Living in Two Dimensions

LIVING IN TWO DIMENSIONS

A vexing problem in the history of human thought is finding one’s position on the boundary between skepticism and gullibility, or how to believe and how to not believe. And how to make decisions based on these beliefs, since beliefs without decisions are just sterile. So this is not an epistemological problem (i.e., focusing on what is true or false); it is one of decision, action, and commitment.

Clearly, you cannot doubt everything and function; you cannot believe everything and survive. Yet the philosophical treatment of the problem has been highly incomplete, and, worse, has not improved much over the centuries, if it has improved at all. One class of thinkers, say the Cartesians, or the academic skeptics some eighteen centuries before them, in their own way, started with the rejection of everything upfront, with some even more radical, such as the Pyrrhonians, rejecting so much that they even reject skepticism as too dogmatic. The other class, say the medieval Scholastics or the modern-day pragmatists, starts with the fixation of beliefs, or some beliefs. While the medieval thinkers stop there, in an Aristotelian way, the early pragmatists, with the great thinker Charles Sanders Peirce, provided a ray of hope. They proposed to update and correct beliefs as a continuous work in progress (albeit under a known structure of probability, as Peirce believed in the existence and attainability of an ergodic, long-run, reachable state of convergence to truth). That brand of pragmatism (initially called pragmaticism) viewed knowledge as a rigorous interplay between anti-skepticism and fallibilism, i.e., between the two categories of what to doubt and what to accept. The application to my field, probability, and perhaps the most sophisticated version of the program, lies in the dense, difficult, deep, and brilliant forays of Isaac Levi into decision theory with the notion of corpus of belief, doxastic commitment, distance from expectation, and credal probabilities.

A ray of hope, perhaps, but still not even close. Not even remotely close to anything useful.

Think of living in a three-dimensional space while under the illusion of being in two dimensions. It may work well if you are a worm, certainly not if you happen to be a bird. Of course, you will not be aware of the truncation—and will be confronted with many mysteries, mysteries that you cannot possibly clear up without adding a dimension, no matter how sophisticated you may get. And, of course, you will feel helpless at times. Such was the fate of knowledge all these centuries, when it was locked in two dimensions too simplistic to be of any use outside of classrooms. Since Plato only philosophers have spent time discussing what Truth was, and for a reason: it is unusable in practice. By focusing on the True/False distinction, epistemology remained, with very few exceptions, prisoner of an inconsequential, and highly incomplete, 2-D framework. The third missing dimension is, of course, the consequence of the True, and the severity of the False, the expectation. In other words, the payoff from decisions, the impact and magnitude of the result of such a decision. Sometimes one may be wrong and the mistake may turn out to be inconsequential. Or one may be right, say, on such a subject as the sex of angels, and it may turn out to be of no use beyond intellectual stamp collecting.

The simplified, philistinified, academified, and glorified notion of “evidence” becomes useless. With respect to Black Swans, you act to protect yourself from negative ones (or expose yourself to positive ones) even though you may have no evidence that they can take place, just as we check people for weapons before they board a plane even though we have no evidence that they are terrorists. This focus on off-the-shelf commoditized notions such as “evidence,” is a problem with people who claim to use “rigor” yet go bust on occasion.

A probabilistic world has trouble with “proof” as it is, but in a Black Swan world things are a lot worse.

Indeed, I know of almost no decision that is based on notions of True/False.

Once you start examining the payoff, the result of decisions, you will see clearly that the consequences of some errors may be benign, those of others may be severe. And you pretty much know which is which beforehand. You know which errors are consequential and which ones are not so much.

But first let us look at a severe problem in the derivation of knowledge about probabilities.