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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: Sun, 1 Sep 2024 13:44:26 -0400
Organization: i2pn2 (i2pn.org)
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On 9/1/24 9:41 AM, olcott wrote:
> On 9/1/2024 7:30 AM, Mikko wrote:
>> On 2024-08-31 12:18:20 +0000, olcott said:
>>
>>> 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.
>>
>> No, it does not. If you want to get an incoherence proven you need
>> to prove it yourself.
>>
> 
> When you try to imagine a can of soup that soup totally contains
> itself that it has no outside boundary you can see that this is 
> impossible because it is incoherent.

Which just proves your ignorance and stupidity as "analogy" is not a 
valid logical form in n Formal System, like set theory.

> 
> It requires simultaneous mutually exclusive properties.
> (a) It must have an outside surface because all physical
> things have an outside surface.

But sets aren't physical things, and thus the "analogy" just breaks.

> (b) It must not have an outside surface otherwise it is
> not totally containing itself.
> 
> When we try to draw the Venn diagram of a set that totally
> contains itself we have this exact same problem.
> 


No you don't as a Venn Diagram shows a mapping of "members" to "sets" 
there is no rule that the set can't also be a member.

>>> Prior to my isomorphism we only have Russell's Paradox to show
>>> that there is a problem with Naive set theory.
>>
>> Which is sufficicient for that purpose.
>>
>>> That these kind of paradoxes are not understood to
>>> mean incoherence in the system has allowed the issue
>>
>> What system? They are understood to indicate inconsistency of
>> the naive set theory and similar theories.
>>
>>> of undecidability to remain open.
>>
>> What is "open" in the "issue" of undecidability?
>>
> 
> No one has ever bothered to notice that "undecidability" derived
> from pathological self-reference is isomorphic to a set containing
> itself. ZFC simply excludes these sets. The correct way to handle
> pathological self-reference is to reject it as bad input.

But it doesn't.

The only way, it seems, to really exclude Pathoogical Self-Reference is 
to ban Self-Reference, which just limits the power of the logic system.

Something you don't seem to understand, maybe because you can't handle 
logic system that allow for things like self-reference.

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