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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable --- truth-bearer
Date: Sun, 1 Sep 2024 08:41:57 -0500
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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.

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


>> 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.

>> 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
> 

"This sentence is not true"
has the same structure as
"this set contains itself".

> "One of themselves, even a prophet of their own, said, the Cretians are
> always liars, evil beasts, slow bellies." (St. Paul: Titus 1:12) ?
> 
>>> Anyway, nice to see that you don't disagree with may observation that
>>> Quines atom is not inherently incoherent.
> 

The seems to be a very stupid thing to say when ZFC
rejects it as incoherent. It is like you are trying
to say that a dead rat is alive because Quine says so.

>> Even ZFC sees that it is incoherent.
> 
> How does ZFC "see" that?
> 

It is not allowed to exist.

>> Quine seemed to be a bit of a knucklehead. He was too dumb to
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