I. INTRODUCTION

In the second edition of his book The Black Swan: The Impact of the Highly Improbable, Nassim Taleb provides a list of the errors that his readers have often made in attempting to understand the message of the book.[1]  The list contains 13 "main errors."  That the list could be so long is a testament to the fact that the philosophy of science in general, (and epistemology and probability in particular), are subjects which are extremely complicated, nuanced, and difficult to grasp.

Another reason why people so easily misinterpreted the message of The Black Swan, however, is the fact that Taleb makes these already complicated philosophical subjects even more opaque and difficult than they need to be.  Taleb is certainly entitled to present his ideas in any way that he wishes, but it is hard to blame his readers for falling victim to errors that could have been avoided if the message was presented more plainly and cleanly.

In the interest of clarifying and refining the message of The Black Swan, I offer in this article as an alternate statement of what I consider to be the main message of the book.  I do not pretend to speak for Taleb himself, and I do not want to be interpreted as authoritatively "translating" his message into plain English.  Instead, what I am doing here is making an argument along the lines of the one contained in The Black Swan in a way that I think is both clearer than Taleb's original formulation and more forceful from a philosophical perspective. 

If this sounds presumptive of me, I hope to show that my alternate statement is implied by Taleb's own postscript essay that was added to the second edition of the book.  In other words, I believe that my argument here is one that Taleb himself could have made in the second edition of the book. 

In the following section I lay out my alternative statement of the central message contained in The Black Swan.  I hope you will agree that, while I have considerably pared down Taleb's central message, nothing of real substance has been lost.  

II. THE CENTRAL MESSAGE OF THE BLACK SWAN: PROBABILITY IS SUBJECTIVE AND SHOULD NOT BE TAKEN TOO SERIOUSLY

That's it.  This simple sentence is the central message of the entire book. 

III. WHY MY ALTERNATIVE STATEMENT OF TALEB'S CENTRAL MESSAGE IS PREFERRABLE TO TALEB'S OWN

I am only half kidding that a dense, 400+ page book can be distilled down into one sentence.  Of course there is much more of interest in the book than this simple little sentence.  But, in an important sense, I think it is true that the major thesis of the book could have been distilled down to these few words.  And that says something very important about Taleb's approach to the topic, because he does not come out and say anything as straightforward as this sentence.

It is unclear whether Taleb had already adopted a truly subjective definition for probability when the first edition of the book was published.  If he was a subjectivist at the time, he did not mention anything about it in the first edition of The Black Swan or his previous book, Fooled by Randomness.[2]  We only learn about subjective probability in the postscript essay contained in the second edition of The Black Swan, and then only briefly.  If Taleb only belatedly came to believe that probability is subjective, this might explain why he did not venture to state his message as plainly as I just have. 

The reason why I bring up the chronology of Taleb's acceptance of subjective probability is that the book would make more sense in many ways if it was read backward.  In the postscript to the second edition Taleb very clearly says that probability is subjective.  "Probability," he provocatively heads a subchapter, "Has to Be Subjective."[3]  A few pages later he goes on to ask rhetorically "Why did we ever take notions of "objective" probability seriously?"[4]  If this had been disclosed to the reader at the beginning of the book, he would have been in a position to more clearly understand the issues involved.

If the reader understood that probability is subjective before learning about economic modelers like Merton and Scholes, for example, he would be in a position to clearly understand why such modeling is absurd if taken too seriously.  He would be in a position to understand that, if probability is subjective, the risk estimates being generated by Merton and Scholes' scientistic models (or anyone else's) could never be anything more than a subjective statement of belief.  Forget all of the nuances of Extremistan and Mediocristan -- all that you need to know is that the models these guys are building are only capable of generating measures of their own belief.         

To criticize economic prediction, or any other prediction, for that matter, from the perspective of subjective probability is extremely powerful.  It is much more powerful, in fact, than trying to convince people that there are two worlds "out there" to consider -- Mediocristan and Extremistan -- dictating that we be flexible in our thinking.  Taleb's approach, for instance, does not shatter the idea of "objective" modeling in the way subjective probability does.  If probability is subjective, the pedestal upholding these dubious methods is completely exploded, and no hope is afforded to the recalcitrant model builder to reach the vaunted heights of "objectivity."  If the model builder is merely being urged to consider that he resides in Extremistan, on the other hand, he may internalize Taleb's warnings and yet retain a glimmer of hope in his heart that he will one day build a model perfect enough to use in a world of full of "randomness."

The concept of "randomness" that Taleb utilizes throughout the book is itself troubling and confusing.  He clearly does not want to speculate about whether "true randomness" exists in the world or whether the world merely appears random and indeterministic when it is in fact not.  From the narrow, applied perspective that Taleb takes, this might make some sense, but it complicates things for him later on when he claims probability "has to be subjective."  If the world truly is indeterministic and random at some level, then this opens the door to the possibility that probability is a "real" physical property "out there" in the world that can be measured, which would completely undercut Taleb's assertion that probability "has to be subjective."  If things like photons can move about without any cause and yet still act in somewhat predictable ways, then who is Taleb to say that probability is not an inherent "physical property" of the things themselves, as Richard von Mises says.[5]

The probabilist I.J. Good observed that if the world is deterministic, we are forced to adopt a subjective definition for probability.  "Whether or not we assume determinism," Good noted, "every physical probability can be interpreted as a subjective probability or as a credibility.  If we do assume determinism, then such an interpretation is forced upon us."[6]  While Taleb does not want to speculate about these questions, he has nevertheless stepped in the arena by stating unequivocally that probability "has to be subjective." For, he provides the indeterminist with no argument that would force him to abandon the idea that probability is a real, physical and "objective" property of things in the world.  He may justifiably say, with I.J. Good, that every probability can be interpreted as a subjective probability, but he has provided us no reason to believe that probability "has to be subjective."

All of this confusion could have been avoided if Taleb was willing to rise above the narrow, applied perspective that he adopts and take on the concepts of "randomness" and "probability" head-on by defining them.  Taleb himself identifies the "central idea" of his book as "our blindness with respect to randomness,"[7] and yet we don't learn how he truly defines randomness until page 198!  It is hard to understand how one can write two thirds of a book before getting around to defining the book's central concept.  This is to say nothing of the fact that the definition he provides is, at best, confusing.[8]  The same is true of the concept of probability, which, amazingly, is not even defined in the 1^st edition of the book.  We learn, as I have noted, that Taleb defines probability subjectively in the second edition of the book, but, again, this definition appears more as a deus ex machina than a clarification of what has already been written.

All of this is not merely semantic quibbling, because Taleb's book is about randomness and probability.  To leave the reader with only a murky understanding of what these concepts are is to invite confusion and error.

It would have been far better for Taleb to note at the very beginning of the book that probability is nothing more than a measure of subjective belief.  And why is it a measure of subjective belief?  Because, as I.J. Good says, we are literally forced to define it that way in a deterministic world.[9]  The social world that Taleb discusses is not necessarily deterministic in the sense that God or prior events predestine outcomes, but it most emphatically is causally deterministic in the sense that every action has a cause.  Every action is purposeful, which means that every action is "caused" by the goal-driven thinking of individual men.[10]  If we knew all of the motivations, ideas and goals of individual men, we would know in advance how they would act.  We of course cannot know these things, but the simple fact that every action has a cause means that probability is not "out there" in the social world.[11]  It is merely a measure of our subjective uncertainty about how people will act.

Highlighting this fact for the model-obsessed empiricist is absolutely devastating.  Pointing out to Robert Merton, for example, that his fancy probabilistic models are only capable of generating subjective estimates of risk is tantamount to throwing his entire life's work in the garbage.  His models are no more "objective" than are any other models -- whether we live in Mediocristan or Extremistan.  Why leave him an escape route by making a subjective claim that we live in Extremistan where his models are blind to Black Swans (a claim that Merton can dispute), when you can kick the chair out from under him altogether. 

By adopting a subjective definition for probability, Taleb stands poised to kick the chair, but he has not yet done so.  In a world where model-building cranks like Merton and Bernanke have done and are doing so much damage, the time has never been riper for Taleb to swing away.                   

[1] Nassim Nicholas Taleb, The Black Swan, 2^nd edition, (New York: Random House, 2010), pp. 331-332.

[2] Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, 2^nd ed. (New York Random House, 2005).

[3] Taleb, The Black Swan, p. 343.

[4] Ibid., p. 346.

[5] Richard von Mises, Probability, Statistics and Truth (New York: Dover, 1981), p. 14.

[6] I.J. Good,  Good Thinking: The Foundations of Probability and Its Applications (Minneapolis, Minn.: University of Minnesota Press, 1983), p. 72. Emphasis added.

[7] Taleb, The Black Swan, p. xxiii.

[8] Taleb ultimately defines randomness in the following way: "Randomness, in the end, is just unknowledge.  The world is opaque and appearances fool us." (Ibid., p. 198) 

To get a sense of just how unsatisfying this definition is, consider the fact that this definition would not only deem the movement of atomic particles to be "random," but it would also deem virtually everything that we are uncertain about to be "random."  At this moment I am unsure whether my girlfriend chose to go to the gym this evening.  Does my "unknowledge" mean that my girlfriend's decision to go to the gym is "random?"  If so, what does that mean?  Sure, I am personally uncertain about what she chose to do, but is it really clear or helpful to use the same word to describe my girlfriend's purposeful decision and the movement of subatomic particles?

Nor does the introduction of the concept of "unknowledge" clarify anything.  Taleb does not offer a definition of "unknowledge," so we are left completely in the dark about what the term means.  It is hard to see how the introduction of a new, undefined term is supposed to clear up our confusion about randomness, let alone help us to understand a philosophical question as profound as the question of whether "true randomness" exists in the world.  Needless to say, this definition was bound to cause confusion.

[9] Good, op. cit., loc. cit.

[10] Ludwig von Mises, Human Action: A Treatise on Economics, 4^th ed. (San Francisco: Fox and Wilkes, 1996).

[11] Mark Crovelli, "On the Possibility of Assigning Probabilities to Singular Cases: Or, Probability is Subjective Too!" Libertarian Papers, 1, 26 (2009).