How the Proof of the Pudding is Really in the Eating

When you want to know the truth you are looking for facts. This seems very evident but Philosophy and especially the field of Epistemology has spend a lot of time to find out if this Statement about Truth is really True.

The first step is to look up the definition of the word “fact“. We use Wordnet to do this. WordNet is a semantic lexicon for the English Language. The database contains about 150,000 words.

Fact: A piece of information about circumstances that exist or events that have occurred.
Fact: A statement or assertion of verified information about something that is the case or has happened.
Fact: An event known to have happened or something known to have existed.
Fact: A concept whose truth can be proved.

The meaning of words changes in history. If you want to know how the meaning is changed you have to look up the Etymology of the word.

Fact: 1539, “action” especially “evil deed,” from L. factum “event, occurrence,” lit. “thing done,” from neut. pp. of facere “to do”. Usual modern sense of “thing known to be true” appeared 1632, from notion of “something that has actually occurred.”

When we combine the result of both dictionaries we see that the original meaning of the word “Fact” is-related to the word “Event”. Later around 1632 it changed into a concept “whose truth can be proved”.

To find more about the meaning of the word Event we can look for all the occurrences of this word in the sentences of English language. One of the scientists who spend a lot of time researching the meaning of the word “Event” is George Lakoff. He defined The Event Structure Metaphor.

A Metaphor Is-A Mapping. A Mapping Is-A Relation between two Domains, the Source and the Target.

The Event Structure Metaphor is one of the most widespread of all the conceptual metaphors in the world. It maps from the source domain of Space to the target domain of Events, and leads to the following concepts:

A State Is-A Location (a bounded region in space).
A Change Is-A Movement (into or out of bounded region).
A Cause Is-A Force.
An Action Is-A Self-Propelled Movement.
A Purpose Is-A Destination.
A Mean Is-A Path to destinations.
A Difficulty Is-A Blockage.
Expected Progress Is-A Travel Schedule.
A Schedule Is-A Virtual Traveler, who reaches pre-arranged destinations at pre-arranged times.
An External Event Is-A Large Moving Object.
A Long-term, purposeful activity Is-A Journey
.

An Event Is-A Blockage that prevents us to Move from One Destination to an other Destination in the Journey called Life. To Move from one Destination to an other Destination we are Propelling our Self. Sometimes we are propelled By something else, An External Event. If this Happens it feels like we are hit by a Large Moving Object.

When we are Hit by an External Event “things get out of hand” or “we are not able to keep a tight rein on the situation” or “we are not going with the flow” or “things take a turn for the worse“.

A Fact is an Event that Causes the Emotion of Frustration (Anger, Irritation, Sadness, Worry,..). An Event Forces us to Move Away from our Original Route, the Path that leads us to the Destination that we wanted to Reach in Life. We have to take a Detour.

What happened around 1632?

Around 1632 Francis Bacon advocated a new method for achieving knowledge, based on careful observation and eliminative induction. Bacon warned that effective reasoning must be freed from the “idolatrous” influence of human nature (Emotions & Imagination).

Francis Bacon started The Age of Enlightenment. The Enlightenment advocated reason as a means to establishing an authoritative philosophical system which would allow human beings to obtain objective truth about the whole of reality. Much later Emmual Kant dedicated his Critique of Pure Reason to Francis Bacon.

What happened?

Facts were moved from the Emotions (Judgement, Opinion) to the Level of the Mind (Truth). With the help of Logic it would be possible to Prove Everything.

According to Aristotle there are four types of truth: universal affirmatives take the form: All S are P, universal negations take the form: No S are P, particular affirmatives take the form: Some S are P, particular negations take the form: Some S are not P. Later so called contingent truths were added. They are dependent on the situation/context.

The Quest for the Eternal Logical Truth is still going on. Many very bright minds have tried to find a solution but the terrible thing is that the Truth of a logical proposition is entirely dependent on the Truth of the Facts that are put into the Proposition. We are again in a State of Infinite Regress.

One of these bright minds was Frank Plumpton Ramsey (1903-1930). Ramsey lived and worked in Cambridge and was befriended with Bertrand Russell, G. E. Moore, J. M. Keynes and Ludwig Wittgenstein. Ramsey created a theory called Pragmatism.

In his paper ‘Truth and Probability’, written in 1926, Ramsey shows that if people in their behaviour obey a set of axioms or rules, the measure of our ‘degrees of belief’ will satisfy the laws of probability. The Truth is highly related to Judgment and “if we have analysed judgment we have solved the problem of truth“.

“..it is, for instance, possible to say that a chicken believes a certain sort of caterpillar to be poisonous, and mean by that merely that it abstains from eating such caterpillars on account of unpleasant experiences connected with them. … An exact analysis of this relation would be very difficult, but it might well be held that in regard to this kind of belief the pragmatist view was correct, i.e. that the relation between the chicken’s behaviour and the objective factors was that the actions were such as to be useful if, and only if, the caterpillars were actually poisonous. Thus any set of actions for whose utility p is a necessary and sufficient condition might be called a belief that p, and so would be true if p, i.e., if they are useful“.

What Ramsey is telling is that “the proof of the pudding is in the eating“.

What happened?

We are finally back to square one! After about 400 years of Enlightment we have to admit that the only way to find the Truth is to find out if what we Think is true is really True. We don’t have to use very complicated reasoning to prove what we are already experiencing in the Real World.

LINKS

About Logic and Alchemy

About the Age of Reason

About Pragmatism and Ramsay

About Truth

About the War of Words

The amount of people that are confused or are creating confusion is growing. It all has to do with Language. New words are created. Languages and Cultures are mixing. New Inventions and Theories are Created and Destroyed. We are in a highly creative phase, the End Game of Time Wave Zero. Is it possible to find the pattern behind this pattern?

The Encyclopedia Britannica is the oldest English-language encyclopedia still in print. It was first published between 1768 and 1771 in Edinburgh and quickly grew in popularity and size. The Brittanica expanded from 3 volumes in 1768 to 32 volumes today.

In France Diderot created the first French encyclopedia in 1745. It started as a translation of the English Cyclopedia of Ephraim Chambers. When he and his co-editor, mathematician Jean d’Alembert, were finished, they created a new work, the ‘Encyclopedie’. At that time it contained everything that was necessary to known about the Western World.

Its aim was “to collect all the knowledge that now lies scattered over the face of the earth, to make known its general structure to the men among we live, and to transmit it to those who will come after us,” to make men not only wiser” but also “more virtuous and more happy“.

Denis Diderot was one of the originators and interpreters of the Age of Enlightenment. This 18th-century movement was based on the belief that Reason could find True Knowledge.

During the Enlightment many scientists hoped that it would be possible to find the Eternal Truth, The Simple set of Rules that would Explain Every Thing. It was just a Matter of Time.

What they did not realize was that Truth is Highly Context Dependent. It is dependent on the Spirit of the Time, the Knowledge and Interpretation of the Writer of the Context, The Status of the Writer and the Genesis of Science.

Not only Knowledge changes but also Words change their meaning all the time. Everything Changes and the only thing that is left is to accept this Fact of Life.

The awareness of the problem of the Eternal Truth has created Cynicism. Scientists especially in the Social Sciences (Post-Modernism, Deconstruction) don’t believe it will be possible to find any objective general accepted pattern or explanation. They are fighting the goals of the highly rational Enlightment with very complicated rational arguments of their own.

When the exponential rise of Novelty predicted by Time Wave Zero (and other comparable models) reaches the Point Omega we will be literally lost in Space. Innovations that took centuries to happen in history will happen in a few days.

It is really true that there are no general Explanations possible? Is Everything Context Dependent?

The problem that the Eternal Change of our primary communication vehicle, Language, is creating is analyzed by many great minds in history. Perhaps the greatest genius was Wittgenstein. At the end of his life his students put all his Observations (he did not believe in Theory) in something called The Blue and Brown Books. In these books he is teaching the Art of Clarification.

Wittgenstein invented a new way of looking at the world called a Family Resemblance. If we gather together members of the same Family, they probably Look Alike, although there is no Distinctive Feature that they all share in Common. A brother and a sister might have the same dark eyes, while that sister and her father share a slightly turned-up nose.

They share a group of features, some of which are more distinctly present in some members of the family, while some features are not present at all. Wittgenstein argues that the different uses of one word and rules share the same Family Resemblance.

A Family is a Vague Set of Relationships that have something in Common but the parts of the set are Different. A Family is a unique set of permutations of distinctive features.

The only way to recognize a Family is to meet the members and create an intuition, a feeling. To do this we have to leave our study room and walk around in Reality. We have to move into the Context instead of floating above The Context.

Floating above the Context is called Imagining. There is nothing wrong with imagining. The imagination (Spirit) is the Mother of Art. Changing Art into a Science Destroys the Beauty of the Work of Art. Just like a Family a Piece of Art shows a pattern but is also shows exceptions of the pattern. The exceptions show a pattern but this pattern also contains a pattern. The world is a self-reference, a Fractal.

Scientists don’t realize that they are creating Fiction. When they would realize that they are producing Fiction they would certainly improve their Style. Scientific Fiction (a Genre) is mostly unreadable for other Scientists and especially for “Normal” people like me.

There are Many Families and there are even Families of Families. Some people have been born with a Talent to Observe one Family. Others are aware of completely different Families. All of them share features but it will never be possible to find The Set of all Sets of features. Finding the set of sets created a huge problem in Mathematics. It was the main reason why Wittgenstein changed his “theory”. He left the field of Mathematics, spend years in complete isolation (he was a teacher) until the people of Cambridge begged him to come back.

It does not help to spend a lot of time to discuss a joint Family. It only creates a War of the Words or a nicer term of Wittgenstein, A Language Game. A major part of Scientific Fiction is about the Quest to find the general Definitions of the set of all sets, The Holy Grail of Science… When we spend too much time to Fight we will never See.

The quest of Objectivity shows itself in the Use of Statistics. Scientists are unable to find the right Context (a Family) but they are also unaware of the Fractal Structure of the Universe. They are also completely unaware about the boundaries of Statistics. They accept the General Truth of Statistics without any awareness of the background.

What is the solution to all these problems?

The fist step is to accept the Spiraling Spiral and Self-Reference as the fundamental Fractal of the Universe. It is really a simple clarifying explanation.

The next step is to determine the Level and the Phase of the Spiral You are in (Style, Chronotope, Family, Network, Field of Reference, Bias). It determines what You are able to See and Do. It defines the Place in Time/Space you are Watching. If You want to move to another Level or State change the State of Your Awareness.

The last step is to feel the Movement of the Force of Life, The Tao,  and connect to this Movement. If you have accomplished this all the Clarifications you are looking for are given to you by the Great Force of Creation, Inspiration.

About the Foundations of Mathematics

In the beginning of the 20th century the mathematicians Bertrand Russell and Alfred North Whitehead wanted to define the eternal foundation of Mathematics.

To build a foundation Mathematicians always start with defining what they “mean”. They use a symbolic language called Logic to do this.

In Logic “=” means Being the Same“. If we would use the mathematical “=” in human languages we would say things like “a House is a House“.

These statements are without any meaning. We believe them but they are not adding something to our knowledge of the world we live in. “=” is called a Tautology in Logic. It is the only statement that is always true.

Mathematics is about changing the left hand and the right hand of the tautology without changing the truth. Mathematicians are always proving that the left and the right in what they mean are the same (=).

To speed up the process of proving, Mathematicians define new symbols that are “based on” other symbols. They use the foundation of “lower” symbols to define higher symbols. This process of mapping is called Abstraction (going UP). A Number is abstracted into the symbol A, called a variable.

Human languages are different from Logic. Depending on the language, the context and the person, terms have a different meaning. Mathematicians don’t like that.

The term Foundation is a Latin term (fundus). In the English language “Foundation means “stable layer“.

In the Dutch language “Foundation” is translated into the term “grond-slag“. “grond-slag” means “hitting” (slag) a pole (paal) into the Earth to build a house on.

A foundation is something that is connecting a foundation (Poles) to another foundation (Earth).

In human language the right and the left are equal AND not equal. They have something “in common“.

When we talk about a foundation most of us See a House. When we communicate we share this picture unconsciously. If we have not lived in a context where houses are build we are not able to share meaning.

When a Dutch person “wants to fund” he has “to hit the pole“. In other places “Laying a Foundation” is a much more gentle process.

Human languages differ from Logic in many ways. The left and the right have something in common but are also different.

The symbols (words) in human languages are connected to real pictures.

A very important difference is the principle of truth.

In mathematics we want to be certain. Mathematical truth is binary, Yes or NO. In human languages we have to believe and believing is an Emotion.

Believing is Seeing and Feeling. We have abstracted a thing that is Seeing and Feeling.

It is situated in our body. We call it Mind. Mind is a Latin word (“mental“) and it means Spirit and Soul.

Spirit is connected to the Imagination and Soul is connected to the Emotions.

We Feel with our Soul and we See with our Spirit (Inspiration, Inspire).

Our Soul moves to something it likes and it moves away from something it dis-likes.

Our Spirit takes us away. Suddenly we get a Flash of In-Sight and we Have to Move.

Soul is gentle. Spirit hits us, like we hit a pole.

Russell used a “Thing called a Set” to create the eternal basis of Mathematics. He defined many operations on the Set. In the end he believed he had succeeded.

Suddenly a nasty problem arose.

The set of all sets created a paradox (The Russell Paradox).

It contained itself and it did not contain itself.

To solve this paradox he defined a new rule (an axiom) that a set had to contain itself. Later others proved that this was not helping him at all. The foundation of Russell proved to be completely unstable.

The reason he failed was related to the boundary of the set. The boundary is not nothing. It can be open or closed to its environment (other sets).

An open boundary looks-like your skin. A closed boundary looks-like an armor. Somewhere the set of sets (of sets of ..) had to close itself but the Set of the Whole could not be found.

One of the companions of Russell, Ludwig Wittgenstein, totally changed its views about mathematics. He did not believe in logic and a foundation any more.

He showed that we are playing games with language. Language is context-dependent. It’s meaning changes all the time.

He also showed that many sciences are simply impossible because they belong to the domain of the emotions.

Examples are Ethics and Esthetics.

Formalizing emotions is impossible. We all know what is right and wrong and beauty is a personal experiences. Nobody is able to tell you what you have-to-like.

Later the Dutch Mathematician Brouwer proved that everything we cannot imagine always leads to a paradox.

Later Gödel created a new problem. Gödel proved that an abstraction (a higher layer) is unable to explain every part of a lower layer.

If we go UP we always loose meaning. The Set of Sets of … cannot contain all sets.

Later Lakoff and Nunez proved that the language of Mathematics acts in the same way as human languages.

Mathematical Truth is not only connected to Seeing (Brouwer) but also to Feeling. The Emotion of believing is necessary to believe mathematics.

Lakoff showed also that in human languages the process of abstraction has an end. It ends when we are unable to imagine what we are talking about (see Brouwer). When we use highly abstract words like “relation” or “furniture” we reason with a part of the set (a prototype) we are using. We use a chair or a table when we use “furniture“. Abstraction without visibility again creates confusion (a paradox).

Now I want to apply the flashes of insight of all the people to show you something about the abstraction called Mind.

(1) Russell: If you think your Mind is a closed environment you’re wrong. You are using the concept of the Set. Your mind is open to other Minds.

(2) Brouwer: If you cannot imagine a Mind it does not exist. Many people see the Brain when they imagine the Mind. The Brain is controlling everything in our body. If we use (1) we have to find a way of explaining how the mind is communicating with other minds. Scientists found the solution. The mind is producing words (speaking).

(3) Wittgenstein showed that speaking is not a reliable tool of communication. Behind words we are exchanging pictures and emotions. Wittgenstein showed that it is impossible to reason about emotions. We cannot reason about the emotional part of the Mind (Soul).

(4) Gödel: Your mind is an abstraction and therefore Your mind is unable to explain everything You Are.

(5) Lakoff: Mind is an abstraction without an image. When you reason about your mind you use a visual (!) sub-set of the Mind. The visual subset we use is “Actor”. Your Cold Analytical Mind (An Actor) controls Your Warm Body. You are a Walking Thinking Mind that is desperatly trying to manage the Instable Fluctuating Emotions (now called Desire) and the Imagination (now called Fantasy). We are back to You again.

The best thing to do is to skip the whole concept of Mind and start to look for something else.

George Lakoff has a theory that is able to give you some insight.

When we are born we come out of a Body and we become a new Body. The Body has to learn to crawl. Crawling gives us the feeling  that we were moving-away (Mother) and moving to-something (Mother?). Crawling is an emotion.

Our most difficult learning process is to learn to stand-“up” and to “keep balance“. In all cultures “Up” is more important than “Down“. Management is always on the upper floor and God is Up  in the heavens and the Devil is Down in hell.

The feeling of “Up” is basically a bias. We are so dominated by our difficult childhood learning process that we Evaluate many things with our “Up-feeling“. Thinking with the “Up” is getting you Down. It kills self-confidence. We believe that we think Up with our head (Brain) and the Brain (Mind) is the manager.

Let’s get back to what You are. You are your Body and your Body is open to its environment.

Lakoff found that the sentences we speak contain metaphors. Many metaphors are connected to the body. We use our organs to define the types of truth. We feel with our heart (com-passion). We feel with our bellies (In-tuition, inner teaching). We also feel with our stomach. Our stomach tells us that we want to express something. Funny enough these places in the Body (the Chakra’s) are independent of Culture. The reason is that every human shares the same body.

When you believe something you will feel this with your heart. You will feel excitement. The rythm of your heartbeat will change. When somebody is explaining something and you don’t see the picture with your inner eye (your imagination) don’t believe him. Ask somebody to draw what he is trying to explain. If your stomach protests ask a question. If you want to do something with what you believe you will feel it in your solar plexus (Navel). Don’t hesitate Act.

Now I want to come back to the foundation Russell was looking for. When you use your body the basic level to reason with is Earth. What we See on Earth is what is and what is does not need an explanation. Trees grow without any theory. The clouds move without any theory.

If you want to develop a theory start to look with attention (Focus). Be aware and watch what is happening on Earth. What is happening on Earth is always Cyclic. The Earth moves around the Sun. The Moon moves around the Earth. The Planets move around the Sun. Seeds turn into flowers and produces seeds again.

When we try to predict these movements we find patterns. These patterns are stages in a cyclic process of enfolding. The patterns are waves and waves are strongly related to Music (Pythagoras). The patterns in Music create overtones. They interfere. Short term Cycles are part of long term cycles. You’re body is a Standing Wave and it resonates with other Standing Waves with the same wavelength.

Out of the analyses of these patterns mathematics was created. Mathematics is about Music and Beauty. A mathematical theory has to be beautiful. If it is not beautiful it is not correct. This is simple. You have to feel enlightened when you understand mathematics. If you don’t get this feeling your teacher does not understand what he is explaining.

The problem of the Set of Sets can now be solved easily. The Whole is part of itself. The Whole is One but also Two. It is OBSERVING itself. It is conscious.

Perhaps now you understand why the Ears are the place in the Body that controls your Balance. Close your Eyes and Listen to the Rhythms in your Body and Nature. Erase your non-existing Mind. Get back to the level of You, Your Body. Observe your Self. Become conscious. Feel the warmth of your skin. Let the images come and observe them without touching them. Feel your gentle Soul move in and out when you breathe. Concentrate on your Belly (the level of In-tuition). Suddenly you get an Insight. Spirit has hit you. You feel full of Joy about the beauty of the Whole. You found the foundation Russell was looking for. Its You.

LINKS

About the Axiomatic Foundations of mathematics

A video interview with Bertrand Russell

The Sad (?) Insight of Ludwig Wittgenstein

Ludwig Wittgenstein
Ludwig Wittgenstein

In 1921 Wittgenstein thought that the Tractatus Logico-Philosophicus had solved all the problems of philosophy.

Later in his life (The Philosophical Investigations, published 1951) he came to the conclusion that he was utterly wrong.

He found out that language itself is the problem.

Language is woven into the fabric of life, and as part of that fabric it works relatively unproblematically.

Philosophical problems arise when language is forced into an abstract environment, where all the familiar and necessary landmarks and contextual clues are absent. The tragedy is that almost nobody understood Wittgenstein at that time.

One of his students in Cambrigde when he still believed in abstraction was Alan Turing. He invented the Turing Machine, one of the foundations of computers and computer languages.

Computer Languages and everything created by a Computer Languages suffers the Problem Wittgenstein identified.

I was a witness to an important part of the history of computing. I was responsible for many what I now would call abstraction-projects.

I have been extremely busy with the creation of E-Learning, Knowledge-Management, Centers of Expertise, Educational Games based on Story Telling etc.

They all failed in the end but the creation-process was fun.

One of the inspiring persons I spoke was Mr. Ikujiro Nonaka. His book The Knowledge-Creating Company was just published.

He showed that knowledge could be divided into formal (again abstract) and informal knowledge.

He defined a 2X2 matrix of the knowledge-tranfer process.

The most difficult of course was the transfer of informal-informal knowledge.

My big mistake was to believe that informal/informal knowledge-tranfer could be supported by a Computer System.

The Computer System itself is formalizing everything. Many years later (about 5 years ago) I came to the same (sad?) conclusion as Wittgenstein (and Bahktin).

What can we do? The only way to transfer “knowledge” is to talk person-to-person in a secure environment.

Some people will understand each other and become friends. They are a small Centre of Expertise.

Many people will think(!) they understand the other. They will go their own way until they realize, perhaps when they are 56 (like me), that in the end your mostly wrong and sometimes right.

Keep meeting and talking! And realize The Creation Process is always Fun.

LINKS

About the War of Words

About the Foundations of Mathematics

How the Proof of the Pudding is Really in the Eating

How to Analyze a Context