Deeper than primes

[Apathia]

But maybe we shouldn't interfere with the attempted dialog between Apathia and Doron. How about setting up another thread as "peanut gallery", where the rest of us can hang out and give our comments? Then Doron will not be distracted by our pesky questions

In choosing to try getting back into a dialog with Doron here, I assumed you would be present. I'm hoping I coulld ground things a little, so that there wouldn't be as many sometimes hostile expressions of frustration between Doron and the rest of us. And that we might just get on somewhat the same track.

But at the moment I'm laughing at my fear that I'm going to fall on my face and have to admit defeat.
Alas! I'll be that bear without a head!

 

[drkitten]

Abstraction of both Relation and Element, which is actually hyper-formalism (in standard formalism only Elements are abstracted but Relations still have a particular meaning).

The implicit definition of "hyper-formalism" here comes very close to being a type of higher-order logic.

I.e. propositional or zero order logic represents propositions : "Tigers are orange and black."
First order logic represents partial propositions where elements are abstracted : "Something exists that is orange and black."
Second order logic represents partial propositions where elements and their properties (such as relationship) are also representable : "Something exists that has two colors x and y."

But this, again, is a well-understood field of mathematics. Interesting, but hardly earth-shaking.

 

[Apathia]

The implicit definition of "hyper-formalism" here comes very close to being a type of higher-order logic.

I.e. propositional or zero order logic represents propositions : "Tigers are orange and black."
First order logic represents partial propositions where elements are abstracted : "Something exists that is orange and black."
Second order logic represents partial propositions where elements and their properties (such as relationship) are also representable : "Something exists that has two colors x and y."

But this, again, is a well-understood field of mathematics. Interesting, but hardly earth-shaking.

Doron's "higher order logic," if that's what it is, concerns itself with a template that every element and relation neccesarily comes in.
There's a field on the template for the element (whatever it's going to be) and one for the relation (whatever its going to be.)
His template is his "X/Y Complementation." He asserts that to have rational meaning (or "researchability" as he puts it), you need both the element and the relation standing with each other in this framework.

Now that's just plain trivial, but here comes the twisterroo.
"Complementarity" means many different things to Doron. It includes dualities such as Mind/Body or Wave/Patricle, split levels of discourse such as Physics/Metaphysics, 2 dimensions defining a plane, and any situation where two elements interact. Seeing that it casts so wide a net, this rule of 2, it involves the twist that any element of the pair can also be the relation field of the template. And any relaltion of the pair can also be in the element field. Any element can be regarded as relational, and any relation can be regarded as an object of discourse itself.
So, allowing this interchangability (that is not necessarily a feature of ordinary linguistics and so comes across as counterintuitive) the complementary field involves not just 2 values but four.

So here Doron gets his truth table of "Complementary Logic,"
where True or False as elemental values are paired with True and False as relational values.

This is also the generator of Doron's Organic Natural Numbers, though he has a different way of approching them based on Local/Non-local Complementarity. But it all comes back to anything goes into the two slots and you pull the lever.

Yes, I'm not speaking with mathematical rigor and precision. I'm a storyteller. a retired English teacher. I confess to my uselessness in the field of Mathematics.
And it's with this incompetance that I claim some insight into what Doron is about. His approach is analogical in nature. He uses the language of Mathematics metaphorically to express his overarching analog.

Perhaps this is why his Complementary Logic as yet has no formal rules of inference, or why his Organic Numbers as yet don't have their own Algebra.
But perhaps they could.

 

[doronshadmi]

Aphatia,

I am going to reply only to you in this thread, exactly because you are not a mathematician, which is limited to the western school of thought.

You are asking for a rule.

Please read again http://www.geocities.com/complementarytheory/UR.pdf in order to see how the concept of rule is nothing but a particular case of hyper-formalism, where
No form has a meaning of its own.

MAFs are simply the Relation\Element Interaction (without any meaning) that can be found under any given cardinal.

You, the mathematician take Relation\Element Interaction (REI) and invent your researchable game, by giving it meaning where rules already have meaning.

By standard formalism, Relations have meaning (the hold the rules) where Elements can be replaced by any other elements that obey the invented\discovered rules.

Higher-order logic is a particular case of Universal Reasoning (Hyper-Formalism) because Higher-order is based on some particular asymmetric MAF.

Again, Relation\Element Interaction is not a dualistic framework exactly as a tree with a one trunk and infinitely many branches (that are related to each other by infinitely many distinct ways, where each way is both general and particular case of the entire tree) is not a dualistic framework.

You still don't get how Hyper-formalism's natural transparency of any meaning, is the best detector of being aware of any meaning (rule, etc...) that is given by the mathematician.

The form without any meaning is the best way to avoid hidden assumptions during mathematical developments.

 

[jsfisher]

Aphatia,

I am going to reply only to you in this thread

If you are unwilling to defend and support allegations you have made, then we may fairly assume you are unable to support them and they are all false.

Yes, you completely misunderstood and misquote Hilbert.
Yes, the whole MAF idea is trivial at best with no interesting example.
Yes, Mathematics has interconnections among all of its branches.
No, you cannot demonstrate any meaningful knowledge of Mathematics.
No, you cannot recognize a metaphor in normal English discourse.
No, English is not your first language; your native tongue is gibberish.

 

[Apathia]

Aphatia,

I am going to reply only to you in this thread, exactly because you are not a mathematician, which is limited to the western school of thought.

You are asking for a rule.

Please read again http://www.geocities.com/complementarytheory/UR.pdf in order to see how the concept of rule is nothing but a particular case of hyper-formalism, where
No form has a meaning of its own.

MAFs are simply the Relation\Element Interaction (without any meaning) that can be found under any given cardinal.

You, the mathematician take Relation\Element Interaction (REI) and invent your researchable game, by giving it meaning where rules already have meaning.

By standard formalism, Relations have meaning (the hold the rules) where Elements can be replaced by any other elements that obey the invented\discovered rules.

Higher-order logic is a particular case of Universal Reasoning (Hyper-Formalism) because Higher-order is based on some particular asymmetric MAF.

Again, Relation\Element Interaction is not a dualistic framework exactly as a tree with a one trunk and infinitely many branches (that are related to each other by infinitely many distinct ways, where each way is both general and particular case of the entire tree) is not a dualistic framework.

You still don't get how Hyper-formalism's natural transparency of any meaning, is the best detector of being aware of any meaning (rule, etc...) that is given by the mathematician.

The form without any meaning is the best way to avoid hidden assumptions during mathematical developments.

Thanks for your reply, Doron.

Indeed, the others were right. I was reading something into you that isn't really what you're about.
It was based on old stuff of yours about "Complementary Logic," but I should drop that because your MAF is not a logic. And since it isn't, one shouldn't expect rules of inference.

So I confess this idea of a complementary frame for all elements of cognition was my own fantasy. I'll not muddy your waters with it again.

You still don't get how Hyper-formalism's natural transparency of any meaning, is the best detector of being aware of any meaning (rule, etc...) that is given by the mathematician.

Actually that's what I like. Forget the "Complemetary Logic." The essence is groundless and structureless. The template is empty of any set fields.
Mathematics can only speak of the stuff it writes on this blamk sheet, but it's that the sheet is blank that allows anything to be written on it.

 

[The Man]

Aphatia,

I am going to reply only to you in this thread, exactly because you are not a mathematician, which is limited to the western school of thought.

You are asking for a rule.

Please read again http://www.geocities.com/complementarytheory/UR.pdf in order to see how the concept of rule is nothing but a particular case of hyper-formalism, where
No form has a meaning of its own.

MAFs are simply the Relation\Element Interaction (without any meaning) that can be found under any given cardinal.

You, the mathematician take Relation\Element Interaction (REI) and invent your researchable game, by giving it meaning where rules already have meaning.

By standard formalism, Relations have meaning (the hold the rules) where Elements can be replaced by any other elements that obey the invented\discovered rules.

Higher-order logic is a particular case of Universal Reasoning (Hyper-Formalism) because Higher-order is based on some particular asymmetric MAF.

Again, Relation\Element Interaction is not a dualistic framework exactly as a tree with a one trunk and infinitely many branches (that are related to each other by infinitely many distinct ways, where each way is both general and particular case of the entire tree) is not a dualistic framework.

You still don't get how Hyper-formalism's natural transparency of any meaning, is the best detector of being aware of any meaning (rule, etc...) that is given by the mathematician.

The form without any meaning is the best way to avoid hidden assumptions during mathematical developments.

You still do not get it Doron, what you are talking about is done and has been done for centuries, it is called language.

The sentence above is just a collection of abstract symbols that have no meaning on their own. What gives them meaning is the alphabet, the definitions, the syntax and the general rules of the language involved, in this case English. It does not matter whether it is Swahili, pig Latina or mathematics none of the symbols (being the MAF) of any language have any meaning on their own. What you’re asking for or seeking to accomplish has been done since the inception of language, symbols as the MAF is already there. If you what to create your own language then you must define your symbols, syntax, rules of usage as well as terminology, which everyone is still waiting for you to do.

 

[Skeptic]

Folks --

Once again, Doron's entire "discovery" is re-stating trivial, well known points as if they are essential, and doing so in incredibly complicated and badly-defined language. That makes up 10% or so of what he writes; the other 90% is simply meaningless.

It's pointless to ask Doron what he thinks, since there's nothing Doron thinks that isn't either (a) meaningless, or (b) found in any first-year logic textbook.

Hey, you asked.

 

[TMiguel]

Aphatia,

I am going to reply only to you in this thread, exactly because you are not a mathematician, which is limited to the western school of thought.

Asking for other people that has already proven to know more then you do to step aside is the first symptom that you are about to talk nonsense, that you are not willing to be showed has so.

You are asking for a rule.

Please read again http://www.geocities.com/complementarytheory/UR.pdf in order to see how the concept of rule is nothing but a particular case of hyper-formalism, where
No form has a meaning of its own.

Pointless, document without content that has been presented many times.

MAFs are simply the Relation\Element Interaction (without any meaning) that can be found under any given cardinal.

Nonsense, cardinality means something; therefore it can not represent something meaningless. Even if we ignore that, something meaningless is totally useless has it tells you absolutely nothing.

You, the mathematician take Relation\Element Interaction (REI) and invent your researchable game, by giving it meaning where rules already have meaning.

Mathematicians limits themselves to find relations, those relations are applicable under certain rules.

By standard formalism, Relations have meaning (the hold the rules) where Elements can be replaced by any other elements that obey the invented\discovered rules.

Higher-order logic is a particular case of Universal Reasoning (Hyper-Formalism) because Higher-order is based on some particular asymmetric MAF.

Meaningless sentence.

Again, Relation\Element Interaction is not a dualistic framework exactly as a tree with a one trunk and infinitely many branches (that are related to each other by infinitely many distinct ways, where each way is both general and particular case of the entire tree) is not a dualistic framework.

Mathematics is not a tree although you can make the analogy has such. If you base your framework on the same principles then different aspects of it will follow the same rules, and because they follow the same rules you are able to relate them.

You still don't get how Hyper-formalism's natural transparency of any meaning, is the best detector of being aware of any meaning (rule, etc...) that is given by the mathematician.

Meaningless sentence.

The form without any meaning is the best way to avoid hidden assumptions during mathematical developments.

There are no assumptions in mathematical development beside the axioms that we know to be true but can not be proven (and they can not be made at any stage). You can not present a mathematical proof whit an assumption, if it has an assumption it is not a proof.

Yet again you failed to comprehend even the most basic elements on how we do math.
You can call you work whatever you want, but there is no math in it.

 

[The Man]

Folks --

Once again, Doron's entire "discovery" is re-stating trivial, well known points as if they are essential, and doing so in incredibly complicated and badly-defined language. That makes up 10% or so of what he writes; the other 90% is simply meaningless.

It's pointless to ask Doron what he thinks, since there's nothing Doron thinks that isn't either (a) meaningless, or (b) found in any first-year logic textbook.

Hey, you asked.

Indeed, Skeptic, I stopped asking Doron what he “thinks” some time ago. I had tried instead to actually get him to look at the current (as well as past) thinking that he so vehemently opposes yet utilizes in his own dissociative manner. That of course has been as effective and meaningful as asking him what he thinks. Certainly I am not above chastising (since I am a scourge) and, as you mentioned before, attempting to humiliate him into waking up, but I still need to do more then just that. If not just for Duron’s benefit then for those others that might gain something even from the re-stating of the trivial, albeit this time from someone who can put it (hopefully) in a more coherent fashion.

 

[ddt]

It seems I'm late to the party . All other participants in the thread have already responded to Doron. I agree with their opinions and sentiments expressed. Doron doesn't address the many questions raised nor will he most probably ever do so; and his latest post doesn't add anything meaningful. A few snippets:

I am going to reply only to you in this thread, exactly because you are not a mathematician, which is limited to the western school of thought.

It is most curious that someone who claims to do mathematics refuses his work to be vetted and inquired by mathematicians. It is tantamount to admitting your work is not mathematics.

The "western school of thought" claim is another untruth from Doron. Mathematics has been influenced not only by Greeks, but by Arabs, Persians, Khwarezmians, and Indians, to name a few. India and China have had flourishing mathematical traditions which are recognized by everyone as being mathematics. Doron's writings are not, and that has nothing to do with "western thought" or "eastern thought".

MAFs are simply the Relation\Element Interaction (without any meaning) that can be found under any given cardinal.

The notion "cardinal" exists within the context of (ZF) set theory, so it is utterly misplaced here. That apart from the question what finding a MAF under a cardinal means - is that like strolling through your garden and finding a slug under a rock?

 

[jsfisher]

The notion "cardinal" exists within the context of (ZF) set theory, so it is utterly misplaced here. That apart from the question what finding a MAF under a cardinal means - is that like strolling through your garden and finding a slug under a rock?

Finding an MAF under a cardinal is similar to finding an acolyte under a priest. Either way, though, the Catholic Church is in denial.

 

[The Man]

It seems I'm late to the party . All other participants in the thread have already responded to Doron. I agree with their opinions and sentiments expressed. Doron doesn't address the many questions raised nor will he most probably ever do so; and his latest post doesn't add anything meaningful. A few snippets:


It is most curious that someone who claims to do mathematics refuses his work to be vetted and inquired by mathematicians. It is tantamount to admitting your work is not mathematics.

The "western school of thought" claim is another untruth from Doron. Mathematics has been influenced not only by Greeks, but by Arabs, Persians, Khwarezmians, and Indians, to name a few. India and China have had flourishing mathematical traditions which are recognized by everyone as being mathematics. Doron's writings are not, and that has nothing to do with "western thought" or "eastern thought".


The notion "cardinal" exists within the context of (ZF) set theory, so it is utterly misplaced here. That apart from the question what finding a MAF under a cardinal means - is that like strolling through your garden and finding a slug under a rock?

A fine post ddt and exemplifies the “Doron dilemma”. Certainly, Eastern and Western philosophies can be considered divergent, but not to the extent that Doron asserts. However, in mathematics there is no divergence, as you so eloquently described. The problem, I think (and as I recall Skeptic pointed out before), is that Doron takes such references as “real”, “irrational” and perhaps even “Imaginary” (or complex) numbers as a philosophical indication of such divergence in mathematics, taking those ascriptions as philosophically literal, as opposed to just defining some classifications. What he has repeatedly indicted, and in some cases stated, is his intent to combine Eastern with Western philosophies in mathematics (which as you note is the already the general basis of mathematics) when the only divergence is just philosophical and not literally mathematical.

 

[doronshadmi]

... because your MAF is not a logic.

It is the essence of Logic (where Logic is already a researchable framework).

By using MAF one can invent\discover anything that is based on Relation\Element Interaction.

 

[Reality Check]

It is the essence of Logic (where Logic is already a researchable framework).

By using MAF one can invent\discover anything that is based on Relation\Element Interaction.

What is your proof that Logic is a researchable framework?

Where is your proof that anything that is based on Relation\Element Interaction can be invented/discovered by using MAF?

What do you mean by "invent\discover"? Does "invent" mean that the "anything" did not exist before and was created by the researcher?

So many questions from a couple of sentences from doronshadmi! I am tempted to ask you what you mean by "the", "essence" and "of"

 

[doronshadmi]

What is your proof that Logic is a researchable framework?

Where is your proof that anything that is based on Relation\Element Interaction can be invented/discovered by using MAF?

What do you mean by "invent\discover"? Does "invent" mean that the "anything" did not exist before and was created by the researcher?

So many questions from a couple of sentences from doronshadmi! I am tempted to ask you what you mean by "the", "essence" and "of"

Please try, for example, to use Logic where there is no interaction between Logical connectives (what I call Relations) and propositions (what I call Elements).

The same holds in the case of Arithmetic where Relations are the operations and Elements are numbers, etc… (actually REI is the Minimal Accepted Form (MAF) of any researchable framework, formal or informal).

One of the new things about MAF is Distinction as a first-order property.

By get MAF one can understand that most of the current mathematical science is based on the particular case of MAFs' distinct elements.

 

[doronshadmi]

I'll not muddy your waters with it again.

Dear Aphatia,

MAF is simply the Minimal Accepted Form that is used to define the minimal terms of some researchable framework.

You, as a mathematician use MAF in order to define your game.

If this game is interesting, more persons will play with it and develop it.

In other words, you as a mathematician have the ability to define some interesting (researchable) framework (you are a significant factor of any given game).

 

[TMiguel]

Please try, for example, to use Logic where there is no interaction between Logical connectives (what I call Relations) and propositions (what I call Elements).

Without any possible relation, there is nothing you can possibly do.

The same holds in the case of Arithmetic where Relations are the operations and Elements are numbers, etc… (actually REI is the Minimal Accepted Form (MAF) of any researchable framework, formal or informal).

There is no accepted form, you can call it whatever you wish, but the intrinsic properties and relation that they imply always holds no matter what you call it. You can chose to ignore, but then you will be missing good tools.

One of the new things about MAF is Distinction as a first-order property.

By get MAF one can understand that most of the current mathematical science is based on the particular case of MAFs' distinct elements.

Pointless, complete nonsense after what has been said.

You, as a mathematician use MAF in order to define your game.

If I wish I can get myself a group of new axioms and create a new field of mathematics of my own. Will it be consistent? Different? Useful?
The answer is never yes on all the 3.

If this game is interesting, more persons will play with it and develop it.

In other words, you as a mathematician have the ability to define some interesting (researchable) framework (you are a significant factor of any given game).

We do not define the rules of the game, there is no point in time where some mathematician could have said that the result of a certain operation is different then what he came up whit in his “original version”. He doesn’t set the rules, he can only find them.

Ps. You are getting extremely repetitive.

 

[Reality Check]

Please try, for example, to use Logic where there is no interaction between Logical connectives (what I call Relations) and propositions (what I call Elements).

The same holds in the case of Arithmetic where Relations are the operations and Elements are numbers, etc… (actually REI is the Minimal Accepted Form (MAF) of any researchable framework, formal or informal).

One of the new things about MAF is Distinction as a first-order property.

By get MAF one can understand that most of the current mathematical science is based on the particular case of MAFs' distinct elements.

Your logic is incorrect.
An example of not being able to "use Logic where there is no interaction between Logical connectives (what I call Relations) and propositions (what I call Elements)" is not any of:

• What is your proof that Logic is a researchable framework?
• Where is your proof that anything that is based on Relation\Element Interaction can be invented/discovered by using MAF?
• What do you mean by "invent\discover"? Does "invent" mean that the "anything" did not exist before and was created by the researcher?

Let us start with somthing really simple: What is your proof that Logic is a researchable framework?

 

[doronshadmi]

Your logic is incorrect.
An example of not being able to "use Logic where there is no interaction between Logical connectives (what I call Relations) and propositions (what I call Elements)" is not any of:

• What is your proof that Logic is a researchable framework?
• Where is your proof that anything that is based on Relation\Element Interaction can be invented/discovered by using MAF?
• What do you mean by "invent\discover"? Does "invent" mean that the "anything" did not exist before and was created by the researcher?

Let us start with somthing really simple: What is your proof that Logic is a researchable framework?

It uses Interactions between Relations and Elements, and this is not a proof but the Minimal Accepted Form that enables to define some interesting axiomatic system, in the first place.

MAF is a pre-axiomatic form where also Relations (unlike in axiomatic systems) have no meaning of their own (in addition to Elements).

By asking about a proof you simply show that you (still) do not get axiomatic of pre-axiomatic frameworks.