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Numquam ponenda est pluralitas sine necessitate

Occam’s Razor is a famous philosophical device, a pragmatic solution when faced with multiple competing hypotheses: always choose the one that necessitates the fewest additional assumptions.

Wikipedia contains this description:

Occam's razor (also written as Ockham's razor and in Latin lex parsimoniae, which means 'law of parsimony') is a problem-solving principle devised by William of Ockham (c. 1287–1347), who was an English Franciscan friar and scholastic philosopher and theologian.

The principle can be interpreted as

Among competing hypotheses, the one with the fewest assumptions should be selected.

In science, Occam's razor is used as a heuristic technique (discovery tool) to guide scientists in the development of theoretical models, rather than as an arbiter between published models. In the scientific method, Occam's razor is not considered an irrefutable principle of logic or a scientific result; the preference for simplicity in the scientific method is based on the falsifiability criterion. For each accepted explanation of a phenomenon, there is always an infinite number of possible and more complex alternatives, because one can always burden failing explanations with ad hoc hypothesis to prevent them from being falsified; therefore, simpler theories are preferable to more complex ones because they are more testable.

I’d argue, however, that the paragraph cited above actually contains at least the seeds of good reasons why it is more than a mere heuristic device. Consider: There is always an infinite number of possible and more complex alternatives, because one can always burden failing explanations with ad hoc hypothesis…. This means that for every concrete question, there is an infinite number of answers; one of them is maximally correct, some are plain wrong, and an infinite number fit the data but make unjustified and unparsimonious assumptions. But then, the simplest explanation that fits the data is actually very special, and not just because it’s more testable, but because of that privileged position. It alone accounts for the observed data without adding extraneous assumptions.

This leaves us with a choice, not just on a heuristic and testing level, but on an epistemological level, too: Do we accept only the one explanation permitted by the data yet spared by Occam’s Razor, or do we accept more explanations? If we do not restrict ourselves to only the simplest working possibility, I do not know of any reason why we should not accept all possibilities. Then, since we have an infinite number of possible explanations, whereof only one is maximally correct, the odds of our choosing the best solution are one out of infinity—which is to say, zero. Neglecting parsimony, then, does more harm than merely making it harder to test our hypotheses: it statistically guarantees that we will choose the wrong explanations!

So:

Occam’s Razor provides a rule for choosing a single explanation with strong heuristic properties and avoiding the arbitrary choice of complex solutions that, statistically, are certain to be wrong in detail.


That’s perhaps a bit abstract, so let’s ground it a bit. This actually came up in a discussion on religious epistemology, where I set up something like this: Agnostic (sometimes called “weak”) atheists make a negative existential claim, not based on the existence of positive evidence for non-existence, but based on the lack of positive evidence for existence. Or, in plain language: I’m not an atheist because I have evidence there’s no god; I’m an atheist because there’s no evidence of a god.

But then, runs a certain standard counter-argument, the agnostic atheist is on the same rational footing as the theist. Neither has evidence either directly supporting their position, nor directly refuting the contrary. (Perhaps, this may go on to say, the ideally rational stance is ‘strict’ agnosticism, apparently meaning a refusal to commit to any stance on likelihood.)

This, however, I reject on the basis of a stronger Occam’s Razor.¹ The reason is this: Theists and I agree on the existence of physical reality, each other, rocks, trees, suns, moons, and so on. When we run out of established physical reality, I stop. The theist goes on to add unsupported assumptions—and that’s where the trouble sets in. After all, if you are willing to accept one god without evidence, why not two? Or three? Or a billion? If you accept (though you cannot demonstrate it) that the universe was designed by God, how can you be sure it wasn’t actually designed by aliens pretending to be God? Or wizards posing as aliens pretending to be God? Or Smurfs dressed up as wizards posing as aliens… Well, you see where this goes. I can extend this list into infinity.²

If you are willing to accept any proposition without positive evidence, on the mere basis of inability or to disprove it, or impossibility of so doing, then either you must regard all such propositions as equally valid; or you must have a method of separating your proposition from the infinite number of other propositions with the same property (the property that it hasn’t been disproven, or is not falsifiable); or you are being completely arbitrary and no longer rational. But you can’t have a rational method for separating it, for if you did, it would have to be positive evidence, and you wouldn’t face this problem to begin; so either you are being arbitrary and non-rational, or you must accept them all.

And if you hold that the infinity of possible explanations is valid territory to enter, then your preferred explanation is wrong. How do I justify this assertion? Suppose that each explanation can be laser-etched onto a grain of sand, and we take all possible explanations and let the wind carry them into the sandy desert. This is an infinity of explanations, and as the text is too small to read, you cannot know which is which. With no positive evidence to point to any one explanation, your choice is arbitrary relative to the truth. Maybe one of these explanations is the correct one—but it’s one grain of sand in the desert; and it is an infinite desert. When you bend down and pick out a single grain of sand, I can be confident that you chose the wrong one.

I prefer a more consistent principle of reason, Occam’s Razor: Choose the simplest explanation that fits observations (id est, that isn’t falsified). If our investigation has been thorough enough, it is the right explanation. If not, then it is a good explanation to start from as we investigate further, and our investigation won’t be cluttered up by arbitrary (and almost certainly wrong) assumptions.

That is why, in the absence of existential evidence either positive or negative, assuming the negative is more reasonable than assuming the positive. We should be agnostic in the strict sense of being prepared to admit additional evidence—but that does not mean we should be holding our breath.


¹ This is pretty close to Hitchen’s Razor; in a way, it’s the two razors put together: Occam’s and Hitchens’s. Mine is a two-bladed philosophical razor!

² Or if not infinity, then at least until the text of my post exceeds storage limitations. I wonder if I could write a Haskell program to generate an infinite list of increasingly unparsimonious complications…

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Petter Häggholm

April 2016

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