Theories, Models, Laws, Hypotheses, and Proof

This sounds like a really boring topic, but I encourage you to read on, because it's actually quite interesting, I think, and very important. I've been reading one of Richard Dawkins's books, and he brought up the topic of two types of "theory" in the English language. This is something I've talked about a lot with others, and it was brought fully to my attention by Kenneth Waltz in his seminal work Theory of International Politics. Understanding the meanings of all those words in the title is absolutely indispensable for understanding all kinds of things in the world around us, from biology to political science, and more. Their definitions, though, seem sometimes a bit fuzzy and they also often overlap. So I'm going to lay down what I believe is the usual sense in which the words are used in science and academia, and the way that I will try to always use the terms in this blog (and in all my academic writing).

Laws: I'm going to start with this one because it's actually the easiest. In spite of that, my school teachers told me the wrong definition! If you thought a law was a theory that had been established for so long that is now accepted as a fact, your teachers were misinformed as well, just like mine. (If not, congratulations!) A law describes a relationship between two or more things. The law of gravity, for example, tells you how fast objects should fall with a given strength of gravity. The format is, roughly: if A, then B. Kenneth Waltz calls many things laws or "law-like statements," things that many others often call theories. He does this because the "theories" (actually law-like statements) do not explain anything, but rather simply describe something (a theory must explain, see below). Laws can be tested. A law can thus be "true," while using "true" to describe a theory is misleading, because a theory cannot be "proved" directly in the way that most people use the word.

Hypotheses: This brings us to the next category. The word "hypothesis" has two separate meanings. One meaning of hypothesis is "a theory I haven't tested yet at all, something I think might be true." The other meaning, sometimes called an "auxiliary hypothesis," is actually a law-like statement that can be used to test a theory. Confused? Let me give an example. If I theorize that plants use the sun to make food, I can test this by inferring a hypothesis from it. An easy one would be "if I put a plant in the dark, it will die." This is a law-like statement: "If no light, then death." It is inferred from the theory, it itself in NOT a theory. If the plant then dies when this happens, I will have shown my hypothesis to be correct. I will NOT, however, have proved my theory to be right. It could be that plants need light for something other than making food, and that the plant died because of that. That would mean that my explanation (the theory behind the hypothesis), though supported by my little experiment, is in fact wrong!

Theories: This brings us to the big one: theory. Like hypothesis, theory also has two meanings. The first is much like a hypothesis "I think this probably works in this way, but I don't know." The second meaning is the one more often used in science: "a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena (e.g. the wave theory of light)" (from Merriam Webster's Online Dictionary). The important part of this rather confusing definition is that a theory explains something. Using our above example, if I say "if no light, then death" for a plant, I haven't explained anything. I've just said that the plant dies, not why. My theory was that plants require light to make food. That is a theory because it explains why a plant needs light. Get it?

As I mentioned, it is extremely difficult or even impossible to prove a theory "right," even one as seemingly straightforward as photosynthesis. Instead of "right" or "wrong," "true" or "false," many people (myself included) instead refer to theories as "good" or "bad." What I mean by this is: the theory works or it doesn't. We figure this out by inferring hypotheses from the theory and then testing them, as with the above example with the plants. If we keep inferring different hypotheses and keep testing them, trying to prove the theory wrong (it's important that we don't just keep testing things we think will support the theory, that's called bias), and we just can't seem to prove it wrong, then we say the theory is good, or that it has a lot of explanatory power, or that it is supported by evidence. 

For example, we might go on to test the amount of glucose in a plant's leaves with and without light. Our theory would lead us to hypothesize that there should be less glucose in the leaves when it's dark. If that is confirmed, then it supports (not proves!) the theory. If not, it actually does not necessarily disprove the theory: maybe darkness causes the plant to break down its own tissue to make glucose. It is sometimes even difficult to prove a theory wrong, too! This is why many different hypotheses must be drawn and tested, preferably by several different, independent scientists. Multiple hypotheses may be correct and support the theory... until one suddenly doesn't.

Another thing scientists like in theories is simplicity. If two theories explain and predict phenomena equally well, then why not use the simpler explanation? Many people misunderstand this principle, however. The important part is the caveat "all other things being equal." If both theories are equally good on all other fronts, then the simpler one is preferable (again, not necessarily "right," but why use use a complicated one if the simple one works just as well?). If one theory explains something more accurately than the other, that one is clearly better, whether it's more complicated or not. Finally, if two theories are completely untested, it is not possible to say which one is better; in that case it does not matter which one is simpler.


Models: An easy one for the last part. A model is basically the same thing as a theory, especially when the theory can be shown as a chart, map, sculpture, etc, which most can. "Model" and "paradigm" are also the same thing.


Proof: I think this has now actually been covered, but let me recap. Hypotheses and laws, as the terms are used here, can be shown to be wrong or right, true or false (if they are selected well). Theories and models cannot be proved correct, and may be difficult to prove wrong, as well. A theory that cannot be proved wrong, by the way, is called unfalsifiable and is considered a bad theory. These usually involve some form of magic. Saying it was magic (or god) does not really explain anything and is not falsifiable, which is why either one will not cut the mustard as a theory.


Anyway, if someone talks about a "proven" theory, they either misunderstand what theories are or (as sometimes in my case) they mean it in the don't-be-pedantic way and are saying that numerous hypotheses have been inferred from it and tested in attempts to falsify it -- and none have succeeded. That would suggest that the theory is a very good one indeed and may even be considered fact, like photosynthesis or that the sun is in the middle of the solar system (yes, that's "just a theory," too, though most reasonable people would consider that a fact!).

A little tangent here: The reason we accept the solar system model (or theory) is because we can hypothesize about the positions of planets, stars etc. so well that we can fly spaceships and robots into space and everything works. The model explains and predicts things in our solar system so well there is essentially no room for doubt. Some have tried, however, using all kinds of complicated theories to put the earth at the center. If you go to crazy lengths, you can make any model fit reality (until a new heavenly body is looked at, requiring the model to be adjusted yet again), but why? The simpler explanation that has been supported by evidence is better, and requires less maintenance work to boot in the case of the solar system.


Keeping these terms in mind and understanding the limitations of each type of "knowledge" is really important. I hope this has helped. I welcome any (polite) comments, as always.