Re: This makes all Analytic(Olcott) truth computable --- truth-bearer

On 9/2/2024 3:22 AM, Mikko wrote:

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:
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On 8/31/2024 3:43 AM, Mikko wrote:

On 2024-08-30 14:45:32 +0000, olcott said:
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On 8/30/2024 8:36 AM, Mikko wrote:

On 2024-08-29 13:36:00 +0000, olcott said:
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On 8/29/2024 3:12 AM, Mikko wrote:

On 2024-08-28 12:14:47 +0000, olcott said:
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On 8/28/2024 2:45 AM, Mikko wrote:

On 2024-08-24 03:26:39 +0000, olcott said:
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On 8/23/2024 3:34 AM, Mikko wrote:

On 2024-08-22 13:23:39 +0000, olcott said:
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On 8/22/2024 7:06 AM, Mikko wrote:

On 2024-08-21 12:47:37 +0000, olcott said:
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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
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*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.
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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.

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Tarski proved that True is undefineable in certain formal systems.
Your definition is not expressible in F, at least not as a definition.
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Like ZFC redefined the foundation of all sets I redefine
the foundation of all formal systems.

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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.
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Then According to your reasoning ZFC is wrong because
it is not allowed to redefine the foundation of set
theory.

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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.

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It <is> the correct set theory. Naive set theory
is tossed out on its ass for being WRONG.

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There is no basis to say that ZF is more or less correct than ZFC.

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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.

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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.
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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
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Wrongo. This is exactly isomorphic to the incoherent notion of a
can of soup so totally containing itself that it has no outside
boundary.

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As I already said, that isomorphism is not needed. It is not useful.

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It proves incoherence at a deeper level.

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No, it does not. If you want to get an incoherence proven you need
to prove it yourself.
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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.
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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.
 

No it has an actual surface. When we pick up a ball
we touch its surface. If is had no outer surface we
could not pick up a ball.

(b) It must not have an outside surface otherwise it is
not totally containing itself.

 It hasn't.
 

If it has no outside surface then it does not physically exist
It is has an outside surface then it does not totally contain itself.
Thus any thing physical or conceptual that totally contains
itself is incoherent.

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.

One set containing another set is shown by a smaller circle
inside a larger circle. A set containing itself cannot be
shown as both smaller than itself and larger than itself.
It can only be diagrammed as an identical set to itself.
Yet again we show that the premise of RP is incoherent
with no need for any actual paradox.

 

Prior to my isomorphism we only have Russell's Paradox to show
that there is a problem with Naive set theory.

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Which is sufficicient for that purpose.
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That these kind of paradoxes are not understood to
mean incoherence in the system has allowed the issue

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What system? They are understood to indicate inconsistency of
the naive set theory and similar theories.
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of undecidability to remain open.

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What is "open" in the "issue" of undecidability?
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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.
 

It is valid in the same way that you can go to the store and
buy a can of sour that so totally contains itself that it has
no outside surface. Quine was a bit of a goofball that derailed
correcting all of the errors in the foundation of logic.
Carnap and the logical positivists were always correct.

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

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Is there someting illegitimate in

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"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?
 

Pathological self-reference is the central issue that
I have spent the last 20 years of my life on.

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

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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".
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ZFC disallows constructing sets that contain themselves.

It is like you are trying
to say that a dead rat is alive because Quine says so.
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Even ZFC sees that it is incoherent.

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How does ZFC "see" that?

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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.
 

ZFC constructs sets in a certain way that does not allow
sets to be members of themselves.

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))

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What makes you think Quine did not understand the distinction,
or that Carnap's understanding was better?

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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?
 

*I merely add missing details to the same idea of analytic*
True entirely on the basis of its meaning now has more details.
An analytic expression of language is any expression of
formal or natural language that can be proven true or
false entirely on the basis of a connection to its semantic
meaning in this same language.
This connection must be through a sequence of truth preserving operations from expression x of language L to meaning M in L.
A lack of such connection from x or ~x in L is construed as x
is not a truth bearer in L.

Anyway, non of the above shows thar the particular isomorphism
mentioned in quoted messages be needed or userful, only that
you think it is.

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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.
 

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer