Occam's razor

Occam's Razor (also Ockham's Razor), is a principle attributed to the 14th century logician and Franciscan friar, William of Ockham that forms the basis of methodological reductionism. It is nowadays usually stated as follows:

"Of two competing theories or explanations, all other things being equal, the simpler one is to be preferred."

When that is ambiguous, Isaac Newton's version may be better:

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

In modern usage, "true" may mean "well established."

The principle is most often expressed as Entia non sunt multiplicanda praeter necessitatem, or "Entities should not be multiplied beyond necessity", but this sentence was written by later authors and cannot be found in his surviving writings. William wrote the Latin Pluralitas non est ponenda sine neccesitate, which translate literally into English as "Plurality should not be posited without necessity".

Dave Beckett of the University of Kent at Canterbury writes: "The medieval rule of parsimony, or principle of economy, frequently used by Ockham came to be known as Ockham's razor." [1]

Occam'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."

Another variant of this law is Thargola's Sword from Nightfall, written by Isaac Asimov and Robert Silverberg: "We must drive a sword through any hypothesis that is not strictly necessary".

Science and Occam's Razor

Occam'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 Occam's Razor does not express any preference in these cases.

For example, after a storm you notice that a tree has fallen. Based on the evidence of "a storm" and "a fallen tree" a reasonable hypothesis would be that "the storm blew down the tree" -- a hypothesis that requires only one assumption--that it was, in fact, a strong wind that knocked over the tree, rather than a meteor or an elephant. 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 less preferable.

Occam's Razor is not equivalent to 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 happens that the best explanation is much more complicated than the simplest explanation because it requires fewer assumptions. Some people have oversimplified Occam's Razor as "The simplest explanation is the best." (or is "the true one")

Statistics and Occam's Razor

There are various papers in scholarly journals deriving versions of Occam'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.

One of the problems with the original formulation of the principle is that it only applies to models with the same explanatory power (i.e. prefer the simpler one of equally good models). A more general form of Occam's Razor can be derived from Bayesian inference and Bayesian model comparison, which can be used to compare models that don't fit the data equally well (see e.g. Duda, Hart & Stork, 2001). These methods will optimally balance the complexity and the power of the model.

Religion and Occam's Razor

In the philosophy of religion Occam's Razor is sometimes used to defeat arguments for the existence of God. None of these applications has been considered definitive because the competing assumptions are not precisely defined. Also, it should be added that the principle is only a guide to the best theory based on current knowledge, not the "truth."

William 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."

Galileo Galilei notably lampooned Occam's Razor in his Dialogue. The principle is represented in the dialogue by Simplicio.

The telling point that Galileo Galilei presented ironically was that if you really wanted to start from small number of entities; one could always consider the alphabet as the fundamental entities, since you could certainly construct the whole of human knowledge out of them. (A view that Abraham Abulafia held much more expansively.)

Adding another layer of Irony, many modern scientists and mathematicians seriously propose that the basic "entities" of reality may be "bits of information", i.e. the digits of binary code, in which case the entities of William of Occam might be seen as foreshadowing the logic of George Boole and modern computing.

Perhaps due to the abstuse nature of medieval logic and the obscure goals of William of Occam as a theologian and logician, discussion and application of Ockham's Razor is frequently full of ironies.

For example, William is widely regarded as a precursor of the Scientific Method because he argued for a degree of intellectual freedom in an time of dogmatic belief, but he might equally be seen as an apologist for Divine Omnipotence, since he was concerned to demonstrate that creation was contingent and the Creator free to change the rules at will: If God is free to make an infinity of worlds with completely different rules from those which prevail in our world, then we are free to imagine such worlds and their logical and practical consequences (within the bounds set by the Church's infallible Dogma).

Thus Ockham's cautious answer to the sophomoric philosophy paradox "Can God make a stone so heavy that He Himself could not lift it?" would be a qualified yes, which is to say that God can do anything which is not a logical contradiction or heretical.

Perhaps the best formulation of Occam's Razor is the one which states that, of equally good explanations for a phenomenon, the best one is the simplest explanation which accounts for all the facts.

See also:

• Falsifiability,
• philosophy of science,
• Hanlon's razor,
• Rationalism,
• Bayesian inference,
• Bayesian model comparison,
• Kolmogorov complexity,
• scientific reductionism

Reference

• Richard O. Duda, Peter E. Hart, David G. Stork (2000) Pattern classification (2nd edition), Section 9.6.5, p. 487-489, Wiley, ISBN 0471056693

External links

• What is Occam's Razor?
• Skeptic's Dictionary: Occam's Razor
• NIPS 2001 Workshop "Foundations of Occam's Razor and parsimony in learning"
• We Must Choose The Simplest Physical Theory: Levin-Li-Vitányi Theorem And Its Potential Physical Applications
• Information Theory, Inference, and Learning Algorithms, by David MacKay, includes an introductory chapter on the automatic Occam's razor that is embodied by Bayesian model comparison.

Other uses

• Ockham's Razor (band)