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Let’s say two geologists study a singular natural process, an eruption of a certain special volcano, and do a series of measurements for one hour, one every minute.

The data points look like this:

Data

Geologist A makes the hypothesis that the process follows a simple cubic relationship: Hypothesis A

Geologist B makes the hypothesis that the process follows a cubic relationship but with an additional periodic term: Hypothesis B

Both hypotheses explain the data equally well if we just focus on the error between the data and the theoretical values (yes, it visually does not look like this, but mathematically the error is exactly the same).

We now could say that occording to Occam’s razor, geologist A’s explanation is simpler and so to be preferred. There is no need to add the periodic wave term to the function, it can be discarded without any downsides.

But a lot of amateur (?) examples about Occam’s razor involve the most stark contrasts and absurd examples – for example:

Intuitively, this makes sense – if we have two explanations of why telephones ring, one of which is “electrical pulses are sent down a wire” and the other is “electrical pulses are sent down a wire, except for my phone, which has magic invisible pixies which make a ringing noise and talk to me in the voices of my friends”, we can be pretty confident in dismissing the second explanation and thinking no more about it – it introduces additional unnecessary complexities into things.

(source: Sci-Ence! Justice Leak!)

Here the question arises when “magic invisible pixies” are ever an acceptable explanation or model.

Compared to the example of the two geologists, there is virtually no evidence at all that lets us conclude that invisible pixies are involved. As bad as geologists B’s hypothesis is, there is evidence to support it; his model is – at least compared to the pixies – still quite tightly bound to the evidence.

Now, “electrical pulses” is the correct explanation and by common-sense standards it is not to be preferred because it is simpler but because it is true; skepticism about it approaches Cartesian levels of doubt. It does not get much more proven true than this. And the “magic pixies” explanation is to be rejected because there is no evidence for it.

It seems that Occam’s razor, as it is often presented in informal discussions and popular literature, has been morphed into an argument against taking an agnostic stance (= rejecting all given explanations/models/hypotheses regarding a phenomenon). I suspect this cannot be right and was not what Occam and the long list of philosophers who supported some version of the razor had in mind.

If we lack good evidence and knowledge, it feels like an affront to common-sense that we just try to make up some explanations and then pick the “simplest one”. Shouldn’t the rational person just say “I don’t know yet how it works” ?

What criteria do two explanations, hypotheses or models have to fulfill so that Occam’s razor can be sensibly applied?

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  • I am not sure what to make of the post. If it is about the boldface question then most of the post is moot, and SEP already has a long article on criteria of parsimony. If, on the other hand, the described anecdotal misapplications are somehow relevant then I do not know what the question is. "Magic pixies" are not explanatory in any relevant sense, so they should be not rejected, but rather not considered at all. A non-explanation can not be a simple (or complex) explanation. Ockham himself did not even talk about "simplicity".
    – Conifold
    Dec 7 '19 at 0:43
  • SEP has a separate article on explanation, as does IEP. What is or is not admitted for consideration strongly depends on maturity of the subject, so there are no general criteria, parsimony is never (supposed to be) decisive by itself, apart from other epistemic criteria, and the choice between judgment and suspension thereof is particularly sensitive also to pragmatic purposes. So the "at what point?" question in terms of parsimony alone seems ill-posed.
    – Conifold
    Dec 7 '19 at 0:59
  • Before considering the "B" hypothesis, one would have to take further samples at intervals other than one minute, to avoid the possibility that the extra factor is an artefact of the sampling rate. If all cases result in the same frequency for the extra factor, then it is worth considering. Dec 7 '19 at 1:54
  • I don't think scientists think of Occam's razor in these types of scenarios. More common considers include things like considering the derivative, does it make sense for a periodic rate of change, is the amplitude within the y-axis error bars, does the coefficient of determination (penalized for additional terms) drop significantly if the periodic term is dropped etc.
    – Cell
    Dec 7 '19 at 15:09

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