The Importance of Being Refutable

Chapter 1, Section 4: The Importance of Being Refutable

If the readers ask: through out the entire framework of scientific methodologies, which point is the most important? I will answer without hesitation: conclusions of a theory must be refutable. If a theory has no chance to be refuted, it then doesn't have explanation power at all. We could say, the essence of all empirical sciences is to generate some statements or conclusions that can be refuted by facts. In other words, science is neither the search of right, nor the search of wrong; science searches for the refutable. If something is refutable but not refuted, then it's confirmed. It's been mentioned previously predicting a phenomenon's occurrence is equal to explaining it. If a prediction is refutable but not refuted, then it's confirmed by facts and we deem the phenomenon explained. Of course the same phenomenon can have different explanations. In the following I will discuss the choice problem of different theories.

What I want to stress here is: a theory impossible to get refuted has no explanation power because it doesn't allow a chance to be verified. Tautology cannot be wrong. If it cannot be wrong under any circumstance, how could it be refuted by facts? A refutable theory must be at least able to be wrong in our thinking. Tautology can't be wrong even in just our mind. Except for tautology, we have other four occasions under which a theory is impossible to be refuted and thus has no explanation power. Discussion of them will come in Section 5 and 6.

Being able to be refuted is important. If the conclusion of a theory is refuted by facts, we have two options: first, we give up the theory and look for something else; second, we add clauses to save the theory, but as mentioned before, the rescue asks for a price and it shall not be too high. A theory having not been refuted today may become refuted tomorrow, and this is exactly the way how science advances. But as long as the theory has not been refuted, we can use it today. The applicability to explain phenomena is the the most important criterion on theories. Right or wrong shall never count.

A predicting sentence or statement expresses a testable or refutable implication, which is derived from a theory. Logically, the rule for implication is very simple: if the occurrence of event A implies that of event B (A→B), then B doesn't occur implies A doesn't either (Not B→Not A). This is the most basic verification method. For example, when it rains (A), there must be clouds in the sky (B). The saying implies that if there is no cloud in the sky (Not B), there is no rain (Not A). If it rains when there is no cloud, then the theory that when it rains (A) there is cloud (B) is now refuted by facts. (Translator: the author doesn't make it clear what is an implication. That when it rains there must be cloud, is both a theory AND an implication, as the theory itself is the most trivial implication.)

To verify the implication of a theory, is to find a counterexample. This is very important. To verify the implication that when it rains there must be cloud (A→B), one needs a counterexample of the implication when there is no cloud it doesn't rain (Not B→Not A). Using the counterexample of the implication when it doesn't rain there is no cloud (Not A→Not B) instead as a verification is indeed a common mistake (In logic, the mistake is called fallacy of denying the antecedent.) When the occurrence of A implies that of B, the nonoccurence of A doesn't imply anything about B. Thus by saying nonoccurence of A implies nonoccurence of B, one is making a mistake, and scholars that fall into the trap are a lot. For example, economics assumes all individuals maximize their activity economically (A), so under certain constraints, everyone works hard (B). Some scholars think people may not maximize their activity (Not A), so under same constraints, not everyone works hard (B). This is obviously a fallacy.

In 1946, an economist named R. A. Lester published a world-famous paper. After an investigation of the policies Boston's private transportation enterprises used to hire drivers, he declared the marginal productivity theory, which is very useful in economics, be wrong (the term "marginal" will be explained later). According to economics, each private enterprise maximizes their profits, so when hiring a truck driver, the productivity contribution by the driver is equal to his wage (this is an implication of the marginal productivity theory). Lester inquired all managers of Boston's transportation companies and found they had no idea of "marginal productivity" at all, so he concluded the theory be wrong: the wages of the drivers are not equal to their marginal productivity contribution. This is another "no rain no cloud" fallacy. (Translator: the analogy is too hidden to be grasped.)

I can give another interesting (but not factual) example to illustrate the "A→B so Not A→Not B" fallacy. There are a group of people, and everyone of them is an idiot thus knows nothing. But economists assume they can maximize their activities. Since the group of people are idiots, this economic assumption is definitely wrong. The idiots think the operation of a gas station is fun, so each opens a station. Because they are idiots, some of them build their stations on high mountains, some in thick forests, and some at sea. As no car will pass by, nobody knows how the stations would survive. Luckily, some of them have their stations built beside roads. After a while, the unlucky ones are eliminated, and only those that build the stations at road sides survive. In fact, they have no idea what they did. The assumption that they know how to maximize is wrong, but survived gas stations are the exact result predicted by the same assumption. So concluding the idiots' gas stations won't be at the most profitable places because they don't know what they do, is fallacy. (Translator: the fallacy for "sane people (A) open gas stations at profitable places (B)" is "insane people (Not A) open their stations at nonprofitable places (Not B)", which has counterexamples.)

Astrology in ancient China was extraordinary and by it eclipses of the sun and the moon can be accurately predicted. I didn't investigate how they did it, but all Chinese children must have heard of the saying Tengu (the heavenly dog) eats the sun. Assuming there is the Tengu to explain the eclipses is of course nonsense, but if that generates accurate predictions, we should accept it. That we replace those ancient eclipse theories with today's, is not because today's is right and the old ones are wrong, but because today's theory has greater generality and can explain many other celestial phenomena. There might be a day today's theory is proved wrong. Tautologies are absolute, but they have no explanation power. Theories with explanation power, on the contrary, could be wrong, but that they are refutable is more important. No matter right or wrong, a theory is useful as long as it explains something. Though there is no Tengu that eats the sun, concluding it cannot be used to explain eclipses is however fallacious. We must clearly separate concepts at any time.