Hi people,

During the last 20 years I developed a new Mathematical theory, which is based on what I call: an included-middle reasoning.

Included-middle reasoning is:

The Art of interactions between independent opposites in non-destructive ways.

If we compare between the excluded-middle reasoning (which is the standard reasoning that standing in the basis of the standard language of mathematics) and Included-middle reasoning, we can find these major differences:

In an excluded-middle reasoning, two opposites are simultaneously contradicting each other, and the result is no-middle(=excluded-middle reasoning).

In an included-middle reasoning, two opposites are simultaneously preventing/defining their middle domain, and the result is a middle(=included-middle reasoning).

The goal of my work is to find a logical reasoning system, which can be used as a common basis for both our morality development and our technological developments.

And I am not talking about the biblical morality model, but on the idea of "power over nature" that is the basis of Descrates' and Bacon's philosophy.

This point of view is the basis of our modern technological civilization that is still directed by this "power over nature" idea, which can quickly lead us to a dead-end street of the history of our life on this planet.

Morality, In my opinion, is first of all our basic reasoning of natural balance with the fragile and complex phenomena of life on this planet, which we are part of it (whether we like it or not) and not "power over nature" of it.

If we achieve this goal, then I think that we improve our chances to survive the power of our technology.

I have found that included-middle reasoning has the properties to achieve this goal, after I developed some fundamental Mathematical works, which are based on its reasoning.

From this point of view, the mathematician's cognition abilities are taken as natural parts of the mathematical research itself, and this approach can be used to develop a gateway between his own morality development and his technical mathematical developments.

The main trigger behind this work is my interpretation to Drake's equation.

If we look at Drake's equation http://www.setileague.org/general/drake.htm we can find parameter L.

L = The "lifetime" of communicating civilizations, or in other worlds, if there is no natural catastrophe in some given planet, then how some civilization survives the power of its own technology?

If we look on our civilization, I think that we cannot ignore L and in this case we should ask every day "how we survive the power of our technology?"

My work for the last 20 years is one of many possible ways to answer this every day question.

Though my research I have found that if some civilization has no balance between its morality level and its technological level, then there is a very high probability that its L= some n , or in other words it is no longer exists.

Now, let us look at our L and let us ask ourselves: "Do we do all what we have to do in order to avoid some n?"

Most of the power of our technology is based on the Language of Mathematics and its reasoning, where the current reasoning is generally based on 0_XOR_1 logical reasoning, and there is nothing in this reasoning which researches the most important question which is: "How do we use this powerful Language in order to find the balance between our morality level and our technological level"?

If our answer is: "The Language of Mathematics has nothing to do with these kinds of questions", then in my opinion we quickly bring ourselves to find the exact n of our L.

In my opinion, in order to avoid the final n of our L, we have no choice but to find the balance between our morality level and our technological level within the framework of what is called the Language of Mathematics.

Furthermore, we should not leave this question to be answered beyond the framework of our scientific methods, because no other framework, accept our scientific method can really determinate the destiny of our L.

My work can be found in http://www.geocities.com/complementarytheo...ry/CATpage.html (http://www.geocities.com/complementarytheory/CATpage.html) and it is hard to follow especially for professional Mathematicians that most of their reasoning is based on the excluded-middle reasoning.

Anyway I would like to share with you my work and I'll be glad to get any detailed questions, comments and insights.

Thank you,

Doron

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My goal is to fulfill the dream of the great mathematician Gottfried Wilhelm Leibniz ( http://www.andrews.edu/~calkins/math/biograph/bioleib.htm )

Actually my number system ( which some arithmetic of it can be found in http://www.scienceforums.net/forums/showpost.php?p=76489&postcount=20 ) is the fulfillment of Leibniz's Monads, and beyond it.

Doron, I just have a bit of advice on the form and substance of your paper. Most visitors to this forum are of a mind of "physicist". Tailoring your language to that audience from a mathematics standpoint and an applications standpoint will put you in better stead for review and comments.

I have a copy of your seminal paper and while I am not a mathematician in the sense that you are, I understood your thesis. You will not blow anyone away by mathematical complexities, but as I suggested, show real application to real problems, even the "morality" problem, which is something we all should pay close attention to.
Geistkiesel.

Dear geistkiesel,

First, thank you for your relpy.

I am not talking about technological developments at the first stage, because my system needs to rebuild its software/hardware architecture from scratch, and only then it can be used in efficient scientific ways.

At the first stage I am talking about the meaning the words “logical reasoning”.

In my opinion the first meaning of these two words is the method that reinforces the probability of the existence of its inventors/users.

Since we are non-trivial forms of complex systems, this method MUST clearly and simply include within its domain, methods that reinforce the probability of the existence of non-trivial complex systems, which can be developed according to it, (at least) without reducing their non-trivial complexity in the long range.

After 2500 years of using False_XOR_True logical reasoning, we find ourselves few steps from self distraction, which is a clear failure of this logical reasoning, that says nothing about our own existence.

Included-middle reasoning is the right answer in this crucial time, because its users are first of all learn to cherish non-trivial complexity right from the first stages of their education process.

For example, the concept of a number is not based anymore only on the quantity concept, but on the non-trivial ordered symmetrical degrees that can be found within any given quantity.

In other words, the quantity concept alone is too weak to give an accurate information about elements that are based on an indivisible combination between the Structure and the Quantity concepts, or in other words, the Natural number is not less then a Structural/Quantitative element, which is totally depends on our own cognition abilities as non-trivial complex systems, in order to be defined.

Young children’s cognition will be exposed from the beginning to understand and cherish their own non-trivial complexity, and they will be grown to adults that do their best in order to develop their own internal/external environment according to this logical reasoning.

In my opinion this is a must have step that any developed civilization should take, in order to exist and flourish.

Survival


Most books that teach the language of Mathematics, ignore our cognition’s abilities to understand and define the fundamental concepts of this language.

Language is a tool that gives the cognition its ability to examine the object, the subject and the value of object/subject relations.

For billions of years, living things have been learning how to deal with internal and external challenges occurring in their ways, and as the phenomena of life becomes more and more complex, it needs better tools of communication that will give it the ability to save and develop life from the single gene to the existence of civilizations.

The language in its both inherited and purchased sides is the most significant environment of life phenomena, and through it life can flourish from generation to generation.

Any language is examined first of all by its ability to connect between at least two opposite properties: the simple and the complex.

This ability is the clearest signature of reality in the global memory of life, and this memory is the guarantee to their existence.

Because of this insight, we as living things have to take extra care when we are using a powerful language like Mathematics, because it has the straightest influence on our own survival.

An imprecise use of this powerful language (when the meaning of “precise” is not just technical formal precision but the ways of using its products to support and develop life) can quickly bring us to a dead-end.

Our abilities to avoid it are connected with our abilities to understand the deep relations between language, reality and the cognition that involved with them.

Through this participation, we can tune our life and lead them away from a dead-end.

The first hints to an imprecise use of this powerful language can be found when we are loosing our abilities to distinguish between the simple and the trivial and between the complex and the complicated.

The opposite of the trivial is the complicated, when by saying “trivial” we mean a non-deep reference between the cognition and the thing(s) it is referred to.

For example: our belief that our models are equivalent to reality, which leads us to the trivial conclusion that what holds in our models also holds in reality.

The indistinguishability between the complex and the complicated appears when the cognition tries to force its trivial conclusions on the reality, but then it become aware to the complexity of the reality and concluding that reality is complicated.

A question that should be asked by any civilization that is using a powerful language like Mathematics is: can we find signs of using Math in an incorrect way?

I think that a very brief look on our civilization gives us too many signs of complicated paths that lead us to nowhere.

If we want to avoid these obstacles, I think we have to include feedback (cybernetic) methods which reflecting the influence of a powerful language like Mathematics language on our life.

By this approach we get at least two main advantages:

a) Quality control based on tuned dynamic balance of the influence of Math language on our cognition, which supports our cognition's abilities to deal with abstract and non-abstract non-trivial complexity of the real life.

b) An improved ability to create deep and versatile relations between opposites, which give us better and more valuable conditions for flourishing life.

So the first step to this goal is to reexamine fundamental concepts .

Let us start by checking our ability to count.

The eye does not see itself until it is aware to its own limitations, and then it can be included as an explored element.

Now please change "eye" by "cognition" and read the above again.

The above point of view leaded me to ask myself what are the minimal conditions that give us the ability to identify and count things?

For example, let's examine this situation:

On the table there is a finite unknown quantity of identical beads > 1
and we have:

A) To find their sum.

B) To be able to identify each bead.

Limitation: we are not allowed to use our memory after we count a bead.

By trying to find the total quantity of the beads (representing the discreteness concept) without using our memory (representing the continuum concept) we find ourselves stuck in 1, so we need an association between continuum and discreteness if we want to be able to find the bead's sum.

Let's cancel our limitation, so now we know how many beads we have, for example, value 3.

Now we try to identify each bead, but they are identical, so we will identify each of them by its place on the table.

But this is an unstable solution, because if someone takes the beads, put them between his hands, shakes them and put them back on the table, we have lost track of the beads identity.

Each identical bead can be the bead that was identified by us before it was mixed with the other beads.

We shall represent this situation by:

((a XOR b XOR c),(a XOR b XOR c),(a XOR b XOR c))

By notating a bead as 'c' we get:

((a XOR b),(a XOR b),c)

and by notating a bead as 'b' we get:

(a,b,c)

We satisfy condition B but through this process we define a universe, which exists between continuum and discreteness concepts, and can be systematically explored and be used to make Math.

It means that what is called Natural number is at least a structural/quantitative information form.

Standard Math axioms that define the Natural numbers ignore our cognition's abilities to define them, and the result is a quantitative-only information form where cardinality (quantity) and ordinality (order) are both well-defined.

By this attitude, Standard Math is not aware of several structural/quantitative information forms that exist within any given quantity > 1, and uses only the wall-defined information forms that have no redundancy and no uncertainty.

By using Organic Mathematics ( http://www.geocities.com/complementarytheory/ONN1.pdf), any number is first of all an information form that can be understood only by cognition/object interactions.

From this point of view, redundancy and uncertainty cannot be ignored and they are taken as "first-order" (fundamental) properties of Math language, which is a paradigm shift of the Natural numbers concept that open for us a gateway to non-trivial complexity.


About non-trivial complexity:

Let us examine the balance concept.

For example: we have two pyramids, pyramid A and pyramid V.

Pyramid A stands on one its surfaces, and in this case we have a trivial balance problem.

Pyramid V stands on one its angular points, and in this case we have a non-trivial balance problem.

The skills of a self aware non-trivial complex system can be measured by its ability to use any balance degree that can be found between A and V polar states, in such ways that at least do not reduce the non-trivial complexity of itself and its environment, in the long range.


About Included-Middle reasoning:

Some analogy:

Let us say that the property of being a glue depends on some mixing between material A and material B.

A and B are not defined (exist) by each other, but when they are mixed together in a particular way, we get the property of a glue.

The most comprehensive principle of this point of view is based on the middle domain that can be found between at least two opposites, when the property of the middle domain is a new thing that cannot be found in each separate opposite.

And this is exactly the main principle of Included-middle logical reasoning, which define most of the time new products, which are the outcome of at least two opposites.

In other words, any non-trivial abstract/non-abstract product is first of all based on constructive associations between opposites as their first-order products, and then the rest of the middle domain elements, are some n>1 order products.

For further information about Included-Middle logical reasoning, please open http://www.geocities.com/complementarytheory/CompLogic.pdf , thank you.



What do you think ?


Doron

Doron Shadmi:

Let us say that the property of being a glue depends on some mixing between material A and material B.

The most comprehensive principle of this point of view is based on the middle domain that can be found between at least two opposites, when the property of the middle domain is a new thing that cannot be found in each separate opposite.

And this is exactly the main principle of Included-middle logical reasoning, which define most of the time new products, which are the outcome of at least two opposites.

This system of reasoning was alredy posited by GWF Hegel in his "Logics" and "Phenomenology of Spirit/Mind". In short, Hegel's dialectics attains 'synthesis' by contrasting the two binary oppsitions of 'thesis' and 'anti-thesis' - i.e., a thesis + an anti-thesis = a synthesis.

As in your glue analogy, if you would take a chemical A as a thesis and a chemical B as an anti-thesis, by combining the two polar oppositions, you would get a synthesis -a totally new material.

What is more striking about Hegel's system is that his dialectics is not merely dialectics in the Platonic sense of the word, but it is "Progressive Dialectics". In that, a synthesis you obtained from a thesis and anti-thesis then becomes a newer thesis, which then is contasted against a newer anti-thesis; accordingly you would get a newer systhesis.

To use your glue anaology again - Once you mix chemical A (thesis) and chemical B (anti-thesis), you would get Chemical AB (synthesis), but suppose you have a chemical CD and it is mixable with the Chemical AB, then you would get a totally new material Chemical ABCD (newer synthesis). With the same token, if you have a chemical EFGH, you may get an even newer synthesis of Chemical ABCDEFGH. . . . So the system is to generate a new idea at a given moment, and it keeps generating newer ideas as time goes by. That is, a synthesis in the 19th century is no longer valid in the 20th or 21st century as its very nature is perpetual flux, modification and change. This is the way in which Hegel attains his "Absolute Idea" (at a given time).

I thought your way of thinking resembles the above. Tell me if anything deviates.
kind regards,

Dear teguy,

First, thank you for your reply.


In other words, any non-trivial abstract/non-abstract product is first of all based on constructive associations between opposites as their first-order products, and then the rest of the middle domain elements, are some n>1 order products.

n>1 order products are the same as your AB.. ABCD... ABDCEFGH... example.

And this idea is older then Hegel's dialectics, actually we can find it in some schools of thought in ancient India.

But I wish to notice that the result of constructive associations between at least two opposites is not just a new thing but also exposes a deeper simplicity that help us to define the balance with our new discoveries.


synthesis in the 19th century is no longer valid in the 20th or 21st century as its very nature is perpetual flux, modification and change.

In my opinion, the Quantum Mechanic Wave/Particle duality phenomena can be interpreted and understood by included-middle reasoning, much better then the Excluded-Middle reasoning, which is still the major logical reasoning of the modern western civilization.

And I add to this list, Information theory, Chaos Theory and Complexity Theory, which in my opinion, are going to be the main subjects of the 21st century.

Actually, my framework (which is based on Non-Euclidian school of thought) is the first outlines to construct a comprehensive Mathematical/Logical framework that gradually will substitute the current linear/mechanic school of thought.

In my opinion the deep meaning of logic, is the method that can help us to survive and flourish day by day in non-trivial ways.

We as individuals and a part of a civilization can survive and flourish if and only if we develop our internal/external constructive dialog between us and our environment, in non-trivial ways.

In short, logic is THE ART OF THE DIALOG that keeps and develops non-trivial complexity which is based on simplicity.

Through this point of view, there is no room to scholastic methods that do their best in order to keep their abstract purity by doing their best to disconnect themselves from the non-linear and non-trivial complexity of daily life.

These scholastic games which are mostly based on the Excluded-Middle principle, are nothing but trivial and closed games of a particular community of people, that try to force their trivial methods on the non-trivial complexity of reality.

This school of thought, leaded mostly by Rene Descrates (1596-1650) and Francis Bacon (1561-1626) http://trumpeter.athabascau.ca/content/v10.3/Jung.html , disconnected 500 years ago between THE ART OF THE DIALOG (that should be the heart of any logical method, which is not based on the dangerous idea of "power over nature") and us as non-trivial complex systems, and developed the linear, mechanic and 0_XOR_1 trivial logic, that disconnected between our morality and our logical reasoning.

And I am not talking about the biblical morality model, but on the idea of "power over nature" that is the basis of Descrates' and Bacon's philosophy.

This point of view is the basis of our modern technological civilization that is still directed by this "power over nature" idea, which can quickly lead us to a dead-end street of the history of our life on this planet.

Morality, In my opinion, is first of all our basic reasoning of natural balance with the fragile and complex phenomena of life on this planet, which we are part of it (whether we like it or not) and not "power over nature" of it.

The most 'dangerous zone' of this "power over nature" idea can be found in the logical reasoning that stands at the basis of the formal and platonic school of thought, where humanity and nature’s non-trivial complexity have no room.

Instead of humanity and nature’s non-trivial complexity, Formalism and Platonism are based on scholastic and artificial methods that look at logic as some scholastic game (in the case of formalism) or a universal principle, which is out of this world (in the case of Platonism).

So as you see "power over nature" has many faces in our modern civilization, and this imbalance can lead us like a pendulum movements, to the opposite side of irrationality which is based on superstitious and some primitive aspects of fundamentalist beliefs.

This cocktail of a weapon of mass destruction and primitive fundamentalist beliefs, are both based on the same "power over nature" idea.

So, from this point of view LOGIC is too important concept to be left in the hands of the current community of academic institutions that still teach only its trivial technical aspects, which are mostly based on 0_XOR_1 axiomatic frameworks that all their products are based on PROOFS that are totally disconnected from THE ART OF THE DIALOG between our morality levels and our technological skills.

In my opinion, we immediately have to find the balance between our morality level and our technological skills, because we are in Galois last night, and if we do not act now to return to full meaning of the LOGIC concept, it will be our last night on this planet.

For more details please look at:

http://www.geocities.com/complementarytheory/MyGoal.pdf

http://www.geocities.com/complementarytheory/TheBestOf.pdf

http://www.geocities.com/complementarytheory/GaloisDialog.pdf

http://www.geocities.com/complementarytheory/Non-Naive-Math.pdf

http://www.geocities.com/complementarytheory/ONN1.pdf

http://www.geocities.com/complementarytheory/ONN2.pdf

http://www.geocities.com/complementarytheory/ONN3.pdf

http://www.geocities.com/complementarytheory/My-first-axioms.pdf

http://www.geocities.com/complementarytheory/MonadCK.pdf

http://www.geocities.com/complementarytheory/9999.pdf

http://www.geocities.com/complementarytheory/Anyx.pdf


The meaning of the Function concept:

What we call a function is (in my opinion) first of all the reflection of our own memory ( http://www.geocities.com/complementarytheory/Function.pdf )

From this point of view, the mathematician's cognition is no longer just a passive observer but also included as an active part of the mathematical research itself.

By this point of view, the language of Mathematics can be used as a very powerful gateway to connect and find the balance between our morality and our technical and logical skills.

Please read my answers to ex-xian at:

http://www.iidb.org/vbb/showpost.php?p=1926183&postcount=13

http://www.iidb.org/vbb/showpost.php?p=1926228&postcount=14

In short we are both observers and participators of the language of Mathematics, and from this point of view obsever_XOR_participator (Excluded middle logical reasoning) is a trivial framework that should be replaced by obsever_AND_participator (Included-middle logical reasoning).


Monadic Mathematics:

In Monadic Mathematics we do two basic things before we start to develop any possible product that can be found within its domain.

1) We clearly show its lowest and highest limitations.

2) We use the Included-Middle logical reasoning, which is the framework that stands in the basis of any existing product, which is the outcome of any possible interactions between at least two opposites.

After we did these two steps, we can talk about anything, which is under these two principles.

I have found that this attitude can lead us to ask interesting questions about the abstract/non-abstract aspects of our life, which lead us to become active participators of our answers, and not just passive observers of them.

In my opinion this is the real value of any living language, formal or informal, that it can be changed by its users, during non-trivial dialogs among them, that also includes within it “pointers” that also related to their common environment.

Form this point of view, I do not agree with Platonic idealism or any Formalistic scholastic closed game.

In short, the Number concept of Monadic Mathematics is the building block of the non-trivial progressive dialog between opposites.

For more details please look at http://www.geocities.com/complementarytheory/GaloisDialog.pdf



Thank you.

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