Science Philosophy and Practice: Ockham's Razor

Introduction

Simplicity is a virtue in any explanation or description. Both understanding and communication are facilitated by keeping concepts and the words that express them as simple as possible without sacrificing accuracy or completeness. This principle has been known, practiced, and codified since ancient times. The best known version of the principle is attributed to English Franciscan nominalist philosopher William of Ockham (or Occam) (c.1288–1347). Though scientists more commonly call it Ockham's razor, it is properly called either the principle of parsimony or the principle of economy, because it shaves away superfluous concepts.

Ockham's razor has been the key principle of scientific method since the beginning of modern empiricism in the experiments of English polymath Francis Bacon (1561–1626) and especially since the standardization of the speculative—empirical cycle (observe, create hypothesis, test hypothesis, observe) in the twentieth century.

Probably the best example of the razor working to improve scientific understanding is the cosmological revolution wrought by Polish astronomer Nicolaus Copernicus (1473–1543). Before his time, the prevailing geocentric view of the universe was bolstered by notions of epicycles and other fanciful mathematical fabrications that “explained” retrograde planetary and lunar motions. By going against religious dogma and positing a heliocentric system, Copernicus was able to explain these motions with a relatively uncomplicated arrangement of ellipses.

Historical Background and Scientific Foundations

Greek philosopher Aristotle (384–322 BC) wrote in De Caelo that assumptions should be as few as possible, consistent with the known facts. In Physics he asserts that the universe has only one mover. In Book Alpha Major of the Metaphysics he refutes his teacher Plato's (c.427–c.347 BC) view that each thing on Earth has an ideal form in a supraterrestrial, intelligible realm. Aristotle's counterargument was that things are substances, and there is no reason to understand any substance as existing doubly, as both itself and its idea, when it could just as well be understood as existing singly.

The principle of parsimony was familiar in medieval scholastic philosophy before Ockham's birth. Like most Aristotelian ideas, it appears in the writings of Italian Dominican philosopher St. Thomas Aquinas (c.1225–1274), notably in Summa Contra Gentiles, in which he argues that because nature does not use two means when one would suffice, we generate superfluity if we perform any task in several ways when we could do it in one way. Moreover, he continued, if there are two or more metaphysical theories of a thing, at most only one of them could be correct.

The principle is also found in the texts of Scottish Franciscan philosopher John Duns Scotus (1266–1308), who may have been Ockham's teacher. The French Franciscan Archbishop of Rouen, Odo Rigaldus (1205–1275), wrote in Commentary on Sentences that to posit many entities when we could posit only one is vain.

Ockham wrote several statements of the principle. Its most common formulation, “Entities are not to be multiplied without necessity,” is attributed to Ockham but does not appear in any of his surviving works. This version has not been found in any text earlier than the 1639 commentary on Duns Scotus by Irish Franciscan theologian John Ponce of Cork (1603–1670). Rather carelessly disregarding the actual history of the principle, Scottish philosopher Sir William Hamilton (1788–1856) coined the term “Ockham's razor” in 1852, though Hamilton did not give credit where credit is due. Ockham's razor would more fairly be called “Aristotle's razor.”

The Principle of Sufficient Reason

The principle of sufficient reason (PSR) claims that everything has a reason or cause as to why it exists. Disproportionately associated with German rationalist philosophers Gottfried Wilhelm von Leibniz (1646–1716) and Christian Wolff (1679–1754), it appears also in the writings of Plato, Aristotle, Thomas Aquinas, and German philosopher Arthur Schopenhauer (1788–1860). It does not oppose Ockham's razor. The two principles complement each other. PSR supports not positing too few explanatory factors, while the razor supports not positing too many. The goal of investigation is to find exactly the right number.

Neither philosophy nor science can seriously challenge either PSR or the razor. They have been involved, at least implicitly, in every important philosophical or scientific contribution since the dawn of rigorous thought in ancient Greece. PSR has been invoked to discredit scientific theories, notably the idea of the spontaneous generation of life. To explain the origin of living beings, such as frogs, by saying that they just oozed out of swamp mud is simpler than talking about zygotes and tadpoles. But that explanation does not fit all the known facts. French biochemist Louis Pasteur (1822–1895) depended more on PSR than on the razor to disprove spontaneous generation.

Applying PSR adds concepts, but only necessary ones. Applying the razor removes concepts, but only unnecessary ones. The closer the harmony between these two opposite tendencies in any philosophical or scientific inquiry, the more defensible that inquiry is. Striking that balance requires both analytic subtlety and speculative comprehension.

Modern Cultural Connections

Ancient and medieval thinkers devised elaborate cosmologies and metaphysical systems to account for the structure and origin of Earth, the nature of things, and the birth, growth, and death of living beings. Many of these constructs have found their way into the doctrines of major world religions and are still difficult or impossible to reconcile with each other or with modern science. Others, such as the humoral theory of the elements and the flat Earth theory, were discredited as new facts came to light and as science applied Ockham's razor to these facts.

Since Bacon, the razor has been applied consistently and pervasively in natural science, but less so in other domains of thought, such as philosophy. It is conspicuously absent from theology. Many philosophers and scientists argue that there is no good argument for not applying it to all these domains because it enables beliefs to be based on facts and deductions rather than legends, traditions, prejudices, and intuitions.

The application of Ockham's razor to science is essentially a simple refusal to believe that which cannot be proved. Scientists form prudent theories from what the facts indicate, not from what either metaphysics or religion tells them the theories ought to be.

While its influence on science has been profound and positive, its influence on society has not been as significant. Many social problems can be traced to superstitions and other erroneous beliefs that the razor might eliminate if applied.

IN CONTEXT: PLATO'S BEARD

American logician Willard Van Orman Quine (1908–2000), following a line of argument begun by English analytic philosopher Bertrand Russell (1872–1970), wrote in From a Logical Point of View that the Platonic doctrine that non—being exists “might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor.” Plato's beard is a paradox of reference. It allows meaningful discussion of entities that patently do not exist, such as unicorns, because these nonexistent entities “exist” as ideas.

At first glance, a sentence without a definite referent might seem nonsensical. Yet the sentence, “Unicorns cannot fly,” makes sense even though the word “unicorn” does not denote anything real. We use Ockham's razor to excise unicorns from our world, which can well be explained without mentioning them. Yet, even though we can never observe them, we can still understand and employ descriptions of them as fictitious creatures with distinct properties, just as if they were real. Plato's beard becomes intellectually troublesome only if we believe in the actual existence of such fictions.

The razor's limited social impact has resulted mostly from its inconsistent application. Ockham himself modified application of the principle by declaring that it did not apply to supernatural concepts of God or scripture. Instead of using it only to eliminate explanations not supported by experience or deductive reasoning, Ockham, serving his faith, used it also to eliminate explanations not in accord with his religious beliefs.

Despite the fact that both the ontological argument for the reality of a supernatural God and the five ways of Aquinas are consistent with the razor, if the razor were accepted universally, then it would directly challenge many superstitions, religious doctrines, and folk beliefs.

Primary Source Connection

What follows is a portion of a transcript of Dr. Anthony Garrett (1957–), a physicist at Cambridge University, explaining some modern applications of Ockham's razor during an April 2000 radio interview with Robyn Williams, host of the Canadian radio show Ockham's Razor.

PHYSICIST ANTHONY GARRETT EXPLAINS THE MEANING OF OCKHAM'S RAZOR

Anthony Garrett: … In the 20th century it (Ockham's Razor) has found mathematical expression within probability theory. So: is this mathematical version the final, precise version of the idea, settled for all time? No, it isn't. Mathematics is precise, and words have shades

of meaning which make them ambiguous; mathematics and words are suited to different things. So today's version of the Razor in probability theory, corresponds to one interpretation of the words, but other interpretations could generate different mathematical realisations. The idea made precise in probability theory is a very important one though, relating theory and practice in some very basic areas of physics. Let me illustrate this.

The new mathematical razor applies whenever there is a set of numerical data that are polluted by noise, by processes we do not know the exact details of, and we are interested in whether there is a signal, hidden in that noise. An example that recurs as data become ever more accurate is whether there are further planets in our solar system. Look at the motion of the outermost planets such as Pluto. We know that Pluto is influenced principally by the gravitational field of the sun, round which it orbits; then by the gravitational fields of the other planets that we know about. But if you look closely enough at Pluto's motion you will still find small deviations from the motion predicted, even taking the known planets into account. The question is: do those deviations contain subtle evidence for any further unknown planets, or are they best explained as noise due to comets and meteors passing by Pluto, dust, and so on? If the answer is Yes, it is more likely that there is another planet, then where do the data suggest that this other planet is orbiting, and how big is it, what is its influence?

To see how this plugs into the idea of Ockham's Razor, imagine hunting for not just one extra planet, but two, three, four and so on. Obviously if we suppose there are enough extra planets we can fit the predicted orbit of Pluto to the observed fluctuations of the orbit very finely indeed. But the mind revolts at the idea of dozens of extra planets; it makes obvious better sense to suppose the fluctuations are due to irregular passing comets, dust, and so on. The physicist Richard Feynman once said that given enough parameters (that means planets in this case) he could fit an elephant to the curve. We call this phenomenon Overfit. On the other hand, with fewer extra planets we cannot fit the data so closely, which is obviously something that you want to do. So intuitively, there is going to be a trade—off between how well you can fit the data and how many extra planets you suppose there are. In other words, how complicated the theory is. This trade—off between goodness of fit to the observations and the simplicity of the theory you're using is made precise in the new mathematical razor. It allows us to say how probable it is that there is zero, one, two or more undetected planets; and if one or more, what is the best guess of where their orbits are and their masses. Both the number of extra planets, and their positions and masses, are chosen so as to allow the best fit to the data. Ockham's Razor is not just “choose the simplest theory that fits the facts,” but “choose the simplest theory that fits the facts well,” and there is a measurable trade—off, between goodness of fit and simplicity of the theory; a trade—off between flexibility and economy.

Ockham's Razor is also the motivation behind unification of physical theory. A good example of this came nearly 100 years ago. The German physicist Max Planck had invented an early version of the quantum theory that explained a baffling phenomenon: the speed of electrons that were thrown off when light is shone at a metal. His equations called for a new physical constant, a new constant of nature, whose value had to be found from the observations he made. But the same idea was then applied to explain the amount of radiation given off by a hot body, an electric fire, for example, and also to explain the wavelengths of light that are absorbed by hydrogen atoms. But of these further phenomena had been experimentally studied and each had required its own physical constant of nature to be set separately from the observations. The new idea related these two extra constants to Planck's and accurately gave their values. Three supposedly separate phenomena had been shown to have the same underlying explanation. The quantum idea was rapidly accepted in consequence.

My last example is from cosmology. When Einstein worked out his general theory of relativity and gravity early in the 20th century, and improved on Newton's venerable theory, there was room for an arbitrary constant, known as a parameter, in his equations. To keep things simple he was tempted to put it to zero, but another consideration weighed even more heavily: he believed on philosophical grounds that the universe was unchanging on the large scale. He believed it was unchanging in how the great clusters of stars, called galaxies, relate to each other. This meant that his number could not be zero, for technical reasons.

IN CONTEXT: OCKHAM'S RAZOR APPLIED TO ABSTRACT LANGUAGE

Ockham's razor implies that relationships between entities are not themselves to be treated as entities. Abstractions, the common aspects among several observed species or individuals, are not to be reified, personified, or otherwise granted entity status. They are not real things, but only ideas or interpretations in the mind of the observer.

Using the word “man” in the singular as a substantive without an article violates this implication of the razor. We would not say “Horse runs,” “Snake creeps,” or “Pig wallows,” but we often say “Man thinks,” “Man builds,” or “Man cares.” “Man” in this context does not refer to anything real. If we obeyed the razor in this regard, we would say “People think,” “Humans build,” or “Human beings care.” As we typically say “Horses run,” “Snakes creep,” or “Pigs wallow,” we acknowledge at least in those cases that we are referring to aggregates of individuals rather than to abstract, non—existent essences or universals.

There is no such thing as the universal “man.” There are only individual human beings. Perhaps this is why the academic journal called Man and World was renamed Continental Philosophy Review in 1998. If philosophers and poets allow such titles as An Essay on Man rather than An Essay on Humankind, then, on the same grounds, ornithologists should be able to use, say, An Essay on Bird rather than An Essay on the Class Aves.

But some years later, it was found that the galaxies were in fact all rushing away from one another. In Einstein's mind, an informal version of the Ockham analysis immediately took place and he reverted to the value zero for his number, which is called the ‘cosmological constant’ today. In this spirit, a translation of the Latin Ockham's Razor, ‘entia non sunt multiplicanda praeter necessitatem’ would be ‘Parameters should not proliferate unnecessarily.’ This particular plot has thickened though: the value of Einstein's cosmological constant is once again in question. Is it zero, or is it very small, and should be chosen so as to best fit the data? We don't know yet. This is why these questions are exciting.

It is a long way from the modest 13th century village of Ockham to modern research laboratories with state—of—the—art technology, proving the secrets of elementary particles and cosmology. Our link is William, and the principle he wrote about which allows us to improve our answers to questions about the universe, according to the data that is coming out of those laboratories. I think he would be pleased.

Anthony Garrett

garret, anthony. “ockham's razor.” interview with robyn williams onaustralian broadcasting corporation's radio national (april 16, 2000).

See Also Science Philosophy and Practice: Postmodernism and the “Science Wars”; Science Philosophy and Practice: Pseudoscience and Popular Misconceptions; Science Philosophy and Practice: The Scientific Method.

bibliography

Books

Baum, Eric B. What Is Thought?. Cambridge, MA: MIT Press, 2004.

Panaccio, Claude. Ockham on Concepts. Burlington, VT: Ashgate, 2004.

Pols, Edward. The Recognition of Reason. Carbondale, IL: Southern Illinois University Press, 1963.

Quine, Willard Van Orman. From a Logical Point of View: 9 Logico—Philosophical Essays. Cambridge, MA: Harvard University Press, 1971.

Rowland, Wade. Ockham's Razor: The Search for Wonder in an Age of Doubt. Toronto: Patrick Crean, 1999.

Rubenstein, Richard E. Aristotle's Children: How Christians, Muslims, and Jews Rediscovered Ancient Wisdom and Illuminated the Dark Ages. Orlando, FL: Harcourt, 2003.

Wassermann, Gerhard D. From Occam's Razor to the Roots of Consciousness: 20 Essays on Philosophy, Philosophy of Science and Philosophy of Mind. Brook-field, VT: Avebury, 1997.

Weinberg, Julius R. A Short History of Medieval Philosophy. Princeton: Princeton University Press, 1964.

Periodicals

Thorburn, William M. “The Myth of Occam's Razor.” Mind 27, 3 (July 1918): 345–353.

Other

Garret, Anthony. “Ockham's Razor.” Interview with Robyn Williams on Australian Broadcasting Corporation's Radio National (April 16, 2000).

Eric v.d. Luft