On 2024-09-01 13:41:57 +0000, olcott said:
> 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 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.
Perhaps physical things in some sense have an outside surface but
that surface is not a part of the thing. We get the imression of
a surface because the resolution of our eyes and other senses is
too coarse to observe the small details of physical things.
> (b) It must not have an outside surface otherwise it is
> not totally containing itself.
It hasn't.
> When we try to draw the Venn diagram of a set that totally
> contains itself we have this exact same problem.
Venn diagrams do not define what is and what is not a set.
>>> 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.
As Quine's atom is a valid set in some contexts that is not a problem.
Anyway, "undecidability" is about logic, not sets.
>>> 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".
OK, but is that structure illegitimate? And does it apply to
the following?
>> "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.
There is nothing in ZFC that could be called "reject" or "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.
ZFC does not "allow" anything. Certain sets can be proven in ZFC to exist
and certain kinds of sets can be proven to not exist, and certain kinds
cannot be proven either way. For example, existence of an uncountable set
can be proven, non-existence of Quine's atom can be proven, neither
existence not non-existence of a set that contains all sets that can
be proven to exist can be proven.
>>> 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))
>>
>> What makes you think Quine did not understand the distinction,
>> or that Carnap's understanding was better?
>
> I totally grok analytic. Quine was a goofball.
Can you prove that wen you use the word "analytic" you are talking
about the same topic as Carnap or Quine?
>> Anyway, non of the above shows thar the particular isomorphism
>> mentioned in quoted messages be needed or userful, only that
>> you think it is.
>
> As soon as there were cans, long before ZFC people
> could have known the a set containing itself is a misconception.
Cans are not relevant. Cantor first presented sets as abstraction
of lists but extended the concept to cover sets that are bigger
than any list.
--
Mikko
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