On 8/20/2024 4:53 AM, Mikko wrote:
On 2024-08-19 12:58:12 +0000, olcott said:
On 8/19/2024 3:14 AM, Mikko wrote:
On 2024-08-18 11:26:22 +0000, olcott said:
On 8/18/2024 5:37 AM, Mikko wrote:
On 2024-08-17 15:47:51 +0000, olcott said:
On 8/17/2024 10:33 AM, Richard Damon wrote:
On 8/17/24 11:12 AM, olcott wrote:
On 8/17/2024 9:53 AM, Richard Damon wrote:
I guess you consider all the papers they wrote describing the >>>>>>>>>> effects of their definitions "nothing"
Not at all and you know this.
One change had many effects yet was still one change.
But would mean nothing without showing the affects of that change. >>>>>>>>
Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless
You are lying. According to that page the word "meaningless"
has two meanings. The other is 'having no real importance or value'. >>>>>>
OK. I always use the base meaning of a term as its only meaning.
That makes things much simpler if everyone knows this standard.
People have different opions about which meaning is the "base"
meaning.
The most commonly used sense meaning at the first
index in the dictionary.
If you want to use this you should say so and specify the dictionary
in the beginning of your opus. You shold not choose a dictionary
that presents obsolete and archaic meanings first.
Base meaning as in the meaning in a knowledge ontology https://en.wikipedia.org/wiki/Ontology_(information_science)
basis that all other sense meanings inherit from.
For example a liar must be intentionally deceptive not merely
mistaken.
For example people may regard you as a liar if you say something untrue >>>> when you were too lazy to check the facts.
I am redefining the foundations of logic thus my definitions
are stipulated to override and supersede the original definitions.
If you want to use definitions other that the first meaning given
by the dictionary, you must present the definition before the
first use in each opus that uses it.
The key term that I am slightly adapting is the term {analytic}
from the analytic synthetic distinction. That is why the
title of this post says Analytic(Olcott)
It took a long time to reverse-engineer the subtle nuances of
the exact details of what needed to be changed.
It seems that you have not yet completed that task.
I have competed the architecture of the task.
We cannot move on to further elaboration until
people quite rejecting the architecture out-of-hand.
*This abolishes the notion of undecidability*
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language.
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
On 8/20/2024 4:53 AM, Mikko wrote:
On 2024-08-19 12:58:12 +0000, olcott said:
On 8/19/2024 3:14 AM, Mikko wrote:
On 2024-08-18 11:26:22 +0000, olcott said:
On 8/18/2024 5:37 AM, Mikko wrote:
On 2024-08-17 15:47:51 +0000, olcott said:
On 8/17/2024 10:33 AM, Richard Damon wrote:
On 8/17/24 11:12 AM, olcott wrote:
On 8/17/2024 9:53 AM, Richard Damon wrote:
I guess you consider all the papers they wrote describing the effects
of their definitions "nothing"
Not at all and you know this.
One change had many effects yet was still one change.
But would mean nothing without showing the affects of that change. >>>>>>>>
Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless
You are lying. According to that page the word "meaningless"
has two meanings. The other is 'having no real importance or value'. >>>>>>
OK. I always use the base meaning of a term as its only meaning.
That makes things much simpler if everyone knows this standard.
People have different opions about which meaning is the "base"
meaning.
The most commonly used sense meaning at the first
index in the dictionary.
If you want to use this you should say so and specify the dictionary
in the beginning of your opus. You shold not choose a dictionary
that presents obsolete and archaic meanings first.
Base meaning as in the meaning in a knowledge ontology https://en.wikipedia.org/wiki/Ontology_(information_science)
basis that all other sense meanings inherit from.
For example a liar must be intentionally deceptive not merely mistaken. >>>>For example people may regard you as a liar if you say something untrue >>>> when you were too lazy to check the facts.
I am redefining the foundations of logic thus my definitions
are stipulated to override and supersede the original definitions.
If you want to use definitions other that the first meaning given
by the dictionary, you must present the definition before the
first use in each opus that uses it.
The key term that I am slightly adapting is the term {analytic}
from the analytic synthetic distinction. That is why the
title of this post says Analytic(Olcott)
It took a long time to reverse-engineer the subtle nuances of
the exact details of what needed to be changed.
It seems that you have not yet completed that task.
I have competed the architecture of the task.
We cannot move on to further elaboration until
people quite rejecting the architecture out-of-hand.
*This abolishes the notion of undecidability*
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language.
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
On 8/20/2024 9:43 PM, Richard Damon wrote:
On 8/20/24 9:45 AM, olcott wrote:
On 8/20/2024 4:53 AM, Mikko wrote:
On 2024-08-19 12:58:12 +0000, olcott said:
On 8/19/2024 3:14 AM, Mikko wrote:
On 2024-08-18 11:26:22 +0000, olcott said:
On 8/18/2024 5:37 AM, Mikko wrote:
On 2024-08-17 15:47:51 +0000, olcott said:
On 8/17/2024 10:33 AM, Richard Damon wrote:
On 8/17/24 11:12 AM, olcott wrote:
On 8/17/2024 9:53 AM, Richard Damon wrote:
I guess you consider all the papers they wrote describing >>>>>>>>>>>> the effects of their definitions "nothing"
Not at all and you know this.
One change had many effects yet was still one change.
But would mean nothing without showing the affects of that >>>>>>>>>> change.
Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless
You are lying. According to that page the word "meaningless"
has two meanings. The other is 'having no real importance or
value'.
OK. I always use the base meaning of a term as its only meaning. >>>>>>> That makes things much simpler if everyone knows this standard.
People have different opions about which meaning is the "base"
meaning.
The most commonly used sense meaning at the first
index in the dictionary.
If you want to use this you should say so and specify the dictionary
in the beginning of your opus. You shold not choose a dictionary
that presents obsolete and archaic meanings first.
Base meaning as in the meaning in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
basis that all other sense meanings inherit from.
For example a liar must be intentionally deceptive not merely
mistaken.
For example people may regard you as a liar if you say something
untrue
when you were too lazy to check the facts.
I am redefining the foundations of logic thus my definitions
are stipulated to override and supersede the original definitions.
If you want to use definitions other that the first meaning given
by the dictionary, you must present the definition before the
first use in each opus that uses it.
The key term that I am slightly adapting is the term {analytic}
from the analytic synthetic distinction. That is why the
title of this post says Analytic(Olcott)
Which, as I pointed out elswhere, basically means you aren't actually
talking about formal systems, as they don't have that distinction,
because there is no sense based truth to be synthetic.
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.
It took a long time to reverse-engineer the subtle nuances of
the exact details of what needed to be changed.
It seems that you have not yet completed that task.
I have competed the architecture of the task.
We cannot move on to further elaboration until
people quite rejecting the architecture out-of-hand.
No, you haven't, because you haven't sat down an listed the axioms of
your Formal System, so you haven't "completed" (or even really
strated) your architecture.
*This abolishes the notion of undecidability*
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language.
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.
But Godel's G *IS* an expression that has a connection through an
INFINITE sequence of truth preserving operations in PA. It just can't
be proven in PA, as proofs require finite sequences in the system.
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
Wrong.
Truth allows an infinte sequence of steps.
Decidability requires a FINITE sequence of steps.
That difference is where undeciability comes into existance.
Requiring Truth to be only established by finite sequences breaks too
much logic, and greatly limits what can be exressed. In particular,
you lose mathematics. Things that we could show must be true or false,
but we can't show which, end up being non-truth-bearers.
We also end up with a system that can't talk about what it doesn't
know yet, as not-yet-known might be unknowable, and thus neither true
or false.
And, you can't let "proofs" use infinite sequences, as that breaks
epistomolgy, as we are finite, and can only know what can be shown
with a finite proof.
On 8/20/2024 9:43 PM, Richard Damon wrote:
On 8/20/24 9:45 AM, olcott wrote:
On 8/20/2024 4:53 AM, Mikko wrote:
On 2024-08-19 12:58:12 +0000, olcott said:
On 8/19/2024 3:14 AM, Mikko wrote:
On 2024-08-18 11:26:22 +0000, olcott said:
On 8/18/2024 5:37 AM, Mikko wrote:
On 2024-08-17 15:47:51 +0000, olcott said:
On 8/17/2024 10:33 AM, Richard Damon wrote:
On 8/17/24 11:12 AM, olcott wrote:
On 8/17/2024 9:53 AM, Richard Damon wrote:
I guess you consider all the papers they wrote describing the effects
of their definitions "nothing"
Not at all and you know this.
One change had many effects yet was still one change.
But would mean nothing without showing the affects of that change. >>>>>>>>>>
Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless
You are lying. According to that page the word "meaningless"
has two meanings. The other is 'having no real importance or value'. >>>>>>>>
OK. I always use the base meaning of a term as its only meaning. >>>>>>> That makes things much simpler if everyone knows this standard.
People have different opions about which meaning is the "base"
meaning.
The most commonly used sense meaning at the first
index in the dictionary.
If you want to use this you should say so and specify the dictionary
in the beginning of your opus. You shold not choose a dictionary
that presents obsolete and archaic meanings first.
Base meaning as in the meaning in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
basis that all other sense meanings inherit from.
For example a liar must be intentionally deceptive not merely mistaken. >>>>>>For example people may regard you as a liar if you say something untrue >>>>>> when you were too lazy to check the facts.
I am redefining the foundations of logic thus my definitions
are stipulated to override and supersede the original definitions.
If you want to use definitions other that the first meaning given
by the dictionary, you must present the definition before the
first use in each opus that uses it.
The key term that I am slightly adapting is the term {analytic}
from the analytic synthetic distinction. That is why the
title of this post says Analytic(Olcott)
Which, as I pointed out elswhere, basically means you aren't actually
talking about formal systems, as they don't have that distinction,
because there is no sense based truth to be synthetic.
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.
On 8/21/2024 3:23 AM, Mikko wrote:
On 2024-08-20 13:45:13 +0000, olcott said:
On 8/20/2024 4:53 AM, Mikko wrote:
On 2024-08-19 12:58:12 +0000, olcott said:
On 8/19/2024 3:14 AM, Mikko wrote:
On 2024-08-18 11:26:22 +0000, olcott said:
On 8/18/2024 5:37 AM, Mikko wrote:
On 2024-08-17 15:47:51 +0000, olcott said:
On 8/17/2024 10:33 AM, Richard Damon wrote:
On 8/17/24 11:12 AM, olcott wrote:
On 8/17/2024 9:53 AM, Richard Damon wrote:
I guess you consider all the papers they wrote describing the effects
of their definitions "nothing"
Not at all and you know this.
One change had many effects yet was still one change.
But would mean nothing without showing the affects of that change. >>>>>>>>>>
Yet again with your imprecise use of words.
When any tiniest portion of the meaning of an expression
has been defined this teeny tiny piece of the definition
makes this expression not pure random gibberish.
Meaningless does not mean has less meaning, it is
an idiom for having zero meaning.
https://www.britannica.com/dictionary/meaningless
You are lying. According to that page the word "meaningless"
has two meanings. The other is 'having no real importance or value'. >>>>>>>>
OK. I always use the base meaning of a term as its only meaning. >>>>>>> That makes things much simpler if everyone knows this standard.
People have different opions about which meaning is the "base"
meaning.
The most commonly used sense meaning at the first
index in the dictionary.
If you want to use this you should say so and specify the dictionary
in the beginning of your opus. You shold not choose a dictionary
that presents obsolete and archaic meanings first.
Base meaning as in the meaning in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
basis that all other sense meanings inherit from.
That page does not define "base meaning".
You will not be understood if you use a private language.
Responses to your messages probably use Common Language. Where you
understand it or not, most readers do, at least to some extent, or
ask clarification and then understand.
*The defined predicate True(L,x) here*
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.
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.
A problem with your method is that it is ofen not known whether there
is a sequence of truth-preserving transformations in F and there is
no method to find out.
Try to show a concrete example of that where self-contradictory
expressions are not needed.
Your definition also requires truth-preserving is defined without
reference to truth. Is there any such definiton?
Because it establishes the notion of truth.
Truth is what my foundational axiom says that it is.
Truth is the connection from an expression of language
to its stipulative meaning. Many of the conventional
logic operations are truth preserving, some are not.
After the architecture of my system is understood and
accepted then we do these further elaborations.
This is all aspects of my categorically exhaustively complete
system of reasoning. Work on the broadest category first and
then progressively narrow to smaller categories.
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.
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.
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.
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.
Lying is not merely a different opinion of "truth".
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.
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:It <is> the correct set theory. Naive set theory
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. >>>
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.
They are just different theories. While the naive set theory is
inconsisen, Cantor's original informal theory is not.
For many purposes sets with urelements are useful. Stratified sets
are also useful for many purposes. Sometimes the notion of classes
(that are not sets and not members of sets or classes but have
sets as members) is used and useful.
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:It <is> the correct set theory. Naive set theory
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. >>>
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.
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.
[[...]]s = list()
s.append(s)
s
Trues in s
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:It <is> the correct set theory. Naive set theory
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. >>>>>
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.
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. Prior to my
isomorphism we only have Russell's Paradox to show
that there is a problem with Naive set theory.
That these kind of paradoxes are not understood to
mean incoherence in the system has allowed the issue
of undecidability to remain open.
The Liar Paradox is isomorphic to a set containing itself:
Pathological self-reference(Olcott 2004) yet we still
construe the Liar Paradox as legitimate.
Anyway, nice to see that you don't disagree with may observation that
Quines atom is not inherently incoherent.
Even ZFC sees that it is incoherent. 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))
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.
Prior to my isomorphism we only have Russell's Paradox to show
that there is a problem with Naive set theory.
That these kind of paradoxes are not understood to
mean incoherence in the system has allowed the issue
of undecidability to remain open.
The Liar Paradox is isomorphic to a set containing itself:
Pathological self-reference(Olcott 2004) yet we still
construe the Liar Paradox as legitimate.
Anyway, nice to see that you don't disagree with may observation that
Quines atom is not inherently incoherent.
Even ZFC sees that it is incoherent.
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))
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:A set containing itself has always been incoherent in its
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. >>>>>>>
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
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.
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.
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:A set containing itself has always been incoherent in its
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. >>>>>>>
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
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.
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.
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:
On 8/31/2024 3:43 AM, Mikko wrote:
On 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:
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. >>>>>
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.
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.
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.
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.
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?
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) ?
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".
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.
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.
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))
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?
*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.
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.
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:
On 8/31/2024 3:43 AM, Mikko wrote:
On 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:
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:A set containing itself has always been incoherent in its
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. >>>>>>>>>
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. >>>>>
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.
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
On 9/3/2024 5:49 AM, Mikko wrote:
On 2024-09-02 12:44:57 +0000, olcott said:
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:
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.
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
In that case nothing physically exists. Every outside surface is
merely an illusion.
Nothing that no outside surface exists.
Since I can touch a cup with my fingers
this proves that the cup and my fingers
have an outside surface.
A set containing itself is isomorphic to a can
of soup containing itself. In both cases they
cannot have an outside surface.
The physically existing thing must have out
outside surface proves that the can does not
physically exist.
The the Venn diagram of a set that includes itself
as a member can at best shown a diagram of a pair
of identical sets with overlapping boundaries proves
that a set containing itself cannot exist. It has
always been a misconception.
For one set to be actually contained within another
one this contained set must with inside of the boundaries
of its container set.
On 9/3/2024 5:49 AM, Mikko wrote:
On 2024-09-02 12:44:57 +0000, olcott said:
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:
On 8/31/2024 3:43 AM, Mikko wrote:
On 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:
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: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.
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. >>>>>>>>>>>
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. >>>>>>>
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.
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
In that case nothing physically exists. Every outside surface is
merely an illusion.
Nothing that no outside surface exists.
Since I can touch a cup with my fingers
this proves that the cup and my fingers
have an outside surface.
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