Special Theory and Tautology

Chapter 1, Section 3: Special Theory and Tautology

We know, the same item would weigh less on a very high mountain, and this can be explained by the theory of gravitation. But before Newton, how would people think of it? We know on a high mountain the temperature will decrease, so we say the cold temperature, due to some reason, can make an item weigh less. This is a theory, but to prove it true, we take the same item to the sea level, place it in a freezing room and then weigh it. As the weight doesn't decrease, the theory of temperature is refuted.

The following will explain, every theory that has explanation power, must be refutable but have not been refuted. The theory that explains the decreased weight by decreased temperature is refuted, though, is it wrong? This is a philosophical problem of great importance.

If we ignore other conditions and deem any refuted theory wrong, then all theories are wrong. So it won't work. Refuted theory can be rescued. Take the weight of an item on a high mountain as an example, though the temperature explanation has been refuted, we can say on top of a mountain the wind is stronger as well. So in another experiment, we store the same item in a freezing room and weigh it with a fan blowing wind. Again we won't get a decreased weight.

We proceed as the surface on a mountain is sloping. So in the freezing room with a big fan, we add a slant, weigh the item on it, and find the temperature explanation again not trustable. No surrender, we see high mountain has a increased altitude. Therefore with a big cost we build the freezing room into the sky. Finally, we reproduce the phenomenon on high mountains, with cold temperature, fan, slant and altitude, the weight does decrease, which makes the temperature explanation proved. This theory is correct, but it's only an ad hoc theory. An ad hoc theory is also a theory, but too specific that there is no general explanation power in it. In the theory there are too many clauses that it would be refuted with the slightest change.

Any scientific theory, if refuted by facts, can be rescued with additional conditions. But the rescue is not without a price and it cannot be too high. If a theory is so specific that it explains only one phenomenon and is not extensible to other ones, the price is overpaid. The measure is right the theory's general explanation power. Power can be big or small. So we should not give up a theory yet without enough explanation power, as today's not-so-general theory might be replace by another general one tomorrow, and before that happens the not-so-general one is the best we can use. (Translator: each step of generalization is a hypothesis and thus requires time to be discovered and verified.)

In this world there are truths, but the is no theory that cannot be replaced by a better one. Science advances not because the right ones replace the wrong, but because the ones of broader explanation power replace the narrower. Human thoughts can move forward, as today's best may get substituted tomorrow by a more useful one. As of today we still don't have a limit line for human imagination. After World War II science has made extraordinary progresses, this makes us believe human thinking might be limitless forever.

A special theory, if it's so specialized that it explains only one phenomenon, like the aforementioned temperature theory for weight reduction on high mountains, is at one extreme of science and cannot be generalized for other use at all. At the other extreme stand the theories that are ridiculously generalized. They cannot be wrong under any circumstance, because they don't have contents. These are the tautologies in philosophy. While a special theory has too many contents, a tautology has none. Any viable theory must sit in between of them two.

Tautologies are the statements that cannot be wrong under any circumstances. For example, I say "a four-footed animal has four legs". How could it be wrong? The second part of the sentence just repeats the first part, so we can never find a situation under which the statement could be wrong. On Earth and Mars, it can't be wrong, nor can it be at any other place of this universe. The statement has perfect generalization, but what does it exactly say? Nothing! It's absolutely right, but we can get no information from it. So the content of a tautology is void and it explains nothing. (Translator: too many "nothing" repeated here.)

However, tautology is never as simple and obvious as "a four-footed animal has four legs". Theories too generalized to be wrong sometimes even cheat college doctors. Let me give some examples.

In economics, an indispensable assumption is: all individuals maximize their economic activity. But activities like smoking or jumping off a building is harmful to oneself. If we insist these activities are maximizing, then the assumption becomes tautology, because this assumption has included all human activity and using it to explain smoking or building jumping cannot be wrong. If human activity can be vaguely and generally explained like this, there'd be no need of economics.

Another example. Once there was an economist, who wanted to figure out whether private enterprises are running at their lowest cost. According to economic definition, all private enterprises, for maximizing private profits, shall try to lower their cost as much as possible. So the investigation the scholar wanted to make is actually tautology, because the definition itself doesn't allow for the existence of a willful cost hold when it can indeed be reduced. On this job, Friedman had his remarkable comment: "A foolish question, of course deserves only a foolish answer!" What is a foolish question? The one to which you can't have a second answer or no answer is wrong.

So tautology is not always as simple and obvious, sometimes even a learned can be tricked. Forty years ago, a Harvard graduate student got his Ph. D in economics, with his thesis named best of school and a certificate honored. Afterwards, the thesis got published and widely propagated. However, Alchian's review for it was even more well-known. He just pointed out, accurately, that the whole thesis of the student was just a tautology and can never be wrong. The review made Harvard really awkward. Just think, a student's tautology even tricked the professors from Harvard's Department of Economics, how can we ever underestimate the "profoundity" of this sort of logic?

Though I say tautologies cannot be wrong and have no contents, that doesn't mean they cannot be important concepts. In fact, many important scientific theories originate from the idea or concept provided by tautology. One strength of tautology is: it's extremely generalized. If we constrain the scope of a tautology, sometimes we may get a theory of content, though quite probably wrong, and if right its explanation power could be astonishing.

We can have some cases in economics. Take the aforementioned maximization and smoking as an example, if the two are taken for granted to be of the same category, as if by definition, then it's tautology and won't give us any content; but if we add some limiting conditions (i.e. constraints), we can then decide under what circumstance one would smoke more, less, or even quit. In this way, the theory now has content and becomes verifiable.

Another more significant example that a tautology changes into a useful theory is the quantitative theory of money in monetary theory. The start point of this theory is obviously tautology: quantity of money (M) times velocity of money (V), is equal to price of goods (P) times quantity of goods (Q). The formula MV=PQ can't be wrong, as the former (MV) and the latter (PQ) are just a same quantity from different angles. Now that it can't be wrong, it becomes a definition and should be written as MV≡PQ (≡ stands for identical to). Obviously it doesn't explain anything. But because the definition offers a angle to view the world, if we constrain it with proper conditions, it becomes the important quantitative theory of money and has great explanation power. Talented Fisher and Friedman successfully pointed out under which circumstance the velocity of money (V) keeps nearly constant and thus the price of goods (P) is connected with the quantity of money (M). Such a successful theory, in the end, derives from the concept of  a tautology.

The Coase theorem that has been popular in economics for more than forty years is taken as a tautology by some people as well. I think the theorem is of great use, because when an intellectual adds constraints to it, a number of theories with explanation power can be derived. Tautology is the same tautology, but in different people's hands, the usefulness could be quite different. Those that take Coase theorem as tautology and ignore it completely, just don't understand it correctly. As for the detail of the theorem, it will not be discussed until Volume 3 of this book.

Now we can make some conclusions about the two extremes. Special theory has too many contents and only explains one thing. It doesn't have general explanation power at all. But special theory is better than no theory. R. Kessel once said: without theories at hand, you cannot win any debate. One thing is explainable is of course better than nothing explainable. However, viable scientific theories always have their generality, or else each phenomenon would require an individual theory and we can only have a mess.

Another extreme is tautology, which cannot be wrong but has no content at all. The explanation power of a tautology is even less than that a special theory. But tautology can have illuminating concepts sometimes and give us a new angle to view the world. Ignoring a tautology completely just because it's empty may make people miss the treasure. Instead, we should pick up the new angle suggested by the tautology and try to add proper constraints to make its content rich. Through this, a theory with good explanation power may arise.

Viable theories that explain a lot always stay in the between of special theory and tautology. Progresses of science usually start from one or the other extreme and then move towards the middle.