Ockham's Razor

[PairTheBoard]

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In fact it is somewhat of a proof. If I run over glass and then park, go somewhere, and come back to my car to find a glass shard in it (and it's flat) I could conclude an infinite number possibilities, including one that involved David S. and Brandi following me and stabbing glass into my tire in order to send a message to 2+2ers at large. The evidence given to me certainly does not negate that possibility, but there is no reason think that likely. Given the small amount of evidence I have, the most probable option is the simplest and easiest. As I get more data I can exclude more theories, although I can still come up with an infinite number. But mathematically, I approach the limit of just one theory, and with all available evidence, it is reasonable to assume what the limit is approaching is the right choice, until I find other evidence that suggests another theory is more likely. When you average out all the unavailable evidence, the simplest theory is easily the most probable choice.

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Right. It was obviously witchcraft.

PairTheBoard

[Philo]

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As I get more data I can exclude more theories, although I can still come up with an infinite number. But mathematically, I approach the limit of just one theory, and with all available evidence, it is reasonable to assume what the limit is approaching is the right choice, until I find other evidence that suggests another theory is more likely.

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I think this is wrong. The empirical justification of a theory does not work with mathematical precision. There are always an indefinite number of theories that are empirically adequate (i.e., that are consistent with all of the available evidence). There is no such thing as 'approaching the right' choice if by that you mean eliminating all but one theory based on the evidence.

Hence the need for Occam's razor. It is not an empirical principle but a heuristic one, which gives us some principled reason for choosing among equally empirically adequate theories.

[wazz]

Thanks for all the input, guys. I'm understanding this a bit better.

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The mutilated and incorrect statement of Ockham's Razor is that 'the simplest explanation is the correct one'. It should take all of about a minute to think of a counter-example.

The best statement of Ockham's Razor is simply, 'a smaller model is more useful than a larger model, if both make sufficiently accurate predictions for your purposes'.

This isn't a really a mind-blowing insight, thus Ockham's Razor is hugely overrated.

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Why isn't it a mind-blowing insight? I never suggested it was but am curious as to why you find this so trivial and don't find any use in Ockham's Razor.

Your first statement bears no relation to the rest of this thread, I feel.

[Borodog]

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The mutilated and incorrect statement of Ockham's Razor is that 'the simplest explanation is the correct one'. It should take all of about a minute to think of a counter-example.

The best statement of Ockham's Razor is simply, 'a smaller model is more useful than a larger model, if both make sufficiently accurate predictions for your purposes'.

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I don't think either one of these is a correct statement of Occam's Razor. 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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This isn't a really a mind-blowing insight, thus Ockham's Razor is hugely overrated.

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I think it would be an incredibly mind-blowing insight for the people that don't actually understand it, which is the majority of people. Occam's razor informs my entire world view. In my opinion it's practically impossible to overrate it.

[Philo]

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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.

[vhawk01]

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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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Yep, thats a better way to put it. In practice we don't really care how likely to be capital T true the explanation is. Thats probably entirely impossible to determine for anything you'd apply the razor to. We just care about selecting one of the infinite explanations that fits the bill. Since you can only go UP infinitely, and cannot go down past some real minimum, we prefer the 'simplest' as a convention.

And I'm with Boro, this is probably the most important concept that exists, for me, and I think its really difficult to overrate it. Its amazing how the two most important, powerful concepts (this and evolution) both seem so ridiculous self-evident and simple, when you finally understand them.

[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]



[/ QUOTE ]

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.

[luckyme]

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And I'm with Boro, this is probably the most important concept that exists, for me, and I think its really difficult to overrate it. Its amazing how the two most important, powerful concepts (this and evolution) both seem so ridiculous self-evident and simple, when you finally understand them.

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Well, they are related, so getting one opens the door to the other.

luckyme

[vhawk01]

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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]



[/ QUOTE ]

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.

[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]



[/ QUOTE ]

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.