Occam's razor
Ockham's Razor (also Occam's Razor), is a principle attributed to the 14th century logician and Franciscan friar, William of Ockham: "Entities should not be multiplied unnecessarily." This is nowadays understood to mean "Of two competing theories or explanations, all other things being equal, the simpler one is to be preferred." The spelling Ockham's Razor is considered to be correct by most historians and philosophers, but the latinized spelling Occam's Razor is more commonly used.
Ockham wrote the Latin Pluralitas non est ponenda sine neccesitate with the literal English translation Plurality should not be posited without necessity. The principle is most often expressed as Entia non sunt multiplicanda praeter necessitatem (Entities should not be multiplied unnecessarily), but this sentence was written by later authors and cannot be found in Ockham's surviving writings.
Ockham's Razor in science
Ockham's Razor has become a basic principle of the scientific method. It is important to note that it is a heuristic argument that does not necessarily give correct answers; it is a loose guide to the scientific hypothesis which contains the least possible number of unproven assumptions and is the most likely to be fruitful. Often, several hypotheses are equally "simple" and Ockham's Razor does not express any preference in these cases.
For example, after a storm a tree is noticed to have fallen. Based on this evidence of "a storm" and "a fallen tree" a reasonable hypothesis would be that "the storm blew down the tree"--a hypothesis which requires only one assumption--that it was, in fact, a strong wind (as opposed to a meteor or an elephant) which knocked over the tree. The hypothesis that "the tree was knocked over by marauding 200 meter tall space aliens" requires several additional assumptions (concerning the very existence of aliens, their ability and desire to travel interstellar distances and the alien biology that allows them to be 200 meters tall in terrestrial gravity) and is therefore inferior.
Ockham's Razor is not equivalent the idea that "perfection is simplicity". Albert Einstein had this in mind when he wrote in 1933 that "The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience" often paraphrased as "Theories should be as simple as possible, but no simpler." It often does happen that the true explanation is much more complicated than the simplest explanation. People often fail to appreciate this, and misquote Ockham's Razor as stating that "The simplest explanation is the true one."
Ockham's Razor has also been referred to as the "principle of parsimony" and the "principle of simplicity" and "K.I.S.S." (keep it simple, stupid). Another proverb expressing the idea that is often heard in medical schools is "When you hear hoofbeats, think horses, not zebras."
Statistical justifications for Ockham's Razor
There are various papers in scholarly journals deriving versions of Ockham's Razor from probability theory and applying it in statistical inference, and also of various criteria for penalizing complexity in statistical inference. Recent papers have suggested a connection between Occam's Razor and Kolmogorov complexity. However, these interpretations are not generally accepted in the statistical community.
Ockham's Razor and religion
In the philosophy of religion Ockham's Razor is sometimes used to defeat arguments for the existence of God and support the rationality of atheism. Ockham himself used his principle to argue that God's existence cannot be deduced from reason alone. These applications of Ockham's razor are not considered definitive, since they often hinge on highly debatable notions of "simplicity". For example, postulating special creation involves some obvious big assumptions--but to claim that evolution is a "simpler" hypothesis requires that one quantify the exact nature and magnitude of the assumptions on which it rests.
Ockham may have been inspired by earlier thinkers. For example, Book V of Aristotle's Physics has the statement "Nature operates in the shortest way possible."
See also: Falsifiability, philosophy of science, Hanlon's Razor, Rationalism, Bayesian inference, Kolmogorov complexity