Topics Science

Question Are there many instances in science (or other disciplines) of Occam's Razor being wrong? What prompts this question is the recent thread in the Religion section about Katrina and the problem of evil but I didn't post it there because of the 'faith' issues of some respondents and philosphers quoted. No visiting alien intelligence new to our planet would plump for, say, Islam though they might have their own non-Occamish explanation I suppose. I mean, generally, does the law of parsimony hold water?

Accepted:
November 12, 2006

Comments

Whether the "law of parsimony" works depends on what it says. Broadly speaking, it says that we should prefer a simpler explanation over a complicated explanation of some phenomenon, all other things being equal. This leaves a lot unspecified: What makes one explanation simpler than another? What does it take for one fact to explain another? What are the "other things" and what does it take for them to be "equal"? What does "prefer" mean? (Believe? Believe more likely to be true? Adopt as a working hypothesis?)

Leaving all of that to one side, there will certainly be cases where the simpler explanation turns out to be false. Suppose a patient has a large collection of symptoms. Perhaps there is one disease that often produces just that collection of symptoms. But there may also be a pair of diseases, the first of which often produces the first half of those symptoms and the second of which often produces the second half. Arguably, parsimony favors the first hypothesis: that all of the symptoms have a single, common cause. However, it sometimes happens that the second explanation is correct -- the two sets of symptoms have different explanations. If the two diseases in the second hypothesis are relatively common and the single disease in the first hypothesis is quite rare, then "parsimony" will usually mislead us in this case.

But this takes us back to the question of what "the law of parsimony" says. If you know that the first disease is very rare and the two diseases in the second hypothesis are relatively common, then perhaps "other things" are not "equal." and so the "law of parsimony" does not favor adopting the more parsimonious hypothesis.

Undoubtedly, scientists do sometimes cite "simplicity", "parsimony", "Occam's razor" and so forth as reasons for favoring one hypothesis over another. When Uranus's orbit deviated slightly from its predicted path, scientists predicted that there was another planet whose gravitational influence caused this deviation. A more complicated hypothesis -- that there were 10 small planetesimals responsible for this deviation -- would have been regarded as multiplying entities beyond necessity. But should we think that there is some sort of "law of parsimony" at work here, or merely a background belief that 1 large undiscovered planet is more likely than 10 smaller undiscovered planets? Many philosophers would argue that there is no single "law of parsimony", but merely different pieces of background knowledge at work in different cases where scientists favor the more parsimonious explanation. For a nice and accessible discussion of this idea, see Elliott Sober's paper "Let's Razor Ockham's Razor", reprinted in "Philosophy of Science: An Anthology", Blackwell, 2006, edited by me (Marc Lange).