Ockham's Razor

[KipBond]

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it is instructive to observe that it is almost always wrong.

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Ops! In an attempt to be contentious I was being a little wayward in my use of language. What I meant of course was that not that Ockham's razor itself was wrong, but any theory it promotes was, in the sense that in any non trivial scenario the will always be a more accurate theory.

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F=ma?

I think you're forgetting the need for empirical adequacy, which any Occam's Razor pretty much assumes.

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I think you mean that Newton's 2nd law is "empirically adequate", even though it is not as accurate as Einstein's theory of special relativity (because mass & time are dependent upon velocity).

But, the point should be noted that "F=ma" is not as accurate of a model as Einstein's -- even though it is very simple, and still widely used (because it is "good enough"). In this sense, it is not "more likely to be true"; rather, Einstein's more complicated model is "more likely to be true".

[Metric]

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The thing is, for any randomly generated program that computes pi correctly for some digits, that program can have add-on lines of code that don't essentially change it. It can have infinitely many add-ons. I don't see any way you could reasonably Pronounce a probalility measure on that space of unbounded finite randomly generated codes. I don't think the proper measure on such a space would even be a probability measure.

If this arguement really has technical merit, somebody has written a peer reviewed paper on it somewhere that you should be able to reference. I doubt you can do that.

PairTheBoard

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If you generate your input program by, say, flips of a fair coin, you are more likely to run into a relatively short self-delimiting program for output string S before you have huge add-ons that essentially do nothing and an enormously huge program for output string S. In fact, the probability that your machine outputs S is dominated by the probability for you to randomly generate the simplest few programs that compute S.

Much has been written about this stuff -- here's a nice little intro that I just googled: http://www.research.ibm.com/journal/...ibmrd2104G.pdf

If you're only interested in the first peer-reviewed papers on the subject, look for the work of Solomonoff and Levin.

[Metric]

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i.e. no cheating allowed).

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"Lets assume that no cheating is allowed.”

“Yes but what happens if someone cheats.”

“We are assuming that no on cheats.”

“Yes I know that, but what happens if nether the less someone cheats.”

… 10 years later…

… no one is allowed to cheat”

“I know that, but what happens if despite that assumption someone actually does….

….
… later…

… cheats”
“but…

….

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If you do cheat, that's fine -- it just means that I no longer care about the result from the point of view of Ockham's razor. Because then any statement about probabilities is directly related to how you cheated, and is no longer a general logical principle connecting generic cause (with no prior) to effect.

[vhawk01]

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The people arguing that OR implies that certain theories are more likely 'true' or 'correct' have different definitions of those words than is meant in an empirical/scientific sense.

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Not really. To wit:

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This is often paraphrased as "All things being equal, the simplest solution tends to be the best one." In other words, when multiple competing theories are equal in other respects, the principle recommends selecting the theory that introduces the fewest assumptions and postulates the fewest hypothetical entities. It is in this sense that Occam's razor is usually understood.

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What definition of "best"? My contention is that the only definition of "best" that can possibly have any meaning is "the most likely to be correct."

Again, if the simplest explanation is not more likely to be true than alternatives containing unnecessary complications, the what benefit is choosing the simpler one? What is the justification? These are the essential questions that keep getting dodged.

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I did my best to show the benefit, but I am at a loss to show the justification. I was always under the impression that the Razor is, in fact, unjustified. The benefit is simply that it is always easier if we can decide on one explanation or theory to talk about, EVEN IF WE REALIZE that there are an infinite number of acceptable ones. We could make any sort of arbitrary selection we wish, but the only one that ISN'T arbitrary is the Razor. Its my understanding that it is just as justified to instead choose the most complicated one, but that it is, in practice, impossible to do so. We can always find a more complicated explanation.

[vhawk01]

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Again, if the simplest explanation is not more likely to be true than alternatives containing unnecessary complications, the what benefit is choosing the simpler one? What is the justification? These are the essential questions that keep getting dodged.

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The answer is this:

OR says nothing about which equally reliable & explanatory theory is "more likely to be true".

You can read a lot about this here:

http://en.wikipedia.org/wiki/Occam's_Razor

We use the simplest of equally reliable & explanatory theories for various reasons: practicality, easier to learn, apply, remember, teach, etc. Once the more complicated model provides a bit more explanatory & reliable predictions, then simplicity takes a back seat when we need to be more accurate.

You can argue that, indeed, it is the case, that the simplest theory is "most likely to be true", and then you could create your own maxim for that. But, that's not Occam's Razor.

But, I think you'll be hard pressed to show that this is the case. It seems to me that more complicated models are usually more reliable & explanatory than simpler models. We still use the simpler models sometimes because they are easier and are 'good enough', but we know they are not "more likely to be true". There may be exceptions, but I think they are rare. Of course, at some point you are going to have to define & present a way to measure "simplest".

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Yeah, this is better than my post.

[vhawk01]

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The people arguing that OR implies that certain theories are more likely 'true' or 'correct' have different definitions of those words than is meant in an empirical/scientific sense.

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Not really. To wit:

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This is often paraphrased as "All things being equal, the simplest solution tends to be the best one." In other words, when multiple competing theories are equal in other respects, the principle recommends selecting the theory that introduces the fewest assumptions and postulates the fewest hypothetical entities. It is in this sense that Occam's razor is usually understood.

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What definition of "best"? My contention is that the only definition of "best" that can possibly have any meaning is "the most likely to be correct."

Again, if the simplest explanation is not more likely to be true than alternatives containing unnecessary complications, the what benefit is choosing the simpler one? What is the justification? These are the essential questions that keep getting dodged.

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I did my best to show the benefit, but I am at a loss to show the justification. I was always under the impression that the Razor is, in fact, unjustified. The benefit is simply that it is always easier if we can decide on one explanation or theory to talk about, EVEN IF WE REALIZE that there are an infinite number of acceptable ones. We could make any sort of arbitrary selection we wish, but the only one that ISN'T arbitrary is the Razor. Its my understanding that it is just as justified to instead choose the most complicated one, but that it is, in practice, impossible to do so. We can always find a more complicated explanation.

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As a matter of fact, Boro, if you interpret the Razor the way you seem to be doing, then what can the phrase "all else being equal" possibly mean? How could any two theories ever be equal in all else, since obviously "probability of being correct" is just about the only relevant "all else" and you are deeming it exactly NOT equal?

[IronUnkind]

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We could make any sort of arbitrary selection we wish, but the only one that ISN'T arbitrary is the Razor. Its my understanding that it is just as justified to instead choose the most complicated one, but that it is, in practice, impossible to do so. We can always find a more complicated explanation.

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There are other non-arbitrary criteria which one might use. Cleverness, for example.

[vhawk01]

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We could make any sort of arbitrary selection we wish, but the only one that ISN'T arbitrary is the Razor. Its my understanding that it is just as justified to instead choose the most complicated one, but that it is, in practice, impossible to do so. We can always find a more complicated explanation.

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There are other non-arbitrary criteria which one might use. Cleverness, for example.

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Thats the same one I'm using.

[Philo]

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If justifying OR is a straightforward empirical matter . . .

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Why do you keep saying this, when that isn't what the people you are arguing with are saying?

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To quote you, you said earlier, "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."

If you think that OR says something like "the simplest theory is more likely to be true," then you think the justification for OR is empirical, rather than, say, aesthetic, pragmatic, or deductive, which are all forms of justification for OR that philosophers have offered.