Tractatus Paradoxico-Philosophicus: A Philosophical Approach to Education

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7/7/2018

Tractatus Paradoxico-Philosophicus - Preface

PREFACE A specter haunts the minds of people all over the world: the thought that societies, their laws and their institutions mean little or nothing to the few wealthy and to the many poor whose population increases without bound. The many subdued by the few through arbitrary hierarchies that preserve themselves through instruction, coercion, containment, and destruction of the many, and through rewards of riches and power for the few. Hierarchies also develop among groups of people, among nations, among conglomerates, and among corporations and institutions. From the perspective of these hierarchies, people themselves appear irrelevant, ergo expendable. This Tractatus addresses some old and new concepts thought essential for the understanding of living organisms (humans included), their environments and interactions. For example, consider concepts such as process, recurrence, organization, closure, paradox and education. Curiously, notwithstanding numerous efforts to bring them to the fore by different authors and in different forms, wide understanding and recognition still eludes them. Maybe their pervasiveness and omnipresence make them invisible to creatures so immersed in them; or maybe thinking about them collides with the resistance to change of societies that believe they require the predictability (triviality) of their members to preserve themselves. The propositions of the Tractatus do not attempt to represent but an incomplete collection of my thoughts about these and related concepts, which I shall address neither with formalisms nor explanations, intending to stimulate in my reader thoughts similar to mine. This I shall do by imagining my reader as an interested observer of the world, a world that includes the observer. While any learning only leads to tentative knowledge, learning indirectly from others, through their writings or sayings, requires reading and hearing between and behind the lines, since an observer can only speak (or write) from its own perspective to the (different) perspective of another observer, as I do now. By your perspective I refer to what and how you think and feel about the world and your fellow humans and about yourself in the midst of them. In this spirit, language in the Tractatus will play the role that marble plays in sculpture or oil in painting. Consequently, even though, to the reader, some statements may seem definitions or explanations, the reader must receive them as metaphors and then interpret them from the reader’s perspective.     I dedicate these thoughts to those who, through their years and experiences, have managed to maintain their minds young and thinking in spite of an “education” dedicated to silence its students, to inhibit their creativity, and to close their minds instead of opening them. To manage that requires courage, because young minds often say what they think and this usually gets them into trouble. In some places, innocent looking places, innocent looking people will torture and kill you if you speak your mind. For example, young minds will clearly see the catastrophic effects of the following recurrence, of which most people live happily unaware: If humans rather instruct than educate their children, these children will instruct their children even more (educating them even less), and they in turn will similarly do with their own children and so on and on. If humans do not perish at the hands of uneducated leaders, sooner than later they will grow into a population of morons who only obey rules, predictable creatures, ants of an anthill, humans no more. The sad (happy?) end of the story: awareness of their own shortcomings will thoroughly escape them.     This shows an example of a recurrence that humans should see (understand) in order to interrupt its course. Ecological cycles (such as those of forests, lakes, rivers and oceans) provide examples of recurrences that humans should see (understand) in order to preserve them. (I propose a philosophical understanding rather than a scientific one since it has to prevent rather than lament: the complexity of these systems renders the scientific understanding inappropriate or, at best, too slow and too late.) Then, consider those recurrences that humans must initiate in order to develop the potentialities of vast sections of their population (for example, women, children and other groups everywhere) whose opportunities for development and education remain hindered or non­existent due to carefully selected archaic and shortsighted cultural, political and economic legacies and practices. Humans should initiate these recurrences by eliminating the instruction of these archaic and shortsighted cultural and economic legacies and practices to the young. Young minds can also comprehend that some individuals or groups amass or have amassed their fortunes taking advantage of the power bestowed on them by hierarchies (designed and sustained by the same individuals or groups) where the few, who exploit the many, provoke rather than prevent social, economic, ecological and other disasters. Moreover, young minds will easily see that, like the politics of power, whose false generosity appeases the people, charity, donations, “good causes”, etc., and, of course, organized religion, activities supported and steered by the wealthy few, cover up the monumental injustice that they inflict; and will also see that such societies not only tolerate these thieves but also often praise and imitate them. This shows a clear example of an unhealthy recurrence.     These incompatible discrepancies of power and fortunes originate dogmatic and irreconcilable ideologies that lead to profound social changes and immense loss of life. Occasionally, these conflicts make more people enjoy the advances of civilization but more often they only increase the wealth and power of those already wielding enough power, wealth and the callousness to provoke these conflicts. Between conflicts, organized religion consoles the poor and calms the conscience of the rich, as they get even richer; hence corruption sets in. These ideas must appear so basic and simple to the reader, and the solution to the problems they unveil so clear and straightforward, that the reader must conclude that the individuals or institutionalized groups appointed (by themselves or others) to make decisions that affect other people, abandon responsibility, education and foresight while striving for power and while exercising it. And since power blurs these shortcomings for those who hold it and for their followers, this recurrence can easily lead to excesses and abuse of that power. Ironically, it seems that this situation perpetuates itself because, as the individuals or groups in these positions and institutions (including universities) abandon thinking and conversation, their power to affect other people increases multifold (an unhealthy recurrence, and a rather unfortunate one since it affects society and its future). Moreover, eventually their most noble goals dwindle and vanish only to reappear as ruthless goals of self­preservation: the silence of their present critics through http://bcl.ece.illinois.edu/Uribe/English/Preface.htm

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containment, confinement and destruction, and the silence of their future critics through more instruction and less and less education. As a result, vast numbers of human beings endure war, misery, hunger, lack of health care, lack of education, etc. Consequently, since equal opportunities belong still to a distant future, humans should in the meantime temper extreme wealth and extreme poverty (society means little or nothing in both cases) by establishing limits to wealth and to poverty. As long as large fortunes exist, democracy cannot exist, except as a delusion, since even though the people occasionally manage to elect the representatives of their choice, those with the large fortunes promptly take over, through influence, bribes, menace or force, and run the nation as if everybody shared their views. Those who dare to oppose them will suffer the consequences as mentioned above.     Even more disturbing: it seems that for all the distance that institutionalized scientists purport to maintain from organized religionists, they appear to join them against improving the lot of the dispossessed and in favor of a status quo. Organized religions, long known as the opium of the people, preach that, after death, the faithful will receive ample consolation for all the miseries of life. Concurrently, institutionalized scientists and technologists join in with their own farce: the promise of a utopian future based on the illusory concept of progress. As with religionists, the future supplants the present so that most humans forget their current misery and oppression. While science and its applications, lacking a philosophical and/or political outlook, sell themselves to the highest bidder with regrettable consequences and with little or no outrage from the “scientists” involved, few raise their voices in an effort to understand the essence of humans and their societies and then share this understanding so that a new, long overdue, society of humans does neither destroy its members nor itself. Perhaps the most insidious recurrence results from a society’s foolish intention to “educate” their young to join an already corrupt society where success comes only from power and wealth no matter at what cost. To achieve this, society uses instruction, organized religion, propaganda, deception and other methods to convince or coerce the reluctant young (already aware of society’s corruption), thus defeating its original intention and entering a self­destructive loop (recurrence) that erases all hope to educate the young for a better society. To address this state of affairs, presently quite ominous, the Tractatus proposes that instead of relying on a logical and scientific understanding, usually dedicated to the search for a “truth”, better to rely on exploring the philosophical possibilities and in using, if needed, logic and science as tools to do the task(s) prescribed by a philosophical understanding.     I sense logical reasoning alone as a disease from which we must distance ourselves as shown in the Tractatus. I believe that this will perturb and perhaps annoy many who consider themselves “well off” and/or “content”; choosing to ignore the miserable state of affairs in the world and to forget those who provoke it, they prefer to welcome, to demand or to adapt to a logical reasoning without conflict or paradoxes. I also believe that this will make uncomfortable those logicians, mathematicians and others who provide that “purified” logical reasoning. Many will understand the thoughts presented here but few, if any, will act accordingly… unless thoughts may also bring about a storm. Many have stimulated my thoughts with their writings and conversations, but since my writing reveals large and small discrepancies with their thoughts I shall give no sources and simply express my unreserved thanks to all of them. I will only mention Jorge Luis Borges, Herbert Brün, Humberto Maturana, Gordon Pask, Bertrand Russell, Heinz von Foerster, and Ludwig Wittgenstein. I would like to extend my special thanks to Jamie Hutchinson and Olga Trullenque Alvarez who have read the manuscript making suggestions that, in one way or another, have contributed to the Tractatus. I owe to my students the inspiration and stimulus to fight for the education of all, including that of those who have lost it.       Urbana, 1991–2006. R.B.U.       Introduction

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INTRODUCTION Order and* chaos: stimulates imagination and creativity. Order or** chaos: inhibits imagination and creativity, allowing some to develop a limitless power to affect the lives of others. * and: the one blends with the other. ** or: the one excludes the other. This Tractatus offers a new, or long forgotten, language-game. It does so, not through definitions or explanations but rather showing, as if uttering the ideas while pointing at them. It invites observers, mostly through metaphors, to explore new ways of seeing (understanding) their environments, and new ways of expressing their desires and interactions. We may find it easy to accept the description of all phenomena in terms of processes or networks of processes. (Consider phenomena such as the movement of a limb, the explosion of a star, the “collisions” of sub-atomic “particles”, the “beginning” of the “universe” and its subsequent transformations, etc.). We may not find it as easy, however, to grasp that a closed network of processes may distinguish itself as an observer of an environment brought forth by the same distinction. Furthermore, consider: (1) that the distinguished environment contains the observer (the closed network of processes) and (2) that from the perspective of this observer, this distinction and further distinctions resulting from the interaction between this observer and its environment appear paradoxical and logical. In other words (paradoxically), for the observer, all possibilities blend into each other (for example, exist and not exist, inside and outside, red and blue and green and… etc.) and (logically), for the observer, the possibilities appear distinguished from each other (exist or not exist, inside or outside, red or blue or green or … etc.). Living organisms, with or without a nervous system, constitute examples of these closed networks of processes. A nervous system, also a closed network of processes, interacts with its environment through closed networks of processes that involve its sensory surfaces as well as its effector surfaces. The nervous system, therefore, interacts with its environment (paradoxically) inside and outside itself and (logically) inside or outside itself. Determined largely by their biology, one or more observers, reasoning logically, distinguish a world “out there” made of objects and events to which they attach (through further distinctions) specific possibilities as a result of perceptual or other characteristics and limitations, as well as a result of attempts at acting socially. Yet these attempts also entail steps towards triviality and away from thinking and paradoxes. Social knowledge, whether “objective” or “subjective”, as practiced by logicians, mathematicians, scientists, technologists and others, provides no exception. An observer may still welcome these attempts, as long as they lead to conversation, thereby avoiding the trivialization (instruction) of one by the other and that of many by the few. Two or more individual observers cannot distinguish a common world “out there” unless some evidence can convince them. From this evidence, logical reasoning allows human observers to draw inferences about the world “out there” that will not hold until some evidence supports them, reinforcing the original distinction of a world “out there”. Since new evidence may prove previous evidence wrong, this process (evidence, inferences, new evidence, new inferences…) has no end, and it may even call into question the original distinction of a world “out there”, which may call into question logical reasoning itself and suggest instead a paradoxical reasoning. No observer “resolves” or “explains” paradoxes without loss. This viewpoint, as shown by the Tractatus, appears essential to such societies that humans should develop through education and art and philosophy. The Tractatus does not say, teach, or explain what to educate; but it shows education as if pointing at it. It also traces the origin of these seemingly outrageous propositions to the source of all propositions: the paradoxical essence of the observer. If humans do not succumb to their self-inflicted shortcomings, what follows should help them see (understand) themselves as well as the consequences of logical reasoning alone as done by logicians, mathematicians, scientists, technologists and others; searching for a truth as if searching for a god, they translate everything into their own language, thus utterly missing the point. Those who practice these disciplines soon forget or fight their paradoxical origin mostly because those who consider themselves “well off” and/or “content” and those who believe they will soon achieve this status, welcome, demand and/or adapt to a logical reasoning without conflict or paradoxes, thus forcing a status quo. From logics to paradoxes Consider a concatenation of words (a sentence) and call it a proposition (a statement) invented by one or more observers to assert or express something in a given context. Propositions may have different meanings for different groups of one or more observers. Reasoning paradoxically, a group of observers may find tentative common meanings for propositions through the language-games that define their forms of life. Reasoning logically, a group of observers may find that some propositions do not refer to themselves and that an observer or group of observers must assign or determine their logic values (e.g., in a two-valued logic: true, false). Other observers may disagree and defend with arguments different values.

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Other propositions refer to themselves (self-referential propositions) and determine their own logic values, e.g., L: “Proposition L has now and here the value true”. One or more observers can choose and assign either logic value (true, false) to L and since L refers to itself it does not allow any arguments to dispute or to support this choice. Some of the self-referential propositions determine their own “logic value” as “true and false”, thus preventing the observer from choosing (distinguishing) “true” or “false”, such as the proposition: P: “Proposition P has now and here the value false”. If one or more observers, adopting a logical reasoning, assume that this proposition has now the value true, they soon have to accept, under that assumption, its value as false. If they assume the value of the proposition as false, soon they have to accept it as true, and so on. For these observers the values oscillate: true, false, true, false ... as they attempt to determine a value. Call this proposition a paradox. Unfortunately many authors who write about paradoxes forget self-reference and the fusion of different possibilities as essential aspects of paradoxes, with the regrettable consequence that many riddles, puzzles, conundrums, etc., pass for paradoxes. The paradox does not allow the observer to assign one value “true” or “false” to the proposition except as part of an oscillation, thus inviting the observer to contemplate paradoxical reasoning and blend both values (all possibilities in this case) into “true and false”. Reasoning logically, the observer can only consider both values as alternating in a time and a space resulting from the observer contemplating the paradox from a logical perspective. Reasoning paradoxically, the observer blends “true” or “false” into “true and false” and hence, no time, no space, nor oscillation result from a paradoxical perspective. With paradoxical reasoning, however, the observer blends, without conflict, all possibilities. Hence, with paradoxical reasoning, the observer also blends paradoxical or logical reasoning into paradoxical and logical reasoning. Therefore, reasoning paradoxically, the observer can also make tentative distinctions in time and space. In a self-referential loop of propositions, derived from proposition L above, such as the one that follows, all the propositions will have either the value true (T) or the value false (F) depending on what value the observer chooses for one of the propositions, say L1 (and no oscillation develops): t1

t2 ...

L1: “L2 has now and here the value true.”

T(F)

T(F)…

L2: “L3 has now and here the value true.”

T(F)

T(F)…

Ln: “L1 has now and here the value true.”

T(F)

T(F)

A self-referential loop of propositions, derived from proposition P above, such as the one that follows, will not allow the observer to attach values to any of its propositions since their values will oscillate logically and blend paradoxically for the observer as before (notice that the values now ripple through the loop of propositions as the observer, reasoning logically, determines the value of each proposition, thus making the oscillation of values slightly more complex than shown here): t1

t2

t3 ...

P1: “P2 has now and here the value true.”

T

F

T ...

P2: “P3 has now and here the value true.”

T

F

T ...

Pn: “P1 has now and here the value false.”

T

F

T ...

...

As proposition P, this paradoxical loop of propositions also suggests paradoxical reasoning to the observer. If an observer takes a narrow band of paper and glues its ends together, the observer forms a ring with two faces (outside and inside) and two edges (right and left or up and down, depending on how the observer holds the ring). Assuming that each face (or edge) of the ring corresponds to a value (T, F), the observer can see the whole ring as a metaphor for the loop of propositions derived from L. If the observer twists one end of the band 180 degrees before gluing it to the other end, the observer forms a Möbius band with one face and one edge (see the Ring and Möbius Band in the following section). As with the paradoxical loop of propositions derived from P that, for the observer traversing the loop of propositions, alternates logically two values (in a time and a space) and blends paradoxically two values into one (no time, no space), for the observer traversing the band lengthwise, this band alternates logically two faces (in a space and a time) and blends paradoxically two faces into one (no time, no space), and alternates logically two edges (in a space and a time) and blends paradoxically two edges into one (no time, no space). Notice that proposition n corresponds to the twist and that any odd number of twists maintains the paradox and that any even number of twists destroys it, introducing a distinction. Logical and paradoxical toroids If instead of a band, the observer has a tube, with a polygonal cross section, that closes on itself forming a toroidal shape with 3, 4, 5 ... or n faces, and each face represents a possibility (e.g., a logic value in a multi-valued logic or a component in a closed http://bcl.ece.illinois.edu/Uribe/English/Introduction.htm

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network of processes and components) the observer has a logical toroid from which the observer may form a paradoxical toroid (one face and one edge) with the appropriate twist (360/3 = 120 degrees for 3 faces, 360/4 = 90 degrees for 4 faces, 360/n degrees for n faces (n possibilities)). Ring and Möbius Band: (2 faces 1 face; 2 edges 1 edge)

Logical and Paradoxical Toroids: (3 faces 1 face; 3 edges 1 edge)

Logical and Paradoxical Toroids: (4 faces 1 face; 4 edges 1 edge)

For the observer traversing the resulting face lengthwise, the paradoxical toroid alternates logically n faces in a space and a time and blends paradoxically n faces into one, eliminating time and space. Reasoning logically, every time the observer returns to the point of departure after every turn around the paradoxical toroid the observer will stand on a different (and, paradoxically, the same) face. The paradoxical toroid also suggests paradoxical reasoning to the observer. Consider now that a logical toroid, as a metaphor for a set of components (the faces of the toroid) that do not change (no processes, no activity), may represent the static stability of non-living things. A paradoxical toroid, however, as a metaphor for a set of components that do change (due to processes) into each other, represents the dynamic stability that lies at the heart of all living organisms and at the heart of the activity of their nervous systems. Reasoning logically, closed networks of changing components look like this (for 2 and 3 components):

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The arrows represent the processes and the times and spaces resulting from the logical perspective chosen. Reasoning paradoxically, the same networks look like this:

The arrows now represent components blending into each other, self-reference and twist (best represented by the corresponding paradoxical toroids). Neither time nor space results from this perspective. From paradoxes to logics Until we know better, it makes sense to assume that as human infants join the world and a society, their nervous systems, not yet subdued by training and instruction but full of curiosity, observe (explore) their surroundings and themselves considering all possibilities, including emotions and feelings, unconstrained by the limitations of a logical framework. Under this assumption, contemplate observing (perceiving) as resulting from the activity of closed loops of processes that, crossing the sensory and motor surfaces, lie inside and outside the nervous system. Since this activity includes all possibilities, these loops must resemble the paradoxical toroids discussed above and play the role of paradoxical contexts where the uninhibited infant observers, reasoning paradoxically (logical reasoning still incipient), make tentative distinctions. Moderate instruction and training can force these observers to consider only part of their paradoxical toroids (a part that each observer can make to coincide with part of the toroids of other observers) so that only logical reasoning emerges. On the other hand, extended rigorous instruction and training can force the observers to untwist their paradoxical toroids (to make a logical toroid). Unlike the first case, which may prove reversible and lead to a somewhat flexible observer, the latter case may prove irreversible and lead to a rigid observer who considers logical reasoning alone. Most observers succumb to these methods of coercion and relinquish the paradoxical view (the whole paradoxical toroid). This reveals the essence and origin of all logical reasoning: a social convenience extricated from a paradoxical context. The extraction, however, reduces a priori the possibilities (the available choices) for these observers. Logical reasoning Logicians and mathematicians have carved and extracted (painstakingly, brilliantly) the whole edifice of logical reasoning out of these same paradoxical loops, so that this edifice may please as many logicians and mathematicians as possible. The carving and extraction, as before, reduce a priori the possibilities (the available choices). The same applies to science and its applications, and to any other activity in which the observers attempt logical reasoning alone. Logical reasoning alone, and a “logical” language derived from it, for all the benefits it has given to humans, mostly allowing them to build and destroy things together, has deprived them of wisdom; and because different groups of humans often do not share the same logical reasoning, it has also stimulated their irrationality, exacerbated by excessive and unnecessary differences in wealth and power. Observers that use only logical reasoning have always attempted to distance it from its paradoxical origin, as shown by the histories of logics and mathematics. These histories reveal an abundance of branches sprouting from these disciplines, most of them, if not all, dedicated to the eradication or isolation of paradoxes. This unveils disciplines concentrated in them, inside their own languages and their growing abstraction; lacking also the philosophical outlook, it makes them increasingly unfit to contribute to a better society of humans. An example Many paradoxical loops have inspired useful or useless applications such as the logical inverter with feedback used as an oscillator (e.g., clock(s) at the heart of digital computers), or the electromagnetic buzzer used in electric doorbells, or the paradox of the liar and many others that inspired and bedeviled many logicians and mathematicians. The example presented below also suggests the insight that paradoxes may bring to logics, mathematics and the sciences, if humans would allow them as part of reasoning; as if humans would listen to troublemakers rather than shutting them up. When an observer enters a room at night, the observer usually turns on an electric light using a switch near the door. The corresponding electric circuit follows. V stands for a source of voltage and L stands for the light. The switch SW allows the flow of current (light on) when closed and prevents it (light off) when open.

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If the room has several doors, the observer would like to have a switch by each door, so that each of the switches can turn on or off the same light. A paradoxical approach to this problem offers an interesting solution, rich in possibilities and meanings. Modify the circuit as follows:

Instead of the switch the circuit has now two rings made of electrical wire. Visualize these two rings as the two edges of a band like the paper ring considered above. If the observer manages to twist this band to form a Möbius band, the two wire rings will form one continuous wire, thus closing the circuit and turning the light on. The observer can do this with a so-called Double Pole Double Throw (DPDT) switch as follows:

With the switch in position A (A closed, B open), the two wire rings remain isolated from each other (light off). With the switch in position B (A open, B closed), the two wire rings cross (twist) into each other forming one continuous wire and turning the light on. The observer may connect as many of these switches around the rings as the observer wishes. Just as in the paradoxical loop of propositions only an odd number of switches in position B (twist) will turn the light on. Notice that the operation of the circuit contemplates logic and paradox, distinction and absence of distinction. If the observer places one switch by each door of the room and wires them accordingly, the observer may turn the light on or off from any of those doors. Moreover, depending on where among the switches the observer connects the voltage source and the light to the wire rings, different operations of the switches result. (I built this circuit with five DPDT switches and it operates as I have described it). A metaphor Imagine a network, say, of a hundred nodes arranged in a 2-D (two-dimensional) matrix of 10x10 elements interconnected horizontally and vertically (a 2-D interconnection of nodes). Make each node an oscillator and its oscillation observable as a light that the node turns on (red) and off (white) with a given frequency. (See top half of the figure below). A basic oscillator consists of a logical inverter within a paradoxical loop (a loop with a “twist” such as the Möbius band). As with a paradox the oscillation develops in a time and a space resulting from the observer contemplating the oscillator from a logical perspective. (Many configurations of elements in a recurrent loop can make oscillators of different kinds and complexities such as electrical, mechanical, optical, biological, etc.). In the network, all nodes oscillate at approximately the same frequency. When a node turns off its light, it sends an excitatory signal to its four neighbors (up, down, right and left, including a wrap-around at the borders of the matrix) so that their lights turn on. This activity coming from the nodes synchronizes the whole network so that it oscillates turning on and off alternate lights (vertically and horizontally) at instants (t1, t2, t3, t4, t5, t6…) and it also provides innumerable paradoxical loops. The wrap-around, structural or not, operates from an even row (column) to an odd one or from an odd to an even one. (I built this network and it operates as described). The dynamic stability of the activity in the network, clearly more complex than that in each of its nodes, offers many paradoxical contexts (all possibilities) where the observer may choose (distinguish) among concurrent alternatives: Observing the activity of the network (lights turning on and off), the observer may concentrate on one light that just turned on, and when it goes off choose one of its four neighbor lights (four possibilities) that now have come on. Then, concentrate on that chosen light and, when it goes off, choose one of its four neighbor lights as they go on, and so on ad infinitum, forming a path drawn by the lights visited. At each light visited by the observer, the four neighbors, as a paradoxical context, alternate logically up, down, right or left and blend paradoxically up, down, right and left. (See the last figure of the logical and paradoxical toroids). http://bcl.ece.illinois.edu/Uribe/English/Introduction.htm

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The observer may also choose to follow the movement of one or more diagonals of lights on. As the network oscillates, these diagonals move up towards the upper left corner of the matrix and down towards the bottom right corner. The observer may also choose diagonals that move up towards the upper right corner and down towards the bottom left corner. For the observer the diagonals, as a paradoxical context, alternate logically, up or down, and blend paradoxically into up and down. The same applies to the diagonals made of lights off, if the observer chooses to follow these diagonals instead. The observer may also choose any group of lights (say 2, 3, 4 … n lights on) and, choosing the moves of each selected light, form patterns that result from the path determined by all the choices. For example, in the bottom half of the following figure, an observer has chosen a group of two lights on (red) in a diagonal. Then, the observer chooses, for each light, a vertical (or horizontal) move but in opposite directions and so on, as shown by the arrows. As the network oscillates this pair will oscillate, for the observer, like a seesaw and will rotate like a windmill if vertical and horizontal moves alternate. (If the number of lights selected for each group increases, the number of possible patterns formed as the observer chooses the neighboring lights increases even more. This happens even for a modestly sized network such as the one considered here. Notice that the observer cannot follow all the possible patterns, thus unavoidably missing the ones not followed, much as any observer can handle only so much and no more of its environment, missing the rest). And many others.

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See animation.

See animation. http://bcl.ece.illinois.edu/Uribe/English/Introduction.htm

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The choices of the observer do not affect the oscillation of the network but without the network’s activity the observer cannot choose. On the other hand, without an observer the activity of the network makes no sense. Adding light sensors to the network, an external (to the network) light may affect the dynamic stability of the network’s activity and some of the neighbors may not turn on when expected or vice-versa, thus changing the number of choices available to the observer. This suggests that the network can have any shape: regular, as shown, or irregular. Since the network does generate light some lights may act as effectors, and so it can interact with another network or with itself (e.g., using a mirror). For an observer, some of the lights may represent effector surfaces and some of the light sensors may represent sensory surfaces of the network. In such a network any activity somewhere in the network leads to further activity elsewhere in the network, including the “external environment” of the network. Inhibiting the activity of some lights, an external stimulus (e.g., light) may lead to the partial or complete isolation of other lights. These will continue to oscillate by themselves, but the activity of the network will disintegrate and cease to oscillate as an entity. Let us now observe the network of oscillating lights as a society of individual organisms (the lights or groups of them) that interact with their immediate neighbors. Under certain circumstances these interactions may correspond to those of a working society, e.g., an anthill, a beehive, a human group. Notice that for an observer not affected by the functioning of these “societies”, these “societies” make no sense except as oscillating networks that just oscillate (no matter how complex the oscillation) as the matrix of lights already described. Imagine a visitor to a foreign land where the inhabitants speak a language the visitor does not understand, and where the inhabitants do not understand the visitor’s language. During some time the visitor may not interact with these people and so the visitor may act only as an observer of them and vice versa as long as none perceives a threat or nuisance in the other. The societies or groups that the visitor may encounter will appear only as networks that just oscillate until the visitor learns the language and joins the oscillation (the dance). The activity of these oscillating networks may sustain some local damage (some nodes stop oscillating, some excitatory or inhibitory signals blocked, etc.) but the network as a whole continues its dance, blending dynamic stability and instability, thus enriching the life of the group or society and that of its members. With major damage the activity of the network may collapse. Notice that the activity (oscillation) in the network as a whole maintains itself because any activity somewhere in the network leads to further activity (integrated, synchronized) elsewhere in the network, activity that returns through many possible paradoxical feedback loops to the original activity considered. (A circle, a sphere, with its center everywhere and with its circumference, shell, nowhere). It should transpire from the above that the original 2-D interconnection of nodes could grow into a multi-dimensional interconnection of nodes and also that the activity of the nodes could grow much more complex than turning a light on or off and that the signals between nodes could also increase in complexity. Living organisms, for example, interact using a variety of carriers for simple and complex signals: electro-chemical, chemical, light, sound, dance, etc., and, of course, human language. The following figure represents the instants (t1, t2, t3, t4, t5, t6 …) of one node (at the center), its neighbors and the neighbors of its neighbors in a multi-dimensional interconnection of nodes. As before, when a node “turns off (white)” all its neighbors “turn on (red)”. With n = 4 the figure represents a 4-D (D1, D2, D3, Dn) interconnection of nodes with 8 possibilities at each node clearly depicted. (If Dn represents time the figure may represent a 4-D space-time manifold). (I built this network and it works as described).

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See animation. (A 1-D (1-dimensional) interconnection of nodes offers to the observer a paradoxical context with 2 possibilities at each node (2 neighbors); a 2-D interconnection of nodes, like the one we have discussed earlier, offers at each node 4 possibilities (4 neighbors); a 3-D offers 6; a 4-D offers 8; and an n-D offers 2n possibilities. (A 0-D offers none).) To contemplate more than four dimensions the reader must imagine or draw the additional nodes and their interconnections to the node at the center, between D3 and Dn, and between –D3 and –Dn, as suggested in the figure. Notwithstanding all this increase in complexity, an unimpeded network of individual elements still oscillates no matter how complex the nodes, their signals, or their observed behavior, and no matter how many dimensions involved in their interactions. http://bcl.ece.illinois.edu/Uribe/English/Introduction.htm

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The essential properties of the 2-D network have not changed: it can take any shape, its activity has no borders, any activity leads to further integrated activity, it resists local and temporary damage, it may interact with other similar networks, and major or permanent damage may disintegrate the network’s activity as an oscillating entity. If ants lose their “language” (signals between nodes) the anthill’s activity disintegrates as an entity. The same will happen to bees and their beehive. And so it will happen to all social organisms (including humans) and their societies, if they lose their “language”. Notice, however, that for a complex set of nodes such as humans in society, a precise and/or limited “language” such as that of ants or bees, implies already a loss. A complex individual, already an entity in itself and not totally subservient to a society (such as an ant in an anthill, a bee in a beehive, etc.), requires a community of complex individuals that will interact with the richness and flexibility necessary to achieve and preserve the best possible life for every individual in the community. Unfortunately most human societies organize into rigid hierarchies that require the predictability (triviality) of their members who will rapidly lose the richness and flexibility of their interactions, reducing them to trivial talk, no different than the “language” of ants or bees. A society may develop, but not of humans. Hierarchies replace thinking and conversation with rituals, secular or religious, where neither thinking nor conversation takes place. This reveals societies uneasy about the present, with longings for a primitive past and with forebodings of a future without humans. Relaxing the arbitrary distinctions necessary to establish and maintain hierarchical societies, to the point of eliminating the hierarchies, will accordingly allow the richness and flexibility of interactions to recover, and thinking and conversation to flourish again. Consider the network of oscillators as a community of observers with a non-hierarchical activity. Consider the perturbations that affect this activity without disintegrating it, but that may constitute stimuli for unpredictable conflicts. The flexibility of the nonhierarchical activity allows it to incorporate permanent conflicts in a new dance (oscillation) or resist passing conflicts and recover its original dance. A non-hierarchical community of individual observers does not require rigid distinctions and, therefore, will overcome otherwise insoluble conflicts. Paradoxical reasoning An observer reasoning logically does not welcome paradoxes. This observer, rejecting a priori most possibilities, deems paradoxes as erroneous reasoning. Therefore, an observer reasoning logically considers “logical reasoning” or “paradoxical reasoning”. For an observer reasoning paradoxically all possibilities count, blending into each other. Consequently, for an observer reasoning paradoxically, to reason “logically” or “paradoxically” blends into reasoning “logically and paradoxically”. A living organism produces and maintains itself as a closed paradoxical network of processes and components that distinguishes itself as an observer of an environment brought forth by the same distinction. A living organism, as a cell or as a multi-cellular organism, needs a favorable environment to survive. It may also play the role of a processor that, interacting with other similar living organisms, may form part of a close chain of processors which, given or making a favorable environment, may lead to a new living organism made of living organisms. To survive, this new organism must provide a favorable environment for the survival of the constituent organisms and for their replacement through reproduction or otherwise. The new state of affairs requires that the constituent organisms relinquish their unpredictability (their paradoxical reasoning) in favor of a predictability (a logical reasoning) demanded by the new organism. This happens, for example, to ants and bees as they submit to the anthill and beehive respectively, the new living organism. Returning briefly to the network of oscillators as a metaphor, each node, in isolation, oscillates unimpeded, enabled by its internal paradoxical loop. As part of the network, however, it must, due to the signals from other nodes, keep its oscillation in step, as the logic of the network demands. The activity of a nervous system, as that of other networks, requires the presence of interconnected oscillators (in this case, one or more neurons within one or more paradoxical loops) that generate and maintain this activity. Thus, the neurons form a network of oscillators called the nervous system. Otherwise, the nervous system’s activity would vanish and with it the many possibilities it offers to living organisms. The three-dimensional structure of the nervous system contains innumerable neurons with innumerable interconnections. Since every neuron connects to many other neurons, the nervous system, notwithstanding its three-dimensional structure, functions in a multi-dimensional fashion independently of the position of neurons and of the restrictions of 3-D space. This gives it the enormous potential to activate a great many paths, including those that involve the environment through effectors and sensors, essentially all possibilities, as in a paradoxical context, where an observer makes tentative distinctions as needed to interact with itself and its environment. Sensors and effectors provide the first tentative distinction: the observer distinguished from its environment, where itself and other observers dwell. An observer, with a nervous system as potentially complex as that of a human infant, emerges into a world already populated and shaped by other human observers. The nervous systems of children develop through interactions with their surroundings and with themselves considering all http://bcl.ece.illinois.edu/Uribe/English/Introduction.htm

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possibilities, including emotions, feelings and other observers, making full use of its effectors and sensors. The children’s nervous system activity offers a paradoxical context (all possibilities) within which their paradoxical and logical reasoning develops. Other observers, some indifferent, some caring, will guide the children’s exploration of their world; some will stimulate their logical reasoning with a restricted view; others will stimulate their paradoxical reasoning with all its possibilities; many will attempt to instruct them on how they see the world. All will influence the children, succeeding in different degrees. A fortunate child will keep its paradoxical reasoning alive and so will contemplate all possibilities in a paradoxical context within which, through independent thinking, will make tentative distinctions as needed. This will lead to a nervous system that maintains its original curiosity, inquisitiveness and ability to exercise independent thinking during the whole life of this human observer. Such an observer will not take the society of humans for granted and will contribute wisely to its improvement without preconceived ideas, prejudices or dogmas that may only arise from logical reasoning alone. A less fortunate child will inhibit its paradoxical reasoning in favor of logical reasoning, developing a nervous system that will lose its original curiosity, inquisitiveness and independent thinking. At best, this child will grow into an indifferent member of the society of humans, one that will instruct rather than educate the young. An unfortunate society with most members immersed in logical reasoning will succumb to the recursion already mentioned in the preface. Soon after their early infancy humans also develop the capacity to reflect upon their actions and thoughts. An unfortunate society inhibits this development through arbitrary hierarchies that limit the possibilities of the nervous system and soon most of its members lack this capacity and live totally unaware of this vacuum within others and within themselves. Rather than relying on logical reasoning and on searching for a “truth”, the Tractatus proposes to rely on paradoxical reasoning and on exploring all the possibilities; thus, logical reasoning appears under a new light. As with paradoxes, no observer may “explain” the Tractatus or any of its propositions without trivialization and loss. The propositions of the Tractatus do not say, teach or explain; they show. They invite observers to elude the comforts of trivialization, to explore and increase, through education, the alternatives, to blend paradoxes and logics, and to elude the instructed distinctions. To accept this invitation requires courage because the Tractatus destroys many cherished notions and habits, tearing away from contemporary “civilization”, forms of life and language.

Tractatus

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Contents

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TRACTATUS PARADOXICO-PHILOSOPHICUS 1

Postulate nothing: no observer, no distinction (e.g., object, event), not even dimensions (e.g., space, time).

1.1

Processes: consider changes (not towards the same), transformations (towards the same but different) or computations (changes or transformations in symbolic structures).

1.2

Recurrence: consider processes that continuously interact, changing, transforming or computing themselves.

1.3

Organization: consider a network of interacting processes.

1.4

Open Organization: consider an organization that does not close on itself so that it cannot maintain the activity of its processes.

1.5

Closed Organization: consider an organization that closes on itself so that any activity among its processes leads to further activity among its processes.

1.51

For the activity of a closed organization, “inside” or “outside” blend into “inside and outside”, leaving no room for “inputs”, “outputs”, “time”, or “space”.

1.52

A closed organization maintains its activity, but it does neither define nor maintain itself (its processes).

2

Organizationally closed organization (self-organized organization): consider an organization that recurrently defines and maintains itself.

2.01

This organization closes on itself so that its processes continuously regenerate the same network of processes.

2.02

This organization defines itself as a dynamically stable unity called Organizationally Closed Unity.

2.03

From the perspective of an organizationally closed unity, “inside” or “outside” blend into “inside and outside”, leaving no room for “inputs”, “outputs”, “time”, or “space”.

2.1

Self-organization: consider the recurrent regeneration of processes that allows organizationally closed unities to continuously change, transform or compute themselves, thus maintaining their organizational closure.

2.11

Since processes and open and closed organizations neither define nor maintain themselves they may only form, inextricably, part of organizationally closed unities.

3

Niche: an organizationally closed unity specifies a possible domain of interactions (shared processes) with its own and other organizations and processes such that without this domain the unity disintegrates.

3.01

Call this domain the niche of the unity.

3.02

The unity shares processes with its niche.

3.1

Cognitive domain: consider the niche and all other intersections of an organizationally closed unity with other organizations and processes.

3.11

The unity shares processes with its cognitive domain.

3.2

Interaction: consider the activity of the processes shared in the intersection of the cognitive domains of one or more organizationally closed unities.

3.3

Perception: consider the activity within the closed organizations that form part of the cognitive domain of an organizationally closed unity.

3.4

Distinction: consider the intersection of a closed organization with one or more processes, thus separating them from their background (other processes).

3.5

Cognition: consider the generation of new closed organizations that share processes with and expand the cognitive domain of an organizationally closed unity.

4

Observer: consider an observer as an organizationally closed unity that shares processes with its cognitive domain.

4.01

An observer perceives, distinguishes and knows within its cognitive domain.

4.1

The cognitive domain of an observer may share processes with the cognitive domain of another observer, such that:

4.11

The observer may perceive, distinguish and know the other observer, which may perceive, distinguish and know the first observer.

4.2

Two or more observers may interact through their cognitive domains forming open organizations, closed organizations and even organizationally closed unities, all made of observers.

4.3

Trivial: consider one or more observers that respond predictably to stimuli.

4.31

Non-trivial: consider one or more observers that respond unpredictably to stimuli.

5

The logical perspective: from this perspective one or more observers distinguish an organizationally closed unity from its

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cognitive domain, thereby adopting the logical dichotomy: the distinguished organizationally closed unity or the distinguished cognitive domain, one or the other. 5.1

For these observers, dimensions (e.g., space, time) emerge together with this distinction.

5.11

So do a processor (the distinguished organizationally closed unity) and an environment (the distinguished cognitive domain).

5.12

For these observers, however, these distinctions appear as “discoveries” (of dimensions, processor and environment) to share with other observers adopting a logical perspective, in a world a priori “out there” and as free of paradoxes as possible.

5.2

If these observers attempt to “explain” the processor, it will appear to them as an open organization (with inputs, outputs, divisions and parts) made of processes (events in time) that produce components (objects in space), but no longer organizationally closed.

5.21

The organizations that constitute the environment of the processor also appear open, with outputs and inputs that match the inputs and outputs of the processor.

6

The paradoxical perspective: from this perspective, one or more observers do not distinguish the organizationally closed unity from its cognitive domain such that the unity and its cognitive domain appear to these observers as a paradoxical continuum or as a paradoxical context.

6.01

For these observers, dimensions, processor and the environment vanish.

6.1

Since a paradoxical perspective implies a paradoxical and logical perspective, these same observers may make tentative distinctions in this paradoxical context as attempts at distinguishing a world “in and out there” to share, at least in part, with other observers.

6.11

This world “in and out there” welcomes paradoxes.

6.12

The paradoxical context (the unity and its cognitive domain) remains untouched and ready for new attempts.

6.2

Paradoxes (paradoxical perspective): consider self-referential sets of different, even conflicting, possibilities such that they blend into each other dissolving their differences and conflicts.

6.3

Logics (logical perspective): consider non self-referential sets of conflicting possibilities that exclude each other without solving their differences and conflicts.

7

An observer observing itself: this leads to the following dilemma:

7.01

From a logical perspective, an observer may observe itself, either at the same location but at different instants (emergence of time), or at the same instant but at different locations (emergence of space).

7.1

An observer observing itself at the same instant and location (a paradoxical, unpredictable observer) reveals a paradox with no logical solution.

7.2

This observer offers a paradoxical context from where the same or other observers, adopting a logical perspective, may extract or deduce distinctions, and then more distinctions from those distinctions treated as new paradoxical contexts so that the world “out there” for these observers slowly emerges.

7.3

The logical observer: consider an observer that adopts only a logical perspective and hence only extracts or deduces distinctions from a paradoxical context and allowed by the logic chosen, such as considering other observers as paradoxical or logical.

7.4

The paradoxical observer: consider an observer that adopts a paradoxical and logical perspective and makes tentative distinctions in a paradoxical context considering all possibilities, such as considering other observers as paradoxical and logical.

8

Living organism: consider an organization that produces and maintains itself as an organizationally closed unity that defines its cognitive domain and that:

8.01

as a paradoxical observer interacts with, and makes tentative distinctions in its own paradoxical context (the living organism and its cognitive domain).

8.02

as a logical observer distinguishes itself from its own cognitive domain as a processor whose space and time emerge together with this same distinction and from which it extracts or deduces further distinctions.

8.1

A living organism, as a paradoxical observer, interacts with and tentatively distinguishes the self-producing organization of a living organism maintaining its organizational closure through a closed network of processes (tentative events in time) that produce components (tentative objects in space) and that continuously regenerate the network of processes.

8.2

A living organism, as a logical observer, may extract distinctions from a paradoxical context, but may not act as a paradoxical observer.

8.3

A living organism, as a paradoxical observer, may act as a paradoxical observer and as a logical observer.

8.4

A living organism, even without a nervous system, defines and supports its own cognitive domain and cognition.

9

Nervous system: consider one or more closed organizations that intersect with a living organism and its cognitive domain,

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expanding it. 9.1

A logical observer distinguishes the nervous system only within the living organism and interprets sensory surfaces and effector surfaces as “inputs” to and “outputs” from the nervous system that match “outputs” from and “inputs” to a world “out there”.

9.2

A paradoxical observer interacts with and tentatively distinguishes the activity of the nervous system as “nerve” impulses that encode only “how much” not “what” the living organism “perceives”.

9.21

Since everything “perceived” translates into nerve impulses, the nervous system does not discriminate (distinguish) between impulses coming from an “outside” world and those originated “within” the nervous system (“inside” or “outside” blend into “inside and outside”).

9.22

For this same observer, the encounter with other observers triggers the invention of a tentative world “in and out there”.

9.23

While some of these observers adjust, share, and thus “confirm”, tentatively the invention, others do not.

10

Environment: logical observers distinguish the intersection of their cognitive domains as a common dwelling and call it their environment.

10.1

The distinction of an environment appears to these observers as an invitation to extract or deduce further distinctions.

10.12 These further distinctions appear to these observers as processes (events in time) that produce components (objects in space) forming open networks of processes and components that exclude these and other observers. 10.2

Language and communication emerge in this way from the activity (of processes) in the nervous system and thus, the logical observer invents a world “out there” independent of the observers.

10.3

Since processes, components, open networks of processes and components, and an environment neither define nor maintain themselves, logical observers may only distinguish (extricate or deduce) them from organizationally closed unities (paradoxical context), which will appear open and no longer organizationally closed (nor paradoxical) for these observers.

10.4

Paradoxical observers interact with and tentatively distinguish an environment as a world “in and out there”, through which they may, with some difficulty, relate to logical observers.

11

Complex: consider paradoxical observers interacting with self-organizing, unpredictable, paradoxical, non-trivial environments that include the observers, thus eluding trivialization.

11.01 Interaction: any limit between the “distinguished” and its “background” vanishes for one or more of these observers interacting with themselves or socially. 11.1

Simple: consider logical observers distinguishing non-self-organizing, predictable, logical, trivial environments that exclude the observers, thus embracing trivialization.

11.11 Distinction: a clear limit between the “distinguished” and its “background” appears essential for these observers in social intercourse. 11.2

Observers cannot trivialize organizationally closed unities.

11.21 Any attempt to trivialize them will either fail or destroy (loss of organizational closure) the organizationally closed unities (also a failure). 11.3

Observers cannot trivialize a complex environment without destruction.

12

Mind: consider the activity of the nervous system that encompasses thinking, perceiving, emotions and feelings.

12.1

Consider emotions and feelings as the paradoxical activities of closed organizations (that cross and include the sensory and effector surfaces) inside and outside the nervous system of a paradoxical observer.

12.11 Therefore, emotions and feelings thoroughly escape the logical observer since the logical observer contemplates only inside or outside the nervous system. 12.2

Just as in the network of oscillators discussed in the Introduction, where external stimuli may drastically reduce the possibilities (number of choices available), so may suitable stimuli applied to the nervous system stunt, in different degrees, its potential for emotional, physical and intellectual expressions.

12.21 The resulting damage, temporary or permanent, often not obvious and sometimes desirable as in a hierarchical environment, where moderate or no thinking at all constitutes a requisite for membership.

13

Language-games: imagine predictable and unpredictable games that observers play, logically, inside or outside and, paradoxically, inside and outside their nervous systems, thus defining their forms of life.

13.1

Meaning: consider the uses that observers give to words in language-games.

13.11 If the language-games change or vanish, so do the meanings of words used by observers. 13.2

Language: consider the language-games trivialized (made predictable) by logical observers, where the meanings of words soon evaporate.

13.3

Explanation: consider the attempts to trivialize a language, e.g., using it only to follow rules while striving for a “logically perfect language”.

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13.4

Communication: consider any attempt to use a trivialized language among observers.

13.5

Thinking: consider the activities involving the nervous system of a paradoxical observer, including emotions and feelings, and thus offering new language-games to the observer.

13.6

Conversation: consider the activities involving the thinking of one or more paradoxical observers, thus offering new language-games to these and other observers.

14

Groups: consider observers interacting through their cognitive domains with other observers forming networks of observers and thereby creating organizations of different sizes and forms, such as open organizations, closed organizations or even organizationally closed unities, all made of observers.

14.01 These groups, originally undistinguished by their members, remain as such for most of their members. 14.1

Integration: members must follow the rules to define and maintain the group.

14.11 Disintegration: groups, whose members do not follow the rules, fall apart. 14.2

Logical observers adopt or reject the rules of the group through language, explanation and communication thus participating in trivial language-games and forms of life deprived of meaning and sense.

14.21 Paradoxical observers think and converse generating paradoxical contexts that lead to new meaningful and sensible language-games and forms of life. 14.22 Consequently, logical observers tend to make the group and its rules rigid and structured while paradoxical observers prefer to make them flexible and unstructured. 14.3

If the activities of the members surpass certain complexity, paradoxes may arise among the rules of their groups.

15

Following rules: consider logical observers merely rejecting or adopting the few distinctions used as rules for their groups and those used to follow rules.

15.01 Since these observers only make distinctions as in following or not following rules, appropriate rewards or punishments can easily entice these and other observers into following rules and transform their groups into hierarchies. 15.02 These observers reinforce their following of rules through language, explanation and communication and with a hierarchical organization for their groups. 15.03 Paradoxical observers do not, and prefer to think and converse. 15.1

Since these rules constitute the essence of their hierarchies, logical observers often exaggerate their relevance and use them, for example, in “education”, with regrettable consequences.

15.2

Logical observers follow rules and pursue the goals of their hierarchies without regard for other observers, young observers included.

15.21 These observers develop a need to protect themselves from thinking, conversation, self-reference, paradoxes, uncertainty and unpredictability. 15.22 Therefore, they nourish a conspicuous ignorance about these “unconceivable” concepts.

16

Pondering rules: consider paradoxical observers thinking and conversing about rules, thereby stimulating other observers to do the same.

16.01 These observers interact and make tentative distinctions as in following rules and not following rules. 16.02 These observers do not form hierarchies; they rather invent and participate in language-games with other rule-pondering observers. 16.1

Rule-following members protect their hierarchies from disintegration by maintaining the number of rule-pondering members as low as possible.

16.2

Rule-pondering observers, however, occasionally manage to join hierarchies of rule-following observers, attempting to make their members think and converse.

16.21 If partially successful, one or more members will leave the hierarchy and will contemplate thinking and conversing. 16.22 If successful beyond all expectations, the hierarchy will disintegrate. 16.23 If unsuccessful, the intruding observer risks an unpleasant expulsion such as would happen to a teacher caught educating his/her students.

17

Hierarchies: consider open organizations with two or more levels made of one or more observers.

17.1

For rule-following observers, the hierarchy follows a simple logic, a consequence of logical reasoning: a member who follows the rules expects promotion and praise; a member who does not, expects demotion or expulsion.

17.11 This simple logic, swiftly assimilated by rule-following members, implies for them that rules only flow (apply) from high to low so that self-reference (and paradoxes) cannot happen. 17.12 However, hierarchies must intersect with closed organizations to maintain their activity; for example, without the following loop hierarchies disintegrate: 17.2

“Rewards” (wealth, power, praise etc.), bestowed on those towards the top; “punishments” (enslavement, demotion or

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expulsion, etc.), bestowed on those towards the bottom; these latter, forced to close the loop that chains them, supply with their labor the “rewards” for those towards the top. 17.21 Other recurrent loops give hierarchies flexibility, but also remain unconceivable to rule-following members. 17.22 As hierarchies grow, these loops weaken and break; rigidity or disintegration result together with the silence of rulepondering members. 17.3

Narrow goals, promotions decided from above and blind loyalties from below inevitably promote the most narrow-minded members towards the top.

18

Hierarchies in society: societies organize within a mixture of closed (non-hierarchical) and open (hierarchical) organizations.

18.1

Within hierarchies only few enjoy the product of the labor of the majority, who toils for survival and relentlessly loses hope of breaking the chains.

18.11 This and the breeding of rule-following observers within this majority ensure the survival, growth and propagation of hierarchies, an unhealthy recurrence that leads to a static stability difficult to disrupt. 18.12 Hierarchical societies replace their long-term goals with narrow short-term goals, similar to the “profits at all costs” of corporations, thus stimulating all their members to abandon their most cherished interests and place business above all. 18.13 In this context, human diversity of interests, curiosity, inventiveness, creativity, ingenuity, emotions, feelings, etc., decline to the point of extinction, so that something called “human” replaces human, with considerable loss. 18.2

Meanwhile, hierarchies take over one or more governments, dictate their own laws and logic, and make their actions (deemed always positive by propaganda and deception) accountable to none.

18.3

Without eliminating the hierarchies, every attempt at improving the life of humans has ended and will end in a failure.

19

Instruction: consider the members of a hierarchy “learning” to follow passively its rules.

19.1

Social relationships among rule-following observers need the predictability of observers with respect to each other.

19.11 Instruction makes observers predictable. 19.2

Instruction reduces the number of possibilities (choices) available to observers, fostering the loss of meaning among observers and their environments.

19.21 For example, rule-following observers call “democratic” and “free” a nation ruled by corporations; “university” and “hospital” institutions run as corporations; “professors” and “physicians” those who neglect their declared vocation to participate as rule-following observers in corporate activities inside and outside their institutions; etc. 19.22 Meanwhile democracy, liberty, university, professors, physicians, etc., and their meanings, cease to exist for these observers and for those who follow them. 19.3

Instruction stimulates social knowledge, explanation, communication, logic, predictability, folly and illegitimate questions, questions to which the questioner already knows the answers.

20

Education: consider observers attempting to develop thinking and conversation and thus making themselves unpredictable with respect to each other.

20.01 Education improves the ability to offer tentative distinctions and interactions, increasing the number of choices available to observers. 20.02 All the observers can pursue and achieve an education as long as they avoid competition, since it begins by excluding thinking and soon it omits conversation. 20.1

Observers may educate themselves and stimulate others to do likewise, as long as they understand uncertainty as welcomed and unavoidable.

20.2

A non-hierarchical society breeds rule-pondering observers thus stimulating the generation of dynamic stabilities and instabilities and avoiding the dehumanizing static or dynamic stabilities, a healthy recursion.

20.21 In this context, human diversity of interests, curiosity, inventiveness, creativity, ingenuity, emotions, feelings, etc., flourish unrestricted. 20.3

Education stimulates individual knowledge, thinking, conversation, paradoxes and logic, unpredictability, wisdom and legitimate questions, questions to which none of the concerned knows the answers.

21

Idleness: contemplate the art neither of following rules nor of not following rules and the art of following rules and not following rules.

21.01 Education contemplates idleness to stimulate thinking and conversation among observers, and to nourish their original uncertainty and unpredictability. 21.1

Paradoxical observers welcome idleness and education, offer tentative distinctions (logic) and interactions (paradoxes), and do not form hierarchies.

21.2

A hierarchy welcomes neither idleness nor education.

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If observers ponder rules and attempt to think and converse they will find life difficult, if not impossible, within hierarchical societies.

21.31 These societies appear as prisons to observers in search of education and idleness.

22

“Reality”: consider a simple environment that, chosen (distinguished) by logical observers, excludes the observers.

22.1

From this point of view, “reality” should conform to some immutable pattern that will require neither more distinctions nor interactions nor choices.

22.2

However, every pattern adopted needs adjustments here and there to eliminate contradictions, to “solve” paradoxes, etc.

22.3

Since logical observers can neither adjust a pattern nor offer a new one, they attempt to induce or coerce reluctant paradoxical observers to do it.

22.4

Paradoxical observers either hide and isolate themselves or develop different avenues (e.g., philosophies, the arts, logics, mathematics, the sciences, etc.) to assuage the demands for a goal that they do not desire.

22.5

Invading hierarchies of logical observers under different guises make of these avenues instruments for instruction.

22.6

Many paradoxical observers surrender to these instruments and abandon their education, their curiosity, inventiveness, creativity, etc.

23

Searching for “Reality”: consider logical observers forming hierarchies to reach for “reality”.

23.1

However, these hierarchies make any decision from the “top” seem appropriate, since it elicits no resistance or criticism from “below” due to implicit or explicit intimidation from “above”.

23.2

Hierarchies stimulate irresponsibility, arrogance and slave holding towards the top and diligence, obedience and slavery towards the bottom.

23.3

Foresight, creativity and imagination vanish at all levels, making of these hierarchies a population of ants in an anthill, predictable creatures, and humans no more.

23.4

“Reality”, chosen (distinguished) towards the top of the hierarchy and accepted towards the bottom remains a firmly adopted delusion as any other unquestioned belief.

24

Tentative realities: consider paradoxical observers that choose (invent) many complex (self-organizing, unpredictable) environments that include the observers.

24.1

Tentative realities correspond to as many or more flexible, unpredictable environments as paradoxical observers involved.

24.2

These observers interact through the processes shared by their paradoxical contexts, defined by the observers and their cognitive domains.

24.21 They interact through tentative environments and playing tentative language-games. 24.3

Since organizationally closed unities define and maintain themselves, they appear to these observers as the only possible unities.

24.31 All the rest appears to these observers as a mere consequence of their activity: tentative environments, with all their tentative distinctions and interactions, offered by paradoxical observers to themselves and to others through education and rejected or adopted by logical observers through instruction. 24.32 All originates and ends in the observers (organizationally closed unities).

25

Propositions and distinctions: while using language, logical observers make distinctions, thereby attaching specific possibilities of truth (true or false), of value (good or bad), of inclusion (included or excluded), of logic (logical or paradoxical), etc., to propositions (including this one) and to sets of propositions (such as books, texts, etc.).

25.1

These observers explain and communicate among each other adopting or rejecting propositions about objects and events, morality, aesthetic, beliefs, etc., as if propositions mirrored a world “out there” (“reality”) separated from the observer of the world.

25.11 These observers adopt a language and theorize. 25.12 This leads to knowledge inspired by logical reasoning alone, to information, to certainty and to scientific understanding alone, to incomprehension and to dogmatism.

26

Propositions and interactions: while playing language-games, paradoxical observers treat propositions (including this one) and sets of propositions (books, texts, etc.) as paradoxical contexts for interactions, considering all possibilities.

26.1

These observers think and converse about tentative objects and events, tentative ethics, tentative aesthetics, tentative beliefs, etc., thereby offering propositions as paradoxical contexts for interactions, as if the world (tentative realities) beheld the observer of the world.

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understanding, to comprehension and to skepticism about logical reasoning alone. 26.2

For these observers any proposition must contemplate its counter-proposition so that proposition and counter-proposition blend into a paradoxical context where the observers make tentative distinctions.

26.21 The same applies to books, texts, etc.

27

Delusions: consider a belief that contradicts an accepted classification of beliefs into true or false.

27.01

Delusions do not affect paradoxical observers since they ponder and contemplate beliefs as true and false.

27.02

Delusions, however, affect logical observers since they only explain and communicate, do not ponder and consider beliefs as true or false.

27.021 Consequently, other observers (or themselves) may easily delude them, singly or collectively. 27.1

For example, the delusion of different observers sharing the same thoughts affects only logical observers who also suffer from similar delusions: that they can share their beliefs, dreams, imaginations, etc., as well as the same truth, the same religion, the same god, etc.

27.11

These delusions, harmless in the mind of one individual, can reach pandemic proportions when, stimulated by hierarchies, they invade the minds of many observers.

27.2

Deprived of an education, humans seek refuge in religion and/or rule following to avoid despair; thus they loose their diversity of interactions.

27.21

And societies replace their dynamic stabilities and instabilities with static stabilities without a future.

28

Humans in society: consider multi-cellular organisms such as ants or bees that ensnare the living cells that compose them; anthills and beehives, as new living organisms, trap the ants and bees that constitute them.

28.01 So it happens with the population of humans in society who increasingly serves the goals of entities made of ensnared, predictable and expendable humans. 28.02 These humans do not notice these changes. 28.1

Most, if not all, past and present societies of humans have used hierarchies, religion and all kinds of persuasion to keep their populations in check, thus reducing or suppressing thinking altogether, and fostering rule following.

28.11 This approach will lead, without doubt, to a new living organism that will ensnare everyone, including those who have proposed and support it. 28.12 As every living organism, the new organism will also encounter death in one way or another (including suicide) carrying everyone along. 28.3

Aware that hierarchies take away their humanity and also their lives, young minds must, with courage and caution, reject, and by all available means, prevent or dismantle hierarchical societies, corporations and institutions, beginning with those based on accumulated wealth.

28.31 This they can achieve by encouraging humans to think and converse, to change from rule followers to rule pondering observers.

29

Thinking and conversing: what observers may not explain or communicate, they may think and converse, e.g., they may:

1

Postulate nothing: no observer, no distinction (e.g., object, event), not even dimensions (e.g., space, time) ...

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