The Inductive Leap

Bill-newby L. G. William Chapman, B.A., LL.B.

The real danger of an inductive leap is not that there might in fact be a black swan; rather the danger is that we imagine things that don’t exist.  It is one thing to hope for the best; it is quite another to imagine only the worst.  How we get to the unfortunate second alternative (imagining only the worst) is both understandable and excusable.  Essentially we prefer to rely upon a quick assessment of a situation rather than a detailed analysis of it, a posture which is arguably natural and healthy. There is, after all, considerable support for the “fight or flight” theory. Besides, thinking is hard; instinctive reaction is by comparison conveniently easier. But just as a dog can mistakenly flee from the pop of a balloon, so too can we become needlessly alarmed by an inconsequential disturbance in our life.  Just because our instinct causes us apprehension doesn’t mean we’re right to be worried.

Thanks to the discovery in 1697 by the Dutch explorer Willem de Vlamingh of black swans in Australia, we’ve learned to mistrust extrapolation from generalizations. That is, we’ve learned to be cautious about extending the application of a conclusion (especially one based on statistics) to an unknown situation by assuming that existing trends will continue.  Nonetheless we succumb to the influence of buzz words or other indicia of panic to which we are accustomed by previous experience. It is hard to find fault with this reaction because it has all the force of background and practical knowledge.  It would be equally unfair to suggest we only expect disappointment in life. Being trepidatious is not the same as being pessimistic; caution should not be confused with despair.  There is however a lesson to be learned; and that is that idle speculation can be misleading.  If we’re going to draw hard conclusions we need hard facts.  Too often we sacrifice one for the other – we throw aside the evidence in preference for a quick and dirty verdict.

If one proposes to be a rational being it requires training of the mind.  Given the standard of universal education it would be absurd to suggest that any particular class of person is less suited than another to clear thinking.  What is however clear is that most of us are by nature disinclined to analytic thinking. It is a rigorous undertaking, one which forces us to contemplate alternatives (a prospect which frequently takes the wind out of the sails of a thesis).  At the very least logical thought requires dissection of a problem.  Breaking up a problem into its constituent elements not only facilitates handling of it, it further obliges the analysis of those elements.  If nothing else this retards the process of examination and inhibits hurried conclusions.  There persists the possibility of misunderstanding and misinterpretation which of course contaminates even the most prudent scrutiny.  Oddly it is the hint of doubt (instinct) which may in such instances trigger the need for professional advice which will hopefully advance the correct evaluation.

Even if one feels that the critical analysis of a particular set of facts is beyond one’s capacity, there is a fall-back situation which may be as relieving.  It requires a more global assessment of one’s situation.  One might for example take the high-level view that there is nothing one can do to alter either the past or the future, that one can only live in the present.  Assuming that is so, the quality of a particular problem can only be usefully managed by confronting it.  To impart unrestricted speculation to the problem does nothing to advance its resolution.  It is frequently attractive to indulge oneself in endless obfuscation but this only builds on the shaky foundation of the initial reaction.  If unsure it is better to resist supposition.  While this may seem to be a fainthearted approach it nonetheless dilutes wild surmise. Oh, and if all that seems far too demanding, remember to add another of those illusive human virtues – patience!

Black and white swans

Deductive Reasoning:
General to Specific

In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class. For example, “All men are mortal. Harold is a man. Therefore, Harold is mortal.” For deductive reasoning to be sound, the hypothesis must be correct. It is assumed that the premises, “All men are mortal” and “Harold is a man” are true. Therefore, the conclusion is logical and true.

Inductive Reasoning:
Specific to General

Inductive reasoning is the opposite of deductive reasoning. Inductive reasoning makes broad generalizations from specific observations. “In inductive inference, we go from the specific to the general. We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory. Even if all of the premises are true in a statement, inductive reasoning allows for the conclusion to be false. Here’s an example: Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald. The conclusion does not follow logically from the statements.”

An inductive argument is an argument that is intended by the arguer merely to establish or increase the probability of its conclusion. In an inductive argument, the premises are intended only to be so strong that, if they were true, then it would be unlikely that the conclusion is false. There is no standard term for a successful inductive argument. But its success or strength is a matter of degree, unlike with deductive arguments. A deductive argument is valid or else invalid.

The phrase “black swan” derives from a Latin expression; its oldest known occurrence is the poet Juvenal’s characterization of something being “rara avis in terris nigroque simillima cygno” (“a rare bird in the lands and very much like a black swan”; 6.165). When the phrase was coined, the black swan was presumed not to exist. The importance of the metaphor lies in its analogy to the fragility of any system of thought. A set of conclusions is potentially undone once any of its fundamental postulates is disproved. In this case, the observation of a single black swan would be the undoing of the logic of any system of thought, as well as any reasoning that followed from that underlying logic. The black swan theory or theory of black swan events is a metaphor that describes an event that comes as a surprise, has a major effect, and is often inappropriately rationalized after the fact with the benefit of hindsight.

While most people are happy with thinking about what they do know, Taleb takes great pains throughout The Black Swan to try and focus his readers on what we don’t know — which is far more relevant to the black swan problem. Unpredictable events by their very nature are things that lie outside our common experience and happen precisely because of this. Therefore a good appreciation of our own ignorance and a full rationalization of where our knowledge ends is essential in dealing with (although not necessarily avoiding) black swan events.