(Subchapter added on November 7, 2017)
Before we start, a little bit of «history of the thought of the author», to guess why this chapter. Maybe one day some boring teachers will make my book analysed by their students, to make them find the origin of these ideas in my mother's breast size, or stuff like that. Seriously, this book is only a continuation of what I learned at school: logic and the scientific method. In that time, the scientist's dream was a «theory of everything», allowing to logically explain everything, from the Big Bang to why their fiancée dropped them.
Young man, my social ideals led me to meet leftists, whose reasoning seemed «scientific». However, I quickly realized that even simple human facts can be explained according to many different theories, while we are not really able to decide between these. Worse, these facts are «fuzzy», making it difficult to fit them into theories similar to the Sets Theory in mathematics. If we try, then the explanations quickly become extremely complex. To no avail, because, as with the Heisenberg uncertainties, what we gain in precision is lost in risk of error (without speaking of the inaccuracies of language, or putting in concepts which varies from a person to another). At the time, for lack of means to really sort this, I had classified the fact in my memory, and tried to do something useful with the few sure theories we had: physics, ecology, social ideals.
Luckily, there was at that time, Place des Capucins in Bordeaux, a macrobiotic store, where I had a first contact with the Yin-Yang dialectic. I Immediately realized its interest for a more accurate analysis of many human situations, without stumbling in the above senseless accumulation of mistakes or complexity.
However, it was only when I discovered spirituality that I really began to master the domain of non-Aristotelian logic, first with Hatha Yoga, then with Buddhism, Kabalah and Taoism. Even the notions of Christianity received in my childhood took a meaning in this light (for example, the notion of communion between the one God and His multiple creatures, which seems so illogical to the rationalist. Yet it is the same logic as for the quantum non-locality)
Today, the global understanding of the world is still hogged by the idiotic war between the «scientists» and the «religious». It is to pass to the next stage that I wrote this book. Well, actually I do not think there can be an unique «theory of everything» similar to the Aristotelian Sets Theory. But at least the tools I describe in this chapter allow for a comprehensive understanding of the world, usable in practice, and without leaving inaccessible areas or taboos.
(Permalink) What do we do with logic? We can make reasoning on simple situations of the everyday life. Example: If the traffic light is green, we start on, except if there is an obstacle preventing us to let the road free. Thus we can find solutions to immediate problems. However any higher or more general view, requires an understanding of the whole life and universe, or at least of whole fields. For that we build theories, which are more complex systems: philosophies, mathematics, morals, religious systems, political, economic or social systems. It is interesting to see in what extend and how these systems can describe reality and allow us to understand it. (By supposing of course that they are logically right. We assume this in this chapter)
Such systems, called axiomatic systems by the logicians, or conceptual systems in spirituality, all have the same structure:
-Axioms, which are statements on facts recognised a priori as true (The three axioms of the Sets Theory, existence or non-existence of God, personal interest higher or lower than collective interest...);
-Logical reasonings which, starting from these axioms, if they are true, will rigorously demonstrate the veracity or the falseness of a series of other statements: the results. These reasonings may use intermediate statements between the axioms and the results.
-Results, which are logical statements supposed to describe aspects of reality other than the axioms, or to lead to effective policies (mathematical theorems, moral principles, laws of physics, games, financial methods...). For instance, if we have the axiom as what all humans are equal, we enact laws protecting this equality.
The above statements are classics for the logicians. However this chapter is to introduce a series of new things.
(Permalink) What does happen if one of the axioms is false? This is very worrying, as all the conclusions drawn from it are false. Even if the reasoning are true. Our theory is doomed, even in the case when experience shows that one of the results is true!
And how to know if an axiom is true or false? Hey, this is not an affair of reasoning nor of logic, it is a matter of looking at how the reality is. Is the traffic light green (axiom)? I look at. If is it, therefore (reasoning) I can move forth (result). Does the human being have a spiritual dimension (axiom)? Wait I look at... Ha, there it is somewhat more complicated. It would however be quite useful to know if I must devote my life to enjoy it at best before nothingness (result 1), or if it is a better deal to sacrifice a transitory happiness in order to obtain eternal life in paradise (result 2). And if the axiom is not known, how to know the result?
I think that two things should be clearly understood here:
-A logical system whatever it is cannot demonstrate the truth of its own axioms. The results may seem true, the reasoning may be rigorously unattackable, but that does in no way imply that the axioms are true. We can only say that if the base is true, then the results are.
-To determine if an axiom is true is not a matter of logic, but a matter of observing reality. This may be quite simple (traffic light) as this may raise subtle or fundamental problems (like the existence of a spiritual dimension). This is the domain of epistemology, to which we will dedicate all the second part. Logic only makes possible to predict still unknown facts starting from already known facts.
This can be summarised in a sketch:
All those appetizing little potatoes represent facts of any nature (physical, moral, spiritual...) or more exactly the logical statements which describe those facts. Those facts are linked by logical reasonings, theories (symbolized by the arrows). But in the shaded elliptic zone, those facts are unknown (Too far, hidden by an enemy, or too expensive to observe...) when they are checkable into the white zone.
-If we can check a fact such as A, then we can use it as axiom for a reasoning or a theory.
-If the theory says that C is true, but we cannot check C, so we cannot know if the theory is true (Popper"s testability).
-But if the theory says that B is true, and we can check this, then the theory is exact (scientific verification of a theory).
-This exact theory then allows to correctly deduct facts such as C, that we are however unable to check (technical application of the theory).
-A theory which predicts an unknown fact E starting from an unknown fact D is not checkable (Popper's testability).
-A theory that we already checked (in the situation A and B) which predicts a checked fact F, allows to show the reality of an uncheckable fact D, and even sometimes E.
Many philosophical and religious systems, starting from axioms in the situation D, however state about facts which are in the situation of F, even in contradiction with what the observation shows. When one has knocked about the world in philosophy, this flaw in reasoning ends up appearing obvious, and even boring to refute. However everything seems to happen as if nobody account with this, with everybody clinging to such or such axiomatic system without noticing that it leads to false beliefs or terrible acts. This is not a problem of logic or reasoning, it is obviously a consequence of the psychological bias we already mentioned in chapter I-8 and about which we shall discuss in chapter II-6. Certain philosophers even twist their brains to «demonstrate» their axioms with reasonings which are like dogs trying to bite their own tails, without noticing that this process may also lead to similarly «demonstrate» any heap of axioms picked in the flea market. Sorry, but when I was studying philosophy in secondary school, this problem appeared obvious to me.
(Permalink) Some known systems somewhat differ of what the logicians usually describe, because they do not always use Aristotelian logic (Taoism...). However the principal purpose of this first part was to assess these non-Aristotelian logics as being of equal statute as Aristotelian logic. We shall thus conclude from this that axiomatic constructions can contain indistinctly:
-Aristotelian or non-Aristotelian reasonings (non-duality, quadripolar logic...)
-Axioms, intermediate statements or results which belong to these logics.
Of course these statements and reasonings will have to relate to objects which comply with them, for which the concerned logic is valid (see chapter I-7). This remark on non-Aristotelian logic will remain implicit until the end of the book. We shall use all the logics there, eventually without specifying it.
(Permalink) In the Western world, we so strongly grasp to this idea of single and perfectly determined objects, that we think as if the whole reality could be entirely described by Aristotelian logical statements, all connected together in a single system by Aristotelian reasonings, as in a microprocessor. A theory of everything. Fortunately, reality is not like this! We already saw that certain objects do not obey Aristotelian logic, but to other more gradated logics. The zones of reality where such objects dwell are inaccessible to Aristotelian logic. We can say that an object or a reasoning belonging for example to quadripolar logic transcends Aristotelian logic. This word must rather be understood in its mathematical meaning (Pi is a transcendent number, as it cannot be the result of any formula), but if minds enters on stage, so it is really a matter of spiritual transcendence (A divine purpose necessarily transcends any temporal or material justification). It could also happen that certain realities transcend any form of logic, Aristotelian or other, and then we shall speak of transcendent reality.
A peculiar definition will be useful: We shall often prefer to qualify a non-Aristotelian statement of transcendent view, in comparison with statements of simpler logics. For instance a quadripolar statement transcends its description with Aristotelian statements.
Even inside Aristotelian logic, we find statements which we cannot predict, undemonstrable. We saw the case of the third axiom of the Sets Theory in chapter I-2. The theorem of Gödel predicts that there are indemonstrable statements in all the axiomatic systems. If non-Aristotelian logics are added, the undemonstrable zones are probably smaller, but I do not know if they disappear completely. In any case if we deal with statements which we can demonstrate by no logical reasoning, there we still have the recourse of epistemology. This enthralling discussion could continue, but it will be necessary for us to introduce other elements only into the second part on epistemology.
(Permalink) What happens if we try to make logical reasonings on a transcendent reality? The question is of importance: Even without seeking subtle spiritual realities, the everyday life does not miss gradated choices, or situations with different mixed aspects which we cannot easily separate in distinct categories. The following sketch symbolises this case:
A transcendent reality is symbolised by a dotted ellipse, i.e. a curved form. We try to describe this curve using Aristotelian logical statements that we represent by segments of straight lines. The articulations between these segments symbolises the exact reasonings which connects these statements together. True axioms, bases of the reasoning, are represented by segments of straight lines with balls.
This sketch nicely returns the idea that all axiomatic systems (philosophies, mathematics, morals...) are artificial mental constructions, scaffolding of reasonings. We of course exclude the false systems, or those which do not refer to this reality.
We see that:
1) That an exact Aristotelian axiomatic system as the one represented can never give an exact representation of a transcendent reality.
Another way to say the same thing is to say the opposite:
1 bis) Any true axiomatic system can describe a transcendent reality exactly, but for this it requires an infinite quantity of reasonings and intermediate steps. (An infinite quantity of tiny segments of straight lines to follow the curve)
2) But sometimes for this it will be necessary for him to resort to shaking or complicated scaffolding, where different types of observation errors (on the axioms) of reasoning or validity (kind of logic) have all the more chances to occur, or uncertainty of the results increases with the number of steps.
3) It may happen, however, that any Aristotelian axiomatic system can give of this transcendent reality, at least in certain zones, a representation accurate enough for a given practical use.
The following sketch shows this time two different Aristotelian axiomatic systems, symbolised by two types of lines (they are really two different systems without common points, although they are tangled up):
We can supplement the three preceding results:
4) Different Aristotelian axiomatic systems can validly claim to approximate the same transcendent reality.
5) Different parts of a transcendent reality can be better or less described by such or such Aristotelian axiomatic system. (For instance, on the sketch, the system with fine lines better describes the left part, while the system with thick lines better describes the right part). We shall say that in this place such system may be more or less valid that another, at this given place. Physics theories like Quantum Mechanics, Relativity and Wave Mechanics are in this situation. The various religions also are in this case.
6) It may happen that several different Aristotelian axiomatic systems, even logically incompatible, have a similar validity for a given transcendent reality. We cannot then attach more value to one than to the other, they are equivalent. It often happens that equivalent systems, even if they are built on very different basis, lead to numerous similar practical conclusions. More, it often happens that:
6bis) the same transcendent reality can be as validly described by different logically incompatible or contradictory Aristotelian conceptual systems. This is often the case in politics, sociology and in religions.
It is necessary to be thoroughly aware of these six points, especially of the 5), as soon as we try to conduct a discussion, even not very subtle. Too many mistakes arise from ignoring them. We cannot do otherwise than to accept that reality is like this, while avoiding to artificially oppose together different systems, even apparently contradictory.
It may happen that some persons prefer such or such system among equivalents, for personna, cultural or psychological reasons. This is perfectly correct as long as these persons do this just in order to more easily apprehend reality with means which are more familiar for them. But it is no longer correct if we start to attach more value or validity to «our» system that to «their», with the risk to lose subtlety of judgement. This is a very basic mistake we all do everyday, while sincerely thinking that we are «true» when others are mistaking or stupid. There is no need for much hate to turn this situation into religious war, social clans, political clans or family disputes.
With due respect to certain mathematicians, the Sets Theory could be in this case, which means that other completely different theories could provide an as much valid base for mathematics and logic. Personally I will propose to keep this theory, but to start from the properties of objects on which we shall reason, choice 1 and 2, as presented in chapter I-2. This would bring as an advantage to place mathematics and Aristotelian logic within a much more general framework of all the possible logics.
The mathematician readers will notice the very relevant analogy with the idea of limited development. (For non mathematicians, see (note 10). For example a series of Aristotelian statements approximates a transcendent quadripolar statement, in the same way than in mathematics several simple functions approximate a transcendent function. Another physical comparison is the fact that we can synthesize any sound wave shape («transcendent») with a series of sine waves of frequencies multiple of that of the considered sound wave. Such an analysis sounds very fundamental, but, in an electronic circuit, it is possible to obtain exactly the same result while adding square waves in place of sine waves! This image nicely shows what can be equivalent conceptual systems.
The approximation of a transcendent reality by a conceptual system goes farther than a simple analogy. In the case of an Aristotelian reality, we can find one (or several) conceptual system which describes it exactly, what in physics we call a mathematical model (Like the differential equations of Maxwell, which describe exactly the propagation of an electric wave along a phone line). In the case of a non-Aristotelian reality, or transcendent, we can also find conceptual systems which describe it, such as mathematical models, but none can do this completely or exactly. Despite this limitation, these systems however remain the best mean for our intellect to understand those realities.
7) If an axiomatic system contains non-Aristotelian statements (that we may represent with curves on the previous diagrams) then it can represent much more precisely a transcendent reality. A quadripolar statement, itself transcendent for Aristotelian logic, can be approximated by several Aristotelian statements. It is what we did in this book, to describe the quadripolar logic, and which also explains why this description can never be complete, or why there can be different descriptions, as we noticed. The following sketch illustrates these two cases.
(Permalink) So far, we were speaking of exact axiomatic systems, that we can obtain only when we apply sincerely the reasoning method and checking methods, while completely mastering our psychological bias. However, not everybody does like that, and so many people build false or non-valid axiomatic systems, that after they brandish as the only truth, while considering everybody else as mad.
Of course, human beings are prone to mistake (and being sincere is not enough to avoid any mistake).
8) But when this mistake begins to lock itself into an autojustification cycle, and people get angry in place of envisioning the mistake, then these false axiomatic systems can be called ideologies. We have four main cases:
- The axiomatic system is true, but various psychological defilements lead people to an exclusive attachment to this system, or to consider that all the others are false. This is common in religions and is a very ordinary cause of religious wars.
- The axiomatic system is true, but used in a domain where it is not valid, as in 5). This mistake, as we shall see in Part 2, is the basic mistake of materialism and especially of positivism, chapter II-7. This leads to distortions which cause is difficult to detect.
- The axiomatic system is speculative, but arbitrarily considered as the only true (Dogmatism). This case is also very common in religions and cults.
- The axiomatic system has false axioms or false reasonings. This is for instance the case of Marxism, chapter VI-10, which positive ideal of social justice was spoiled by materialism, clan mind and violence.
It is to be noted that the word «ideology» is often used in a pejorative sense, in such an extent that we must avoid a non-pejorative use of it. Anyway in the beginning it was used by the Marxists, to name their though systems which were precisely ridden by the errors above. So I shall always use this word in the pejorative meaning defined in 8).
When people want to impose their ideology by force, we can speak of fundamentalism. If they simply do a segregation toward the tenants of another opinion, we can speak of sectarianism.
8 bis) (Added in March 2012) The simplest case of ideology is the opinion, (chapter V-12) when a neurosis of hate/attachment is associated to an unique idea (concept). We however need some nuances in the word «opinion», which is used to name very different things, good of bad.
Some epistemologists say that everything is opinion, as we have no mean to obtain an absolutely safe knowledge. In reality, there are knowledges which are safer than others. For instance, we can reasonably hold the opinion that two plus two equal four, as there is very little chances that this turns out to be a mistake. An intermediary case is to say that Earth is flat: this for long seemed a reasonable knowledge. Then it became a popular belief, and today it is nutter. At the other extreme, we find prejudices such as racism, or idiocies like opposition to women driving (it is resurfacing again, yes).
So there are three cases, that the common language does not clearly discriminate:
- The reasonable knowledge, based on exact reasoning and checked knowledge. Even if we are not fully protected from mistakes, any criticism or alternative appears as madness or deliria.
- Choices, such as for instance to admit or not the existence of God, or a lifestyle. By lack of mean for checking, Human Rights guarantee to the persons the freedom of such choices, including in public.
- Prejudices, association of a neurosis of hate/attachment to a concept. This can be a serious psychological trouble, such as racism or sexism, leading to social troubles like discriminations. But it can be a simple preference, for instance toward a political party. But even here, the neurosis will allow us to see only the bad sides of others, and only the good side of ours, while making us blind to any questioning. This also leads to social dysfunctions.
Even science is not exempt of prejudices or arbitrary opinions, and we find scientists «pro» or «anti» such or such theory. Some even go as far as calling their «adversaries» idiots, while thinking to represent alone the «true science»! This is really pity, and it would be much better, in front of two theories which cannot be decided between by experiments, to keep both in mind. This is anyway a requirement in science papers, and it is what I do in this book. And we are to see in 9) a very general way to proceed.
(Permalink) The pure analytic mind is able to develop and understand a given axiomatic system in a very efficient and comprehensive way, but only synthetic mind or meditation is really able to understand the points 1) to 8) without being entangled into that axiomatic system. Only this perspective allows the though to really use and master an axiomatic system, in place of being locked in as in a trap. To the contrary of a common prejudice, meditation (or synthetic or global thought) and the logical reasoning (or intellectual or analytical thought) are not opposite, but they apply to different cases (and in more complementary). (And, contrary to a more recent prejudice, there is no more superiority of meditation over analytical mind, and there are also means to get trapped with the use of meditation alone, as in spiritual materialism, or in some cults. The fair and appropriate use of any of the two requires the mastery of the other. True intelligence uses both, and is thus able, not only to play into a given axiomatic system, but also to play from a system to another, and to feel which one of them fits at best the real situation.
9) The understanding of transcendent realities can really appear only when our conceptual mind begins to easily play with different conceptual systems on the same subject. We begin to feel that there is «something» inexpressible but real and consistent behind these various equivalent conceptual buildings, which explains all of them without being reducible to any of them. This is the very important realisation of the non-conceptual mind, the key for upper spiritual unfolding and ultimate understanding of reality.
This point is really important for any scientific or rational approach of such transcendent domains, which can be undertaken only with the appropriate non-conceptual mind. Conceptual statements about such transcendent domains always contains coarse or subtle mistakes or limits, and thus cannot be said scientific neither rational. Accordingly the human languages are mostly conceptual, and this makes that non-conceptual knowledge can be transmitted only by parabolas, images, meditation exercises, and this book is not an exception.
Several religions (Esoteric Judaism, Buddhism, Taoism) precisely refer to non-conceptual mind, and consider that its absence is a «veil» which forbids to understand reality. In Buddhism, a person enjoying this capacity is called an Arya, and it is considered as an important realization.
We could also say that fundamentalism (religious or atheist) is a consequence of a caricatural lack of non-conceptual mind. What common language calls to take oneself too seriously!
Physics could be in this case too. Today the two most advanced theories (Relativity and Quantum Mechanics) are two incompatible Aristotelian axiomatic systems. Physicists consider this as a defect, and they are seeking for an unique Aristotelian axiomatic system uniting both. But until now (2010), nothing proves that this is possible. But even if it is not, the two current theories remain unified in an non-Aristotelian non-duality. (See chapter IV-4 a better way to solve this problem)
(Permalink) 10) A vicious case is when a false conceptual system (false axioms or false reasonings as well) seems to be a valid approximation of a peculiar transcendent reality. This case can be opposed to:
10bis) A true conceptual system does not look valid for a peculiar transcendent reality.
Such situations can indeed happen, for instance in physics with the aether theory, which seemed to explain «nearby all the physics». In spirituality also, both statements «God exists» and «God does not exist», at least one of then being necessary false, lead both to valid and very useful theories, respectively in spirituality and in physics. So the fact that a conceptual system seems valid (or not valid) for a given transcendent reality is not a proof that this system is true (or false) neither that its axioms are true (or false). This situation can be a source of many mistakes in a sincere search for reality, and it is difficult to escape the need of a progressive try and mistake process. But it can above all be a very practical mind control method, for instance when a dictator, a sect leader or a stalker «interprets» our thoughts or deeds in a different conceptual system than our own, in order to «show» that we had in fact irrational or guilty motivations. If the difference between the two systems is implicit, or in a far domain, it is difficult to find where is the perversity, and often people are entangled into these misleading mind processes.
(Permalink) I apologise to have presented the above results only with images and not with a text describing a rigorous demonstration; that would have been too long and perhaps impossible. In fact my purpose was rather to present things in an understandable manner with sketches, and then to draw some pragmatic conclusions, as we shall now see with concrete examples.
In Christianity, God is an esoteric entity at the origin of the existence and Who gives it its significance (I speak here about the Christian God, not of the bearded psychopath of Roman dogmatism or American anti-Darwinian fanatics). The first Christians considered Him as a character, but refused to give Him an image (they were called iconoclasts, and this tendency was strong up to the 8th and 9th centuries). We find a similar idea in Islam, where the face of God cannot be contemplated by any human. However He is still described as a character. The North America Indians had a similar view of their Great Spirit, Who could be personified or represented by forces of nature. India also personifies God, but in three aspects symbolised by three distinct characters. If we go a little further in study of the esoteric Brahmanism, or variants such as Shivaism, it is clearly recognised that this personification applies to abstract but fundamental aspects of reality, «energies» or tendencies of the mind. Buddhism completely evacuates the idea of creation or divinity at the origin of existence, and replaces it by the concept of Emptiness (chapter V-10), from where the appearance of universes can emerge. Taoism explicitely gives up any reasoning or concept as means to understand the ultimate reality, which it poses as intrinsically transcendent: the Tao. At last, funny joke, the physical science which deliberately eliminated any «abstract» or divine concept to refer only to matter, is now deeper and deeper immersed into esoteric when it studies the infinitely small or the origin of the Universe.
The least that we can say is that these conceptual systems are often contradictory! But it would however be false to say for instance that the Buddhism refuses God: simply this system speaks of transcendence (the emptiness) without using the concept of personal god which is the basis of the Christian thought system. So there is no real contradiction, or the contradiction at the level of the concepts is irrelevant at the transcendent level. Thus we must not be astonished to hear today the Dalaï Lama concerned with the Christian spirituality, while at the time of Lenin his Lamas at St Petersburg got round the communist ban with stating that they did not believed in God.
What I say here, it is that these various approaches are all attempts to approximate a transcendent view using more ordinary concepts, and that they are more or less equivalent in terms of validity.
Here also, examining a logical subject (that some may found abstract, not to say abstruse) lead to a very interesting practical consequence, able to generate a fair amount of peace and happiness: it clearly appears that it is stupid to bring religions in conflict together, especially through war, discrimination or persecution. At last we may consider that such or such religion is better or more efficient in such or such domain. Culturally certain persons choose one of them, but personally I feel happy to have at least some basic understanding of all. It is quite practical, when we want to explain something to somebody, to use his own concepts, without having to first convert him to our own religion.
Even if we eliminate all the false or arbitrary theories, psychology is the very field where no assertion can really be univocal. Such action, such feeling may have several causes, and even causes that no psychologist will ever be able to imagine, and nobody can say which of these causes acted. We can imagine any psychological theory we want, and always find examples which are explained by this theory, but it is very difficult to find psychological laws which are really true for everyone. I would like that the psychologists, including the most rationalist to the most far-fetched New Age, all show some modesty, and in particular fairly recognise that:
-Even if a law is statistically verified, we cannot deduce that it inevitably applies to a given individual. (This is mathematically asserted! To «forget» this is a legal fraud!)
-Even if it is demonstrated that a given individual has acted in a way according to an identified psychological mechanism, we cannot deduce from it that a similar behaviour of another individual is due to the same mechanism neither to the same motivations.
-The silly play of psychological interpretation «you did this because you seek to compensate for that...» does not have any value as long as it does not rely on tests and precise evidences (which are difficult to obtain). It is however a very common mind control process or denigration method.
-Speaking with a psychologist can influence us (it is the purpose besides...) causing the mechanisms proposed by the psychologist to be integrated into our personality, thus modifying any further interpretation.
-There is a two ways interaction between theory and observation, when for example a Freudian makes Freudian dreams, a Jungian makes Jungian dreams, etc... In this way any theory (including the worst wild imaginings and the sects) can become «true».
-An analyst of any kind can see others only through his own personality, his own psychological bias. In such conditions, any analyst, social inquirer, educator etc... can exercise his profession only if he has completed his own analysis, in order to eliminate his own psychological bias! Otherwise he cannot pretend to any objectivity. At a pinch, a clinician may use only more objective methods (psychometric tests with interpretation grids...). Any person who pretends to do psychology, psychological expertise or education, without fulfilling such conditions, is necessarily a mad, a manipulator or a charlatan. This result was already known by the psychoanalysts, and is developed in part 2 on epistemology.
-In short that psychology is a subtle play where should involve only perfectly balanced persons, sincere, honest with themselves and perfectly respectful of others, with for only motive to help others to free themselves from their bad psychological mechanisms, to build a simple, straightforward and happy mind.
Everyone heard about Buddhism divided between different vehicles, and even between various schools. Studies in Buddhist philosophy perfectly assume this situation, and different axiomatic systems or varied conceptual divisions are usually presented by the same professor to the same disciples to explain the same notion. In particular Emptiness (chapter V-10) is taught according to the views of four different philosophical currents, from the simplest to the most subtle, and this although the oldest among these currents do not have any more followers today. Studies are presented like this to gradually refine the mind of the students, to make it more flexible, and to fight attachment to a given system. The fact that several different axiomatic systems can be more or less good approximations of the same reality is clearly recognised here,since at last a thousand years (the great treaties of Buddhist philosophy or non-conceptual mind are dated from the 5th century). The fact that meditation and analytical mind are complementary is also perfectly recognised, and thus intellectual analysis is a large part of Buddhist studies, even if their purpose is basically meditation. A much more abrupt way is to define Emptiness as «the non-duality between the fact that things appear and the fact that they do not have any intrinsic existence» (His Holiness Sakya Trizin). This sentence which clearly refers to a non-Aristotelian association, is a completely clear and sufficient definition... if we understand what non-duality is! You just have to sit on your meditation cushion long enough... The Zen Buddhism shows itself still more unbearable, with sitting in silent meditation for hours, and its koans, absurd little statements with for explicit purpose to blow up our «rational» way of thinking!
The physicists are all together looking for an unified physics theory, which would account in an univocal way of all the possible physical phenomenon. We are still far from this, and the today physics theories are often contradictory (on the level of the concepts), for instance the Quantum Mechanics and the Relativity. To make such an unified theory possible requires that the whole physics be Aristotelian (non-transcendent) a thing that we cannot state a priori. If it is not, we shall still be able to make physics, but we shall have to make do with apparently contradictory Aristotelian theories, or learn to think with a non-conceptual mind. This would not be the most difficult thing the physicists already achieved, and anyway not a pretext to make sadomasochist theories about «unknowability».
(Permalink) We can note that when a system contains paradoxes, most people avoid the paradoxical zone, when they do not straightforwardly denegate its very existence. On the contrary, we may go and see what takes place there... With keeping in mind that, if we cannot demonstrate that one of the two terms is more true than the other, then selecting one of them is necessarily a choice. And especially a creative choice. Each of the two terms leads to a different system. One of them could be far more interesting, or on the contrary both terms are as interesting each other, but different. We use this process in various places in this book, in domains such as the creation of the world, spirituality, the notion of God, and even ethics. But I suggest that mathematicians and physicists may also use this method in their theories, when these theories are no longer able to make valuable predictions (paradoxes, infinite values, integration...) Peculiarly in physics: never such a situation was able to stop nature, it necessarily made its own choice.
In the Sets Theory, the axiom 3 is here to avoid a paradox, to which nobody found any use. The axiom 2, as what a set cannot be a part of itself, was also added to avoid circular references (another kind of paradox). (I saw passing some day an article in a vulgarisation review which said that eliminating the second axiom builds a different Sets Theory, but I do not find any reference on it on the Net.)
(Permalink) Sometimes in an axiomatic system, the reality of the central axiom cannot be demonstrated, whereas all the constructions made with it seem to match very precisely with reality. This is the case with axioms such as the concept of God, or as the singular point in the Big-bang, without which we would not even exist. We could deduce from this success of the whole theory that the basic indemonstrable axiom is true; but it is necessary to be very careful, as such indemonstrable and unobservable facts often reside at the centre of transcendent zones of reality, where ordinary reasonings are no longer effective. It is necessary to show some intellectual modesty in our assertions, and to be aware that, when knowledge approaches these points, what actually takes place here may be completely different of what we imagined, that this may force our mind to discover new paradigms and superior logics. Or that what we believed to be sure and known, happens to have a completely different significance. For instance, persons who admit the existence of God find in this idea a quite simple explanation of their spiritual life, when persons who refuse God see in this absence a simple understanding of the material world. Despite this blatant contradiction, both see into this apparent efficiency a confirmation about their own opinion on God.
My own hypothesis on God (Chapter IV-6 and chapter V-6) or about the origin of the universe ( third part and fourth part) are far from being so naive, and they may explain such an apparent contradiction.
Classical exemple of singularity in physics is the central point of a black hole. In logic, we have the «collection of all the sets» aimed at by the third axiom. In arithmetic, the zero is a singularity, as we cannot define a division by this number, and this one only. Other common examples of singularities are the zero point of the Big Bang, or God.
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