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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable --- truth-bearer
Date: Thu, 29 Aug 2024 11:12:34 +0300
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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.
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.

-- 
Mikko