Читать книгу Safe Haven - Mark Spitznagel - Страница 13

Aristotle is generally considered to be the earliest and foremost developer of the idea of deductive reasoning, or sullogismos. Deduction is “top‐down” logic, whereby general rules or premises are applied to particular cases or conclusions. This contrasts with induction, which is “bottom‐up” logic and goes in the opposite direction, whereby particular cases or premises are applied to reach a general rule or conclusion. Examining the geometry of a die to estimate the frequency that any side will come up over repeated rolls is deductive reasoning. Reasoning in the other direction, by repeatedly rolling a die and using those results to estimate the geometry of the die, is inductive reasoning. (We will be rolling the dice in both directions in this book.)

A syllogism applies deductive reasoning to draw a valid conclusion from assumed premises. One example is the syllogism called modus tollens or “denying the consequent.” It is the main logical method to avoid mistakes of reason in science—what Feynman has described as “what we do to keep from lying to ourselves.” It is an ideal BS filter (so don't be too surprised if you haven't encountered it in the context of investing).

A modus tollens takes the form of “If H, then O. Not O. Therefore, not H” (with H for hypothesis and O for observable). There are two premises—an explanatory hypothesis, made up of an antecedent and consequent, paired with an observable; brought together, they yield a conclusion, which follows logically from the premises. The logic goes, if a statement is true, then so is its contrapositive.

Think of this example of modus tollens involving my dog Nana:

 If Nana is good at catching groundhogs, then I won't have a groundhog problem.

 I have a groundhog problem.

 Therefore, Nana isn't good at catching groundhogs.

We can see that a modus tollens serves the specific role of falsifying or eliminating a hypothesis. But neither it, nor anything else for that matter, can ever be used to verify a hypothesis as true. When we pair our proposed hypothesis with a minor premise that is an observable fact, we have a well‐constructed test of that hypothesis. Modus tollens, then, is the logical principle of the empirical sciences, and the scientific method itself; it allows us to clarify our ideas and move them away from mere metaphysics. Scientific rigor demands that we be able to pose, experimentally test, and ultimately falsify theories or conjectures in this way. When, like sleuths, we disqualify false theories whenever we can, then step by step we approach the truth. It's all very Sherlock Holmesian: “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

Most significantly, the twentieth‐century Austrian philosopher of science Karl Popper constructed his whole falsification principle around it—as the fundamental demarcation between science and pseudoscience. “Universal statements are never derivable from singular statements, but can be contradicted by singular statements,” as Popper wrote in The Logic of Scientific Discovery. “Consequently, it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to universal statements.”

So far, we have been discussing cost‐effective risk mitigation as if it were something worthy of our attention—something that exists. Even uttering the phrase presupposes it. (And this is why no one ever really utters the phrase “cost‐effective” in the context of risk mitigation in investing. Have you noticed?) Taking such a conclusion for granted is begging the question.

It might even appear that we did this in our principle number three. However, the principle only claimed what risk mitigation should be, not necessarily what it always is. Cost‐effective risk mitigation could still be only theoretical, and not actually possible.

So, instead, we need to treat this principle as a conditional premise. It is an explanatory hypothesis, and this conveniently suggests our own modus tollens syllogism for safe havens, which we will be testing and investigating over and over:

 If a strategy cost‐effectively mitigates a portfolio's risk, then adding that strategy raises the portfolio's CAGR over time.

 Adding that strategy doesn't raise the portfolio's CAGR over time.

 Therefore, it does not cost‐effectively mitigate the portfolio's risk.

What we have here is a natural, testable conjecture about safe haven investing. And it's important to understand what this hypothesis testing can and cannot do. It can only refute or falsify the hypothesis. If a safe haven strategy does not raise a portfolio's CAGR over time, then the null hypothesis—that the strategy cost‐effectively mitigates the portfolio's risk—does not hold. If it disagrees with experiment, it is wrong—it is not a cost‐effective safe haven strategy. What we cannot do, however, is prove that something is a cost‐effective safe haven strategy. Such is the scientific method.

To illustrate why you can't prove things in reverse, it's important to note that I could not have posed this syllogism instead, as the inverse of our premises: If a strategy does not cost‐effectively mitigate a portfolio's risk, then adding that strategy lowers the portfolio's CAGR over time. That would be deductively invalid; it mistakes a sufficient condition for a necessary condition. Observing that adding the strategy raises the portfolio's CAGR over time actually proves nothing about cost‐effective risk mitigation. This is because there are other ways that the strategy could have raised the portfolio's CAGR; the strategy needn't have even mitigated risk at all, and it may have even added risk. We would need to delve deeper into the source of that outperformance. (As Hemingway said, “Being against evil doesn't make you good.”)

This is equivalent to the fallacy of affirming the consequent: If “O is true,” can we then conclude that “H is true”? Thinking that we can is a mistake often committed even in the physical sciences: “If my theory is correct, then we will observe this data. We observe this data; therefore, my theory is correct.”

In my previous example with Nana, what if I don't have a groundhog problem? Can I proudly claim that my Nana is good at catching groundhogs? After all, there could be myriad other possible reasons that I don't have a groundhog problem. Maybe they were scared off by our resident fox. Or perhaps my son has been playing in our woods with his bow and arrow and ghillie suit.

We would similarly mistake sufficiency for necessity with the fallacy of denying the antecedent. In this case, we might conclude that I have a groundhog problem as a logical consequence of knowing that Nana is not good at hunting groundhogs.

All knowledge is a hypothesis; it is all conjectural and provisional, and it can only ever be falsified, never confirmed.

Now, a critical part of this scientific method is the way we go about choosing the very hypothesis that we are putting to the test. We specifically need to avoid ad hoc hypotheses that simply fit our observations. They are always there, ripe for the picking. We need logical explanations that are independent of and formed prior to those observations.

Scientific knowledge is not just to know that something is so; it is just as important to know why something is so.

The deductive thinking behind my hypothesis “Nana is good at catching groundhogs” was so important because it's going to hang around as sort of our working hypothesis until I manage to falsify it. Did I have a sound deductive reason to think that her skill, if it exists, would really result in the disappearance of groundhogs? Skilled or not, does she prefer to spend her summer days sleeping indoors? (As a Bernese Mountain Dog, she much prefers snow and air conditioning.) Does she more often chase or get chased by the groundhogs?