Occam's Razor

From SkepticWiki

1 Definition
- 1.1 "Simpler Theory"
2 Versions of the Razor
3 Rationale
4 Examples of Application
5 Fallacious Application
6 Related Articles
7 References

[edit] Definition

A central maxim of skepticism, that given two explanations that equally describe a given situation, the simplest one is most likely to be the correct one.

Occam's razor concerns the choice of which alternative theory to tentatively accept; it by no means constitutes proof that the simpler theory is, in fact, correct.

[edit] "Simpler Theory"

There are several misconceptions to the meaning of the word "simpler", for example:

Creationist: Since Occam's Razor says the simplest explanation is most likely to be correct, then my explanation is "Goddidit!". What could be simpler than that?

It's very tempting to believe that "simpler" means "fewer words", but meaning of a "simpler" explanation has a very precise definition in the context of Occam's Razor.

Formalized, Occam's Razor states [1]:

1) Unfalsifiable theories should be rejected as useless. This is an epistemological position, and is based on the simple observation that an unfalsifiable theory can not be used to learn anything that you do not already know.

2) Any claims within a theory which are not logically necessary to account for the testable claims of the theory, must be rejected. This is just an extension of (1), since such a theory could always be split into one theory which possesses no such claims, and one theory which is unfalsifiable.

3) Given two theories which make exactly the same testable claims, if those two theories differ in any way which is not simply semantic, then at least one of them must possess claims which are not logically necessary to account for its testable claims.

That third one is more difficult to justify, although Logical Positivism may provide the answer. It was shown that it is possible to construct a formal scientific logical language in which everything is defined in reference to observations. Points (1) and (2) above indicate that if such a formal language exists, then any theory which is not rejected by point (1) or (2) must be expressible in that formal language. Having done that, it is clear (well, maybe not so clear) that the expression of such a theory in that formal language must be unique. That is, two theories which make exactly the same testable predictions, and which make no claims which are not logically necessary to produce those predictions, must have exactly the same representation within that formal scientific language, which means that they only differ semantically.

[edit] Versions of the Razor

As originally stated by William of Ockham, a franciscan friar: "Pluralitas non est ponenda sine necessitate" (Plurality should not be supposed without necessity)

Isaac Newton expressed this as: "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances."

Colloquially, the KISS Principle (Keep it simple, stupid!) and the analogy "When you hear hoofbeats, think horses, not zebras" express the same idea.

[edit] Rationale

There are infinitely many possible "theories" that can explain a given set of facts. Consider the following two possible laws of nature:

1. The force of gravity diminishes with the square of the separation of two bodies.

2. The force of gravity diminishes with the square of the separation of two bodies, until December 21, 2012, at which time it will become a linear proportion.

Both of these laws predict equally well the observed effects of gravity in the universe. We cannot say for certain that the second one is wrong. However we may tentatively accept the first one as correct in the absence of any contradictory data, since it is simpler. Without Occam's razor, there would be any number of different rival theories, and the pursuit of general knowledge would become impossible.

[edit] Examples of Application

A classic example is the choice of the Copernican model of the Solar System over the Ptolemaic model. While these equally well described the observed motion of heavenly bodies (at least to 15th century standards), the Copernican model was accepted as being the simpler, not requiring equants and crystal spheres. (Later, the Keplerian model of the Solar system was accepted over the Copernican model, mostly because of its improved accuracy but also because Kepler's ellipses finally eliminated the need for epicycles.)

More recently, the results of the Michaelson-Morely experiment could be explained by supposing that objects contract and their time slows down when they move relative to the luminiferous ether. Alternatively, objects contract and time slows down when they move relative to anything at all. The ether idea was discarded from physics as an unnecessary arbitrary construct.

[edit] Fallacious Application

Here are some examples of fallacies associated with incorrect use of the razor.

Fallacious Argument #1:

The existence of the universe may be attributed to the complex interactions of numerous elementary particles, which are described by equations so complex that they are inaccessible to anyone who has not spent years studying them. Alternatively, the existence of the universe may be attributed to God. Since the second is a simpler explanation, it is more likely to be true.

This argument is fallacious since it assumes that the concept of "God" is simpler, since it can be referenced with fewer words. The attributes that God would need to have to create the universe are at least as complex as those used in fundamental physics.

Fallacious Argument #2:

Chemical interactions can be described in terms of 91 naturally occurring elements, or in terms of the four elements known to the ancient alchemists. Since the second theory postulates fewer entities, it is more likely to be correct.

This argument is fallacious since the two theories do not equally well describe the observed facts. Occam's Razor can only be applied when the theories have (so far) been equally accurate.