Deeper than primes

[doronshadmi]

You didn’t even know that there was such thing has an axiom before I even mentioned it.

Please don't be ridiculous.

Give an example of an axiom of mainstream mathematics, except for “1 is different from 0” cause I already given you that one.

ZF Axiom of extensionality: X and Y are the same set if they have the same members.

 

[TMiguel]

ZF Axiom of extensionality: X and Y are the same set if they have the same members.

Wrong! You taken that out of Wikipedia, I made sure they didn’t have main stream math axioms (or Arithmetic axioms). You took a Zermelo-Fraenkel set theory axiom.
Here are another examples of mainstream math axioms you don’t find on the web:

There is a number a, that added to a any number b equals b. a+b=b
And to this number “a” we call it zero “0”
There is a number c, that multiplied to any number d is equal to d. cxd=d
And to this number “c” we call it one “1”

You don’t know what axioms are, you never heard of it before, you don’t know what you are talking about.

QED!

 

[ddt]

ZF Axiom of extensionality: X and Y are the same set if they have the same members.

Wrong! You taken that out of Wikipedia, I made sure they didn’t have main stream math axioms (or Arithmetic axioms). You took a Zermelo-Fraenkel set theory axiom.

To be fair to Doron, you didn't ask for an axiom from arithmetic, so the answer shouldn't be discarded on that account.

I would like to remind, though, that doron up until 3 months ago was not aware of the axiom of extensionality. You might re-read the "A collection of infinitely..." thread from post 1328 on to see it took some 150 posts to drive home the existence and implications of the Axiom of Extensionality.

 

[TMiguel]

To be fair to Doron, you didn't ask for an axiom from arithmetic, so the answer shouldn't be discarded on that account.

I referred main stream mathematics and clearly given the example of the axiom 0 is different from 1. What else could I be possibly talking about?

 

[jsfisher]

I referred main stream mathematics and clearly given the example of the axiom 0 is different from 1. What else could I be possibly talking about?

I agree with ddt. I do not take main stream mathematics to mean just arithmetic.

 

[doronshadmi]

To be fair to Doron, you didn't ask for an axiom from arithmetic, so the answer shouldn't be discarded on that account.

I would like to remind, though, that doron up until 3 months ago was not aware of the axiom of extensionality. You might re-read the "A collection of infinitely..." thread from post 1328 on to see it took some 150 posts to drive home the existence and implications of the Axiom of Extensionality.

Understanding of fundamental notions has nothing to do with time.

I definitely did not drive to your home about "The axiom of the Empty set" as can be clearly shown by your reply, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=3816786&postcount=1359 .

The Axiom of an empty set is:

"There exists set X such that given any set Y, Y it is not a member of set X."

There is no guarantee that there is a unique X by this axiom, because ONLY by this axiom there must be also set X that is not a member of set X (for example: {} is not a member of {} (and {} exists only if it is not a member of {}, which gives us more than a one unique {}, without the Axiom of Extensionality)).


Again, a unique empty set does not exist without at least two axioms, which are:

The axiom of an empty set AND the Axiom of Extensionality.

I am not going to open again this disagreement between us on this case, in this thread.

 

[jsfisher]

Again, a unique empty set does not exist without at least two axioms, which are:

The axiom of an empty set AND the Axiom of Extensionality.

Why do you continue to make such an issue of this? In ZFC set theory, the empty set exists and it is unique. There is absolutely no rule of linguistic ethics forbidding naming an axiom about the empty set The Axiom of the Empty Set, even though that axiom may not be complete in every possible way characterizing the empty set.

You don't like the name given to one of the axioms. So what?

I am not going to open again this disagreement between us on this case, in this thread.

How can you honestly not claim to do something that you have already done?

 

[doronshadmi]

Why do you continue to make such an issue of this? In ZFC set theory, the empty set exists and it is unique. There is absolutely no rule of linguistic ethics forbidding naming an axiom about the empty set The Axiom of the Empty Set, even though that axiom may not be complete in every possible way characterizing the empty set.

You don't like the name given to one of the axioms. So what?



How can you honestly not claim to do something that you have already done?

The relevant part to this thread, taken from ddt's reply in http://www.internationalskeptics.com/forums/showpost.php?p=3816786&postcount=1359 is:

"Set theory without extensionality seems quite uninteresting to me."

In other words, ddt's fundamental notion is limited to the particular case of no Entropy (clearly distinct elements) as a first-order property of the entire framework.

This is, by the way, also your limitation, jsfisher, because you do not get my argument about the non-unique state of set X by using only the axiom of an empty set.

 

[jsfisher]

The relevant part to this thread, taken from ddt's reply in http://www.internationalskeptics.com/forums/showpost.php?p=3816786&postcount=1359 is:

"Set theory without extensionality seems quite uninteresting to me."

In other words, ddt's fundamental notion is limited to the particular case of no Entropy as a first-order property of the entire framework.

You are getting a lot of mileage out of this entropy term. Perhaps you should define it as some point.

Be that as it may, ddt meant exactly what he said. Your "in other words" are irrelevant, misguided, and little more than gibberish.

 

[ddt]

Understanding of fundamental notions has nothing to do with time.

You are (deliberately?) misunderstanding why I brought this up. As anyone can see from the referenced posts, it took you a freaking 150 posts to actually listen to what other posters were saying about the Axiom of Extensionality and its implications. That's rather bizarre for someone who claims to have been working for 20 years on his own variant on set theory and has been repeating again and again that "Cantor was wrong", etc.

In other words: it's quite disengenuous of you to bring up this particular axiom, given the above. Think of one you actually thought of yourself, instead of one that nearly literally had to be hammered into your skull. I'm not interested in re-iterating that bizarre discussion.

I definitely did not drive to your home about

You don't think I'd give you my home address, do you?

The relevant part to this thread, taken from ddt's reply in http://www.internationalskeptics.com/forums/showpost.php?p=3816786&postcount=1359 is:

"Set theory without extensionality seems quite uninteresting to me."

The onus would be on you to show that set theory without extensionality would be interesting, not the reverse.

In other words, ddt's fundamental notion is limited to the particular case of no Entropy as a first-order property of the entire framework.

Bollocks. The words "entropy" and "first-order property" did not appear in that thread. You've invented them later, without actually defining them. We're still waiting for that...

 

[Skeptic]

The problem with Doron's work is that he thinks that some trivial point or definition he had recently read about (or had made up) is the "key to everything" in math that everybody else had missed.

For the record, primes in mathematics -- more precisely, in number theory -- are "deep" for reasons that have nothing whatever to do with this odd definition of "enthropy". Doron simply doesn't know enough mathematics to know that.

Doron -- why don't you read a basic primer about number theory?

 

[doronshadmi]

You are (deliberately?) misunderstanding why I brought this up. As anyone can see from the referenced posts, it took you a freaking 150 posts to actually listen to what other posters were saying about the Axiom of Extensionality and its implications.

Let us reverse it.

Evan after 150 posts, you still do not get http://www.internationalskeptics.com/forums/showpost.php?p=4117701&postcount=306 and http://www.internationalskeptics.com/forums/showpost.php?p=4117773&postcount=308 .

 

[doronshadmi]

The problem with Doron's work is that he thinks that some trivial point or definition he had recently read about (or had made up) is the "key to everything" in math that everybody else had missed.

For the record, primes in mathematics -- more precisely, in number theory -- are "deep" for reasons that have nothing whatever to do with this odd definition of "enthropy". Doron simply doesn't know enough mathematics to know that.

Doron -- why don't you read a basic primer about number theory?

The "deep" about Primes, is limited to the particular case of clear distinction, as a first-order property of the entire framework.

Did you read http://www.geocities.com/complementarytheory/UR.pdf?

I'll be glad if you air your view about it.

 

[jsfisher]

Let us reverse it.

Evan after 150 posts, you still do not get http://www.internationalskeptics.com/forums/showpost.php?p=4117701&postcount=306 and http://www.internationalskeptics.com/forums/showpost.php?p=4117773&postcount=308 .

Doron, since you, yourself, are clearly having trouble following your own point, post to post, as evidenced by your sequence of non sequiturs, do you really expect us to follow it?

 

[doronshadmi]

Doron, since you, yourself, are clearly having trouble following your own point, post to post, as evidenced by your sequence of non sequiturs, do you really expect us to follow it?

Please don't be ridiculous.


Since you and your friends here do not know how to start, I'll give you some help by this dialog:

Glad to see you around here. How you doing?

Well, I have read your article and I have several questions, but in here I will show two general comments:

i) The MAF, when defined as "any possible relation between A, B and C that is not limited to any particular order", is defined as "any possible relation between A, B and C in any order". Then you say that in a MAF "There is no particular order and there is no particular distinction between the elements.", that is to say, a MAF is any relation between anything.

http://philosophy-forums.com/showthread.php?p=30891

Do not copy posts from other forums. This is a violation of copyright.

Replying to this modbox in thread will be off topic  Posted By: Lisa Simpson

My answer:

Thank you, I'm doing fine.

I really like your analysis of my work.

You are right about MAF.

By using MAF we ignore any particular meaning that may be given by some definition, and all we care is about the form.

I have found that MAF ,if it is researchable, is not less than Relation\Element Interaction (it can be called REI).

An anti-foundationalist reduces its belief to Relation (everything is relative to each other).

A foundationalist reduces its belief to Element (everything is derived from an Elementary building-block).

No researchable framework can be found, unless REI can be found, where this framework is not Relation-only and not Element-only.

We have shown that no Singularity (going beyond any interaction) is researchable, or in other words, a researchable framework is at least the interaction between anti-foundationalism and foundationalism beliefs.

Let A be Foundationalist beliefs.

Let B be Anti-Foundationalist beliefs.

MAF is *__*, in this case, where:

* A,B                  * A
|            and       |
* A,B                  * B

Without MAF *__* , A and B are not comparable and not researchable, in the first place.

In other words, Relation (notated by "__") \ Element (notated by "*") Interaction (REI) enables a researchable framework, which is not Relative-only (__) and not Element-only (*), but it at least MAF.

 

[jsfisher]

Please don't be ridiculous.


Since you and your friends here do not know how to start, I'll give you some help by this dialog:

...improbably dialog snipped...

This is far more likely:

I did read your Universal Reasoning document. I found the Introduction uncharacteristic of your other writings. Then I realized it was a very long carbon copy of someone else's work. You might want to review standard manuscript style about how to properly present long quotations. You don't want to be accused of plagiarism, after all.

As for the rest of the document, it was classic doron in style and content. Rather than any sort of intelligent development of concepts and relationships using the words and the powers of expression, you resort to pointless substitutions, inconsistent terminology, meaningless diagrams, and, of course, gibberish.

I also note that document does not really build on nor develop the concepts expressed in the Introduction.

 

[ddt]

I referred main stream mathematics and clearly given the example of the axiom 0 is different from 1. What else could I be possibly talking about?

I agree with ddt. I do not take main stream mathematics to mean just arithmetic.

Thanks, jsfisher. But basically, we're going to argue about what is a true Scotsman, so let's leave it with that.

You don’t know what axioms are, you never heard of it before, you don’t know what you are talking about.

Doron indeed has on several occasions shown not to comprehend what axioms are.

Here are another examples of mainstream math axioms you don’t find on the web:

There is a number a, that added to a any number b equals b. a+b=b
And to this number “a” we call it zero “0”
There is a number c, that multiplied to any number d is equal to d. cxd=d
And to this number “c” we call it one “1”

Well, you'd find them if you look at the Wiki lemma about Group Theory. They're both the Inverse Element Axiom for a group, once stated for the addition group and once for the multiplication group.

I wouldn't call them axioms in the context of arithmetic. Arithmetic, IMHO, builds on Peano's axioms for the natural numbers and on top of that, the definitions of Z, Q and R. Based on that, the existence of an inverse element is merely a theorem.

Let's have a good mathematical discussion about that in the R&P forum .

 

[doronshadmi]

This is far more likely:

I did read your Universal Reasoning document. I found the Introduction uncharacteristic of your other writings. Then I realized it was a very long carbon copy of someone else's work. You might want to review standard manuscript style about how to properly present long quotations. You don't want to be accused of plagiarism, after all.

As for the rest of the document, it was classic doron in style and content. Rather than any sort of intelligent development of concepts and relationships using the words and the powers of expression, you resort to pointless substitutions, inconsistent terminology, meaningless diagrams, and, of course, gibberish.

I also note that document does not really build on nor develop the concepts expressed in the Introduction.

Another example of your inabitiy to grasp new ideas.

You simply unable to say even a one valueable thing about http://www.internationalskeptics.com/forums/showpost.php?p=4117959&postcount=315 , isn't it?

 

[ddt]

I did read your Universal Reasoning document. I found the Introduction uncharacteristic of your other writings. Then I realized it was a very long carbon copy of someone else's work. You might want to review standard manuscript style about how to properly present long quotations. You don't want to be accused of plagiarism, after all.

The paragraphs from "In logic, three kinds" to "associated with this style of reasoning" are a verbatim copy of the wiki article on logical reasoning.

The most hilarious is the reference, though. Doron references this part with [2]: T.J. Menzies, “Applications of Abduction: Knowledge Level Modeling". However, Menzies' paper does not contain that quote. The paper is merely given as an unquoted reference in the wiki article.

So, Doron doesn't even know how to properly give references...

 

[Apathia]

Please don't be ridiculous.


Since you and your friends here do not know how to start, I'll give you some help by this dialog:

Glad to see you around here. How you doing?

Well, I have read your article and I have several questions, but in here I will show two general comments:

i) The MAF, when defined as "any possible relation between A, B and C that is not limited to any particular order", is defined as "any possible relation between A, B and C in any order". Then you say that in a MAF "There is no particular order and there is no particular distinction between the elements.", that is to say, a MAF is any relation between anything.

However, such stipulative definition of MAF is so general and abstract that it does not define anything. I mean, by that definition, any relation between any element is a MAF: everything is a MAF! But that explains/defines nothing.

Regarding the traditional rules to make a definition, one rule suggests that a definition should not be too wide as to include everything, and your definition is definitely too wide.

ii) Regarding your main problem: "Is it possible to define a framework where anti-foundationalist and foundationalist can agree with each other?"

You correctly define:

A foundationalist believes that there are beliefs that do not need any justification by other beliefs. Therefore these beliefs can be used as an objective base ground to justify other beliefs.

An anti-foundationalist believes that there are no beliefs that do not need any justification by other beliefs. Therefore no belief can be used as an objective base ground to justify other beliefs, and beliefs are relative to each other.

Now, how does a MAF define a framework where anti-foundationalist and foundationalist can agree with each other? If the MAF criteria is too general as to accept any relation, then it also accepts the disagreement between anti-foundationalist and foundationalist.

I mean, MAF does not define a framework where anti-foundationalist and foundationalist can agree with each other because MAF does not define a framework. MAF only says "we can relate anything with anything", but that is already just another foundationalist belief that an anti-foundationalist is well prepared to reject.

My answer:

Thank you, I'm doing fine.

I really like your analysis of my work.

You are right about MAF.

By using MAF we ignore any particular meaning that may be given by some definition, and all we care is about the form.

I have found that MAF ,if it is researchable, is not less than Relation\Element Interaction (it can be called REI).

An anti-foundationalist reduces its belief to Relation (everything is relative to each other).

A foundationalist reduces its belief to Element (everything is derived from an Elementary building-block).

No researchable framework can be found, unless REI can be found, where this framework is not Relation-only and not Element-only.

We have shown that no Singularity (going beyond any interaction) is researchable, or in other words, a researchable framework is at least the interaction between anti-foundationalism and foundationalism beliefs.

Let A be Foundationalist beliefs.

Let B be Anti-Foundationalist beliefs.

MAF is *__*, in this case, where:

* A,B                  * A
|            and       |
* A,B                  * B

Without MAF *__* , A and B are not comparable and not researchable, in the first place.

In other words, Relation (notated by "__") \ Element (notated by "*") Interaction (REI) enables a researchable framework, which is not Relative-only (__) and not Element-only (*), but it at least MAF.

http://philosophy-forums.com/showthread.php?p=30891