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A Dialogue on Occam’s Razor

Previously: Please Stop Misunderstanding Occam’s Razor.

What is Occam’s Razor? It is an academic principle attributed to 14th Century English Franciscan William of Ockham (apparently we’ve all been butchering his name all this time, who knew?). It is stated thusly:

Entities should not be multiplied without necessity.

It’s not very precise, like my “we decide to go with” statement. So consider the following disagreement with several people trying to be more precise about what they mean:

//

Andy: Consider two hypotheses about where dinosaur bones came from: Either there were literal dinosaurs that lived and died, whose bones we now found; or Satan carefully laid dino bones around the world in such a way that we would be deceived into believing there were actual dinos. By construction they cannot be distinguished by any experimental test. So why are we debating them? There’s no way to tell the difference so we might as well accept that they’re equally valid.

Betty: Surely not! Clearly the hypothesis of actual dinosaurs is vastly simpler than the one with Satan faking dinosaurs, with no loss in predictive power. Therefore, by Occam’s Razor, we conclude that it is more likely that dinosaurs actually existed.

Carl: Wait wait, how do we know that this is how the world works? By what test can we distinguish and verify the “actual dinosaurs” hypothesis?

Betty: There is no test, even in principle; if Satan is very clever he can make all the experiments look the same. But there’s no reason why the Universe would be overly complicated. Occam’s Razor says the simpler explanation is more likely to be true, and “actual dinosaurs” is simpler.

Carl: I agree that it’s simpler, but that doesn’t imply anything about whether it’s true. The Universe just is the way it is. We don’t know that it’s simple, though we might wish it was. The Universe might have a bunch of ZEVOs running around, and it doesn’t care that we can’t tell the difference.

Betty: So you reject Occam’s Razor?

Carl: No no, I accept it, but you are misunderstanding its implication. The “Actual Dinos” hypothesis is simpler, has fewer moving parts, fewer hidden variables. Therefore, it opens itself up to greater testability than the “Satan’s Trick” hypothesis. A complicated explanation like Satan’s Trick can explain anything, because all the relevant variables are hidden underneath a magical entity that can’t be reduced or tested for, whereas Actual Dinos makes predictions that can be tested. Remember that “The strength of a theory is not what it allows, but what it prohibits; if you can invent an equally persuasive explanation for any outcome, you have zero knowledge.” We can’t falsify Satan’s Trick but we may falsify Actual Dinos; all Occam’s Razor asks of us is that we prefer the hypothesis that is “simpler” in the sense of being “more testable.”

Diane: I think you’re all very confused.

Carl: What do you mean?

Diane: You are all getting part of the story right. Yes, the hypotheses cannot be experimentally distinguished. Yes, “Actual Dinos” is the simpler explanation. And yes, simpler often implies potential testability, but in this case does not. See, the problem is that there are not only two hypotheses, but that the possibilities are innumerable.

Andy: What do you mean?

Diane: See, we are considering two potential hypotheses, but for a given fact there are infinite hypotheses that can explain it. They take the form “Dino Bones + X”, where X takes infinitely many forms: Actual Dinos, Satan, A Fairy That Turns Dirt Into Bones, etc. You can multiply these without end as well; “Satan + Satan 2” or “Dirt Fairy + Actual Dinos” of “Ten Satans + Three Dirt Fairies” constitute real possibilities in the solution space.

The problem here is probabilistic: any possibility that is strictly more complex–here let’s say I mean “more inputs” or “more assumptions” or “requires more things to be true”–are probabilistically less likely than ones that are less complex. To do this really carefully requires some mathematical rigor, but more or less it’s just a question of avoiding the Conjunction Fallacy.

In short, Linda is more likely to be a bank teller than to be both a bank teller and active in the feminist movement, and something like this is all Occam’s Razor boils down to.

//

And so they all internalized Diane’s amazing description, changed their minds immediately, and lived rationally ever after.

To sum up,
Andy (incorrectly) believes hypotheses with identical predictions are equally likely;
Betty (incorrectly) believes the Universe is simple and so simple hypotheses are preferred ontologically;
Carl (incorrectly) believes a testable hypothesis is more likely to be true than an untestable one;

And Diane (correctly, in my view) identifies Occam’s Razor as a probabilistic statement which almost completely reduces to the avoidance of the Conjunction Fallacy.

One thought on “A Dialogue on Occam’s Razor

  1. This is very interesting, I’m reminded of a talk by Yudkowski which I cannot find at the moment, and Huemer has written about OR before.

    https://fakenous.net/?p=708

    Maybe you’re preserving the last interpretation of OR that hasn’t already been shredded to pieces from one thinker or another. I still wonder if any stronger version can still be preserved.

    Some people think about thought as a hierarchical structure where the more basic beliefs are the foundation for less basic beliefs. Conclusions lay on top of premises. Claims that are nearer to the base of the structure might be considered “simpler” beliefs, and must be considered with more confidence than less simple/basic beliefs.

    Like

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