[Borodog]

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A correct statement of Occam's razor is, "The simplest explanation that fits the data is the most likely to be correct.[/b]



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A number of respondents have said something like this. As I understand it, Occam's razor is not about which theory is more likely to be 'correct'. Occam's razor has nothing to do with how likely a theory is to be true, but instead is a principle that directs us how to choose among theories, on non-empirical grounds, that are equally likely to be true given the evidence.

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I couldn't disagree more. This doesn't even make sense. If the simpler explanation were not more likely to be true, what is the justification for the razor at all? The very point is that they are NOT equally likely to be true given the evidence. Hence the razor.

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I don't think thats quite right. There is really no reason to think any theory, X, is more likely to be correct than another theory, X+invisible blue goblins. Its just that there are an infinite number of more complicated theories, and we couldn't ever have ANY meaningful consensus or discussion about any theory if we just accepted any of the infinite as 'equally good.' They are still equally likely, I think, whatever that means. They just aren't as...easy to talk about? To think about, maybe.

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This is silly. They are certainly all not just as likely to be correct. That is the principle the razor embodies.

If I can't find my keys, and it were REALLY just as likely that invisible blue goblins stole them and altered my memory so that I don't remember where I left them as it is that I just forgot where I put them, and hence an infinite number of other theories, then it would LITERALLY be the case the the chances that I just forgot where I put them would be 0%, when obviously it is near 100%. This is patently ridiculous. The only way this is avoided is if the simple explanations is MORE likely than alternative explanations that invoke extraneous ad hoc hypotheticals.

I repeat, if the simpler explanation were not more likely to be correct, then parsimony would be a useless concept.

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That is a misapplication of the concept. To stick with your keys scenario, the two (or infinite) competing theories are:

You forgot where you put your keys
and
You forgot where you put your keys and invisible blue goblins watched you do it.

Both of these are equally likely.

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No, they aren't. You have totally sidestepped my entire argument. If this were actually true, then the chance that I simply forgot where I put my keys is literally 0%. The only way to avoid this farcical result is to conclude that the simplest explanation is literally more likely than the alternative explanations. That's the entire point of the principle of parsimony (Occam's Razor).

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There is absolutely no difference in explanatory power.

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I would argue that yes, there is a difference in explanatory power; that unneccesary ad hoc hypotheticals reduce the explanatory power, even if the theory accounts for all the evidence in question.

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Its just the second one involves a whole bunch of unnecessary information.

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Here's the crux: SO WHAT? If the one involving the unnecessary information is really just as likely, how is the unnecessary information "bad"? What exactly does it mean for the simplest explanation to be "better" in such a crazy world? That you have to type less to describe it, even though an infinite number of alternative theories are just as likely, and hence the odds of the simple theory being the correct one are 0%? Why think up any theory at all if it isn't more likely than any alternative? Such a premise would render science pointless, not to mention impossible.

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Your scenario is different because there are real differences in outcome or explanatory power to the two theories.

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How so? [img]/images/graemlins/confused.gif[/img]