Relational Logic

Establishing the Foundations

Relational Logic

Ontological and epistemological foundations

Having established the gnostic foundations for our new society, we are now in a position to rebuild the whole of the world of learning in a thoroughly systematic and methodical manner.

To do this, we need to add two further layers to the foundations. These are the ontological and epistemological layers, which constitute relational logic, the system of co-ordinates or framework for the discipline of omniology. Relational logic is the skeleton that supports the coherent body of knowledge that we shall build out of the rubble of the Tower of Babel. I look at these two layers together because they are so closely interrelated it is not possible to talk fully about one without considering the other.

To remind you, when I began this reconstruction process some nineteen years ago, I imagined that I was a computer that switched itself off and on again so that it had no programs within it to execute, not even a bootstrap program to load an operating system from its external environment. From this totally empty beginning, from this tabular rasa, I then imagined that I had the task of organizing all the world's knowledge into a coherent whole.

I started this project because I wanted to prove beyond any doubt whatsoever that the aims of the artificial intelligence community can never be fulfilled, that the world's problems cannot be solved by everlasting technological growth, and that we human beings are not machines and nothing but machines.

My friends say to me, why go to all this trouble? All you need to do is meditate, whether formally or informally. That gives you all the proof you need. I know this now, but this was not enough for me. I was educated as a mathematician, which taught me the importance of rigorous proof in establishing true and certain knowledge, a method of proof that is more demanding than scientific proof. To illustrate this point, there is a well-known joke that mathematicians like to tell about themselves:

An engineer, a physicist, and a mathematician were holidaying in Scotland. Glancing from the train window, they observed a black sheep in the middle of a field. "How interesting," observed the engineer, "all Scottish sheep are black!" To which the physicist responded, "No, no! Some Scottish sheep are black!" The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."

So in order to prove that I am not a machine and nothing but a machine, I adopted the mathematical method of reductio ad absurdum. In this method of proof, you assume the opposite of what you want to prove, then deduce a contradiction, an absurdity.

Reductio ad absurdum is a very powerful way of proving mathematical facts, the most famous example of which is Euclid's proof that there are an infinite number of primes. Euclid assumed that there are a finite number, of which one is the largest. He then derived a number that is not divisible by any of the finite number of primes, but which is larger than the largest one, thus proving the theorem.

I'm not using the method of reductio ad absurdum directly, because I cannot start with such an advanced notion as that of proof. I need a much simpler beginning. Besides which, relational logic, as the framework for the discipline of omniology, does not belong to mathematics. It lies beneath the foundations of mathematics.

Indeed, mathematics today doesn't have a sound foundation, despite the call of David Hilbert in 1900 to ensure that mathematical reasoning is soundly based. For in 1931, through the most tortuous process of reasoning you can possibly imagine, Kurt Gödel showed in his Incompleteness Theorems that it is neither possible to prove every theorem in arithmetic from the axioms of arithmetic, nor to prove that these axioms are consistent. The notion of truth in mathematics is stronger than that of proof.

That might seem to indicate that my approach is deeply flawed. Not so. It is the purpose of relational logic, not only to give mathematical reasoning a solid foundation, but also to ensure that all our learning is based on the Truth. In this way, I have proved my initial hypothesis beyond a shadow of a doubt. My experiment in learning has led me to a wonderful sense of Wholeness, of Consciousness, that has no divisions or borders within it. This experience, this deep inner knowing, contradicts the hypothesis that I am a machine and nothing but a machine, for a machine manifestly has divisions and borders within it. I have no doubt that anyone else repeating this experiment in learning will have a similar experience.

As I am imagining that I am a computer, I inevitably must use the language of computer science, the language of our times, to describe my insights. But this does not require any special technical knowledge. Even though my business background is in the data processing industry, what I am saying is just common sense, because that is what we all share.

All I am doing here is making explicit what is implicit in each and every one of us. I need to do this, because in a computer, nothing is implicit. All knowledge and information in a computer must, of necessity, be expressed in symbolic terms. There is no tacit knowledge in a computer, to use a term introduced by Michael Polanyi in Personal Knowledge.

Pattern recognition

To establish the ontological and epistemological foundations for omniology, we need to look more carefully at the Datum of the Universe, and the patterns of data that emerge from it. While in one sense, these patterns form a seamless ocean of data, prior to existence, they are not actually without form. There are a multitude of patterns within it, which I can abstract.

So my overall approach to creating a synthesis of all knowledge is pattern recognition, for this lies at the heart of creative learning. I am particularly interested here in discovering what patterns are common to the physical and nonphysical universes, to my outer and inner worlds, to science and religion, and to the West and the East.

Now to reveal these common patterns, it is most important that I do not make any artificial boundaries between these various domains. For if I did, I would have a fragmented, divisive view of the world, and not find the Wholeness that I am seeking. I therefore cannot begin with the three eyes that Ken Wilber refers to in Eye to Eye: The Search for the New Paradigm and The Marriage of Sense and Soul, for this would immediately fragment my view of the totality of existence before I had even begun to look at it.

For those unfamiliar with Ken's work, these three eyes are the eyes of flesh, mind, and contemplation, related to science, philosophy (and the humanities in general), and esoteric religion. As he points out, valid knowledge of each of these three realms can be learnt in essentially the same way in three steps: through instrumental injunction, direct apprehension, and communal confirmation (or rejection).

However, he does not really start at the beginning with his synthesis. Although he has immense depth and breadth, his transpersonal philosophy is not yet sufficiently abstract to be able to see the totality of existence as one coherent whole.

For myself, if I am to see the patterns that underlie all three realms, I need an eye that can see the Whole, the totality of existence, at a glance. I call this eye the eye of Intelligence. It is what is sometimes called the Witness by spiritual teachers.

Now Intelligence cannot see in the dark, it needs light to be able to see the patterns of experience with clarity, without distortion. That light is provided by Consciousness, which emanates from the Whole like the light from the Sun, or rather from a laser, for this light is more like the coherent light of a laser beam than the dispersed light from the Sun.

With the coherent light of Consciousness to lighten my way, what patterns can I see in the ocean of data that provides the foundation of the Universe? Most particularly, are there any patterns in this data that are independent of any interpretation, of any beliefs and assumptions that we might make about the nature of existence?

Indeed there are. To create a model or map of all these patterns, I use the word entity to represent each and every one of them. Entity has a Latin root that derives from the present participle ens of the verb esse, 'to be'. In turn, ens derives from the Greek on, the present participle of einai, again meaning 'to be'.

Now ontology also has the same Greek root; it means the 'study of being', of what exists. So to establish the ontological foundations of my experiment in learning, I can do so by studying the characteristics of all the entities in the Universe, prior to any interpretation.

I use the word entity rather like a mathematician uses the symbol x to denote a number in a function or an equation. Entity can represent anything, not only objects. For events, processes, systems, civilizations, languages, religions, emotions, and a host of other types of entity also exist.

Note also that entity does not denote only that which is real. Mythical creatures, such as unicorns and dragons, and fictional characters, such as Jane Eyre and Tom Sawyer, are also entities in my model. For if they were not, my model would not provide me with a complete representation of the totality of existence. So entities can be both real and imaginary. If we are to be completely clear in our reasoning, it is vitally important not to confuse what exists with what is real.

Entity is a symbol for everything that exists, including both the totality of existence itself and the learning process that creates this vision of the Whole. This last point no doubt sounds impossible when viewed from the mechanistic perspective that still dominates Western reasoning. While "a map is not the territory that it represents", as Alfred Korzybski pointed out in Science and Sanity, any map that is to represent the totality of existence must include both the map and the process of creating the map in the territory being studied.

Indeed, this is essential if we are to understand what is causing the pace of change to accelerate hyperexponentially in society today. We need to look inwards to consciously model our own learning process to see where we have come from and where we are heading.

Escher's lithograph Drawing Hands well illustrates this process. But it is not as impossible as it looks when we sense the action of the Logos arising from within. In this way, both the map and the process of creating the map arise simultaneously. Because there is no division between the map and its creation, they gain clarity together in an iterative fashion.

So it is not only in Jesus Christ that the Logos is made flesh, as John the Evangelist wrote in the fourth gospel. The Logos, the primary organizing principle in the Universe, is not exclusive; it is acting through all of us every moment of every day. The Logos is what gives us all life and so can also be called Life. Of course, this primary, life-giving energy is not called the Logos in every culture. In the East, it is called the Dharma, Tao, and Rita. Ramesh Balsekar refers to this fundamental energy as Consciousness-in-action, which is exactly what it is.

Guiding principles

So how is the Logos leading me to create a coherent model of the totality of existence? Well to do so, I need to establish a few rules or guiding principles, just as Descartes did in his philosophy. The guiding principles I use are simplicity, clarity, consistency, and integrity.

The first two of these are reasonably self-explanatory. But the last two need a little explanation. By consistency, I do not mean noncontradictory. What I mean is "constant to the same principles of thought or action", to use a definition in the Concise Oxford Dictionary.

Now if I am to be consistent in my reasoning, in this meaning of the word, I need to treat all entities in my model in exactly the same fashion. If I consider any entities to be special, then I am being inconsistent. So I do not look at space, time, and matter any differently from any other entities. The physical universe therefore does not provide the overall context for my reasoning.

What is more, if I am to discover what it truly means to be a human being, I cannot treat human beings any differently from any other beings or entities in my model. To be consistent in my reasoning, free from anthropocentric considerations, there are no beings that are more special than any other.

Most particularly, I cannot regard this being that I am in any special way. In this thought experiment, while I am a human being, I am imagining that I am also both a machine and an extraterrestrial. I am doing this because I wish to uncover the underlying principles that maintain the Universe as a unity, as an integral whole. And I cannot do this if I make any assumptions about the relationship between the brain and the mind, for instance, just because I am a human being.

Besides which, I have no direct experience of my brain. I have never seen it, and I know nothing of its structure. Indeed such knowledge is not necessary if I am to answer Ramana Maharshi's well-known question "Who am I?" If I wish to debug a computer program, I do not do so by attaching an oscilloscope to the electronics. Similarly, if I wish to free myself from any mental disturbances that I might have, I do not take drugs. For me, the only sure way of healing myself, and hence of helping to heal our sick society, is to understand the root causes of these disturbances.

This approach to learning comes directly from the enterprise modelling methods of information systems architects in business. The highest level models developed using these techniques show the underlying structure of a business, independent of organization and technology, independent of whether the tasks are being performed by human beings or machines. The distribution of work to human beings and machines comes later in the design process.

This leads me to the fourth guiding principle, that of integrity. Integrity means two things, wholeness and honesty. So to maintain my integrity, it is vitally important that I leave nothing out. If I omit anything from my map making just because it doesn't fit some preconceived notion that I might have, I lose my integrity. So I need to follow E. F. Schumacher's maxim for map making, "accept everything, reject nothing", which he described in A Guide for the Perplexed.

Integrity, meaning honesty, is also of the utmost importance in the search for the Truth. If I judge some situation or individual, including myself, as being good or bad, desirable or undesirable, then I am not being true. A gap opens up between 'what is' and what I would like it to be, a point that Krishnamurti made over and over again in his teachings.

As often happens then, emotions arise, clouding the Intelligence, thus violating the second of my guiding principles, that of clarity. But that's OK. That is 'what is'. The point is that, in my experience and that of many others, the search for the Truth takes many years of constant practice. Every time we stray from the principles we set ourselves, we just return to them. In this way our path will one day take us to the pathless land. For all paths, whatever they might be, lead eventually to the Truth. This must be so, for it is Truth that is guiding us to our destination.

So to return to the first of these principles, that of simplicity. If we wish to understand how the Universe is designed, we do not begin with the arcane mathematics of the physicists. We can only begin with simplicity, for complexity arises out of simplicity, not the other way round.

On interpretation

To begin interpretation, I simply look at the differences and similarities in the patterns of data in my experience. Entities with similar properties I put in one set, and those with different characteristics I put in other sets. Or as David Bohm put it, if we wish to bring order to our reasoning, "we give attention to similar differences and different similarities".

This reminds me of the Sanskrit word smriti, which is translated in Buddhism as 'attentiveness' or 'mindfulness'. This is a pity, because it is not the mind that it is attentive to everything that is happening in the moment, it is Intelligence. Nevertheless, the approach to learning that I am describing here is a natural extension of the Buddhist way of attentiveness. As in Buddhism, this way of learning is essential if we are to awaken our consciousness, to be free from delusions.

A key point here is that the act of interpretation inevitably involves comparison. But this does not mean making judgements. Some spiritual teachers say, "don't compare", meaning "don't judge". This is sound advice if we want to free ourselves of the pain that arises when we compare, that is judge, our situation in life to that of others.

But to deal with the practicalities of daily life, we often need to make comparisons, to be discriminatory. For example, if we need someone to install a new shower, we call a plumber not a psychotherapist. But this does not mean that one is judged more worthy as a human being than the other.

Of course, it is the egoic mind that judges, while it is the heart that sees the innate goodness in all beings. This means that if we are to see the differences and similarities between the various data patterns of our experience without judgement, it is most important that we do so through the heart. The intellect must be the servant of Intelligence, not its slave.

Notice that in simply making nonjudgemental comparisons between data patterns, I do not begin with any assumptions or axioms. Relational logic is a nonaxiomatic form of reasoning. So while I am borrowing the concept of set from mathematics, I am not constrained by the axioms of set theory. This is because I am working below the foundations of mathematics. So sets are just simple common or garden groupings of similar entities, a way of doing mathematics that we teach children in primary school today.

The reason that we do this is because the concept of set, which is the basic concept in semantics, is more fundamental than that of number, the basic concept in mathematics, as the former Soviet dissident, Valentin Turchin, points out in The Phenomenon of Science. Indeed, it was not until the concept of set was introduced by Cantor, that Frege and Russell were able to establish a sound definition of the concept of number in mathematics.

So semantics is a more fundamental discipline than mathematics. A multitude of mathematical equations cannot possibly enhance our understanding of the Universe if the conceptual model on which they are based is flawed.

Generalization relationships

I now need a way of identifying the similarities and differences between the entities of my experience. I use the terminology of entity-relationship modelling in computer science to do so. I use the word attribute to denote those properties that entities in a set share. I then can see that many of these sets of entities in themselves have common properties, which I can group into classes.

I have two principal ways of representing the relationships between these entities and classes. The first is as tables, rather like a telephone directory lists telephone subscribers with the attributes of name, address, and telephone number. In computer science, these tables are called relations because they can be defined in terms of the mathematical theory of relations. But it is not necessary to know this to understand the function of the tables; they are very simple.

Tables are a most convenient way of organizing information and knowledge. They show in a concise way the relationships between related entities, albeit implicitly rather than explicitly. In recent years, dictionaries have begun to depict some related sets of words in tables, rather than just describe them alphabetically, a development that indicates that the power of the table in presenting information and knowledge in a coherent fashion is well acknowledged.

Following is an example of a table in my model. It is a table of the class of quadrilaterals, giving each type of quadrilateral, its name, shape, and defining attributes. Note that I am using British English terms here. In the USA, a trapezium is a trapezoid and a trapezoid is a trapezium, for some curious reason.

Class name

Quadrilateral

Attribute name name shape
Defining attributes

parallel sides equality of adjacent sides angle

Attribute values square opposite pairs equal right

oblong opposite pairs unequal right

rhombus opposite pairs equal oblique

rhomboid opposite pairs unequal oblique

trapezium only two

kite none two pairs equal

trapezoid none

The second way I depict relationships in relational logic is by various types of semantic diagram. Here, I mostly use the notation developed by object-oriented modellers in software engineering.

The first of these diagrams is a class diagram, showing the relationships between classes. For example, following is a class diagram for the subclasses of the class of quadrilaterals. Here I can represent relationships that it is not easy to depict in a table. For example, a rectangle is an abstract class consisting of the square and oblong classes, which can be instantiated.

This is an example of a set of hierarchical relationships, known as generalization relationships in object-oriented modelling and in relational logic. Each level up the hierarchy represents a more general concept than the previous level. Developers of special purpose thesauri use the terms broader terms and narrower terms to denote these relationships.

Perhaps the most familiar example of generalization relationships is the classification of the species by Linneaus. This has twenty different levels, each of which has a name, from kingdom, through class, order, family, genus, to species and subspecies. So the class of mammals has within it the order of primates, which in turn includes the species homo sapiens.

As you might expect, there is an ambitious project on the Internet to document the Tree of Life. So far it mainly uses scientific terms, and there is still much to do. For instance, there is little yet on mammals, the class of animals to which we belong. But this site does give some indication how biologists view the interrelationships of the species in a hierarchical fashion.

The key point about generalization relationships is that subclasses generally inherit attributes from their superclasses. For example, the females of all mammals suckle their young, whether they are dogs, lions, horses, whales, human beings, or whatever.

In relational logic, the superclass that contains all other classes within it is the entity class. The entity class thus plays a similar role in relational logic as the object class does in the Smalltalk and Java programming languages. But, again, it is not necessary to know this to understand relational logic.

Aggregation relationships

Another familiar example of hierarchical relationships are aggregation relationships. In relational logic, as in computer science and mathematics, these are known as 'part-whole' or 'a-part-of' relationships, in contrast to the 'is-a' or 'is-a-kind-of' relationships between classes and their superclasses in generalization structures.

(In a similar manner, the relationships between classes and their attributes, implicit in tables, can be represented in semantic diagrams as 'has-a' relationships. For instance, a person has a name, sex, height, weight, nationality, and so on.)

A familiar example of aggregation relationships is the human body, which consists of organs, cells, molecules, atoms, protons, electrons, neutrons, etc. Another example is from the business world, where conglomerates can consist of companies, divisions, departments, branches, sections, and teams, although not all these levels are present in every organization.

Here wholes consist of an aggregation of parts, which, in turn consist of smaller parts. So, as Arthur Koestler observed, in such relationships every whole is a part of a greater whole. For this reason, he called these wholes/parts holons, a term that Ken Wilber has made much use of in his recent writings. However, I don't use the word holon in relational logic because the word does not have universal applicability as Ken seems to think it has. Holon, in the way that Koestler used the term, does not apply to generalization relationships.

Just as the entity class is at the top of the generalization structures, the Absolute Whole is at the top of the aggregation structures. This does not mean that the entity class bears any special relationship to the Absolute. The entity class is just a part of the Absolute Whole, just like every other entity.

One other major type of hierarchical relationships that I highlight in relational logic are family relationships. We can look at these in two ways. In human terms, looking forwards in time, an individual has children, who have children, and so on and so forth. Looking backwards in time, we all have two parents, who have two parents, back into the dim mists of time.

How many zillions of ancestors we all have, even if we only go back to the beginning of sexual reproduction, is quite unimaginable. Just going back to the beginning of this millennium, we each have some 2³⁰ ancestors at a conservative estimate, around a billion. Now this is larger than the entire population of the world at that time. The reason for this, of course, is that cousins with common ancestors have frequently married, thus greatly reducing the actual number of ancestors we had living in the year 1000. The implications of this are that we are all cousins to each other. If only we could live in this way, as one big happy family.

Nonhierarchical relationships

Be that as it may, we can combine the descendant and ancestor relationships and depict them in one diagram, called a relation chart in the family history program, Reunion for Mac. However, in relational logic, I use a different way of representing these relationships. Here, rather than using a class diagram, I use an instance diagram, again borrowed from object-oriented modelling. Here is an example of such a diagram:

As you can see, we have now moved away from hierarchical relationships, into the much more complex area of nonhierarchical relationships, which form networks, webs, or heterarchies. It is not easy to classify nonhierarchical relationships. In language, we can use many parts of speech to denote such relationships. For instance, we can use transitive verbs like loves, sends, attracts, heats, pulls, and manages; prepositions, like between and above; and adverbs like more beautiful than or smaller than.

In relational logic, I make no special attempt to express these nonhierarchical relationships in symbols; they are far too complex. I know that they are there, and when necessary I investigate them. But then I am moving out of relational logic into some speciality, like systems design. It is hierarchical relationships that give a sense of order and structure to our knowledge, not nonhierarchical relationships

Despite this, hierarchical relationships have had something of a bad press in recent years. This is because they are associated with patriarchal, authoritarian organizations, like the churches, the military, business enterprises, and educational establishments. The belief appears to be that the death of Western civilization will mean that hierarchical structures in society will disappear.

How can this be? Hierarchies are of the essence to organization, including the natural world. So to ignore these hierarchical relationships, as some systems theorists do, to put all the emphasis on the Web of Life, is to deny the fundamental organizing principle of the Universe.

To resolve this issue, Ken Wilber, in Sex, Ecology, Spirituality, makes the key distinction between domination hierarchies, which are pathological, and actualization hierarchies, which are life-enhancing. There has been some attempt within the business world in recent years to move from domination to actualization hierarchies, through the concept of empowerment. But, in actuality, little progress has been made. The slogan "do your own thing - the way we tell you" pervades the commercial world, as an article in the Harvard Business Review of May-June 1998 pointed out.

The unifying structure of the Universe

To round off this section, let me return to the opening paragraph and explain how relational logic serves as the ontological and epistemological foundations for the Paragonian Society.

When I look at all the forms, structures, and relationships in the Universe, I can see a structure that underlies them all, independent of any interpretation. This is how I describe it:

The underlying and unifying structure of the manifest world of form is an infinitely dimensional network of hierarchical relationships.

I call this statement the first part of my data model (I describe the second part on the next page). It is a curious statement because it says something about all the entities in the Universe that is prior to any meaning that is given to these entities. Yet it is of the utmost power. For as Arthur Koestler observed, "arborization and reticulation are complementary principles in the architecture of organisms and societies".

It is this data model, which shows the unifying structure of all the entities in the Universe, that provides the ontological foundation for omniology. As you can see, it is not really possible to see this layer prior to interpretation. It is only when the conceptual model is reasonably well developed that it is possible to see the underlying structure of the Universe.

The key point about this view of the underlying structure of the Universe is that this structure exists in whatever part of the Universe I might look at. In other words, every part of the Universe contains within it the structure of the Whole.

Now such a property of the Universe is not unlike the property of a hologram. When a holographic image of an object is broken into pieces, each piece contains an image of the object as a whole. We can thus say that the Universe is holographic, in a similar manner to Karl Pribram, David Bohm, and several other researchers in the world today.

So just like a hologram, every partial image that I create of the Universe contains within it a representation of the Whole. I can look at this image in greater or lesser detail depending on the scope of the image, again, not unlike the hologram. When I stand back as far as possible, I can see the totality of existence, but with comparatively little detail. But when I focus my attention on some part of the Universe, as I do, for instance, when studying psychology or computer science, I can see the Universe in much greater detail, but always in the context of the overall Whole.

Another important characteristic of this underlying structure is that of self-similarity, rather like the properties of fractals discovered by the mathematicians in recent years. It is therefore not surprising that fractal mathematics can produce artificial images that closely represent Nature as it really is. These images are a reflection of the unifying structure of the Universe.

Finding a way of describing this unifying structure back in 1980 answered a question that I had asked myself as a sixteen year old: What can we know about knowledge that we don't yet know, that is beyond the frontiers of science. The answer, of course, is that we can know its structure.

Knowledge about knowledge

So what about the epistemological foundation of omniology? Well, epistemology derives from the Greek word episteme meaning 'knowledge'. Thus the Greeks had two words for knowledge, gnosis and episteme. The way I use words derived from them is that gnosis denotes deep inner knowing, while episteme denotes symbolic knowledge. This is a distinction that has been made in many cultures, as Ken Wilber points out in The Spectrum of Consciousness.

Epistemology then is the science or study of symbolic knowledge. The result of such a study is, of course, knowledge. So epistemology produces knowledge about knowledge or metaknowledge.

Where then is knowledge about knowledge in my conceptual model of the Universe? Well, it consists of the class and attribute names that are italicized in the example of the table that I gave earlier. I can collect all these class and attribute names into a pair of tables that provide knowledge about all the classes and attributes in my model.

Alternatively, I can represent all these classes and their relationships to each other in gigantic class model. I have never attempted to depict these tables and semantic models on paper; they are far too big and complex. However, I can see this knowledge about knowledge quite clearly with my inner eye. It is this that provides the epistemological foundation for omniology.

Putting it all together

So having demolished the three pillars of unwisdom that support the Tower of Babel that represents the world of learning today, I now have almost established the gnostic, ontological, and epistemological foundations for the discipline of omniology.

I call the gnostic level, the deep inner knowing of God or Consciousness, the ontological level, the data model, free of interpretation, and the epistemological level, the semantic model, which provides knowledge about knowledge. Without these three levels, we cannot really call our knowledge of ourselves and the world we live in scientific.

It is on this solid base that we can establish the foundations for the Paragonian Society. The gnostic and ontological levels are common to us all, regardless of cultural background. It is only at the epistemological level that differences appear, for we all interpret our experiences in different ways. Also, in our specialized work, we focus our attention on different parts of the Universe, so have different detailed knowledge of these various domains.

But even here there are commonalities. When I see the colour red, it is much the same as what others call red. However, if I look at some Chinese writing or an X-ray, these patterns are quite meaningless to me, while they are quite meaningful to Chinese and medical practitioners. So our semantic models and the body of knowledge that we build on them are quite different depending on our own unique background.

I am reminded when I look at the incredible simplicity of relational logic of M. Jourdain's question to his philosophy teacher in Molière's Le Bourgeois Gentilhomme: "What? when I say: 'Nicole, bring me my slippers, and give me my nightcap,' is that prose?" To which the philosopher replied, "Yes, Sir". "Good heavens!", exclaimed M. Jourdain, "For more than forty years I have been speaking prose without knowing it."

As it is with prose, so it is with relational logic. For many thousands of years, we have all been using relational logic without knowing it. Even Aristotle used relational logic in developing syllogistic reasoning, which provides the foundation for Western logic and mathematics. He could have done nothing different.

But I have not quite finished outlining relational logic. There is a second part to the data model that I need to explain. This I do on the next page.

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