Occam's razor



Numquam ponenda est pluralitas sine necessitate.

Plurality must never be posited without necessity.

You may decry some of these scruples and protest that there are more things in heaven and earth than are dreamt of in my philosophy. I am concerned, rather, that there should not be more things dreamt of in my philosophy than there are in heaven and earth.

Occam's razor is a logical razor which states that one should never make more assumptions than the minimum necessary to explain something; or, if you don't have explicit evidence to believe that something is true, then you should not. It is named after the 14th-century English philosopher and theologian  (or Occam or Ockham), born c. 1285. Died 1347/49.

The mathematical proof by Ray Solomonoff that any sequence of observations is best predicted by Occam's Razor in a computable environment (a.k.a. Solomonoff induction) should be considered in light of the fact that all mainstream physics models (such as the Standard Model) are computable. On the other hand, underground mind-controlling gerbils might be biasing physicists into computability chauvinism so as to prevent humans from discovering the true laws of nature, which would lead them to the hoards of jewels and gold deep within the underground gerbil colonies. So those rational enough to be concerned with the possibility of underground mind-controlling gerbils should consider Occam's Razor to be a "rule of thumb".

History
Although William of Ockham did not “invent” (discover?) the principle of parsimony, he can be credited with inventing his eponymous razor. The principle of parsimony is engrailed across 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. Unnecessary entities, popular with the scholastics, were cloven from the body of theory by Ockham — hence Ockham’s razor. In his extant works, William of Ockham only phrased it thusly: Numquam ponenda est pluralitas sine necessitate. (Plurality [of entities] must never be posited without necessity.) But the best known version is a paraphrase by the 17th-century scholar John Ponce, who did not construe it as a razor, nor did he eponymously name it — Ponce referred to it as an axiom vulgare (a “banal axiom”) used by the scholastics. Entia non sunt multiplicanda praeter necessitatem. (Entities are not to be multiplied beyond necessity.) For example, William of Ockham and other medieval nominalists used the razor to dismiss abstract objects as flatus vocis, “vocal breeze”.

During the late eighteenth century, 1786 to be exact, the empiricist John Horne Tooke urged that we should eliminate John Locke’s conclusions about “the abstraction, complexity, and generalisation, etc., of ideas,” in favour of “the substitution of compositions of terms”, and that “the greatest part is that [Locke’s] essay does indeed merely concern language”; in other words, that there is no need for reifying ‘ideas’ — multiplying entities beyond need — when all we need is language.

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 Invisible Pink Unicorns… nor zebras (unless you live in a savannah).

Getting it right
Occam's razor is often misinterpreted.

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.

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".

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.

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. Also, the first hypothesis has predictive power: if you unplug the television from the mains, it ceases to function.

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:

1+X=2

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

X=G

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

Meaningful precision
One common question among people just beginning to learn high-level physics is "why learn Newtonian physics if it's 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 tonne 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 tonnes 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, a fallacious overprecision in this example.

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.

Getting it wrong
Occam's razor is a principle of logic that is often invoked but rarely properly understood… It's a useful rule of thumb to help clarify one's thinking, not a strict logical necessity. Failure to understand Occam's razor, however, can lead to very slopping thinking.

Confusing the razor with knowledge division
Some confuse Occam's razor with a class of knowledge divisors that separate the empirical/falsifiable from the supernatural and pseudo-scientific (such as Popper's falsifiability theory) or even Hume's fork, which separate ideas and concepts from matters of fact. While there may be a few distantly related commonalities between these and Occam's razor, the earlier deal with dividing categories of knowledge while Occam's razor deals with the complexity of arguments for a given explanation.

Using the razor as a handwave tool
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 — if not outright unknowable — 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 abiogenesis could spontaneously happen or 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.

Occam's octoechos
Occam's octoechos is an observation that the mental process of Occam's razor - pursuing simplicity - does not necessarily avoid making assumptions which are difficult - if even possible - to reconcile with each other.

Occam's duct tape
The opposite mental process to Occam's razor — avoiding simplicity and making as many (potentially) unnecessary assumptions as possible — is sometimes referred to as Occam's duct tape.

Crabtree's bludgeon
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.

Alder’s Razor
Alder's razor was devised by the Australian mathematician and philosopher Mike Alder. Alder seems to have been inspired by Newton’s “hypotheses non fingo”, initially dubbing his razor “Newton’s flaming laser sword”, although Alder’s razor better represents a species of Percy Bridgman’s Operationalism. 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."

The opposite mental process to the flaming laser sword is Newton's arc welder or Alder's duct tape — avoiding (open) debate to obviate experiments or debating documented experiments to keep a question unsettled.

Whitehead’s principle of abstraction
Whitehead’s principle of abstraction is named after the mathematician A.N. Whitehead. It was suggested by Whitehead to Bertrand Russell as he was writing Our Knowledge of the External World. However, it was first introduced by Russell in his Principles as a means of “supporting the reality of relations” (CTCT, loc cit.). Russell stated, during his 1914 lectures, that it could “equally well be called ‘the principle which dispenses with abstraction, and clears away metaphysical lumber.’” The principle of abstraction was mainly employed by Russell to make ontologies more economical viz. by substituting equivalence classes — mere “logical constructions” — for suspect “fictitious metaphysical entities” (1914a, 134). For instance, Russell suggested that physical objects could be constructed as classes of their “aspects” or “perspectives” (Russell 1914a, Lecture 3) and proposed Whitehead’s method of constructing the points and instances of physics from sense data by “extensive abstraction” viz. as the limit of of successively enclosed or nested regions containing a specific point (1914a, pp. 114, 121).

Russell’s Construction principle
Russell’s construction principle was attributed to the mathematician and philosopher Bertrand Russell by Rudolf Carnap (CTCT, loc cit.; Carnap called it “Konstruktionsprinzip”), and may be defined thusly: “Wherever possible, logical constructions are to be substituted for inferred entities.” Russell used this principle inter alia to deal with the problem of “non-referring names”: Russell demonstrated that by paraphrasing names such as ‘Pegasus’ or descriptions such as ‘the present king of France’ into predicate Logic, we need not be committed to any nonexistent entities, whilst maintaining that these still are meaningful expressions.

Sundry relata
The conjunction of Whitehead’s principle of abstraction and Russell’s construction principle provided Carnap a starting point for his own project i.e. although Whitehead and Russell’s particular tools were unsuitable for his own directivities, “a formally similar kind of construction would make it possible to arrive at the kinds of discrete and atomistic sense-data needed for science.” (CTCT, loc. cit). Carnap baptised his methodology as “quasi-analysis”, and it appears in the first sketch of his Aufbau system (ASP 1922a, pp. 4-6).

Logical atomism and neutral monism loom large in the milieu of particularly Russell’s work, but also Whitehead’s work, and to a lesser — more indirect — extent, Carnap’s early work; the spectre of the second dogma of empiricism also seems to be, albeit unwittingly, present in the early forays of Whitehead, Russell, and Carnap.

In fact, Russell was deeply influenced by his empiricist predecessor Jeremy Bentham, who in his “theory of fictions” observed that to explain a term, we do not need — as is still standard practice in today’s dictionaries — to compose a synonymous phrase, we need only explain all sentences in which we propose to use the term; this process is now called, thanks to Russell’s innovations, “contextual definition”. Verily, Bentham’s motives were parsimonious: he wanted to be able to introduce one, or another, useful term without being charged with assuming some controversial object(s) for it to refer to, and hence, Bentham’s “theory of fictions” enabled him to dismiss the seeming object or objects as merely innoxious fictions.

Trump's razor
When there are several explanations for any one of Donald Trump's policies, assume the most stupid one applies.