A Discourse on Paradigms

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Abstract

This reflexive paper attempts to describe and justify my present philosophical position, my worldview. The appendices contain definitions and brief descriptions of the concepts of paradigm, epistemology, and
ontology and elaboration of other concepts that are mentioned in the article. This is based on a reflexive paper written for EHRD 651 – Models of Epistemology and Inquiry, Fall 2008.

1. Introduction

In this paper I attempt to describe my understanding of the problem of knowledge as it has evolved over time and the self-critique of the process of thinking about ontology and epistemology.

I do as bidden, and I bring the message
Whether it give thee counsel or offense1

The great value of reflexion has been stated by great minds throughout history.

The unexamined life is not worth living.2

True loss is for him whose days have been spent in utter ignorance of his self.3

For the sake of intelligibility I will state my present positionality which is a hybrid of foundationalism4 and post-structuralism.

Many of my musings haven been pilfered from various sources, ancient and contemporary, western and eastern, including podcasts and Wikipedia.5 Even though this is reflexive paper, that is I am looking at myself, questioning myself and engaging in a dialog with myself, it will often appear that I am referring to a different person. There are two reasons for this, (1) the beliefs that I held previously reflect an ontology and epistemology that are so different, I dare say alien, to my present ones that I am forced but to regard them as belonging to a different person; (2) since I am of the understanding that the concept of person and self are but constructs and do not refer to any objective independent entity, in Buddhist terminology Sankhara6 , I am linguistically forced to pretend to assume the position of an outside observer. Of course that is still a defective way of viewing the situation since it is basically impossible to posit a proper “observer ” for those who hold a post-structuralist worldview.

The world is but a show, vain and empty,
a mere nothing, bearing the semblance of reality.
Set not your affections upon it.

…. the world is like a vapor in the desert,
which the thirsty dreams to be water
and strives after it with all his might,
until when he comes unto it, he finds it to be mere illusion7

Disciples, this I declare to you: All conditioned things are subject to disintegration – strive on untiringly for your liberation.8

Know that the world is even as a mirage rising over the sands,
that the thirsty mistakes for water.
…. Abandon it to those who belong to it …. 9

The theoretical framework chosen for this paper is “Fowler ’s Stages of Faith Development” (Cited by Momen, 1999, p. 146). James Fowler developed an analysis of individual faith development based on Piaget’s work on cognitive development, Erik Erikson’s psycho-social development, and Kohlberg’s study on moral development.10

2. Certainty and Uncertainty in Worldviews

According to Fowler ’s theory, this corresponds to stage 3, synthetic-conventional. During this stage we “establish a life narrative and construct a personal ideology.”
 
Why would something that has no empirical evidence be accepted so uncritically?11 How could myths be so misunderstood?12 I think that the reason is not logical but rather psycho-logical. The universe even as experienced in daily life is far too complicated to be comprehended and accepted in toto. Thus, we create simplified models of our experienced reality to reduce it to a manageable size by passing it through a mental filter. The filter we put in place is culturally conditioned. Its validity is reinforced every day by interacting with people who are using similar (mostly overlapping) filters and by using selection bias. The latter entails the disregard of all dissonant ideas and the acceptance of those conforming to the personal reality filter.

The good news is that these filters can be discarded and replaced with new ones. What we can not do is to not have one. The action of interpretation is integral to our understanding of reality. We can not have knowledge without interpretation. Even in the positivist paradigm, data by themselves are nothing. We need to frame data inside a theory to make sense out of them.

In my opinion, what brings about this process of change is cognitive dissonance. That is the phenomenon by which our filters are removing so much of unacceptable reality that their function becomes unacceptable. We are restricting our worldview so much that is can not cope with the variety of our experiences anymore. The function of a filter is to produce useful, consistent information from its environment. The moment that the filter has to remove so much that it can not create anymore a consistent model of reality, it will have failed its function.14 At this point we can replace our filter with a “better ” one or live in an alienated state which occurs when our model failed us, but we are not able to replace it with anything else. Hence our world stops making sense and we feel strangers to ourselves.

People who live a stable and isolated life never need to change their filters and at most need to tweak then once in a while. Others need to replace them frequently. It all depends on the stability of their environment. It is no surprise that people who attend university or move to a different location do experience this cognitive dissonance. This is usually not a pleasant process, it is equivalent to experiencing an earthquake.

When one abandons fundamentalism one steps on a slippery slope that starts from “absolute certainty” and could end in “radical skepticism” of the ‘brain in a vat’ type15 because a fundamentalist worldview is an “all or nothing” one.

One has to find an epistemology that could work for me. No improvised and rigged epistemology can be so strong that it will stand up to the Medusean gaze of logic, rationality, facts, and skepticism16.

The quest for the modality for the acquisition of knowledge is an ancient one. Plato wrote about knowledge in his dialog called Theaetetus.17 In this dialog, Socrates and Theaetetus discuss three definitions of knowledge: knowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions were shown to be unsatisfactory. The conversation ends with Socrates’ announcement that he has to go to court to answer to the charges that he has been corrupting the young and failing to worship Athenian Gods.

The Fowler stage for fundamentalism is the “synthetic-conventional”. The successive one is the “individuative-reflective” stage at which literal interpretation is rejected, but no connections are yet made to other spiritual strands. According to Fowler most people stop at this level.

The next stage is the “Conjunctive” stage, the one where people start seeing patterns of interrelatedness. It should be noted that according to Fowler most people never reach this stage. This stage can be the springboard for more questions, and searches.

For these have passed over the worlds of names,
and fled beyond the worlds of attributes as swift as lightning.18

What is important is the freedom from fear to investigate all and everything. If one accepts that all is interrelated, then anything one would discover, can only enrich a person. It is my firm conviction that all of the significant stories in the Holy Writings19 can be classified as myth.20 21

The final stage of Fowler ’s classification is the “Universalizing” stage. This fifth stage has been described in a mystical work as the realization that

…. all the variations which the wayfarer in the stages of this journey beholds in the realms of being proceed from his own vision.
Thus, for that they move on these three differing planes, the understanding and the words of the wayfarers have differed; and hence the sign of conflict does continually appear on earth. For some there are who dwell upon the plane of oneness and speak of that world, and some inhabit the realm of limitation, and some the grades of self, while others are completely veiled.22

I believe that a progressively widening ontological circle should include Buddhism, albeit as a philosophy rather than a religion. Most people choose either a Western philosophical position or Buddhism since they appear to most as being mutually exclusive. I however am not of this opinion23.

I have been intrigued by what I consider the three ultimate ontological questions. That is, is there a (1) Truth, a single Reality in which “we live and move and exist?”24 (2) Free will? (3) Self? These three questions are not new, the Buddha examined them, albeit in different culture, about two and a half millennia ago.

Here I do not even pretend to be able to formulate a coherent and even less a comprehensive argumentation of my present understanding. Any such attempt would be sheer mockery of any one’s intellect. I will thus limit myself to presenting some personal observations.

I approach Question (1) in the light of the cosmological, teleological, and transcendental arguments,25 which I accept based on the “argument to the best explanation.”26 However, that brings us only as far as Deism and certainly not Theism. I, as many before me, have asked where we all fit in this

Then to the rolling Heaven itself I cried,
Asking, “What Lamp had Destiny to guide
Her little children stumbling in the dark?”
And “A blind understanding!” Heaven replied.27

The answer, explicit or implicit, of question (2) determines much in our society. For instance how we approach Queer Theory. It is not a choice. That is just a political correct way of stating that it is (pre)determined, that is we have no control over it, we are not free agents. In my opinion, the opposition to Queer Theory is not so much religious bigotry and traditionalism, but its subtle but still devastating implications on free will. Anything that diminishes our understanding as free agents, masters of our destiny, independent entities is considered an attack and provokes even violent reactions. Few have the stomach to dispassionately contemplate what this poet has so vividly described

This all is a chequer-board of nights and days,
Where Destiny with men for pieces plays:
Hither and thither moves, and mates, and slays,
And one by one back in the closet lays.28

Today we would have used the analogy of a ‘robot’ instead of ‘chess piece,’ but the concept remains the same. It is ironic that when money and safety are at stake we forget all these niceties and accept the fact that human behavior is more determined that we like to admit. Millions of dollars are spent on commercial and political propaganda. We send our children to schools, madrasas and Sunday schools. We now have public lists of sexual perverts, which totally contradicts the ethos of personal responsibility and punishment in our judicial system. These people have served their sentence, why do we not leave them alone to pursue whatever they want to pursue? Apparently, when the well being of defenseless children are at stake we are forced to face the truth.29

Questions (2) and (3) are expounded upon by the Dalai Lama (2005, p. 46) with peerless clarity using the framework of the Theory of Emptiness30

One of the most important philosophical insights in Buddhism comes from what is known as the theory of emptiness. At its heart is the deep recognition that there is a fundamental disparity between the way we perceive the world, including our own experience in it, and the way things actually are. In our day-to-day experience, we tend to relate to the world and to ourselves as if these entities possessed self-enclosed, definable, discrete and enduring reality. For instance, if we examine our own conception of self hood, we will find that we tend to believe in the presence of an essential core to our being, which characterises our individuality and identity as a discrete ego, independent of the physical and mental elements that constitute our existence. The philosophy of emptiness reveals that this is not only a fundamental error but also the basis for attachment, clinging and the development of our numerous prejudices. According to the theory of emptiness, any belief in an objective reality grounded in the assumption of intrinsic, independent existence is simply untenable. All things and events, whether ‘material’, mental or even abstract concepts like time, are devoid of objective, independent existence. To intrinsically possess such independent existence would imply that all things and events are somehow complete unto themselves and are therefore entirely self-contained. This would mean that nothing has the capacity to interact with or exert influence on any other phenomena. But we know that there is cause and effect …. Yet in a universe of self-contained, inherently existing things, these events could never occur! So effectively, the notion of intrinsic existence is incompatible with causation; this is because causation implies contingency and dependence, while anything that inherently existed would be immutable and self-enclosed. In the theory of emptiness, everything is argued as merely being composed of dependently related events; of continuously interacting phenomena with no fixed, immutable essence, which are themselves in dynamic and constantly changing relations. Thus, things and events are ‘empty’ in that they can never possess any immutable essence, intrinsic reality or absolute ‘being’ that affords independence.

I like to juxtapose the above philosophical discourse with the following verse from a famous poet

For in and out, above, about, below, This is nothing but a magic shadow-show,
Played in a box whose candle is the Sun, Round which we phantom figures come and go.31

Much, much more could be pondered on and written about these most interesting and intriguing subjects, but all papers have an end, thus

Enough – The written summary I close,
And set my Seal:
The Truth God only Knows.32

3. Appendices

I present here definitions of terms used in the paper that are usually misunderstood by people lacking in classical education. Thus, their common use is quite different from their original meaning. Afterward I further elaborate my thoughts about topics and concepts that I have touched upon.

Appendix A –

Paradigm, or scientific paradigm was defined by Kuhn (1996, chap. 5) as

  • what is to be observed and scrutinized
  • the kind of questions that are supposed to be asked and probed for answers in relation to this subject
  • how these questions are to be structured
  • how the results of scientific investigations should be interpreted

The Merriam-Webster On-line Dictionary defines a paradigm as a philosophical and theoretical framework of a scientific school or discipline within which theories, laws, and generalizations and the experiments performed in support of them are formulated; broadly: a philosophical or theoretical framework of any kind33.

Appendix B – Ontology

Ontology is the study of the nature of being, existence, or reality. The four main ontological approaches are realism (the idea that facts are out there just waiting to be discovered), empiricism (the idea that we can observe the world and evaluate those observations in relation to facts), positivism (which focuses on the observations themselves, attentive more to claims about facts than to facts themselves), and post-modernism (which holds that facts are fluid and elusive, so that we should focus only on our observational claims).

Appendix C – Epistemology

Epistemology, also called the “theory of knowledge,” is the study of knowledge. When we believe in a proposition it means that we accept this proposition to be true34. This does not necessarily mean that this proposition is true. A belief in a true proposition is real knowledge. This is schematically shown in Fig. 1.35 The
theories on acquisition of knowledge are empiricism, rationalism, and constructivism.36

Fig 1: Justified True Belief

While this schematic is very illustrative as most Venn diagrams are, it is ill-defined. We might be able to find out the elements of the set of beliefs using questionnaires and/or interviews. However, determining which of those elements are “true” is basically begging the question since the means of finding out how to determine whether a proposition is true or false is the aim of epistemology itself. The situation is further complicated by the “Gettier Problem” that challenges the “justified true belief ” concept that Plato proposed in Theaetetus.37

Appendix D – Myth

The word “myth” does not mean “common but untrue belief,” rather it means “a sacred story involving symbols that are usually capable of multiple meanings.”  The term itself has no reference to truth or falsehood. Indeed, to its source culture, a myth by definition is “true,” in that it embodies beliefs, concepts, and ways of questioning and making sense of the world. I would state that the truth of a myth has nothing to do with history or science but with a culture that tries to explain reality in its most basic core, which is spiritual is a sense that it is about
us but not us at the same time. It could be argued that in this sense a myth is tautologically true. It is true because it is defined to be true by the people who share the myth.38

Similarly in mathematics we know that definitions are true and thus do not have to be proven. Likewise, mathematical axioms or postulates are true from a foundational point of view. Their truth is necessary for the building an intelligible theory.

Where in common speech the term myth is used, I would use the term “delusion.” Common language also confuses the terms “fact” and “theory” by placing them in opposition to each other. Facts are events and objects that we can measure and describe, while theories are explanations of these events and facts. We shall see that the fundamentalist mindset has a strong dislike to theories because any rational explanation of reality has the potentiality of contradicting their own explanations and thus is a thread to eliminate if possible and avoid otherwise.

The common use of word “theory” should be replaced with the terms “hypothesis” or more appropriately , “conjecture” since a hypothesis has to be testable and falsifiable, while a conjecture does not have this requirement.

Appendix E – Critique of Common Paradigms

It is my opinion that many popular paradigms present inconsistencies that are so serious as to be fatal. I will present my critique using an semi-serious and ironic Platonic dialog method where I talk to myself. In the first paradigm I question is the positivist:

“Only empirically verified statements can be relied upon.”
“Have you empirically verified this belief?”
“Well . . . ”

Then an interpretivist:

“All opinions are relative and no one is preferable over another.”
“Are you sure about this?”
“Yes!”
“Are you absolutely sure?”
“Oh ….”

A critical theorist:

“This oppressed group has to be emancipated. Laws have to be repelled, modified or created to ensure their equality with everyone else. We need to change society.”
“How about your paradigm? Do you not posit experienced worlds that present personal, multiple truths?”
“Yes, that is how we study and document oppression.”
“Do some people deny the existence of this type of oppression?”
“Yes, unfortunately many types of denial exist, such as ‘citation of the exception’ or ‘color blindness.’ ”
“Is their experienced reality not just as valid? Are you not by your activism and advocacy imposing your worldview on others who do not share it?”
“I am working for a just cause”
“So not all experienced realities as equally valid?”
“Definitely!”
“How does that fit your paradigm?”
“Hmmm ….”

And finally a literalist who relies on her or his favorite religious or political text:

“For me it is easy to know what the truth is, I just read the Book”
“How do you know that this book is correct?”
“Because the book itself says so.”
“Is that not circular logic, begging the question?”
“I know in my heart that it is true.”
“Would that not mean that your book is not really your standard for reality? Your standard is actually then your own personal feeling/opinion/intuition?”
“Well, I need to ask my . . . ”
“So it is not your book, nor your opinion of it that is your standard, it is the opinion of someone else?”
“I know that I am right and you are wrong.”
“And you base that on?”
“Stop confusing me, go away ….”

However, I do not think that the problem is with a particular paradigm itself, but with its scope of application. That is, the type of questions that we can ask within these paradigms. Within the positivist paradigm we can only ask question about measurable entities. By definition value statements and propositions about absolutes and abstracts are not in its purview. While it has been applied to the social sciences, it has yielded but few results.

Similarly an interpretivist or critical paradigm can only describe personal states, subjective and restricted in time and space. No generalizations are warranted, no absolutes can be invoked.

Critical theory can not prove a form of oppression, it can only describe it as experienced by the people who claim that they experienced it. However, critical theory can use results from positivist research. For example it could use an objective metric of inequality of wealth distribution such as the Gini Index39 because wealth, power and opportunity in society are closely connected. Indeed, figure 2 clearly shows that in the USA wealth is distributed more unequally than in other developed countries.

Fig. 2

Sacred and ideological texts can not explain or describe objective reality it can only give meaning to our experiences and make “ought” statements.

It is my firm conviction that an absolute, independent truth does exists, however I am also strongly convinced that we are not able to grasp it. No methodology is capable of finding out the absolute truth, not the scientific method, neither participant observation, not revelation, inspiration or intuition. They all are useful tools that give answers when applied within their proper dominion.

I think that are overoptimistic regarding our ability to make truth statements. The scientific method has basically given up on the claim to be able to find truth and has first retreated to the position that we can only dis-prove hypotheses never prove them.40 We can repeat experiments and come up with the same results, but we still would face the problem of induction.41 For example, there is no scientific way that we can prove that tomorrow the sun will come up.

We also know that the cornerstone of the scientific method, which is the measurement of events has an inherent limitations. I would like to mention the Heisenberg Uncertainty Principle42 that shows that no matter how precise our instruments, there is an inherent, unavoidable barrier that can not be breached. The following
inequality shows this principle mathematically

Delta x Delta pgeq frac{h}{2}

The main thing to notice is that the right side of the inequality is a constant and the left side represent the measurement precision. Thus, we realize that measurement precision can only reach a certain point and can not be improved thereafter.

Another scientific phenomenon shows that measurements have insurmountable limitations are the Planck quantities. Those are the smallest amount of time, length, mass, electrical charge and temperature that can be measured.43 The so-called “God Equation”, the equation that embodies mathematically Einstein’s Theory of General Relativity44 contains π, which is an irrational number.45

G_{mu nu } + Lambda_{g mu nu} = frac{8 pi G}{c^4}T_{mu nu}

Irrational numbers in decimal form have a non-repeating infinite number of decimals. Thus, using this equation we can not obtain precise results, only approximate ones. Bottom line, the cornerstone of the scientific method, the measurement of experimental outcomes, is by the very nature of reality not only an approximate tool but a tool that can only reach a certain level of accuracy and then has to cease its quest. It seems that the universe is telling us

Love is a veil betwixt the lover and the loved one;
More than this I am not permitted to tell.46

The practitioners of the Scientific Method have now taken the position that the value of this method is pragmatic. That is, it works, it works very well when used in physics, chemistry, biology, geology, etc.. We can ask question about many, but not all subjects and obtain answers that are repeatable and independent from the observers or experimenter. The methodology is self-validating, but only empirically, pragmatically. We can not make any sweeping statements about any inherent validity of the scientific method. If, when applied to a certain type of inquiry it is able to yield reliable answers, then it is warranted to apply the scientific method in this area. It is important to realize that we do not have any objective, independent, general criterion that is able to predict the applicability of the scientific method.

Even the empyrean realm of abstract ideas, Plato’s stomp ground, does not offer much solace. Truth statements can also not be generalized in mathematics. Axioms and postulates are true, but arbitrarily so. The five Euclidean postulates are the basis of Euclidean geometry. A different set of postulates will create an
equally valid geometry such as hyperbolic and spherical geometry. Gödel’s Incompleteness Theorems47, while they are difficult to completely understand, imply that it is impossible to find a complete and consistent set of axioms for all of mathematics.

On a more pragmatic level, even the issue of mathematical proof is not as clear-cut as previously thought. Modern theorems can be very complicated and take hours to go through. Often not even having a PhD in mathematics guarantees that one has sufficient knowledge to follow the explanation. The end result is that now mathematicians consider a theorem to have been proven when a sufficient number of mathematicians has gone through the proof and agreed with its conclusion. The interpretivist implications of this situation are apparent.48

Appendix F – Fowler ’s Stages of Faith Development

  1. Intuitive-projective faith, age 3 to 7.
  2. Mythic-literal faith, age 7 to 11, corresponding to Piaget’s concrete operations.
  3. Synthetic-conventional faith, around adolescence, establish a life narrative and construct a personal ideology.
  4. Individuative-reflective faith, young adulthood, assumes responsibility for own commitments, lifestyles, beliefs, and attitudes. Realization that own view is only one of many possible worldviews, rejection of literal interpretations of narratives and myths learned in childhood.
  5. Conjunctive faith, mid-life, sensitivity to patterns of interrelatedness. Development of an appreciation as source of non-logical insight.
  6. Universalizing faith, awareness of an ultimate environment that is inclusive of all being. Universal, affirming, transcendent viewpoint. Often considered subversive by established authorities.

Stage 5 is uncommon and 6 is rare. Stage 3 corresponds to an orthodox adherence to traditional religious beliefs. Stage 4 entails critical analysis and self-reliance for interpretation. Stage 5 is characterized by a symbolic and paradoxical interpretation of religious concepts.

Appendix G – An Excursus on Mythology

Most think that mythology is synonymous with ancient Greek fiction. I have come to realize that mythology is pervasive among all ancient religions and will be illuminated by their connections. Whoever has some understanding of the power and depth of myth will realize that the story of the Fall of the Garden in Eden49 and the story of the discovering of suffering by the young Siddhartha are equivalent. Indeed, it is mythical narration about what happened ages ago when humanity acquired consciousness and moreover happens every time a child discovers that it is a distinct being from its mother and there is a world out there beyond her nurturing protection.

Thus, ere thou didst issue from thy mother ’s womb,
I destined for thee two founts of gleaming milk,
eyes to watch over thee,
and hearts to love thee50.

This is a loss truly to be mourned and thus unsurprisingly has been mentioned in the highest world literature. An even greater loss is its complete misunderstanding by many. Another great myth that is missed by all who remain at the “Synthetic-Conventional” stage,51 is the myth of the “Death/Rebirth of Nature” which is the cyclical counterpart of the “From Chaos to Cosmos” creation myth. This also is a very ancient myth and is told as the story of Inanna and Dumuzi52 and the binding53 of Jacob in Genesis chapter 22.

The myth of a special killing at the beginning of time is (was) very widespread. It was the agent that changed the Chaos into Cosmos. An ancient version of the principle of conservation of energy demanded that to obtain order from disorder something valuable had to be offered in exchange. A mythical reverse entropy, mors tua vita mea. Originally it was the killing of the quintessential enemy, a sea monster, a dragon, the personification of chaos, the unrestrained and thus dangerous forces of nature

you broke the heads of the dragons in the waters. You crushed the heads of Leviathan54

In a variant of this myth the ‘enemy’ is replaced with a ‘friend’ to make it even more valuable, but the outcome is the same55

…. the Lamb who was slaughtered from the founding of the world.56

However this sacrifice can be also cyclical, or more precisely “seasonal”

…. women were sitting there weeping for Tammuz.57

The cosmos-creating battle is also thought to re-occur at the end of our age in the Book of Revelation (20:1-2,10), probably because the cosmos needs to be reorganized. Thus we have a confluence of origin, consummation and cyclic variations of this myth. I am of the opinion that here we are touching a very basic, if
not foundational, mythology combining the themes “creative sacrifice”, “dying god”, axis mundi and “titanomachy” of comparative mythology.58 Sadly, also this profound myth has been stripped of its profound meaning and has been trivialized by a crude historization and has been used to separate humans in ‘us’ and ‘them’ for two millennia now.

Notes

1. Sa’dí, 1184-1283 CE
2. Socrates, Apology 38a
3. Bahá’u’lláh, Words of Wisdom, No. 21
4. http://plato.stanford.edu/entries/justep-foundational
5. http://en.wikipedia.org and http://it.wikipedia.org, guilty as charged.
6. In English “conditional things” or “volitional formations,” http://en.wikipedia.org/wiki/Sankhara
7. Bahá’u’lláh, Gleanings, Section 153, Paragraph 8
8. The last words of the Buddha, Mahaparinibbana Sutta.
9. Selections from the Writings of ‘Abdu’l-Bahá, 157.2
10. See Appendix F – Fowler ’s Stages of Faith Development for a brief description of these stages.
11. The logical fallacy “argument from authority,” ipse dixit
12. Regarding a proper definition of myth see Appendix D – Myth.
13. or bad news, if you like or have an interest in the status quo
14. See chapter 6 & 7 of Kuhn (1996).
15. A similar but much more scientifically dignified and sophisticated position would be to state than the universe and all that it contains are but collapsed quantum wave functions, http://en.wikipedia.org/wiki/Wavefunction_collapse
16. The sad story of Medusa is an interesting subject for Critical Feminist Theory, http://en.wikipedia.org/wiki/Medusa. The very ancient mythical theme of the woman and the snake is a fascinating field of study, e.g. Gilgamesh and the Huluppu-Tree, see Lauter and Rupprecht (1985)
17. http://plato.stanford.edu/entries/plato-theaetetus. Interestingly, Theaetetus is an important mathematician whose work was incorporated by Euclid into his The Elements (Artmann, 1999, p. 12). A major revision of this book was done in 364 CE by Theon and his daughter Hypatia. Her gruesome murder by a Christian mob has been considered to mark of the end of the Hellenistic Age, http://en.wikipedia.org/wiki/Hypatía_of_Alexandria
18. Bahá’u’lláh, The Seven Valleys, The Valley of Knowledge. Regarding the term “kingdom of names” see Lyotard, Pefanis, and Thomas (1992, p. 31) for a corresponding modern understanding.
19. I use this term inclusively, Vedas, Buddhist Canon, Hebrew Bible, New Testament, and Qur ’an.
20. For an excursus on this topic see Appendix G – An Excursus on Mythology
21. There are other stories that are not mythical such as court records, genealogies and geographical descriptions, but they can hardly be considered significant.
22. Bahá’u’lláh, The Seven Valleys, The Valley of Unity
23. Note that Buddhism is non-theistic rather than atheistic. It does not consider the concept of a deity relevant to its main purpose which is the end of suffering.
24. Epimenides of Knossos, Cretica. He was a poet, philosopher and seer. He is quoted twice in the New Testament, Acts 17:28 and Titus 1:12
25. http://en.wikipedia.org/wiki/Proof_of_god
26. http://en.wikipedia.org/wiki/Historical_method
27. Omar Khayyám, Rubáiyát 33
28. Omar Khayyám, Rubáiyát, 49
29. An interesting piece of psychological research has been done on candidates for parole. The purpose was to find the most reliable predictor on relapse. What was found that the most reliable one was a simple test where the candidates had to follow with a pencil a somewhat complicated pattern without lifting the pencil. Those who completed the task had the lowest relapse rate. This test was more accurate that all the other psychological tests including extended interviews.
30. http://en.wikipedia.org/wiki/Shunyata
31. Omar Khayyám, Rubáiyát, 46
32. Jami Noureddin Abdurrahman, Salámán and Absál, 30
33. http://www.m-w.com/dictionary/paradigm
34. this can be understood at both a personal and social level
35. http://en.wikipedia.org/wiki/Image:Classical-Definition-of-Kno.svg
36. For a discussion of the philosophical terms see Stanford Encyclopedia of Philosophy at http://plato.stanford.edu
37. http://en.wikipedia.org/wiki/Gettier_problem
38. See Karl Jaspers, http://plato.stanford.edu/entries/jaspers/
39. http://en.wikipedia.org/wiki/Gini_index
40. See Karl Popper, http://plato.stanford.edu/entries/popper
41. http://plato.stanford.edu/entries/induction-problem/
42. http://en.wikipedia.org/wiki/Uncertainty_principle
43. http://en.wikipedia.org/wiki/Planck_units
44. http://en.wikipedia.org/wiki/General_relativity
45. more precisely, transcendental
46. Jalálu’d-Dín Rúmi (1207-1273 CE), The Mathnaví
47. http://en.wikipedia.org/wiki/Gödels_incompleteness_theorems
48. For example, the proof of the famous Fermat’s Last Theorem by Andrew Wiles was published in the Annals of Mathematics in an article consisting of 108 pages. Most non-mathematicians will not even understand the first sentence of the introduction. See http://math.stanford.edu/~lekheng/flt/wiles.pdf
49. in, not of, see Genesis 2:8. Eden means ‘valley’ in Sumerian. Its almost-geographical location is lower Mesopotamia at a branching of the Euphrates and its almost-chronological setting is the Neolithic or early Bronze Age, 5500 – 3000 BCE.
50. Bahá’u’lláh, The Hidden Words, Persian 39
51. Fowler ’s Stage 3, the last one that is reached by all
52. The Electronic Text Corpus of Sumerian Literature, http://www-etcsl.orient.ox.ac.uk/
53. The Jewish term is Aqeda
54. Psalm 74:13
55. All variations of the same myth are equally true, see Claude Lévi-Strauss, http://en.wikipedia.org/wiki/Claude_Levi-Strauss
56. Revelation 13:8
57. Ezekiel 8:14
58. http://en.wikipedia.org/wiki/Comparative_mythology

References

Artmann, B. (1999). Euclid – The Creation of Mathematics. New York, NY: Springer.
Dalai Lama. (2005). The Universe in a Single Atom – The Convergence of Science and Spirituality. New York, NY: Morgan Road Books.
Kuhn, T. S. (1996). The structure of scientific revolutions (3rd ed.). Chicago: University of Chicago Press.
Lauter, E., & Rupprecht, C. S. (1985). Feminist Archetypal Theory : Interdisciplinary Revisions of Jungian Thought. Knoxville: University of Tennessee Press.
Lyotard, J.-F., Pefanis, J., & Thomas, M. (1992). The Postmodern Explained. Minneapolis, NM: University of Minnesota Press.
Momen, M. (1999). The Phenomenon of Religion, A Thematic Approach. Boston, MA: Oneworld Publications.

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