
>>>>>>>> publication/315367846_Minimal_Type_Theory_MTT
>>>>>>> Does not define any theory.
>>>>>>>
>>>>>>>> https://www.researchgate.net/
>>>>>>>> publication/331859461_Minimal_Type_Theory_YACC_BNF
>>>>>>> The article 315367846_Minimal_Type_Theory_MTT says that "Types must
>>>>>>> be expressly stated in Minimal Type Theory" but the syntax allows
>>>>>>> untyped quantification.
>>>>>>>
>>>>>>>> https://www.researchgate.net/
>>>>>>>> publication/317953772_Provability_with_Minimal_Type_Theory
>>>>>>> This article uses @ as definition article but a comment in the
>>>>>>> syntax says that := is used.
>>>>>>> None of the articles defines what is a valid proof in Minimal Type
>>>>>>> Theory.
>>>>>>>
>>>>>>>> We need such a language so that we don't stupidly fail to
>>>>>>>> understands how this can convert expressions of language into
>>>>>>>> non-truth-bearers having no truth value.
>>>>>>>> Until we do this we get confused into believing that such
>>>>>>>> expressions are in any way undecidable.
> So is the Liar sentence false or not?
> 
>>>>>>>>>> Apparently this cannot be expressed concisely and correctly in
>>>>>>>>>> any formal logic system.
>>>>>>>>> A self reference cannot be expressed in an uninterpreted formal
>>>>>>>>> language.
>>>>>>>>> Sometimes some symbols and expressions are interpreted to
>>>>>>>>> represent themselves or other symbols or expressions. For
>>>>>>>>> example, the symbol 0 of arthmetic can be interpreted to mean the
>>>>>>>>> symbol 0 and the term S0 the sqence of symbols S and 0.
>>>>>>>>
>>>>>>>> LP := ~True(LP)
>>>>>>>> has all of its semantics encoded in its syntax, thus no
>>>>>>>> interpretation required.
>>>>>>>
>>>>>>> Without decoding no semantics can be extracted from the syntax.
>>>>>>>
>>>>>> LP := ~True(LP) obtains its entire semantics from the expression.
>>>>>
>>>>> But none of your arguments have talked about an expression that
>>>>> derives itself from that expression
> 
> 
>>>>>> Because of the cycle in the directed graph of its evaluation
>>>>>> sequence LP cannot derive its semantic meaning from anything else:
>>>>>> ~True(~True(~True(~True(~True(~True(...))))))
>>>>> But the p that can be developed as a statement in the languaged,
>>>>> based on the idea in the metalanguge that must be true if and only if
>>>>> it is false, doesn't.
> 
> 
>>>>>> Normally expressions derive their semantics from a knowledge
>>>>>> ontology inheritance hierarchy.
>>>>>> https://en.wikipedia.org/wiki/Ontology_(information_science)
>>>>> Right, like Godel's expression G specifically derives its semantics
>>>>> from the natured of the system F and the mathematics the system F
>>>>> creates. And, in the meta we can construct a mathematical statement
>>>>> in F, whose truth is the direct opposite of its provability, and thus
>>>>> must be True and Unprovable, as it can't be False but Provably True.
> 
> 
>>>>>> of the set of general knowledge of the world encoded as Rudolf
>>>>>> Carnap meaning postulates using something like Montague Grammar.
>>>>>> Each unique sense meaning has its own GUID.
>>>>> WHich is irrelevent here, as Formal systems don't have that problem.
>>>>> Your problem
>>>> In my type theory based system there is no need for any separate
>>>> language and meta-language.
> *Need*? You can always construct a metalanguage.
> 
>>>> Rudolf Carnap meaning postulates are arranged in an inheritance
>>>> hierarchy where each unique sense meaning is assigned its own GUID.
>>>> The language is something like Montague Grammar.
>>>> LP := ~True(LP) is rejected as semantically incorrect.
>>> but the existing systens aren't built on your "Type Theory" so you need
>>> to show that it works in THOSE systems to use it,
>> Discard all inferior systems.
> 
> 
>>> I guess you are just admitting that you don't understand what you are
>>> talking about, and your "logic" assumes you can just make up crap and
>>> call it true,
>> We axiomatize all the basic facts of the world (facts that cannot be
>> derived on the basis of other facts).
>> Then we plug everything else into an inheritance hierarchy knowledge
>> ontology.
>> Anything that cannot be derived by applying Truth preserving operations
>> to these basic facts is either untrue or unknown.
>> This gives us a True() predicate that always works except for unknowns.
> Wonderful. So not always.
> 
>> It certainty does not get totally confused by self-contradictory
>> expressions. These simply cannot be derived by applying truth preserving
>> operations to basic facts.
> Yeah, it can't decide their truth value.
> 

That is like me saying that you are to stupid to
correctly determine the truth value of this sentence:
"What time is it?"

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer