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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable --- truth-bearer
Date: Sat, 31 Aug 2024 07:18:20 -0500
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On 8/31/2024 3:43 AM, Mikko wrote:
> On 2024-08-30 14:45:32 +0000, olcott said:
> 
>> On 8/30/2024 8:36 AM, Mikko wrote:
>>> On 2024-08-29 13:36:00 +0000, olcott said:
>>>
>>>> On 8/29/2024 3:12 AM, Mikko wrote:
>>>>> On 2024-08-28 12:14:47 +0000, olcott said:
>>>>>
>>>>>> On 8/28/2024 2:45 AM, Mikko wrote:
>>>>>>> On 2024-08-24 03:26:39 +0000, olcott said:
>>>>>>>
>>>>>>>> On 8/23/2024 3:34 AM, Mikko wrote:
>>>>>>>>> On 2024-08-22 13:23:39 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 8/22/2024 7:06 AM, Mikko wrote:
>>>>>>>>>>> On 2024-08-21 12:47:37 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Formal systems kind of sort of has some vague idea of what True
>>>>>>>>>>>> means. Tarski "proved" that there is no True(L,x) that can be
>>>>>>>>>>>> consistently defined.
>>>>>>>>>>>> https://en.wikipedia.org/wiki/ 
>>>>>>>>>>>> Tarski%27s_undefinability_theorem#General_form
>>>>>>>>>>>>
>>>>>>>>>>>> *The defined predicate True(L,x) fixed that*
>>>>>>>>>>>> Unless expression x has a connection (through a sequence
>>>>>>>>>>>> of true preserving operations) in system F to its semantic
>>>>>>>>>>>> meanings expressed in language L of F then x is simply
>>>>>>>>>>>> untrue in F.
>>>>>>>>>>>>
>>>>>>>>>>>> Whenever there is no sequence of truth preserving from
>>>>>>>>>>>> x or ~x to its meaning in L of F then x has no truth-maker
>>>>>>>>>>>> in F and x not a truth-bearer in F. We never get to x is
>>>>>>>>>>>> undecidable in F.
>>>>>>>>>>>
>>>>>>>>>>> Tarski proved that True is undefineable in certain formal 
>>>>>>>>>>> systems.
>>>>>>>>>>> Your definition is not expressible in F, at least not as a 
>>>>>>>>>>> definition.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Like ZFC redefined the foundation of all sets I redefine
>>>>>>>>>> the foundation of all formal systems.
>>>>>>>>>
>>>>>>>>> You cannot redefine the foundation of all formal systems. Every 
>>>>>>>>> formal
>>>>>>>>> system has the foundation it has and that cannot be changed. 
>>>>>>>>> Formal
>>>>>>>>> systems are eternal and immutable.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Then According to your reasoning ZFC is wrong because
>>>>>>>> it is not allowed to redefine the foundation of set
>>>>>>>> theory.
>>>>>>>
>>>>>>> It did not redefine anything. It is just another theory. It is 
>>>>>>> called
>>>>>>> a set theory because its terms have many similarities to Cnator's 
>>>>>>> sets.
>>>>>>
>>>>>> It <is> the correct set theory. Naive set theory
>>>>>> is tossed out on its ass for being WRONG.
>>>>>
>>>>> There is no basis to say that ZF is more or less correct than ZFC.
>>>>
>>>> A set containing itself has always been incoherent in its
>>>> isomorphism to the concrete instance of a can of soup so
>>>> totally containing itself that it has no outside surface.
>>>> The above words are my own unique creation.
>>>
>>> There is no need for an isomorphism between a set an a can of soup.
>>> There is nothing inherently incoherent in Quine's atom. Some set
>>> theories allow it, some don't. Cantor's theory does not say either
>>> way.
>>>
>>
>> Quine atoms (named after Willard Van Orman Quine) are sets that only 
>> contain themselves, that is, sets that satisfy the formula x = {x}.
>> https://en.wikipedia.org/wiki/Urelement#Quine_atoms
>>
>> Wrongo. This is exactly isomorphic to the incoherent notion of a
>> can of soup so totally containing itself that it has no outside
>> boundary.
> 
> As I already said, that isomorphism is not needed. It is not useful.

It proves incoherence at a deeper level. Prior to my
isomorphism we only have Russell's Paradox to show
that there is a problem with Naive set theory.

That these kind of paradoxes are not understood to
mean incoherence in the system has allowed the issue
of undecidability to remain open.

The Liar Paradox is isomorphic to a set containing itself:
Pathological self-reference(Olcott 2004) yet we still
construe the Liar Paradox as legitimate.

> Anyway, nice to see that you don't disagree with may observation that
> Quines atom is not inherently incoherent.
> 

Even ZFC sees that it is incoherent. Quine seemed to be
a bit of a knucklehead. He was too dumb to understand that
analytic/synthetic distinction even when Carnap spelled
it out for him: ∀x (Bachelor(x) := ~Married(x))

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