(Learning from not understanding)

Raymond Smullyan, Professor of Mathematical Logic and part-time magician, writes of an incident he experienced when six years old. It was so intriguing that the child would remember it for all of his life:

This is a paradox in the tradition of the Greek word (which means "conflicting with expectations"). It is a variant of the announced "surprise inspection" or "unexpected examination". One could find a similar pattern in a note you will read in a bus station, announcing that "The last bus of today will not come".

Philosophers, those people who love wisdom, proposed many paradoxes and akin logical "bugs" like aporias or antinomies. Psychologists in their turn found life abundant of "double binds", cognitive dissonance, and so many other blocks. Artists in their turn demonstrated to our eyes and fingers impossible perceptions "that can't be". Writers like Franz Kafka and George Orwell exposed the schizophrenia of totalitarian systems. Private and corporate lives are full of unavoidable absurdity, puzzles and intrinsic contradictions. Therefore, you may believe that I will write here to deplore paradox for its negative instances. However, my goal is paradoxically different.

The aim of the paper is to look at this disquieting field in a profitable way. I will not try to define precisely what paradoxes are. I observe that, quite often, one man's clear idea is another man's paradox. I do not even feel bound to consider exclusively "regular", traditionally recognised or logically credible paradoxes. I will not be analysing what is and what is not a flawless paradox. I will not (heaven forbid) try to solve paradoxes. I will inquire into the usefulness of things that act upon ordinary people's minds as if they were paradoxes.

The following will then be good enough for my definition: For this paper a paradox is something (a statement or a thought, an image, a question, an instruction, a dilemma, but also a situation, even a feeling) that "blows our mind".

The premises or perceptions leading to an experience of paradox are acceptable, my eyes cannot cheat me, and the reasoning appears to be sound and self-evident to my common sense and my intuition. It may even be compelling to logical thought. However, the meaning implied or the conclusion appear impossible. It had better be a joke. The feeling of paradox is most often irritating. It goes against my common sense. It undermines my faith. Some unquestionable values and deep beliefs, my very intellectual makeup must be threatened if I take this seriously. I feel tired to think further. I better laugh it away. Or I quit. I am so busy with other business.

However, in time, I learned something fascinating: This "paradoxical" gut feeling is always a symptom of touching a limit of my mind - a frontier or a foundation. The feeling of paradox is a "detector of the Unknown". It is then a priceless tool. The means to perceive what we do not know and cannot conceive are rare.

Let me recollect some other classical examples of paradoxes:

An example of paradoxical ruse:

The anatomy of a semantic paradox looks simple. It is a circle. A vicious circle. Like the legendary Ouroboros serpent, it swallows itself by the tail. It puzzles us like an engraving by Escher.

A good paradox creates its own world, impeccable in form, and then makes it impossible in meaning. Being self referential, it is waterproof to critical sense and to any external evidence.

The strongest paradox known in history is probably the one "of the liar": a correct statement that ends up in havoc: I read: "This statement is false." A medieval formulation of it is this imaginary argument between Socrates and Plato:

If this is true, it is false. If it is false, it is true. This is not normal. This is not what I learned in school. The disciplined mind needs to solve this.

My favourite example of a mild feeling of paradox is to tease you: "I will now create, because I please so, a piece of truth that I challenge you to refute if you can. 'There are only two kinds of people: Those who believe that there are only two kinds of people, and those who don't.'"

Let me point at this finding: we can create paradoxical experiences.

The reader may still wonder whether all these fallacies are worth considering, beyond sheer curiosity. I believe that the matter is more serious. Let me quote a few paragraphs from the autobiography of Bertrand Russell, an author of the monumental "Principia Mathematica". He relates how the paradoxes ended his "logical honey moon":

Let me conclude from this testimonial that paradoxes are a true challenge to Logic in general and not only to the naive occasional thinkers.

With this, I will stop discussing the form and cultural calibre of paradox.

In daily life, paradox is often an illness to cure.

As a bug in the mind, paradoxes are frequently the very form in which difficult problems are created and in which wrong solutions induce and perpetuate the crisis they are meant to prevent or resolve. Many self-perpetuating organisational illnesses can be identified in such dysfunctional blind spots. The study and the diagnosis of paradox are a gold mine of original, often paradoxical solutions to blocked situations and impossible problems.

This extension of paradox to "everything experienced as a paradox" takes the discussion out of philosophy, into the practical province of action in everyday life.

Parents, teachers, lovers and leaders sometimes give paradoxical instructions that paralyse and beat the mind: "Be spontaneous!" "Be natural!" "Be yourself!" "Go to your room and don't come out until you have a smile on your face!" "Don't take notice of my presence!" "You should trust me!" "Why don't you want to love me?" "I want you to love me of your own free will!" "Discipline must be freely accepted!" "Don't think evil!" "Please ignore my previous mail". Orders of this kind are impossible to obey from the very moment they are uttered. They create "double binds". This is a provocation to madness or at least, to duplicity and double-talk. These "games of not playing a game" create the problem they pretend to prevent. The skill to detect such paradoxical orders allows one to cope with them or to evade them.

Image paradoxes are coercing the spectator (or the victim) to perceive things that can't be, according to common sense; Impossible triangles, water flowing down - upwards, hands drawing each other. I use such and other illusions to help people learn that seeing is not always believing. There are few means to persuade people to become more critical with the obvious.

Situational and organisational paradoxes are less studied scientifically (or I do not know enough about their study). Some of them may stem from the self-fulfilling prophecy or compelling paradigm of a founding father that will confirm itself for a long time before being exposed as Utopia. Others are, I think, "ways to hell paved by good intentions", group-think and perverse effects of cultural bias in big organisations. A whole political system can become one in which, as my mother - a historian - used to say, even "the past is most difficult to foresee" and contradiction is carefully cultivated between thought, speech and action. In such worlds good is bad, truth is lie, ugly is beautiful and everybody is born a sinner and a suspect doomed to prove his innocence forever. Orwell and Kafka describe such tyrannies at their extreme.

We need "organisational ghost busters" specialising in the dangerous activity of exposing sick "visions", institutional blindness, fanatic optimism, lethal allegiances, altruistic money-making, shallow strategies and corporate schizophrenia of various other kinds.

Let me stop here the list of evils generated by paradox.

The positive question starting this paper was: "Why is Paradox so fascinating?" It is time to propose my answer: "Because it is a master tool". I will try to explain this through my own way of rediscovering and using it.

Paradox is fascinating because it can be wonderfully useful. It makes reason bend beyond itself.

I understood as I kept teaching and growing older that, in everyday life, paradox is not only a "bug in the mind" but also a Master tool.

Paradox is a teaching instrument.

Carefully administered, its puzzlement enables me and the people I work with, to detect things beyond the field of what we already conceive. "Just as sight recognises darkness by the experience of not seeing, so imagination recognises the infinite by not understanding it." (Proclus, 412-485 AD)

I realise that this is quite a strong statement. I do not want to appear mystical. On the contrary, paradoxes allow a rational approach to our inner limitations caused by ready-judged ideas, stubborn beliefs about undecidable issues, unshakeable values and other convictions, too deep or too obvious to be a likely subject of critical discussion.

One of my favourite classroom koans is to lure the participants into an exercise of inventing things impossible to imagine. Believe it or not, wise people do fall into this trap and, more important, discover from it, something they neglected.

The unease and the confusion of paradox are privileged ways of bordering what we do not understand. A Zen saying reminds that "the foot feels the foot, when it feels the ground". In the best Socratic tradition the intuition of being helplessly ignorant where I had no doubt, allows me to open and learn new things.

The exasperation of Paradox not only challenges people to grow but also gives them a hint where to go. It points at a frontier, a conceivable limit of the unknown, of the impossible and of the necessary. The inevitable discussion after my koan is about realms, rules and definitions, about what is possible and impossible. Existence, reality and the limits of the mind suddenly intrigue most un-philosophical people. They sense something we all learned to forget: that in the mind, protected with question marks, quotes, parenthesis and attention marks, one could transgress and reframe almost anything. Nothing is impossible to imagination and to thought if there are no rules and no limitations. Even error should not be ruled out, as it could be productive. Much more than this, it may be that part of this imagining and trespassing into the unknown and into the impossible, can be tested for feasibility and transferred into real life.

Paradox is an instrument for creating change, newness and surprise.

This is why I am so fascinated with Paradox.

George Bernard Shaw expresses best this enchantment in a phrase I am never tired to quote: "People see things and ask: Why? I dream of things that never where and ask: Why not?" In this perspective paradox is an instrument of exploding the size of freedom by multiplying choices in the mind.

Change is something else.

Things that are truly new appear paradoxical. I believe that this is because they are "out of the system" of our current understanding. On the other hand, to navigate change and to create newness one must be at ease with the unfamiliar and the contradictory. Change agents must learn to live with the unknown untamed for a while. To cope with the never-ending surprise of our world, familiarity with paradox is a necessary school of Change. Someone mentally accustomed to live with vagueness, complexity, ambiguity is better prepared to produce newness and to cope with newness.

I derive from this belief a practice of strategy in the terms of James Carse who suggests "preparing for surprise", to complete our customary "preparing against surprise". I will even consider another class of creative strategy: "preparing the surprise".

Learning to live with things unknown instead of compulsively trying to reduce Newness to something already controlled is a key to change management.

I found useful to apply this tool in change management consulting and in adult education. I also found that far from being my invention, this artifice is ancient. For several thousands of years the Sufi, Tao and Zen methods were perpetuated in apprentices' minds by means of amazing allegories and unanswerable questions. I guess that the Greek sophists, Heraclitus, Socrates and the Talmudists did the same.

By using paradox I take issue with a very respectable attitude. A scholar like R. M. Sainsbury presents only three possible treatments of a paradox: "(a) Accept the conclusion ... but explain why it seemed unacceptable; (b) Reject the reasoning as faulty; (c) Reject one or several premises, explaining why they seemed acceptable." As an uninhibited pragmatist and "psycho-logician" I need to observe three more possibilities: (d) Misunderstand or refuse to consider the statement altogether; (e) Live humbly or peacefully with the paradox unresolved; (f) Transcend or transgress the frame of reference given, the one that makes the situation impossible. This last one is a method of the Zen masters.

The Zen teacher formulates koans, questions impossible to answer. The desired solution is (maybe) to gain autonomy from the question itself. It is formulated with the intention to exasperate the learner to such an extent that he would in the end break the "catch" in a sudden illumination that all the rules can be disobeyed and transgressed. This is, in intellectual terms, a satori.

Now let me end without an end, by a touch of vagueness. I will let the reader conclude all these thoughts about how we learn from what we do not understand while I only offer an obscure story.

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Hughes, P., Brecht, G., VICIOUS CIRCLES AND INFINITY, Penguin Books, Harmondsworth, 1984

Laing, R., D., Knots, Tavistock, London, 1970

Plato, Parmenide, in Platon, Oeuvres completes, II, Gallimard, Bourges, 1990

Tchouang-Tseu, L'Oeuvre Complete, in Philosophes Taoistes, Bibliotheque de la Pleiade, NRF Gallimard, Bourges, 1985

Reps P., Zen Flesh, Zen Bones, Penguin Books, Harmondsworth, 1986

Russell, B., The Autobiography of Bertrand Russell, Unwin Books, London, 1975 (pp 150, 154)

Sainsbury, R.,M., Paradoxes, Cambridge University Press, Cambridge, 1988

Smullyan, R., WHAT IS THE NAME OF THIS BOOK?, Penguin Books, Harmondsworth, 1985

Watzlawick, P., Weakland, J., H., Fisch, R., CHANGE, W.W. Norton & Company, New York, 1974