Postulate Fewer Entities

Critical Thinking by Adam on 2007-10-06 08:06

“God has chosen the world that is the most perfect, that is to say, the one that is at the same time the simplest in hypotheses and the richest in phenomena.”

Gottfried Leibniz, Discours de métaphysique, 1686

If you were to take a look in my refrigerator right now, you might see a bottle of water. Let’s say that you wanted to form a theory about how that bottle got there. (Actually, it doesn’t matter much if you want to or not - our brains do this sort of theory-forming automatically.) Which of the following theories would you be most likely to come up with?

  1. A thief broke into my house the previous evening and, as part of his skullduggery, placed the bottle of water in the fridge.
  2. Space aliens used particle-transporter technology to beam the bottle into its current location.
  3. Quantum fluctations caused a large cloud of particles, which just happened to be shaped exactly like a bottle of water, to appear in the fridge. (Presumably, there is an anti-particle version of the same bottle that appeared at the same time in my neighbor’s fridge.)
  4. At some point in the recent past I purchased the bottle of water from a local store and placed it in my fridge to keep it cold.

I’m going to guess you chose the last option. But why? You have an equal amount of evidence for any of these occurrences. Empirical observation does not favor any of these theories over any other.

Leibniz’s quote above hints at Occam’s razor, which is an indispensable tool for judging the merit of theories for which we have imperfect information. And outside the realm of carefully controlled scientific experimentation, we are almost always judging theories from highly imperfect information.

What makes you pick the fourth theory above the others? That is, what makes Occam’s razor work?

The obvious answer here is that you’re playing the statistics. The likelihood of the first three theories is very low, whereas the fourth choice is extremely likely.

There’s a less obvious component to Occam’s razor, however: a theory has the most merit when it postulates the existence of a minimum of new entities or forces, but explains a large quantity of known phenomena.

The top three theories for the bottle in the fridge all required a great number of previously unexplained entities: a burglar with an odd approach to stealing, space aliens who came all this way just to fool about with bottle transportation, quantum behavior that doesn’t match anything that has ever been observed before. Each of these explanations leave us with a net negative of knowledge, because now you have to find explanations for all the new entities that have been dreamed up in order to make the theory work.

Does that mean that the simplest explanation is always the right one, so that we need not bother to collect further evidence? Of course not. Empirical observation may provide evidence which we can use to better judge available theories, or form new ones. But the new evidence will be judged with the same underlying principle: how can we make the data fit, using the simplest explanation possible? If I report that I did not place the bottle of water in the fridge, the next theory you would jump to is that someone else - perhaps someone who came to visit my house recently - placed it there. This fits the data that we have, while keeping our explanation as simple as possible.

One comment per 'Postulate Fewer Entities'

  1. Xyla says:

    I always notice professional skeptics breaking occam’s razor. They jump over backwards through many hoops to disprove something which is simply explained by something they don’t believe in.

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