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On 9/1/2024 7:30 AM, Mikko wrote:Perhaps physical things in some sense have an outside surface butOn 2024-08-31 12:18:20 +0000, olcott said:When you try to imagine a can of soup that soup totally contains
On 8/31/2024 3:43 AM, Mikko wrote:No, it does not. If you want to get an incoherence proven you needOn 2024-08-30 14:45:32 +0000, olcott said:It proves incoherence at a deeper level.
On 8/30/2024 8:36 AM, Mikko wrote:As I already said, that isomorphism is not needed. It is not useful.On 2024-08-29 13:36:00 +0000, olcott said:Quine atoms (named after Willard Van Orman Quine) are sets that only contain themselves, that is, sets that satisfy the formula x = {x}.
On 8/29/2024 3:12 AM, Mikko wrote:There is no need for an isomorphism between a set an a can of soup.On 2024-08-28 12:14:47 +0000, olcott said:A set containing itself has always been incoherent in its
On 8/28/2024 2:45 AM, Mikko wrote:There is no basis to say that ZF is more or less correct than ZFC.On 2024-08-24 03:26:39 +0000, olcott said:It <is> the correct set theory. Naive set theory
On 8/23/2024 3:34 AM, Mikko wrote:It did not redefine anything. It is just another theory. It is calledOn 2024-08-22 13:23:39 +0000, olcott said:Then According to your reasoning ZFC is wrong because
On 8/22/2024 7:06 AM, Mikko wrote:You cannot redefine the foundation of all formal systems. Every formalOn 2024-08-21 12:47:37 +0000, olcott said:Like ZFC redefined the foundation of all sets I redefine
Formal systems kind of sort of has some vague idea of what TrueTarski proved that True is undefineable in certain formal systems.
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.
Your definition is not expressible in F, at least not as a definition.
the foundation of all formal systems.
system has the foundation it has and that cannot be changed. Formal
systems are eternal and immutable.
it is not allowed to redefine the foundation of set
theory.
a set theory because its terms have many similarities to Cnator's sets.
is tossed out on its ass for being WRONG.
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 nothing inherently incoherent in Quine's atom. Some set
theories allow it, some don't. Cantor's theory does not say either
way.
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.
to prove it yourself.
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 isIt hasn't.
not totally containing itself.
When we try to draw the Venn diagram of a set that totallyVenn diagrams do not define what is and what is not a set.
contains itself we have this exact same problem.
As Quine's atom is a valid set in some contexts that is not a problem.No one has ever bothered to notice that "undecidability" derivedPrior to my isomorphism we only have Russell's Paradox to showWhich is sufficicient for that purpose.
that there is a problem with Naive set theory.
That these kind of paradoxes are not understood toWhat system? They are understood to indicate inconsistency of
mean incoherence in the system has allowed the issue
the naive set theory and similar theories.
of undecidability to remain open.What is "open" in the "issue" of undecidability?
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.
OK, but is that structure illegitimate? And does it apply to"This sentence is not true"The Liar Paradox is isomorphic to a set containing itself:Is there someting illegitimate in
Pathological self-reference(Olcott 2004) yet we still
construe the Liar Paradox as legitimate.
has the same structure as
"this set contains itself".
There is nothing in ZFC that could be called "reject" or "incoherent"."One of themselves, even a prophet of their own, said, the Cretians areThe seems to be a very stupid thing to say when ZFC
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.
rejects it as incoherent.
It is like you are tryingZFC does not "allow" anything. Certain sets can be proven in ZFC to exist
to say that a dead rat is alive because Quine says so.
It is not allowed to exist.Even ZFC sees that it is incoherent.How does ZFC "see" that?
Can you prove that wen you use the word "analytic" you are talkingI totally grok analytic. Quine was a goofball.Quine seemed to be a bit of a knucklehead. He was too dumb toWhat makes you think Quine did not understand the distinction,
understand that analytic/synthetic distinction even when Carnap
spelled it out for him: ∀x (Bachelor(x) := ~Married(x))
or that Carnap's understanding was better?
Cans are not relevant. Cantor first presented sets as abstractionAnyway, non of the above shows thar the particular isomorphismAs soon as there were cans, long before ZFC people
mentioned in quoted messages be needed or userful, only that
you think it is.
could have known the a set containing itself is a misconception.
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