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Metaphysics

Parsimony (In as few words as possible)

Toni Vogel Carey wonders whether nature loves simplicity.

Webster’s Ninth gives this definition of ‘parsimony’:

1) The quality of being careful with money or resources; the quality or state of being niggardly: stinginess. 2) Economy in the use of means to an end; economy of explanation in conformity with Occam’s razor.

It is the ‘explanatory’ meaning that is of primary interest to philosophers, although the line between it and means-end “principles of least effort” as Nicholas Rescher calls them, is rather fuzzy; and neither sense is far removed from thriftiness with a dollar (pound, euro, renminbi). All are principles of economy.

What Webster’s does not mention is the aesthetic aspect of parsimony, although it is conspicuous both in art and science. Think of Hemingway’s story in six words: “Baby shoes for sale. Never worn.” Or consider the rapt description by François Jacob, Nobel laureate in medicine, of the double helix configuration of DNA: “This structure was of such simplicity, such perfection, such harmony, such beauty even, and biological advantages flowed from it with such rigor and clarity, that one could not believe it untrue.”

History of the Principle

As Webster’s suggests, the locus classicus of conceptual parsimony is the principle of Ockham’s Razor, so named – or rather misnamed – for the English monk William of Ockham (or Occam), c.1285-c.1349 AD. Given that the Scots are known for parsimony in the economic sense, we might expect this principle to have Scottish roots; and it does. Ockham was preceded at Oxford, if not actually taught there, by John Duns Scotus (d. 1308), who also has precedence in the Razor principle in two seminal statements:

Pluralitas non est ponenda sine necessitate:
Plurality is not to be posited without necessity.
Frustra fit per plura, quod potest fieri per pauciora.
What can be done with fewer would in vain be done with more.

This principle was not entirely new with Duns Scotus either. It goes back to Aristotle’s statement in De Caelo that the number of postulates should be “as few as possible, consistently with proving what has to be proved.” Thomas Aquinas offered a similar formulation in the thirteenth century. But according to W.M. Thorburn in Mind 27, it was Duns Scotus who “fully and finally established” the principle.

The Scientific Revolution rejected almost everything Aristotelian and medieval. Yet it did nothing to distance itself from this scholastic doctrine. On the contrary, Newton made it his first ‘Rule of Reasoning’ in the Principia Mathematica (1687):

“We are to admit no more causes of natural things than such as are both true and sufficient to explain the appearances. To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.” (Translated from the Latin.)

The first statement of the principle in English dates from 1852, and comes from another Scot, William Hamilton. It was Hamilton who introduced the term ‘Parcimony’ (sic) to replace the older ‘Frugality’, and Hamilton who coined the term ‘Occam’s Razor’ in 1866, presumably unaware of the priority of his countryman Duns Scotus in its formulation.

“There exists a primary presumption of philosophy. This is the law of Parcimony: which prohibits, without a proven necessity, the multiplication of entities, powers, principles or causes; above all, the postulation of an unknown force where a known [force] can account for the phaenomenon. We are, therefore, entitled to apply ‘Occam’s Razor’ to this theory of causality”

Hamilton has long had a bad reputation, not because he named the Razor after the wrong guy, but because he applied it to “the multiplication of entities” – thus, as Thorburn put it, turning what had been “a sound rule of Methodology into a Metaphysical dogma.” That seems a bit unfair, since Hamilton’s emphasis was clearly on eschewing spurious forces, which was entirely in keeping with best Newtonian practice.

Adam Smith’s Parsimony

Between Newton in the seventeenth century and Hamilton in the nineteenth, Adam Smith in the eighteenth brought together all the key aspects of parsimony: its association with Scotland, its importance in scientific explanation, its aesthetic component, and of course, the monetary connection. Smith had no interest in penny-pinching for its own sake: what he stressed was prudence – foregoing short-term for long-term gain, which he considered essential to building and maintaining the wealth of nations. (Wall Street, take note.)

In an early essay that influenced his later works, but was published only posthumously, Smith defined natural philosophy as “the science of the connecting principles of nature”— the “invisible chains” (recall his “invisible hand”) which “bind together” the “jarring and discordant appearances” presented to our senses. Here, as elsewhere, his writing abounds with allusions to beauty and art. “Like the musician,” he says, those who spend their lives “in the study of the connecting principles of nature” acquire “a nicer ear” about such things.

According to his first biographer, Dugald Stewart, Smith considered simplicity more important than conformity to fact. Particular events may happen merely by accident; but the business of the natural philosopher (scientist) is to discover the unifying non-accidental order beneath the phenomena, Newton’s law of gravitation being Smith’s paradigm case in point, being “the greatest discovery that ever was made by man.”

Like Smith, A.O. Lovejoy, who pioneered the history of ideas, described his discipline as seeking “to correlate things which often are not on the surface connected.” More recently, Herbert Simon pointed n Simplicity, Inference and Modelling (2001) to the beauty in “finding pattern, especially simple pattern, in the midst of apparent complexity and disorder.” Simon construes parsimony itself as “pattern in the phenomena” and places it “at the root of what we mean by a scientific law.” Distinguishing between simplicity and parsimony, Simon does not think we should seek “the absolutely simplest law,” but “the law that is simplest in relation to the range of phenomena it explains, that is most parsimonious.”

Less Is More

Parsimony is a two-sided coin – less on one side, more on the other. Dugald Stewart pointed both to the number of phenomena for which a good theory accounts (more), and to the simplicity by which it explains them (less). The aim, writes the philosopher of biology David Hull parsimoniously, is to “explain a lot by a little.” In fact, the ultimate aim is a Theory of Everything. As Newsweek blazoned in 1988, “cosmologists are determined to understand how the world came to be, and to explain it with such elegant simplicity that … their equation for the universe can be stenciled onto T-shirts.”

Whether this goal is achievable is another question. We discover “the simple beneath the complex,” the mathematician Henri Poincaré once remarked in Science and Hypothesis (1952), “and then the complex from the simple, and then again the simple beneath the complex, and so on… For science to be possible we must stop where we have found simplicity” – even though the simplicity is only apparent and the stop only temporary.

We live in a positivist, reductionist, empiricist age, more prone to bury the principle of parsimony than to praise it. (Empiricism is the doctrine that all knowledge is gained only through experience, and positivism, that metaphysical principles illegitimate because unscientific.) This has not always been the case. Scholars say that Copernicus favored a heliocentric over a geocentric system not because it accorded better with the data, but because of its greater simplicity. Galileo declared in Two New Sciences (1638) that nature “habitually employs the first, simplest, and easiest means,” and that “no one of judgment believes that swimming or flying can be accomplished in a simpler or easier way than that which fish and birds employ by natural instinct.” Darwin wrote in the Origin of Species that “natural selection is continually trying to economize every part of the organization.” Using Newton as his model, Darwin argued that it is more parsimonious to consider three species of rhinoceros as being related by descent than to consider them separately created. He compared the rhinoceros to the fall of a stone, and pointed out that Newton attributed the fall to gravity, not to “the direct volition of the Creator.” Finally, Einstein disclosed that while he started out a “skeptical empiricist,” the problem of gravitation converted him into “someone who searches for the only reliable source of Truth in mathematical simplicity” – which for Einstein, his assistant Helen Dukas writes, meant beauty.

Less merely for the sake of less, however, is not more. In plotting curves, for example, we want the line linking the points on a graph to strike the Goldilocks (just right) balance between smoothness (simplicity) and jaggedness (exact goodness of fit).

Parsimony and Its Detractors

There are those at the empiricist end of the spectrum, such as the philosopher of biology Elliott Sober, who has written extensively about simplicity. In From a Biological Point of View (1994) Sober says he would just as soon “razor Occam’s Razor.” Whether or not “a simpler curve is preferable to some more complex alternative,” he thinks, “has nothing to do with simplicity and everything to do with predictive accuracy.” Detractors tend to see parsimony and accuracy as fundamentally conflicting values, whereas proponents of parsimony believe the two go together like love and marriage. To them, simplicity is beauty, and beauty truth. Scottish empiricist philosopher David Hume criticized the “love of simplicity” as “the source of much false reasoning in philosophy” while his friend Adam Smith emphasized invisible connecting principles and ranked simplicity above facticity.

From its inception in 1660 the Royal Society was the hub of international scientific activity. But by the time Newton became its president in 1703, the level of hostility between his mathematical faction and the Baconian experimentalists was threatening to bring down the organization. Today there is less acrimony, but the disagreement still persists. Francis Crick, of double-helix fame, wrote in his 1988 autobiography What Mad Pursuit that “elegance and simplicity are, in biology, dangerous guides to the correct answer,” and “the only really useful constraints are contained in the experimental evidence.” On the other hand, his colleague Rosalind Franklin declared the double helix “just too pretty not to be right.”

The conflict, then, is not between scientists and philosophers, but between those with an empiricist and those with a theoretical bent. Inductivists may take a jaundiced view of parsimony because they seek it on the surface of things; and not finding it there (sometimes despite long effort) they conclude that it is not to be found anywhere. Theorists look for simplicity, not on the surface, but underlying the phenomena.

Simple vs. Simplistic

What some call simple, others would call merely simplistic. The philosopher of science Joseph Pitt, who cites the “dubious, but extremely powerful, claim that nature is simple,” takes Carl Hempel’s D-N (‘deductive-nomological’) model as a paradigm of scientific simplicity. This model achieved a good deal of currency in mid-twentieth century philosophy of science, but its brand of explanation is pretty simplistic: Why did aspirin cure my headache? Well, aspirin generally cures headaches.

One thing paradigms of simplicity like E = mc² have, and the D-N model lacks, is a high degree of mathematization. Galileo famously proclaimed that the book of nature is written in the language of mathematics, without which we cannot understand a single ‘word’ of it. What makes this language fundamental, rather than just a dialect physicists happen to favor, is that mathematics is reducible to logic, the basis of all reasoning – as Bertrand Russell showed in 1903 in The Principles of Mathematics.

But mathematics is apparently not the key to parsimony, if only because mathematics itself can be quite sophisticated. For another, mathematics can be used too simplistically. Attempts have been made to reduce parsimony to a simple exercise in counting. In other words, what can be done with one would in vain be done with two. As W.V. Quine pointed out, in most contexts the number 5.23 constitutes a correction of 5.21, but merely a refinement of 5.2; and this “simpler hypothesis” (5.2) is “ten times likelier to be confirmed” than 5.23, just because “ten times as much deviation is tolerated.” Here simplicity meets confirmability and convenience.

On the other hand, the economist Paul Samuelson has shown in his much-used textbook Economics that sometimes “two transactions are simpler than one.” The introduction of money added a step to the old barter form of exchange, and in that respect made the transaction more complex; yet the net result was simplification, because more time and trouble are usually involved in trading chickens for apples than in trading chickens for money and money for apples.

When we finish counting, then, we still have simplicity to deal with. As Nicholas Rescher points out in Aesthetic Factors in Natural Science (1990), the number of fundamental physical constants grew from one in Newton’s time (the strength of gravity) to eight in the twentieth century; yet that growth did nothing to cool the ardor with which scientists pursue parsimony. And Rescher thinks we should pursue it, “not so much for its own sake – because of the aesthetics of the thing – but because this is cost-effective as a strategy for problem-solving.” Whether or not nature favors simplicity, “we should certainly do so... [as a] methodological tool of inquiry.” He calls this ‘Methodological Simplificationism’, or “the presumption of simplicity.”

“Nature is Pleased with Simplicity”

Ockham’s Razor is not always relevant, let alone a determinator between theories. Obviously it will not adjudicate between two theories that are equally parsimonious. Take the hoary philosophical question whether the appearances of physical things are caused by external objects or, as Bishop Berkeley thought, by God. By the criterion of Ockham’s Razor, it seems a matter of indifference whether we are realists or idealists.

Nonetheless, parsimony figures on virtually all lists of the higher values of science. In fact, one thing that stands out about these lists is how similar they are. In Monad to Man (1996), Michael Ruse cites “aesthetic or conceptual elegance,” the “ring of truth” conferred by greater simplicity, the “unifying power of bringing many disparate elements under a very few overarching hypotheses, and fertility.” One might quibble with the details of Ruse’s classification, but it has the ring of familiarity. We are used to treating elegance, unifying power and fertility as givens in science, no less than we treat the need for conformity to fact and predictive accuracy as givens.

The philosopher William Lycan is someone who calls the principle of parsimony “ultimate.” The fact that we “prefer neater systems of beliefs to messy ones full of pathways that lead nowhere” is something he chalks up in Judgement and Justification (1988) simply to “Mother Nature.” And as we saw, Newton too declared without explanation or qualification that “nature is pleased with simplicity.” Herbert Simon also thinks parsimony is present in nature, but he goes on to consider “how we are so fortunate to find nature structured in this way.” His answer is natural selection, which he suggests operates tends to operate in hierarchical, parsimonious order, or what Darwin described in the Origin of Species as an increasing “division of physiological labor.”

Some are intuitionists about the principle of parsimony, and do not demand justification of it. Others, with a more empiricist bent, require that parsimony lead to predictive success. The empiricists have found it hard to analyze parsimony their way; but the intuitionist way resists any analysis at all. As Rescher notes, Ockham’s Razor can be construed as a presumption or a principle of method rather than as a true-or-false proposition; and in one statement of it, both Ockham and Duns Scotus do construe it that way. Of course, some may demand justification for relying on this way of solving problems. But if nothing else, to take parsimony as a given, sans explication, is one way to describe it in as few words as possible.

Toni Vogel Carey is an independent scholar who writes about philosophy and the history of ideas. She is a regular contributor to Philosophy Now, and serves on its US Advisory Board.