A set as a member of itself is incoherent

[Pete Olcott]

All this talk, and you have stayed tightly
focused on the _word_ . Okay, you don't like
the _word_ .

<unsnip>

What are you going to call a set x that has an
infinite 'ni' sequence
-- that is, x ni x' ni x'' ni ...
where x ni x' := x' in x .
*How do you label the concept*

</unsnip>
*emphasis added*
I put my question back, which you had snipped.
You don't even try to answer me.

It is totally gibberish to me. It does not directly
pertain to the mathematics of semantics.

*HOW DO YOU LABEL THE CONCEPT*

https://plato.stanford.edu/entries/nonwellfounded-set-theory/
AKA Pathological Self-Reference (a specific type of incoherence).

(copied from elsethread)

https://www.quora.com/What-is-a-Well-founded-set-in-simpler-terms

What is the answer to my question?

I gave you the BASE meaning of well-founded from which
more specific meanings inherit. Perhaps you are not bright
enough to understand this?

Naturally, the only possible explanation for _you_ not
answering _my_ question is that _I_ don't understand _you_ .

https://en.wikipedia.org/wiki/Ontology_engineering
Unless you understand the basic idea of ontological engineering you will never understand my answer.

The basic idea of ontological engineering is quite simple.
Concepts are entirely comprised of other concepts and can thus be decomposed into these constituent parts.

Only when one sees exactly how concepts fit together according to the principle of compositionality will one fully understand what {well founded} actually means.

https://en.wikipedia.org/wiki/Principle_of_compositionality
In mathematics, semantics, and philosophy of language, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them.

That I have not memorized the specific details about one single instance of {well foundedness} totally misses the whole point.

[Jim Burns]

Post by Pete Olcott

All this talk, and you have stayed tightly
focused on the _word_ . Okay, you don't like
the _word_ .

<unsnip>

What are you going to call a set x that has an
infinite 'ni' sequence
-- that is, x ni x' ni x'' ni ...
where x ni x' := x' in x .
*How do you label the concept*

</unsnip>
*emphasis added*
I put my question back, which you had snipped.
You don't even try to answer me.

It is totally gibberish to me. It does not directly
pertain to the mathematics of semantics.

*HOW DO YOU LABEL THE CONCEPT*

https://plato.stanford.edu/entries/nonwellfounded-set-theory/
AKA Pathological Self-Reference (a specific type of incoherence).

(copied from elsethread)

https://www.quora.com/What-is-a-Well-founded-set-in-simpler-terms

What is the answer to my question?

I gave you the BASE meaning of well-founded from which
more specific meanings inherit. Perhaps you are not bright
enough to understand this?

Naturally, the only possible explanation for _you_ not
answering _my_ question is that _I_ don't understand _you_ .

https://en.wikipedia.org/wiki/Ontology_engineering
Unless you understand the basic idea of ontological
engineering you will never understand my answer.

[...]

Post by Pete Olcott
That I have not memorized the specific details about
one single instance of {well foundedness} totally
misses the whole point.

I have a concept that needs a label.

You have taken upon yourself the responsibility of
providing labels for the concepts which I want to use
-- by declaring that that the labels I (and others)
are using are "wrong" somehow.

This is the job you have claimed. Provide me with a
label for that concept. Saying that the label I used
is "wrong" does not do that. Do your job.

The alternatives to you providing a label are
(i) ignoring you (the actual very reasonable option)
(ii) not using that concept.

Option (ii) is Orwellian, the-all-powerful-Olcott-
-will-tell-you-what-to-think-say-thank-you.
I would prefer not to think that that is where you
are headed, but you aren't leaving me a lot of
room to find a different way to see what you are
trying to do.

[Pete Olcott]

Post by Jim Burns

Post by Pete Olcott

All this talk, and you have stayed tightly
focused on the _word_ . Okay, you don't like
the _word_ .

<unsnip>

What are you going to call a set x that has an
infinite 'ni' sequence
-- that is, x ni x' ni x'' ni ...
where x ni x' := x' in x .
*How do you label the concept*

</unsnip>
*emphasis added*
I put my question back, which you had snipped.
You don't even try to answer me.

It is totally gibberish to me. It does not directly
pertain to the mathematics of semantics.

*HOW DO YOU LABEL THE CONCEPT*

https://plato.stanford.edu/entries/nonwellfounded-set-theory/
AKA Pathological Self-Reference (a specific type of incoherence).

(copied from elsethread)

https://www.quora.com/What-is-a-Well-founded-set-in-simpler-terms

What is the answer to my question?

I gave you the BASE meaning of well-founded from which
more specific meanings inherit. Perhaps you are not bright
enough to understand this?

Naturally, the only possible explanation for _you_ not
answering _my_ question is that _I_ don't understand _you_ .

https://en.wikipedia.org/wiki/Ontology_engineering
Unless you understand the basic idea of ontological
engineering you will never understand my answer.

[...]

Post by Pete Olcott
That I have not memorized the specific details about
one single instance of {well foundedness} totally
misses the whole point.

I have a concept that needs a label.

More head games.

[mitch]

Post by Pete Olcott

Post by Jim Burns

Post by Pete Olcott

All this talk, and you have stayed tightly
focused on the _word_ . Okay, you don't like
the _word_ .

<unsnip>

What are you going to call a set x that has an
infinite 'ni' sequence
-- that is, x ni x' ni x'' ni ...
where x ni x' := x' in x .
*How do you label the concept*

</unsnip>
*emphasis added*
I put my question back, which you had snipped.
You don't even try to answer me.

It is totally gibberish to me. It does not directly
pertain to the mathematics of semantics.

*HOW DO YOU LABEL THE CONCEPT*

https://plato.stanford.edu/entries/nonwellfounded-set-theory/
AKA Pathological Self-Reference (a specific type of incoherence).

(copied from elsethread)

https://www.quora.com/What-is-a-Well-founded-set-in-simpler-terms

What is the answer to my question?

I gave you the BASE meaning of well-founded from which
more specific meanings inherit. Perhaps you are not bright
enough to understand this?

Naturally, the only possible explanation for _you_ not
answering _my_ question is that _I_ don't understand _you_ .

https://en.wikipedia.org/wiki/Ontology_engineering
Unless you understand the basic idea of ontological
engineering you will never understand my answer.

[...]

Post by Pete Olcott
That I have not memorized the specific details about
one single instance of {well foundedness} totally
misses the whole point.

I have a concept that needs a label.

More head games.

You are getting too predictable.

This is what you say when you *refuse* to answer
questions.

By the way, you should address Mr. Burns remarks
about the Orwellian character of your research
program,

< begin quote >

This is the job you have claimed. Provide me with a
label for that concept. Saying that the label I used
is "wrong" does not do that. Do your job.

The alternatives to you providing a label are
(i) ignoring you (the actual very reasonable option)
(ii) not using that concept.

Option (ii) is Orwellian, the-all-powerful-Olcott-
-will-tell-you-what-to-think-say-thank-you.
I would prefer not to think that that is where you
are headed, but you aren't leaving me a lot of
room to find a different way to see what you are
trying to do.

< end quote >

The difference between Mr. Burns and me is that
I immediately assumed you to be intelligentsia
of Orwellian persuasion the moment you began
using nonsensical Latin phrases intended for
rhetorical debate.

Cocktail party talk.

mitch

[Jim Burns]

Post by mitch
By the way, you should address Mr. Burns remarks
about the Orwellian character of your research
program,

I think I may have made a mistake there.

I think it is possible that the answer to my question
"What do you, Peter Olcott, call a set with no
infinite "ni"-sequence?"
is
"Coherent"
and that Peter Olcott has given that answer.

Post by mitch
It would seem that what I mean by incoherent is
ill-founded.

In other words (if they are using terminology
consistently) ill-founded set that are define
incoherently.

I remembered last night (vaguely) Peter Olcott saying
something like that, after I tried to list all the things
that he could POSSIBLY have considered a label for that
concept.

If I am reading him correctly, then he would not be
Orwellian, merely stupid to a forget-how-to-breathe
level of toxicity. Honestly, I consider even that level
of stupidity an improvement over being Orwellian.

Though I doubt Peter Olcott would consider this an
apology (as who would like being called extremely stupid?)
this is _in effect_ an apology -- assuming I am reading
him correctly now.

[mitch]

Post by Jim Burns

Post by mitch
By the way, you should address Mr. Burns remarks
about the Orwellian character of your research
program,

I think I may have made a mistake there.
I think it is possible that the answer to my question
"What do you, Peter Olcott, call a set with no
infinite "ni"-sequence?"
is
"Coherent"
and that Peter Olcott has given that answer.

Post by mitch
It would seem that what I mean by incoherent is
ill-founded.

Yes.

But, I wonder what word we will now have
to use instead of "coherent"....

https://en.wikipedia.org/wiki/Coherent_space

http://www.paultaylor.eu/stable/prot.pdf PDF page 61

https://mathoverflow.net/questions/7058/coherent-spaces


mitch

[Pete Olcott]

Post by Jim Burns

Post by Pete Olcott

All this talk, and you have stayed tightly
focused on the _word_ . Okay, you don't like
the _word_ .

<unsnip>

What are you going to call a set x that has an
infinite 'ni' sequence
-- that is, x ni x' ni x'' ni ...
where x ni x' := x' in x .
*How do you label the concept*

</unsnip>
*emphasis added*
I put my question back, which you had snipped.
You don't even try to answer me.

It is totally gibberish to me. It does not directly
pertain to the mathematics of semantics.

*HOW DO YOU LABEL THE CONCEPT*

https://plato.stanford.edu/entries/nonwellfounded-set-theory/
AKA Pathological Self-Reference (a specific type of incoherence).

(copied from elsethread)

https://www.quora.com/What-is-a-Well-founded-set-in-simpler-terms

What is the answer to my question?

I gave you the BASE meaning of well-founded from which
more specific meanings inherit. Perhaps you are not bright
enough to understand this?

Naturally, the only possible explanation for _you_ not
answering _my_ question is that _I_ don't understand _you_ .

https://en.wikipedia.org/wiki/Ontology_engineering
Unless you understand the basic idea of ontological
engineering you will never understand my answer.

[...]

Post by Pete Olcott
That I have not memorized the specific details about
one single instance of {well foundedness} totally
misses the whole point.

I have a concept that needs a label.

In order for categorically (adverb form of category) exhaustively complete reasoning to not take enormously more time than is available one must completely examine every aspect of the elements of the problem domain at the highest relevant levels of abstraction before proceeding to one additional increment of specificity.

Since I have given you a totally effective label very many times you are dishonest when you say that you need a label. You don't really need a label at all. You need a set of axioms proving my point.

I have to create the MTT's automated inference engine before providing these axioms.

[Shobe, Martin]

On 7/22/2017 1:28 PM, Pete Olcott wrote:
[snip]

Post by Pete Olcott
Since I have given you a totally effective label very many times you are
dishonest when you say that you need a label.

What was it? [Keep in mind that what you are supposed to be labeling is
the concept that set theorists call well-founded].

Post by Pete Olcott
You don't really need a label at all. You need a set of axioms

proving > my point.

Post by Pete Olcott
I have to create the MTT's automated inference engine before providing these axioms.

I ain't holding my breath.

Martin Shobe

[Peter Percival]

Post by Pete Olcott
I have to create the MTT's automated inference engine before providing these axioms.

I know nothing about automated inference engines, but don't they need to
embody the axioms? So don't you need to know what they are before you
create MTT's automated inference engine? So why not post them to sci.logic?

[Pete Olcott]

Post by Pete Olcott
I have to create the MTT's automated inference engine before providing these axioms.

I know nothing about automated inference engines, but don't they need to embody the axioms? So don't you need to know what they are before you create MTT's automated inference engine? So why not post them to sci.logic?

I am going to design the inference engine and the axioms concurrently. Instead of wasting time learning how to do conventional proofs, I am simply going to reverse-engineer the best way to do them.

If you understood my categorically (adverb form of category) exhaustive system of reasoning you would understand that this is the best way to proceed.

To describe this in simplistic terms, I simply use a process of elimination to zero in on the best possible solution on the first attempt.

I have the MTT expression to Directed Acyclic Graph compiler almost complete. I am probably going to work on the inference engine / set of axioms next.

I had been planning to implement the programming language first, this will have to wait unless the inference engine requires it.

Some axioms definitely require a programming language, for example defining the semantics of > for digit strings.

[Peter Percival]

Post by Pete Olcott

Post by Peter Percival

Post by Pete Olcott
I have to create the MTT's automated inference engine before
providing these axioms.

I know nothing about automated inference engines, but don't they
need to embody the axioms? So don't you need to know what they are
before you create MTT's automated inference engine? So why not
post them to sci.logic?

I am going to design the inference engine and the axioms
concurrently. Instead of wasting time learning how to do conventional
proofs, I am

Oh, quite right, you don't want to waste time learning stuff!

Post by Pete Olcott
simply going to reverse-engineer the best way to do them.
If you understood my categorically (adverb form of category)
exhaustive system of reasoning you would understand that this is the
best way to proceed.
To describe this in simplistic terms, I simply use a process of
elimination to zero in on the best possible solution on the first
attempt.
I have the MTT expression to Directed Acyclic Graph compiler almost
complete. I am probably going to work on the inference engine / set
of axioms next.
I had been planning to implement the programming language first,
this will have to wait unless the inference engine requires it.
Some axioms definitely require a programming language, for example
defining the semantics of > for digit strings.

I recall that when you were asked to prove that '5 > 3' is true you told
us that '5 > 3' was an axiom. Way to go!

[Pete Olcott]

Post by Peter Percival

Post by Pete Olcott

Post by Peter Percival

Post by Pete Olcott
I have to create the MTT's automated inference engine before providing these axioms.

I know nothing about automated inference engines, but don't they
need to embody the axioms? So don't you need to know what they are
before you create MTT's automated inference engine? So why not
post them to sci.logic?

I am going to design the inference engine and the axioms
concurrently. Instead of wasting time learning how to do conventional
proofs, I am

Oh, quite right, you don't want to waste time learning stuff!

Post by Pete Olcott
simply going to reverse-engineer the best way to do them.
If you understood my categorically (adverb form of category)
exhaustive system of reasoning you would understand that this is the
best way to proceed.
To describe this in simplistic terms, I simply use a process of
elimination to zero in on the best possible solution on the first
attempt.
I have the MTT expression to Directed Acyclic Graph compiler almost
complete. I am probably going to work on the inference engine / set
of axioms next.
I had been planning to implement the programming language first,
this will have to wait unless the inference engine requires it.
Some axioms definitely require a programming language, for example
defining the semantics of > for digit strings.

I recall that when you were asked to prove that '5 > 3' is true you told us that '5 > 3' was an axiom. Way to go!

The way that knowledge works is that there is a set of facts and rules used to combined them.
The relations between single digit integers is a set of facts.
The relations between multi digit finite strings is a set of facts combined with an algorithm (finite string transformation rules).
The same thing goes for natural language.

[Peter Percival]

Post by Pete Olcott
The way that knowledge works is that there is a set of facts and rules

And how do people learn what the facts and rules are?

Post by Pete Olcott
used to combined them.
The relations between single digit integers is a set of facts.
The relations between multi digit finite strings is a set of facts
combined with an algorithm (finite string transformation rules).
The same thing goes for natural language.

You seem not to know that natural language has ambiguities.

[Peter Percival]

Post by Pete Olcott
Only when one sees exactly how concepts fit together according to
the principle of compositionality will one fully understand what
{well founded} actually means.
https://en.wikipedia.org/wiki/Principle_of_compositionality In
mathematics, semantics, and philosophy of language, the principle of
compositionality is the principle that the meaning of a complex
expression is determined by the meanings of its constituent
expressions and the rules used to combine them.

So is it your belief that some meaningful word sequence (it may be "well
founded" or something else) can only have one meaning? You have noticed
no ambiguity in language?

You're a dribbling idiot, aren't you? Need I point out that you do not
actual need to dribble to be called (by me anyway) a dribbling idiot?
(And let us not stop to consider the dimwitted football (soccer to you
maybe) player...)

Also, why have you cross-posted this to a C# group?

[mitch]

Post by Pete Olcott
Only when one sees exactly how concepts fit together according to the
principle of compositionality will one fully understand what {well
founded} actually means.

Hey genius.

Well-founded relations are a generalization
of the well ordering that characterizes the
natural numbers.

Well ordering can be expressed by the idea
that every set of natural elements has a
least element.

A well-founded relation is defined with respect
to a context -- a class of objects in relation
to one another. The relation is well-founded
in this context if every subset has an R-minimal
element.

https://en.wikipedia.org/wiki/Well-founded_relation

And, following your link about ontology, I come
to

https://en.wikipedia.org/wiki/Formal_concept_analysis

https://en.wikipedia.org/wiki/Formal_concept_analysis#Concept_lattice_of_a_context

https://en.wikipedia.org/wiki/Formal_concept_analysis#Concept_algebra_of_a_context


Pretty much, you are clueless with respect to how
your words relate to mathematics.

Maybe you should have taken more than just Calculus I.

mitch

[Pete Olcott]

Post by mitch

Post by Pete Olcott
Only when one sees exactly how concepts fit together according to the principle of compositionality will one fully understand what {well founded} actually means.

Hey genius.
Well-founded relations are a generalization
of the well ordering that characterizes the
natural numbers.
Well ordering can be expressed by the idea
that every set of natural elements has a
least element.
A well-founded relation is defined with respect
to a context -- a class of objects in relation
to one another. The relation is well-founded
in this context if every subset has an R-minimal
element.
https://en.wikipedia.org/wiki/Well-founded_relation
And, following your link about ontology, I come
to
https://en.wikipedia.org/wiki/Formal_concept_analysis
https://en.wikipedia.org/wiki/Formal_concept_analysis#Concept_lattice_of_a_context
https://en.wikipedia.org/wiki/Formal_concept_analysis#Concept_algebra_of_a_context
Pretty much, you are clueless with respect to how
your words relate to mathematics.

I will use more precise language for you:
I am creating the syntactic formalization of all** semantics.
** Formal language and natural language.

Post by mitch
Maybe you should have taken more than just Calculus I.
mitch

[mitch]

Post by Pete Olcott

Post by mitch

Post by Pete Olcott
Only when one sees exactly how concepts fit together according to the
principle of compositionality will one fully understand what {well
founded} actually means.

Hey genius.
Well-founded relations are a generalization
of the well ordering that characterizes the
natural numbers.
Well ordering can be expressed by the idea
that every set of natural elements has a
least element.
A well-founded relation is defined with respect
to a context -- a class of objects in relation
to one another. The relation is well-founded
in this context if every subset has an R-minimal
element.
https://en.wikipedia.org/wiki/Well-founded_relation
And, following your link about ontology, I come
to
https://en.wikipedia.org/wiki/Formal_concept_analysis
https://en.wikipedia.org/wiki/Formal_concept_analysis#Concept_lattice_of_a_context
https://en.wikipedia.org/wiki/Formal_concept_analysis#Concept_algebra_of_a_context
Pretty much, you are clueless with respect to how
your words relate to mathematics.

I am creating the syntactic formalization of all** semantics.
** Formal language and natural language.

OK