Occam's razor

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{{cquote|'''Numquam ponenda est pluralitas sine necessitate.'''<br />
Plurality must never be posited without necessity.|||William of Ockham, ''Questions and decisions in the four books of Sentences of Peter Lombard''(c. 1317-1319)<ref>Ockham, W., ''Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi'' (''ed. Lugd., c''. 1495), ''i, dist''. 27, ''qu''. 2.</ref><ref group=note>According to the Encyclopaedia Britannica’s articles on [https://www.britannica.com/biography/William-of-Ockham#ref227467 William of Ockham], Peter of Lombard’s book — [https://www.britannica.com/topic/Four-Books-of-Sentences ''The Sentences''] — was “the official textbook of Theology in Universities until the 16th century” (cf. §1 “Early Life”, paragraph 2.), and Ockham over a period of two years — 1317-1319 – lectured on ''The Sentences''. Furthermore, Ockham’s lectures over this period were “set down in written commentaries” (§1 “Early Life”, paragraph 2), but ''only'' the commentary on “Book I” of Lombard’s ''Sentences'' — called “''Ordinatio''” — was “actually written by Ockham himself” (loc. cit)</ref>}}

{{cquote|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.|||Nelson Goodman, ''Fact, Fiction, and Forecast''<ref>''Fact, Fiction, and Forecast'' (1st ed., Cambridge, Mass.: Harvard, 1955), p. 39.</ref>}}

'''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 14<sup>th</sup>-century [[England|English]] philosopher and [[Theology|theologian]] '''{{wpl|William of Ockam}}''' (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<ref>[https://wiki.lesswrong.com/wiki/Solomonoff_induction Solomonoff induction], ''LessWrong''.</ref> (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 control|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]] [[philosopher]]s, 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''.<ref>[https://www.britannica.com/biography/William-of-Ockham William of Ockham: English philosopher] by Paul D. Vignaux, ''Encyclopaedia Brittanica''.</ref><br/>
In his extant works, William of Ockham only phrased it thusly:
{{cquote|''Numquam ponenda est pluralitas sine necessitate.''<br>
(Plurality [of entities] must never be posited without necessity.)}}
But the best known version is a paraphrase by the 17<sup>th</sup>-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.<ref>Johannes Poncius’ commentary on John Duns Scotus's ''Opus Oxoniense'', book III, ''dist''. 34, ''q''. 1. in John Duns Scotus ''Opera Omnia'', vol.15, Ed. Luke Wadding, Louvain (1639), reprinted Paris: Vives, (1894) p.483a</ref>
{{cquote|''Entia non sunt multiplicanda praeter necessitatem.''<br>
(Entities are not to be multiplied beyond necessity.)<ref group=note>‘Entity’ was used in the scholastic tradition as a ''category neutral'' term, i.e. ‘entity’ doesn’t determine any particular category, e.g. in the way that ‘object’ determines the category of ‘substances’; rather, an entity could be any of the following: an object, a cause, an explanation, a description, an assumption, a set of assumptions, a proof, …etc.</ref>}}
For example, William of Ockham and other medieval nominalists used the razor to dismiss abstract objects as ''flatus vocis'', “vocal breeze”.<br />
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.<ref>Taken from Quine, W.V.O., ''From Stimulus to Science'' (1995), p. 6</ref><ref>Tooke, John Horne, ''The Diversions of Purley'', vol. 1. London, 1786; Boston, 1806.</ref>

==In science==
Its scientific application is to select priority between developing [[Scientific theory|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 Unicorn]]s… 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: [[Fucking|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 [[Martian]]s. 5. Who are in orbit in their [[flying saucer]]. 6. Which is [[Russell's Teapot|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:

<math>K = \frac{mv^2}{2}</math>

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 [[Relativity|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==
{{cquote|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.|||[[Steven Novella]]<ref>''The Skeptics' Guide to the Universe: How to Know What's Really Real in a World Increasingly Full of Fake'' by Steven Novella et al. (2018) Grand Central Publishing. ISBN 9781538760536.</ref>{{rp|157-158}}}}

===Appeal to simplicity===
Appealing to simplicity is a logical fallacy that frequently comes with a reference to Occam's razor. This is due to a common misconception that Occam's razor states to select the simplest explanation, rather than the one that requires the fewest assumptions.

===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 [[Pseudoscience|pseudo-scientific]] (such as [[Karl Popper|Popper's]] [[falsifiability]] theory) or even [[David Hume#Hume's law|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 [[creationism|creationist]]s sometimes use Occam's razor [[Logical fallacy|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]]. [[Essay:What God would have to be|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 [[skeptic]]s to fall for this one, citing Occam's razor as [[evidence]] itself, rather than finding evidence to refute a concept.

==Related ideas==
[[File:Newtonwithlightsaber.jpeg|thumb|right|200px|It's as if Inigo Montoya woke up in [[Fun:Star Wars|Coruscant]].]]
=== 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 [[Ad hoc|very different cognitive process]] exhibited in [[Crank|certain kinds of people]], which states:
{{cquote|No set of mutually inconsistent observations can exist for which some human intellect cannot conceive a coherent explanation, however complicated.<ref>[http://www.bmj.com/content/343/bmj.d8233 At the Christmas party] by Tony Delamothe (2011) ''British Medical Journal'' 343. doi:10.1136/bmj.d8233.</ref>}}

===Alder’s Razor===
'''Alder's razor''' was devised by the [[Australia]]n mathematician and philosopher Mike Alder. Alder seems to have been inspired by Newton’s “''hypotheses non fingo''”,<ref>Newton, Issac, “General Scholium”, in Principia (second edition)</ref> initially dubbing his razor “Newton’s flaming laser sword”, although Alder’s razor better represents a species of Percy Bridgman’s [https://plato.stanford.edu/entries/operationalism 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."<ref>[http://www.philosophynow.org/issues/46/Newtons_Flaming_Laser_Sword Newton’s Flaming Laser Sword] by Mike Alder (2004) ''Philosophy Now''.</ref>

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 [https://plato.stanford.edu/entries/whitehead/ A.N. Whitehead]. It was suggested by Whitehead to Bertrand Russell as he was writing ''Our Knowledge of the External World''.<ref>A.W., Carus, ''Carnap and Twentieth-Century Thought; Explication as Enlightenment'', (Cambridge University Press, fourth edition, 2010) p.147n [CTCT hereafter]</ref> However, it was first introduced by Russell in his ''Principles''<ref>Russell, Bertrand. “Definitions and methodological principles in theory of knowledge.” ''The Monist'' (1914): 582-593.</ref> 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.’”<ref>Russell, Bertrand. ''Our knowledge of the external world''. (Routledge, 1914a, p.51) [1914a, hereafter]</ref>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).<br />

=== Russell’s Construction principle ===
Russell’s construction principle was attributed to the mathematician and philosopher [https://plato.stanford.edu/entries/russell/ 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.”<ref>Russell, B., 1914b p. 155. “The relation of sense-data to physics.”''Scientia'', 16(16) [1914b, hereafter].</ref> 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). <br />
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. <br />
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.<ref>[http://talkingpointsmemo.com/edblog/the-continuing-triumph-trump The Continuing Triumph of Trump’s Razor] by Josh Marshall (May 11, 2017 4:32 pm) ''Talking Points Memo''.</ref>

==See also==
*[[Begging the question]]
*[[Hanlon's razor]]
*[[Parsimony]]
*[[Thomas Aquinas]], who had a response
*[[Pierre D'Ailly]]
*[[Conspiracy theory]]
*[[Extraordinary claims require extraordinary evidence]]

== Notes ==
{{reflist|group=note}}

==References==
{{reflist|2|80%}}

[[Category:Assessing pseudoscience]]
[[Category:Evaluating arguments]]

Categories: Assessing pseudoscience, Evaluating arguments