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I never bought into the razor.

For example, if I have two hypotheses A and B with equal evidence, the razor would have me pick the simpler one. But personally in my mind, I create a sort of credence-distribution over the two hypotheses and hold the resulting distribution as my belief.

This can put us into some really interesting situations. For example, maybe you consider the hypothesis of the Flying Spaghetti Monster to have credence zero (and all other god hypotheses). But because there are an infinite number of possible hypothesis, it's possible that when you integrate over their credences you get a non-zero credence. Then, your belief in god would be a credence-distribution over all possible beliefs in god.

Are there philosophers who think this way?

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  • Mathematically, given two hypotheses that generate the same data set, the one which can be expressed in the shortest way is the one most likely to be true. This has been shown mathematically. The problem is determining minimum descriptive length. Usually we make guesses about what constitutes simplicity. – Daniel Goldman Nov 8 '17 at 22:27
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    @DanielGoldman, do you have any references for your claim that it can be shown mathematically? – Kenshin Nov 19 '18 at 11:55
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I don't know of any particular philosopher that thinks in that way. From what you explained, I tend to agree with your view, but what I can give you in terms of an answer is something else.

I wouldn't say that your view is actually a disagreement with Occam's Razor. The issue here is that Occam's Razor is so much used and have so many different "versions" that it tends to get fuzzy. Probably the most common version - at least informally - is that when two hypothesis explain equally well the same phenomenon, the simpler one should be preferred. The problem is that it is not trivial to define neither "equally well" nor "simpler".

It's hard to know exactly what Occam(Ockham?) meant by it, but a more understandable version is: "One should not multiply entities unecessarily". That makes a lot more sense because all it states is that you should not have things in your theory that aren't necessary, i.e. prefer simplicity.

So, for example, suppose we have two theories to explain "why the sky is blue": A) because of light scattering; B) because of light scattering and my shoes are blue. In that case, notice that A is clearly simpler than B, but that's only because B is the same as A, but with unecessary entities added.

And that's why I think your model is not a disagreement with Occam's Razor, since you can do as you said while still using Occam's Razor as a criteria to assess different hypothesis.

  • But you're making the assumption that blue shoes are unnecessary, whereas I don't believe that. I have a credence of 99.999...99% that they're unnecessary, but I still have a non-zero credence that they're important. – Mike Izbicki Aug 16 '12 at 18:40
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    @MikeIzbicki I understand, but in that case you can transfer your belief distribution to the theories themselves. So you have for example 99.9% in A and 0.1% in B, but that distribution is directly influenced by the fact that B is A plus low probability "blue shoes". The fact that A is sufficient to explain the fact without the blue shoes is exactly what makes B have a much lower probability. So Occam's Razor is a criteria you can use to compare, even if you want to turn the result of that comparison into a probability distribution. – Koeng Aug 16 '12 at 22:03
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Ockham's Razor is a maxim. Maxims are succinct principles or rules that are used to guide actions. The razor guides us to prefer the theory (or theories) that posit(s) the least total number of entities while satisfactorily explaining the phenomena in question over theories that explain the same phenomenon but posit more entities. As the razor's Wikipedia article says:

The razor asserts that one should proceed to simpler theories until simplicity can be traded > for greater explanatory power.

Let's look at your examples to see how this bears out. You say:

if I have two hypotheses A and B with equal evidence, the razor would have me pick the simpler one.

The razor hasn't been appropriately deployed here. Where you say "simpler one" you really mean that the razor would have you pick between hypotheses A and B in virtue of the number of explanatory posits they individually put forth. Specifically, if there are more explanatory posits in A than in B, and A and B both satisfactorily explain all of the relevant observations, then B is simpler than A.

But personally in my mind, I create a sort of credence-distribution over the two hypotheses and hold the resulting distribution as my belief.

I'm going to try not to step on any toes here. No matter how you slice it, the content of your belief is almost undoubtedly not the "resulting distribution" of a "credence-distribution over the two hypotheses." It's easy to see why it can't be: when someone asks you if you believe A or B, your answer will never be "the resulting distribution of a credence-distribution over the two hypotheses." That may describe how you came to hold the belief you hold, but that process is not the content of that belief.

This can put us into some really interesting situations. For example, maybe you consider the > hypothesis of the Flying Spaghetti Monster to have credence zero (and all other god hypotheses). But because there are an infinite number of possible hypothesis, it's possible > that when you integrate over their credences you get a non-zero credence. Then, your belief > in god would be a credence-distribution over all possible beliefs in god.

Here you've given some great examples of when to use Ockham's Razor because you've invoked explanatory posits that unduly complicate a reasonable analysis of the applicability of Ockham's Razor.

Questioning Ockham's Razor means questioning the role of theoretical simplicity and the number of proffered explanatory posits. The only problems you bring up with the razor are borne of "credence distributions." What exactly are credence distributions? No matter what your answer is, they will also be explanatory posits of your theory. By definition, more explanatory posits makes your theory more complicated. In principle there's no reason you can't bring new explanatory posits into a theory, but as the Ockham's Razor wikipedia article says, they must offer some explanatory power. Including "credence distributions" in your theory doesn't seem to explain any more than a theory without them, and in fact seems to create problems where there were none.

Are there philosophers who think this way?

I would be extremely surprised if there were philosophers who think this way.

  • Credence distributions are just subjective probability distributions, and are basically the foundation of modern artificial intelligence. For example, if I hold a 20% credence that god does exist and 80% that he does, that is a credence distribution. – Mike Izbicki Aug 16 '12 at 18:42
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Read the paper Friederich Nietzsche and the seduction of Occam’s razor by Danesh-Meyer, Helen V.Young, Julian, 2010. It states the risk of assuming a single root cause for a plethora of symptoms in the medical context. Interesting and enjoyable read.

In my opinion, in evaluating data mining models that seek multiple explanatory variables to describe a situation, the method based on the statement mentioned above, from Wikipedia, is of significant value: "The razor asserts that one should proceed to simpler theories until simplicity can be traded for greater explanatory power"

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I've begun seeing Ockham's razor as being a statement about cognition and learning, and not about the construction of reality. Human understanding works best by successive approximation. Think about coming up with the coefficients in a Taylor series one at a time, vs. trying to figure out multiple at once. Trying to figure out multiple at once is computationally much harder. Having to fit multiple variables simultaneously is much harder than fitting them one at a time.

Possible support for this comes from Grossberg 1999 The Link between Brain Learning, Attention, and Consciousness, in which we aren't even conscious of observations unless they sufficiently match a model we already have in our brain. We learn very well when the difference between what we know and what we're being presented with is not too large.

Imagine Charles Darwin employing Ockham's razor to the cell, using it to say that the cell probably isn't very complex (details). That would have been a demonstrably wrong application of the razor. The razor doesn't address ontological complexity, despite it often being used that way. Instead, it says that the best way to understand the cell is by bits and pieces. An alternative, today, would be to cease all study of the cell until a computer simulation can be programmed which perfectly simulates cells. This would obviously never work. One could rephrase the razor: "Don't bite off more than you can chew."

One property of successive approximation is that you stop when the next increment does not make things any better. Ockham's razor says that it is here that you stop.

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Occam's Razor says that you cannot multiply causes beyond necessity, as in: if one ninja could take out the president, you can't posit that two or more were involved. Unless you have evidence of more than one. "Plurality must never be posited without necessity". If a hypothesis is insufficient to explain something, then Occam's razor does not apply. Occam's Razor does NOT say "oversimplify things".

I don't have sources to cite. I draw my conclusion from reading the works of William of Occam. If I ever write a book on it, I'll cite it immediately.

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