Occam's Razor

Ockham's razor, commonly spelled Occam's razor, is a problem-solving principle that states in its most simple form: among competing hypotheses, the one with the fewest assumptions should be selected, or in other words: the simplest explanation is usually the right one.



Overview

A "razor," in philosophy, is used to "shave away" unnecessary information. A razor can also be used to shave away unnecessary assumptions or conclusions. While this post focuses on Occam's razor, there are several other common razors including Grice's razor, Hanlon's razor, and Hitchen's razor.

Occam's razor is commonly thought of today as: the simplest explanation is usually the right one. However, the interpretation of Occam's razor has shifted over the centuries as various schools of thought took hold.

The original Occam's razor states: "Entities should not be multiplied unnecessarily." [8] The basis of Occam's razor can be found in the following two logical principles, both written by William of Ockham:

  • The Principle of Plurality - Plurality should not be posited without necessity.
  • The Principle of Parsimony - It is pointless to do with more than what can be done with less.

Occam's razor can "separate two theories that make the same predictions, but does not rule out other theories that might make a different prediction." [8] It is applied in a wide range of disciplines, used frequently as a tool in making quick decisions and coming to initial conclusions before more comprehensive information can be obtained.


Who is Occam?

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Occam (or Ockham), is actually a rural town in southeast England in the county of Surrey. It is in that town that William of Ockham was born.

Surnames are best believed to have started in Europe in the mid-11th century. Prior to that, towns were small enough that every citizen simply had one name. As towns expanded, there began a need to identify individuals more specifically. While in modern times most cultures adopt a system of patronymic surnames, in the medieval age occupational and locative surnames were more common. Accordingly, William of Ockham was known as such because as he rose to significance he began to be known by his place of provenance.

William of Ockham was a Franciscan friar and an influential philosopher and theologian who lived from approximately 1285 to 1349.*

We know very few details about Ockham's early life, even the years of his birth and death are contested [7]. Most of what is commonly cited are estimations of dates extrapolated from later events in his life. For example, scholars don't know his exact birth year, but do have a record of his ordination in 1306. From there we can surmise he was born around 1285, though some scholars say as late at 1288.

Scholars have inferred that because he joined the Franciscan Order, his early education likely took place in a Franciscan house. After that we know he pursued a degree in theology from Oxford University but he was never able to complete it because in 1323 he was summoned to papal court on charges of heresy.

A century earlier, a theologian and the Bishop of Paris, Peter Lombard, wrote Libri Quatuor Sententiarum, or the Four Books of Sentences. Sentences, essentially, was a book that argued for and against various controversial claims and it quickly became the standard theological textbook in medieval universities.

It was quite customary for high-achieving Oxford students to write commentaries on Sentences because, "by commenting on this book, students would learn the art of argumentation while at the same time developing their own views." [10] Albert the Great, Thomas Aquinas, Gabriel Biel, even Martin Luther and John Calvin read it and wrote about it. For more than 400 years, no other theological book (other than the Bible itself) was cited more frequently.

As a student at Oxford, Ockham wrote commentaries on several of Aristotle's works, as well as Peter Lombard's Sentences. It was Occam's commentary on Sentences, and his contradictory views to Thomas Aquinas that the papacy viewed as heretical and was the reason he was summoned to papal court.

William was a deeply religious man who was perpetually in conflict with the papacy and the orthodoxy, though he never renounced Catholicism. William embraced fideism which is the epistemological view that God, and faith by association, are independent of reason. He wrote "God's existence cannot be deduced by reason alone." This is in direct contrast to the views of his predecessor Thomas Aquinas (1224 - 1274):

Aquinas perfected the great “medieval synthesis” of faith and reason and was canonized by the Catholic Church; Ockham destroyed the synthesis and was condemned by the Catholic Church. Although it is true that Aquinas and Ockham disagreed on most issues, Aquinas had many other critics, and Ockham did not criticize Aquinas any more than he did others. [10]

In Avignon, the new home of the papal court after Rome, William of Ockham was on a form of house arrest for four years. Through this ordeal Ockham became convinced that the papacy was corrupt and he fled the country with other Friars on trial in Avignon including Michael of Cesena. He and the other friars were welcomed by the court of Louis of Bavaria, who had his own reasons for opposing the papacy. William and the other friars were excommunicated from the Church and they were searched for but never captured.

Ockham spent the rest of his life in Bavaria as a political activist writing treatises against the papacy. "Ockham died sometime between 1347 and 1349, unreconciled with the Catholic Church.  All of Ockham’s works have been edited into modern editions but not all have been translated."  [10]

Ockham was a major force of change at the end of the Middle Ages. He was a courageous man with an uncommonly sharp mind. His philosophy was radical in his day and continues to provide insight into current philosophical debates.
...
The principle of simplicity is the central theme of Ockham’s approach, so much so that this principle has come to be known as “Ockham’s razor.” [10]

* Records from this period of William's life are sparse. However, because of his influence, some have been recovered. As always, I will vet my sources carefully and I will provide all sources below in the bibliography.


What is Occam's Razor?

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Occam's razor, also known as the Principle of Parsimony, is a mental model that is used to guide the initial phases of theory building and selection. Occam's razor holds that between two competing hypotheses the simpler theory is usually the right one. Occam's razor can "separate two theories that make the same predictions, but does not rule out other theories that might make a different prediction." [8] It is applied in a wide range of disciplines, frequently as a tool in making quick decisions and coming to initial conclusions before more comprehensive information can be obtained.

It's important to state that Occam's razor is not a law or scientific principle and cannot justify a position in and of itself. However, it can be incredibly useful in the scientific process by helping decide which ideas to investigate first due to what is known as “underdetermination of theories by data” [9].

For any given phenomenon, there is an infinitely large body of complex explanations. Each failing explanation can be supplemented with an ad hoc hypothesis to prevent falsifiability. When in an environment like this, Occam's razor says that simple theories should be chosen over more complex ones for many reasons, not the least of which that simpler theories are more testable. [1]

For Ockham, the principle of simplicity limits the multiplication of hypotheses not necessarily entities. Favoring the formulation “It is useless to do with more than what can be done with less,” Ockham implies that theories are meant to do things, namely, explain and predict, and these things can be accomplished more effectively with fewer assumptions. [10]

Robert Novella explains Occam's razor with a mathematical example:

Two points on a graph can be described by an equation for a straight line, equations for exceedingly complicated circuitous lines, and equations for every type of line in between these two extremes. All of these equations and their resulting lines could be made to pass through the two original points, thereby fitting all the available data. Occam’s razor would recommend the simple linear relationship of a straight line as the best candidate until the additional evidence of a point off this line warranted advocating a more complex solution. [12]

Sharon Kaye at John Carroll University wrote another easy to understand explanation of Occam's razor that I reproduced here:

Suppose your car suddenly stops running and your fuel gauge indicates an empty gas tank. It would be silly to hypothesize both that you are out of gas and that you are out of oil. You need only one hypothesis to explain what has happened.

Some would object that the principle of simplicity cannot guarantee truth. The gas gauge on your car may be broken or the empty gas tank may be just one of several things wrong with the car. In response to this objection, one might point out that the principle of simplicity does not tell us which theory is true but only which theory is more likely to be true. Moreover, if there is some other sign of damage, such as a blinking oil gauge, then there is a further fact to explain, warranting an additional hypothesis. [10]

History of Occam's Razor

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The history and attribution of Occam's razor is muddled and complex. The basis of Occam's razor was a well-established line of thought by time of William's birth. John Punch, who is credited with the exact wording of Occam's razor, said that it was "a common axiom" (axioma vulgare) of the Scholastics. In fact, as far back as Aristotle (~350 B.C.) philosophers have understood and valued simplicity in the scientific process. Aristotle wrote, "we may assume the superiority, other things being equal, of the demonstration which derives from fewer postulates or hypotheses." 

Robert Grosseteste, one of the world's most famous thinkers, wrote nearly 100 years before William of Ockham:

That is better and more valuable which requires fewer, other circumstances being equal… For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly, in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal. [4]

The precise words of the most commonly agreed upon definition of Occam's razor are: entia non sunt multiplicanda praeter necessitatem. In English that translates to: entities must not be multiplied beyond necessity. Those precise words are absent from all of William’s extant academic writings.

With that being said, William of Ockham wrote in Commentary on the Sentences of Peter Lombard: "Nmquam ponenda est pluralitas sine necessitate" [Plurality must never be posited without necessity]. Additionally, in Summa Totius Logicae , William wrote “Frustra fit per plura quod potest fieri per pauciora” [It is futile to do with more things that which can be done with fewer].

Ockham advocates simplicity in order to reduce the risk of error. Every hypothesis carries the possibility that it may be wrong. The more hypotheses you accept, the more you increase your risk. [10]

William is not credited with the exact wording of the principle nor for the coining of the term.  William "never even makes an argument for the validity of the principle, [but] he uses it in many striking ways, and this is how it became associated with him." [10]

Occam's razor has taken recent forms that are different, and often stronger, than the original intention of the Principle of Parsimony. These are quoted from Paul Gibbs from UC Riverside, though he does not provide citations: [8]

  • "If you have two theories that both explain the observed facts, then you should use the simplest until more evidence comes along"
  • "The simplest explanation for some phenomenon is more likely to be accurate than more complicated explanations."
  • "If you have two equally likely solutions to a problem, choose the simplest."
  • "The explanation requiring the fewest assumptions is most likely to be correct."
  • "Keep things simple!"

William J. Hall, a paranormal writer, said it another way: "Occam’s razor is summarized for our purposes in this way: Extraordinary claims demand extraordinary proof." Lastly, the literary icon Sherlock Holmes's classic aphorism is Occam's razor-adjacent: “If you eliminate the impossible, whatever remains, however improbable, must be the truth.”

Some of these re-writings stray from Occam's razor and align more closely with the broader title of "The Principle of Parsimony" or "The Rule of Simplicity." Again, Occam's razor is not used to choose between theories that make different predictions, only to provide guidance in developing a theory.


The Use of Occam's Razor

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As stated above, Occam's razor is applied in a wide range of disciplines to shave away unnecessary elements and information. Occam's razor is used frequently as a tool in making quick decisions and coming to initial conclusions before more comprehensive information can be obtained.

Medicine

Occam's razor is used is modern medicine by doctors looking for a diagnosis. In this context, doctors should look for the most likely cause of a patient's symptoms.

After graduating from medical school, new doctors have just spent eight or more years learning hundreds, if not thousands, of unique medical conditions. Additionally, doctors are increasingly required to specialize and learn new, intricate variations of conditions. Medical diagnoses follow a pattern that aligns with the Pareto Principle: roughly 80% of patients will have 20% of conditions.

Dr. Theodore Woodward, a physician, a professor, and a Nobel-Prize nominee, is credited with coining the aphorism: "When you hear hoofbeats, think of horses not zebras."*

When a doctor encounters a patient, the doctor should should assume the most likely cause and work from there.

Medical students learn early in their career that it is preferable to propose a single diagnosis to explain a host of symptoms with which a patient is presenting, rather than a separate diagnosis for each symptom. A patient, therefore, presenting with headache, neck stiffness, fever, and confusion is more likely to have meningitis than to simultaneously have a brain tumor, whiplash, tuberculosis and acute porphyria. This is a very practical use of Occam’s razor. [12]

Shane Parrish wrote it this way, "For example, a person displaying influenza-like symptoms during an epidemic would be considered more probable to be suffering from influenza than an alternative, rarer disease. Making minimal diagnoses reduces the risk of over treating a patient, or of causing dangerous interactions between different treatments." [13]

* The precise original phrasing is unknown, but it nearly universally credited to Dr. Woodward.

Theology

Occam's razor has been used by both atheists and theologians in attempts to prove and disprove the existence of God, or a higher power.

Consider, for example, the debate of creation versus evolution. Creationists will make the argument that it's more simple to believe that God created life than the the occurrence of the Big Bang followed by an "astounding series of interrelated coincidences." [2] "Many religious people regard the existence of God as the simplest possible explanation for the creation of the universe." [13]

Evolutionists counter by saying that that "explanation supposes that God exists, and we have no empirical evidence that he does." [2] Thomas Aquinas, in Summa Theologica, wrote: "it is superfluous to suppose that what can be accounted for by a few principles has been produced by many."

[Aquinas] considered the existence of God to be a hypothesis which makes a huge number of assumptions, compared to scientific alternatives. Many modern atheists consider the existence of God to be unnecessarily complex, in particular, due to the lack of empirical evidence. [13]

Taoist ideals can be seen as a profound example of the use of Occam's razor in theology. Taoists believe in simplifying everything in existence to its most basic form. "In Taoism, everything is an expression of a single ultimate reality (known as the Tao.) This school of religious and philosophical thought believes that the most plausible explanation for the universe is the simplest - everything is both created and controlled by a single force." [13]

The Development of Scientific Theories

Occam’s razor, or the Principle of Simplicity, is frequently used by scientists especially for theoretical matters. As stated above, simple theories are preferred for a myriad a reasons, not the least of which is that simpler theories are more easily tested. Complex hypotheses, in being harder to test, can lead to repeatability issues which begins to unhinge the falsifiability criterion. 

For these reasons, it is common to begin with the simplest solution consistent with current data, and then to allow new data to come and increase the complexity of the hypothesis. In  other words, "Scientists choose to opt for the simplest solution the current data permits while remaining open to the possibility of future research allowing for greater complexity." [13] 

In A Brief History of Time, physicist Stephen Hawking advocates for Occam’s razor:

"We could still imagine that there is a set of laws that determines events completely for some supernatural being, who could observe the present state of the universe without disturbing it. However, such models of the universe are not of much interest to us mortals. It seems better to employ the principle known as Occam's razor and cut out all the features of the theory that cannot be observed." [14]

Isaac Newton also held the principle of simplicity in high regard. When developing his three universal laws of motion, he wrote: “we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” [6] Accordingly, he wrote the three laws of motion with the fewest underlying assumptions possible.

Occam's Razor in Natural Science

The theory behind Occam's razor goes back at least as far as Aristotle who wrote, "nature operates in the shortest way possible." As an example, the second law of thermodynamics is often rewritten as The Principle of Minimum Energy. This law states that, wherever possible, the use of energy in nature is minimized. Physicists can use Occam’s razor to assume that everything will use the minimum amount of energy necessary to function. Objects will move to the point of minimum potential energy and, biologically, as various actions become habits they use less neurological energy to complete that action. 

Geocentric vs. Heliocentric Models of the Solar System

The ancient debate in astronomy between competing theories of our solar system is a good example of the scientific community applying and accepting Occam's razor.

Robert Novella wrote,

"It is commonly perceived as absurd and almost comical that so many people for so long accepted as fact the geocentric model of the solar system in which the sun and planets orbit around a stationary earth. The philosopher Ludwig Witgenstein, when confronted with this attitude, is said to have commented: 'Yeah, but I wonder what it would have looked like if the sun had gone around the earth.' The point is, of course, that it would have looked exactly the same. Both the geocentric model and the heliocentric model (earth in orbit around the sun) make the same predictions as to the movements of the sun in the sky." [12]

The problem with geocentrism involved more subtle and sophisticated observations. Under geocentric theories there were still several unexplained mysteries including, "the brightening of the planets, the bizarre retrograde paths of their orbits, the apparent daily and yearly movements of the stars, including the sun, and the fact that Mars and Venus never strayed far from the sun compared to the other planets." [9] In defense of these mysteries, Ptolemy devised a host of complex relationships needed to satisfy the geocentric model.

Centuries later, Copernicus developed a much simpler theory wherein the sun was at the center and the planets and their moons rotated around it. This new theory explained all that Ptolemy's model did as well as accounted for all of the mysterious celestial motions described above. This model, which was not only much simpler but also had much more explanatory power led, in part, to the Copernican revolution which ushered in the modern view of astronomy and natural science.

Einstein vs. Lorentz

Albert Einstein and Hendrik Lorentz are both physicists that created mathematical models to explain the space-time continuum. Unsurprisingly, from two of the greatest minds of the 20th century, they each arrived at the same conclusion: that objects in motion experience time at a slower rate than objects at rest.

However, Einstein's and Lorentz's underlying calculations were different. Lorentz based his calculations on changes that he suggested occurred in "the ether." However, because of a lack of empirical evidence, modern science doesn't hold that the ether exists. This leads to problems when considering the falsifiability criterion and the principle of simplicity.

Phil Gibbs wrote it this way:

"The canonical example is Einstein's theory of special relativity compared with Lorentz's theory that ruler's contract and clocks slow down when in motion through the ether.  Einstein's equations for transforming spacetime are the same as Lorentz's equations for transforming rulers and clocks, but Einstein and Poincaré recognised that the ether could not be detected according to the equations of Lorentz and Maxwell.  By Occam's razor it had to be eliminated." [8]

In other words, because Einstein's explanation used no references to the ether, his explanation eventually won over Lorentz's. 

As a final note within this example, Albert Einstein wrote his own version of Occam’s razor when developing his theory of special relativity that read: "it can scarcely be denied 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." [5]

Continental Drift

The denial and acceptance of continental drift is an example where Occam's razor was completely rejected only to be vindicated decades later. Mapmakers and mariners were the first to notice that the coastlines of Africa and South America were complimentary and almost appeared as if they "once fit together like a huge jigsaw puzzle." [12]

Meteorologist Alfred Wegener was responsible for coining the term for the mega-continent, Pangaea. Pangaea is Greek for "all the land" and it appeared in Wegener's book, On the Origin of Continents and Oceans (1915), that codified the thoughts behind continental drift.

American scientists nearly universally rejected the idea of migrating landmasses on a basis on insufficient fossil and geological evidence. Wegener's theory ultimately failed in the same manner as Lorentz's, the conclusion was right, but the attribution was wrong. Wegener, in attempting to explain the colossal forces needed to move continents, invoked gravity. This idea was ridiculed because, mathematically speaking, gravity is far too weak to move such enormous land masses. 

The idea was untouched for several decades until Arthur Holmes, a Scottish geologist, proposed a more plausible mechanism. Holmes proposed that beneath the earth's surface was a "mosaic of rigid and fractured plates." [12] He further theorized that these plates were moved by convection currents in the earth's mantle powered by radioactive decay.

With the assistance of other geologists and physicists, Holmes eventually proposed the "paradigm-shattering theory called plate tectonics, which now underpins our modern understanding of geology and the evolution of the earth itself. Full acceptance still took many years but when the evidence for plate tectonics became incontrovertible, continental drift finally had a plausible mechanism for its assumption that delayed acceptance for decades." [12]

Crime Solving and Forensic Work

Occam's razor is commonly used in detective work, in conjunction with other tools and mental models of course.

Shane Parrish wrote a simple explanation:

A woman is statistically more likely to be killed by a male partner than any other person. Should a female be found murdered in her locked home, the first person police interview would be any male partners. The possibility of a stranger entering can be considered, but the simplest possible solution with the fewest assumptions made would be that the crime was perpetrated by her male partner.

By using Occam’s razor, police officers can solve crimes faster and with fewer expenses. [13]

Conspiracy Theories

This is a small and slightly obscure use of Occam's razor I came across during my research. Josh Clark, from HowStuffWorks, briefly explains the use of Occam's razor against conspiracy theorists. He posts the questions: Was President John F. Kennedy assassinated by a lone gunman, or was his death the result of a CIA plot?

Josh Clark continues,

Usually, it's skeptics who lock horns with conspiracy theorists, using the razor as proof that conspiracists are too far-reaching in their explanations. Take, for example, the assassination of President John F. Kennedy. The idea that he was killed by a single, overzealous Communist gunman is a much simpler explanation than the idea that he was murdered by a CIA conspiracy, which would involve treachery on levels unseen in U.S. history to that point.

But does the fact that one explanation is simpler mean it's correct? Conspiracy theorists can produce all manner of circumstantial evidence that points to many different plots. But according to Occam's razor, this extra evidence would be considered irrelevant in the face of the lone gunman explanation. In this case, Occam's razor only serves to fuel the debate when it's used to discount conspiracists' theories. [2]

Counterarguments To Occam's Razor

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Occam's razor, as with all heuristics, is not above contradiction and should not be used to prove or disprove theories. Aristotle erroneously believed that the principle of simplicity was so strong as to not require observation or experimentation. And even recent scholars have gone so far as quote it as if it were an axiom of physics, not as the heuristic rule of thumb it is meant to be.

Shane Parrish reminds us:

"There are exceptions to any rule, and we should never blindly follow a mental model which logic, experience, or empirical evidence contradict. The smartest people are those who know the rules, but also know when to ignore them. When you hear hoof beats behind you, in most cases you should think horses, not zebras - unless you are out on the African Savannah." [13]

When attempting to prove or disprove a theory using Occam's razor, one runs into two main problems. First, determining whether or not something is "simple" is subjective. Second, there is no evidence that holds that simplicity inherently equals truth.

"Simple" is Subjective

Simplicity is a subjective topic. It's possible for two sides of the same issue to both use Occam's razor in defense of their argument. Think back to the section above, "Uses of Occam's Razor: Theology," one group believes the existence of God to be the simplest solution, while the other group considers the inverse to be the more simple option. In the section, "Uses of Occam's Razor: Conspiracy Theories," one group believes it to be more simple for the lunar landing to have been faked, while the other group believes it more simple to have been real.

Occam's razor can unfortunately also feed into the confirmation bias in which we use it to merely back up our preexisting notions. For example, someone who already believed in God may use Occam's razor to back up those convictions.

As a final note in this section, one must avoid giving overt importance to semantic simplicity. A simple-sounding hypothesis does not necessarily have fewer assumptions than a competing, yet verbose, alternative.

Simplicity is Not Inherently True

As a counterargument to the use of Occam's razor in modern medicine, Dr. John Hickam wrote "Hickam's Dictum" which states that "A man can have as many diseases as he damn well pleases." [11] He made the argument that a person may be suffering from any number of complex conditions, and at no point should a potential diagnosis be precluded from consideration merely because it does not fit Occam's razor.

Experienced clinicians note that patients often do have more than one condition. Robert Novella explains it this way:

As we age, the number of chronic conditions we may have tends to increase, and our susceptibility to acute ailments also increases. Further, one disease often predisposes us to other diseases and disorders. For example, patients with diabetes often develop kidney failure, heart disease, and nerve damage. Often, diseases may occur in a cascade of cause and effect, like a trail of tumbling dominoes. The end result is that Occam’s razor, although very useful as a starting point, often breaks down under the complexities of reality. [12]

Phil Gibbs, from UC Riverside says that Occam's razor "can work well in philosophy or particle physics, but less often so in cosmology or psychology, where things usually turn out to be more complicated than you ever expected.  Perhaps a quote from Shakespeare would be more appropriate than Occam's razor: 'There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.'." [8]

Lisa Randall, in her book Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe, explained her issues with Occam's razor:

The world is more complicated than any of us would have been likely to conceive. Some particles and properties don’t seem necessary to any physical processes that matter—at least according to what we’ve deduced so far. Yet they exist. Sometimes the simplest model just isn’t the correct one.

Conclusion

Occam's razor fits well into the modern scientific method and it's likely that the scientific method was intentionally made with a preference towards simplicity. However, given sufficient information, Occam's razor should never be used in place of the scientific method. It should never be depended upon to make or defend a conclusion.  "As arbiters of correctness, only logical consistency and empirical evidence are absolute." [8]

Use caution when using this razor, and when observing others use the razor. Being such a short statement that can be written so many different ways, it can be stretched and bent to fit the agenda of the user. Just remember, Occam's razor proves nothing, it is just a mental model, a heuristic device, a rule of thumb.

Harlan Coben, in his book Fool Me Once, reminds us to consider the original purpose of Occam's razor:

Most people oversimplify Occam’s razor to mean the simplest answer is usually correct. But the real meaning, what the Franciscan friar William of Ockham really wanted to emphasize, is that you shouldn’t complicate, that you shouldn’t “stack” a theory if a simpler explanation was at the ready. Pare it down. Prune the excess. [3]

I'll leave you with a final quote of unknown origin, though often attributed to Albert Einstein: 

"Everything should be made as simple as possible, but not simpler."


Bibliography

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WORKS CITED

[1] Baker, Alan. “Simplicity.” Stanford Encyclopedia of Philosophy, Stanford University, 29 Oct. 2004, plato.stanford.edu/entries/simplicity/.
[2] Clark, Josh. “How Occam's Razor Works.” HowStuffWorks Science, HowStuffWorks, 4 Oct. 2007, science.howstuffworks.com/innovation/scientific-experiments/occams-razor.htm.
[3] Coben, Harlan. Fool Me Once. WF Howes Ltd, 2017.
[4] Cunningham, Jack, and Mark Hocknull. Robert Grosseteste and the pursuit of religious and scientific learning in the Middle Ages. Springer, 2016.
[5] Einstein, Albert. “On the Method of Theoretical Physics.” Philosophy of Science, The University of Chicago, Apr. 1934, www.jstor.org/stable/184387.
[6] Four Rules of Scientific Reasoning from Principia Mathematica. The University of Alabama, apex.ua.edu/uploads/2/8/7/3/28731065/four_rules_of_reasoning_apex_website.pdf.
[7] Gál, Gedeon, 1982. “William of Ockham Died Impenitent in April 1347.” Franciscan Studies, 42: 90–95.
[8] Gibbs, Phil. “What is Occam's Razor?” Edited by Sugihara Hiroshi, What is Occam's Razor?, University of California Riverside, 1996, math.ucr.edu/home/baez/physics/General/occam.html.
[9] Harnad, S. (ed.) (1987) Categorical Perception: The Groundwork of Cognition.New York: Cambridge University Press
[10] Kaye, Sharon. “William of Ockham (Occam, c. 1280—c. 1349).” Internet Encyclopedia of Philosophy, www.iep.utm.edu/ockham/.
[11] Miller, Wallace. “Letter from the editor: Occam versus Hickam.” Seminars in Roentology, Elsevier, July 1998, www.seminarsinroentgenology.com/article/S0037-198X(98)80001-1/pdf.
[12] Novella, Robert. “The Razor in the Toolbox.” The New England Skeptical Society, Apr. 2001, theness.com/index.php/the-razor-in-the-toolbox/.
[13] Parrish, Shane. “Mental Model: Occam's Razor.” Farnam Street, Apr. 2017, www.farnamstreetblog.com/2017/05/mental-model-occams-razor/.
[14] Schneider, Laurel C. Beyond monotheism: a theology of multiplicity. Routledge, 2008.

UNCITED:

- Hugh G. Gauch, Scientific Method in Practice, Cambridge University Press, 2003.
- Roald Hoffmann, Vladimir I. Minkin, Barry K. Carpenter, Ockham's Razor and Chemistry, HYLE—International Journal for Philosophy of Chemistry, Vol. 3, pp. 3–28, (1997).