Theory vs. theorem, what’s the difference?

I have a new theory. I should point out that it is not a theorem. You may wonder what the difference between a theory and a theorem is. You probably don’t wonder, but just in case you do I am going to tell you.

A theory is a generalized explanation for how the world works. It is often abstract, generalized and contemplative, but also cool. I have found that forming theories can cover for a lot of staring off into space and doing nothing! It’s probably not as good as fishing that way because you have to explain that you are contemplating. If you are holding a fishing pole, you don’t have to explain that you are fishing. Still, when someone asks, “What are you doing?” you can just say “contemplating,” as if you know what that means.

Anyway, a theorem involves a lot more work. A theorem is a statement that has been proven on the basis of previously established statements. Right there it gets more complicated than a theory because you have to actually know what you are talking about. You have to be consistent with previous statements or other theorems. And a theorem has to be true. I think I’d rather fish.

Another cool thing about theorizing is that you don’t really have to prove anything. In fact, theories cannot generally be “proven.” All a theory has to do is suggest a hypothesis that can be tested. If an experiment is performed and the result does not support the theory, the theory is considered incorrect. In other words, the key attribute of a theory is that it can be shown to be false.

Non-scientists sometimes use the words “theory” and “hypothesis” interchangeably. But you don’t really have to test a hypothesis to have a theory. By carefully avoiding hypotheses, one can talk theoretically with little actual effort. If no one ever does the experiment, they can never be proven wrong. This is one of the major advantages of being a political scientist.

Hypotheses can be useful in their own way, though. Probably the easiest way of coming up with a “hypothesis,” if you are sure you want to go to that much work, is to write your idea out as an “If ... then” statement. For example, if there is artificial intelligence, then there must be artificial stupidity. Or, if you torture data correctly, then it will confess.

So my new theory is this: “In theory there is no difference between theory and practice, but in practice there is.” This is based on a lifetime of observations that in theory everything is clear but nothing works. However, in practice everything works, but nothing is clear. Now keep in mind that this is a theory, not a theorem, and I don’t need to prove this at all.

However, my new theory does suggest a testable hypothesis. For example, an “if ... then” statement might look something like this: “If everything is clear but nothing is working, then the idea is a theory.” This might be useful in evaluating government programs. It could also be used to classify mechanical systems.  “If everything is working, but nothing is clear, it is practical.” Another way of phrasing this latter idea as a hypothesis is “if it ain’t broke, then don’t fix it.” If everything works and everything is clear, then it is a theorem.

I actually thought about trying some experiments on this theory. As I tried to apply practice to theory, I discovered that nothing works and nothing is clear. That always seems to be the problem with my theories! Or maybe that’s the problem with my practice. Now I’m confused. Anyway, all this is speaking theoretically, I suppose. Or am I speaking hypothetically? I always get confused about that. Of course, that’s Roget’s fault because he lists them as synonyms for each other. One thing is clear. I am not speaking theoremetically.

Gary McCallister, .(JavaScript must be enabled to view this email address), is a professor emeritus of biological sciences at Colorado Mesa University.

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