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dudeicus comments on Occam's Razor - Less Wrong

37 Post author: Eliezer_Yudkowsky 26 September 2007 06:36AM

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Comment author: dudeicus 23 March 2011 03:25:47PM -1 points [-]

Occam's Razor is "entities must not be multiplied beyond necessity" (entia non sunt multiplicanda praeter necessitatem)

NOT "The simplest explanation that fits the facts."

Now thats just purely definition. I think both are true. I think there are problems with both. The problem with Occams razor, is that yes its true, however, it doesn't cover all the bases. There is a deeper underlying principle that makes Occams razor true, which is the one you described in the article. However summing up your article as "The simplest explanation that fits the facts" is also misleading as in, while it does seem to cover all the bases, it only does so if you use a very specific definition of simple which really doesnt fit with everyday language.

Example: Stonehenge, let me suggest two theories, 1. it was built by ancient humans, 2. it fell together through purely random geological process. Both theories fit with the facts, we know that both are physically possible (yes 2. is vastly less probable, ill get to that in a second). Occams razor suggest 2. as the answer, and "The simplest explanation" appears to be 2. also. Both seem to be failing. The real underlying principle as to why Occams razor is true, is statistics, not simplicity. Now dont get me wrong, I understand why "The simplest explanation that fit the facts" actually points to 1., but then you have to go through this long process of what you actually mean by simplest, which basically just ends up being a long explanation of how "simple" actually means "probable".

Anyways, I'm just arguing over semantics, I do in fact agree with everything you said. I just wish there was no Occams razor, it should just be "The theory which is the most statistically probable, is usually the right one." This is what people actually mean to say when they say "The simplest explanation that fits the facts."

Comment author: JohnH 22 April 2011 03:32:05AM 2 points [-]

In statistics generally the model that has the least variables and is the most statistically probable is the one used. See things like AIC or Bayesian Information Criterion on how to choose a good model. This means that Occam's razor is accurate. Given that is is possible to continuously add variables to a model and get a perfect fit but have the model be blown apart with the addition of an additional observation that is not otherwise influential, then, unless you are defining probability to include an Information Criterion, your formulation is less useful.

Comment author: JoshuaZ 22 April 2011 03:40:54AM 3 points [-]

Occam's Razor is "entities must not be multiplied beyond necessity" (entia non sunt multiplicanda praeter necessitatem)

NOT "The simplest explanation that fits the facts."

The form you list it in is the historical form of Occam's Razor, but it isn't the form that the Razor has been applied in for a fairly long time. Among other problems, defining what one means by distinct entities is problematic. And we really do want to prefer simpler explanations to more complicated ones. Indeed, the most general form of the razor doesn't even need to have an explanatory element (I in general prefer a low degree polynomial to interpolate some data to a high degree polynomial even if I have no explanation attached to why I should expect the actual phenomenon to fit a linear or quadratic polynomial.)

Comment author: adamisom 22 December 2011 10:35:01PM 0 points [-]

I may be missing something here -- Occam's Razor is "entities must not be multiplied beyond necessity" (entia non sunt multiplicanda praeter necessitatem)

NOT "The simplest explanation that fits the facts."

-- but isn't the post using the first definition anyway? So even if he explicitly wrote the second definition instead of the first, he was clearly aware of the first since that's what corresponds with his argument.