Bronze-level articleOccam's razor

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Logic and rhetoric

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Plurality must never be posited without necessity.
—William of Ockam, 1495

Occam's razor is a principle which states that one should never make more assumptions or assume more causes than the minimum necessary to solve a problem or find a cause for something. The "razor" is used to "shave away" the unrequired bits from a solution. It is named after the 14th century English philosopher and theologian William of Ockam (or Occam).

The following fact cannot be overstated: Occam's razor is merely a rule of thumb, not a proof; sometimes the more complex solution is the correct one.


[edit] History

Although the principle bears his name, William of Ockam did not invent it. The concept is found in the writings of many other medieval philosophers, including Duns Scotus, Thomas Aquinas, and Durand de Saint-Pourcain, and has roots as far back as Aristotle. Willliam of Ockam was one of its most prolific exponents, and he became involved in a long theological conflict with Pope John XXII because of it, therefore Ockam's name has been associated with the principle.

[edit] Expressions of the principle

William of Ockam often expressed the principle as Numquam ponenda est pluralitas sine necessitate (A plurality [of causes] should never be posited unless necessary), but the best known version is a paraphrase by the 17th century scholar John Ponce: Entia non sunt multiplicanda praeter necessitatem (Entities are not to be multiplied beyond what is necessary).

[edit] Occam's Razor in science

Its scientific application is to select priority between developing theories of equal predictive power. The "simpler" theory with fewer (or less onerous) assumptions is probably the most appropriate one. For example, if you see hoof-prints on your local walking trail, think horses, not unicorns.

[edit] Fucking it up

[edit] In science Occam's razor evaluates only hypotheses with similar predictive power

Each hypothesis being evaluated must be able to predict the same final state. If a theory has no predictive power (such as Goddidit) then it is automatically excluded due to being impossible to evaluate.

[edit] Predictive power does not mean inclusive power

A theory which can include evidence is not the same as a theory which can predict results. The test of a theory comes from being able to generate results from base data or predict additional discoveries, not the power to use ad hoc reasoning to back-fit new data to the theory. A simple example would be fitting a polynomial of degree 399 to 400 data points: it might fit those 400 perfectly, but is the end behavior likely to be a good extrapolation or a really bad one?

A classic example of generating an excuse that creates infinite inclusive power (but not so much predictive power) is "the lord works in mysterious ways."

[edit] A theory must still be scientific

For the scientific use of Occam's razor to actually come into effect, a hypothesis must first satisfy the standard requirements of the scientific method; in particular, it must be falsifiable. Trying to use science to evaluate an unscientific theory is like trying to use metallurgy to evaluate a restaurant: forking stupid.

[edit] What is a "term?"

Often people use "term" as a synonym for "word" and imagine that the theory which can be described in the simplest way is selected by Occam's razor. This is not the case; one must carefully (and honestly) separate all assumptions being made.

For example, a simple-minded evaluation would say "my television functions because of electricity" is as "simple" as "my television functions because of Martians." But to actually evaluate these:

  • 1. My television contains circuitry. 2. My television draws power from the mains which I can show is used by the circuitry. 3. The power from the mains going through the circuitry is what makes the television function.
  • 1. My television contains circuitry. 2. My television draws power from the mains which I can show is used by the circuitry. 3. The power from the mains going through the circuitry is not what makes the television function. 4. It functions because of Martians. 5. Who are in orbit in their flying saucer. 6. Which is invisible and undetectable. 7. And powers my television in a way that is also invisible and undetectable. 8. And requires no obvious additional components in my television.

It should now be clear which of these would actually be regarded as containing the least number of additional terms.

[edit] Naming an unknown

You cannot explain anything by simply replacing an unknown with an unknown which has a different name. If the hypothesis offers no clue how the result is reached, it is not simple, it is useless. For example:


It is not clear here whether X is a number, many numbers, or an operation of some kind. Based on this alone, the simplest explanation would be that X is 1. The Goddidit explanation would be


Where G is defined as "the correct answer." It should be fairly obvious that we have simply renamed the unknown, and know no more that we did to begin with about the unknown's identity.

[edit] Meaningful precision

One common question among people just beginning to learn high-level physics is "why learn Newtonian physics if they're wrong?" The answer provides a good example of the practical use of Occam's razor in selecting theories.

Let's say we have a one metric ton car moving at 36 kilometres per hour, and we want to find out how much kinetic energy it has. Newton gives us the simple equation

K = \frac{mv^2}{2}

The car weights 1000 kilograms and is travelling at 10 metres per second, so we get an easy figure of 50,000 joules from a straightforward calculation. The Einsteinian method, hated by wiki markup the world over, includes relativistic change in mass, at the cost of performing various sorcery to get it. This gives us a value of 50,000.00000000004 joules.

"But isn't the Einsteinian working more accurate, then?" Those who understand mathematics probably recognise the fallacy here immediately, but for those who don't: the original measurements, in tons and kilometres per hour, simply don't have the precision needed to calculate a hundred-billionth of a joule, so the Einsteinian precision is actually an illusion.

Since the Einsteinian method imparts no meaningful additional level of accuracy, Occam's razor tells us to use the Newtonian method, because it gets the same result with far fewer terms, which is why the Newtonian physics equations are still used for most calculations involving macroscopic objects travelling at non-relativistic velocities.

[edit] Common misuse

Woo-meisters and creationists sometimes use Occam's razor incorrectly as a handwave to avoid facing the fact that the point they are arguing requires a completely unknown mechanism (paranormal powers, Goddidit, Aliensdidit, etc.) to work properly. This claim states that Occam's razor prefers to assume that a god (or similar device) does exist and it's simpler to believe Goddidit than that natural selection and evolution could create the complexity of life. This ignores the incredible complexity such an entity would require, and that since very few religions totally deny the existence of observable natural mechanisms, they are arguing that the entity exists in addition to all of the terms their opponent is assuming. It's also quite easy for skeptics to fall for this one, citing Occam's razor as evidence itself, rather than finding evidence to refute a concept.

[edit] An answer to Occam's razor

In his Summa Theologica, St. Thomas Aquinas quoted an argument for the non-existence of God based on the principle of Occam's razor, and answered it in the following fashion:

Objection 2. Further, it is superfluous to suppose that what can be accounted for by a few principles has been produced by many. But it seems that everything we see in the world can be accounted for by other principles, supposing God did not exist. For all natural things can be reduced to one principle which is nature; and all voluntary things can be reduced to one principle which is human reason, or will. Therefore there is no need to suppose God's existence.

On the contrary, It is said in the person of God: "I am Who am." (Exodus 3:14)

[...] Reply to Objection 2. Since nature works for a determinate end under the direction of a higher agent, whatever is done by nature must needs be traced back to God, as to its first cause. So also whatever is done voluntarily must also be traced back to some higher cause other than human reason or will, since these can change or fail; for all things that are changeable and capable of defect must be traced back to an immovable and self-necessary first principle, as was shown in the body of the Article.[1]

[edit] Occam's duct tape

The opposite mental process to Occam's razor — to avoid simplicity, to leave no entity unmultiplied and to make as many unnecessary assumptions as possible when pondering an idea — is sometimes referred to (in jest) as Occam's duct tape.

[edit] Crabtree's bludgeon

It's as if Inigo Montoya woke up in Coruscant.

Crabtree's bludgeon is an observation which serves as a foil to Occam's razor, characterizing a very different cognitive process exhibited in certain kinds of people, which states:

No set of mutually inconsistent observations can exist for which some human intellect cannot conceive a coherent explanation, however complicated.[2]

[edit] Newton's flaming laser sword

Newton's flaming laser sword, also known as Alder's razor, is another sort of razor devised by the Australian mathematician and philosopher Mike Alder. It represents a sort of logical positivism that is a common thread among the sciences. It states: "What cannot be settled by experiment is not worth debating."

Alder characterizes the flaming laser sword as "much sharper and more dangerous than Occam's razor."[3]

[edit] See also

[edit] Footnotes

  1. Summa Theologica FP Q2 A5
  2. At the Christmas party, British Medical Journal
  3. Newton’s Flaming Laser Sword, Philosophy Now
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