Occam's Razor
by Joseph Rowlands

The law of parsimony, or Occam's razor, suggests that among competing hypotheses, the simplest should be selected. Which one is simpler? The one with the fewest number of assumptions.

This is a powerful tool. For any particular set of data, there are usually many possible explanations for why it is true. If you're trying to figure out why there are dirty dishes on the counter, a simple explanation is that your roommate left them there. A more complicated theory that would also explain it is that you had some kind of seizure that left you acting normally, but without memory of any of it. Or that you have a split personality, and the other personality took over and made a mess. Or that a burglar broke into your home without you noticing, ate some food and left dirty dishes, and didn't leave any other trace. You can go on and on and on. Occam's razor removes all of these convoluted theories and leaves the simple one. Your roommate didn't wash his dishes like usual.

Occam's razor is controversial, though. There are lots of reasons why people reject it or think that it leads to false conclusions. There are examples in the history of science where the simplest theories ended up being wrong. So while it seems useful, is it valid? And if so, why? And why does it lead to errors sometimes? Is that simply a misapplication of the razor?

One particular criticism made against Occam's razor is that there's no reason to think that reality is somehow partial to simple explanations. The argument here is a metaphysical argument. It suggests that Occam's razor may work some of the time, but it's not grounded in the facts. If reality isn't concerned with simple solutions, and complex solutions are sometimes or even often true, then does that invalidate the justification of the razor?

This particular criticism has an implicit assumptions. It assumes that Occam's razor is based on a metaphysical principle. The same is true when Occam's razor is put to an empirical test, checking the frequency it leads to correct or incorrect results. In this view, the justification is based on the statistical likelihood, or some underlying causal explanation of that likelihood.

There's a different approach to justifying the razor, though. It doesn't have to be based on whether it usually leads to correct conclusions, or on a preference by reality for simpler solutions. These are metaphysical claims. But what about an epistemological justification for the razor?

Instead of saying that simpler solutions are right more often, or that reality somehow prefers them, what if the justification for the razor is based on inductive reasoning? When a simple explanation is given, the number of assumptions are small. A more complex argument has far more assumptions that have no supporting evidence.

Say you have one thing that needs to be true in order to explain the behavior. In the case of the dirty dishes, you only have to assume that your roommate left them behind. You may have reasons to believe this is true, such as that he has done it before, that the dishes seem to have the food that he eats, and that he had the opportunity to do it. While you don't know for sure that he did it, it's a simple theory that is supported by a bunch of evidence.

Now when you look at a competing theory, like a burglar broke in, ate something, left the dishes, but didn't steal anything and didn't leave any sign of breaking in, you have less likely theory. While it could perfectly explain the results, it has so many assumptions that must all be true, it becomes less justified by the data.

Reason doesn't simply require that assertions not contradict the data or existing knowledge. Assertions need to be supported. The more assumptions made in explaining a theory, the large the burden of proof that needs to be met and hasn't been. For the burglar case, you'd have to provide evidence that a burglar did it. You'd have to provide evidence that someone broke in. You'd have to provide support for the explanation that after breaking in they only dirtied some dishes. You'd have to provide support that the roommate wasn't around at the time. You'd have to provide support that the burglar could have a motive that explained eating and dirtying dishes while not leaving any other trace.

This is an epistemological argument for Occam's razor. It is not saying that the simple theory is more likely to be true. It is saying that the simple theory has a smaller burden to overcome. If we take the single data point as supporting evidence for either theory, we're still left noting that significantly large requirements needed to accept the complex theory. So we accept the simple explanation, not because it is more likely, but because it is the one best justified by the evidence. We can imagine many scenarios where the more complicated theory might end up being true in the end.

This is an important point. Inductive arguments are not guarantees of success. We can interpret the evidence the best we can, but it's always possible that we're missing critical information. So when cases are shown where Occam's razor ended up leading to the wrong conclusion, this isn't really a problem. Of course it can. The important question is, given the evidence at the time, which of the theories or explanations was best supported by the evidence. We can't dismiss the methods of inductive reasoning simply because they can fail when we have limited or faulty information. We do the best we can with what we know, and the possibility of error does not invalidate the process.

It is sometimes said that Occam's razor only applies when the theories are equal in every other respect. That seems to mean that if both theories are consistent with all of the evidence, with no evidence against either of them, we should take the simpler approach. The example I gave could be viewed as not exactly equal, as it is difficult to imagine a motivation of a burglar acting that way. But we could massage the details a little to get something that avoids this issue.

But is this the only case where Occam's razor applies? Do both theories need to be equal? If we think of the razor as an embodiment of an epistemological principle, it's not necessarily true. The principle is that assertions need to be supported by the evidence. The more assertions, the more support they need. It then seems perfectly reasonable to pick a theory that seems to be slightly worse in other ways, but that has less unsupported assertions.

One example is the different models of the solar system. Do planets revolve around the sun or the earth? There were times when the evidence was more consistent with the earth-centered explanation, which had many additional assumptions. But by adding those assumptions, the data was explained. The sun-centered model, on the other hand, started with much less accuracy.

Kepler eventually figured out that elliptical orbits were needed to explain the movement of the planets, instead of the circular movement that was expected. But he only went through that process because he believed that the sun-centered model had far less assumptions and was in some ways an inductively higher quality theory than the earth-centered view.

Of course, as a razor, the goal is to remove certain arguments. For that to work, the context needed for the razor needs to be consistent. The context that all else is equal between the theories is an appropriate context for a intellectual razor. But if we look at the principle behind the razor, we can see that it applies in every comparison of theories or explanations.

Discuss this Article (9 messages)