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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable --- truth-bearer
Date: Thu, 29 Aug 2024 21:09:22 -0400
Organization: i2pn2 (i2pn.org)
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On 8/29/24 9:36 AM, olcott wrote:
> 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.

And what does that have to do with the question?

ZF doesn't have sets that contain itself either, it is just ZFC without 
the axiom of Choice, or ZFC is just ZF + axiom of Choice.


> 
>> They are just different theories. While the naive set theory is
>> inconsisen, Cantor's original informal theory is not.
>>
>> For many purposes sets with urelements are useful. Stratified sets
>> are also useful for many purposes. Sometimes the notion of classes
>> (that are not sets and not members of sets or classes but have
>> sets as members) is used and useful.
>>
> 
>