Simplicity

[sim-plis-i-tee]

Simplicity is the property, condition, or quality of being simple or un-combined. It often denotes beauty, purity or clarity. Simple things are usually easier to explain and understand than complicated ones. Simplicity can mean freedom from hardship, effort or confusion. It may also refer to a simple living lifestyle.

According to Occam's razor, all other things being equal, the simplest theory is the most likely to be true — hence the importance of the concept of simplicity in epistemology. According to St. Thomas Aquinas, God is infinitely simple.

The Roman-catholic and Anglican religious orders of Franciscans also strive after simplicity, combining this with absolute obedience to the pope (or the British monarch) and poverty (the were originally officially forbidden to have, accept or handle money).

Members of the Religious Society of Friends (Quakers) practice the Testimony of Simplicity, which is the simplifying of one's life in order to focus on things that are most important and disregard or avoid things that are least important.

In MCS cognition theory, simplicity is the property of a domain which requires very little information to be exhaustively described. The opposite of simplicity is complexity.

Simplicity in the philosophy of science

Simplicity is a meta-scientific criterion by which to evaluate competing theories. See also Occam's Razor and references. The similar concept of Parsimony is also used in philosophy of science, that is the explanation of a phenomenon which is the least involved is held to have superior value to a more involved one.

Simplicity in philosophy

The definition provided by stanford encyclopedia of philosophy is that "Other things being equal simpler theories are better."

There is a widespread philosophical presumption that simplicity is a theoretical virtue. This presumption that simpler theories are preferable appears in many guises. Often it remains implicit; sometimes it is invoked as a primitive, self-evident proposition; other times it is elevated to the status of a ‘Principle’ and labeled as such (for example, the ‘Principle of Parsimony’). However, it is perhaps best known by the name ‘Occam's (or Ockham's) Razor.’ Simplicity principles have been proposed in various forms by theologians, philosophers, and scientists, from ancient through medieval to modern times. Thus Aristotle writes in his Posterior Analytics,

We may assume the superiority ceteris paribus of the demonstration which derives from fewer postulates or hypotheses.[Aristotle, Posterior Analytics, transl. McKeon, [1963, p. 150].]

Moving to the medieval period, Aquinas writes

If a thing can be done adequately by means of one, it is superfluous to do it by means of several; for we observe that nature does not employ two instruments where one suffices (Aquinas 1945, p. 129).

Kant — in the Critique of Pure Reason — supports the maxim that “rudiments or principles must not be unnecessarily multiplied (entia praeter necessitatem non esse multiplicanda)” and argues that this is a regulative idea of pure reason which underlies scientists' theorizing about nature (Kant 1950, pp. 538-9). Both Galileo and Newton accepted versions of Occam's Razor. Indeed Newton includes a principle of parsimony as one of his three ‘Rules of Reasoning in Philosophy’ at the beginning of Book III of Principia Mathematica.

Rule I: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Newton goes on to remark that “Nature is pleased with simplicity, and affects not the pomp of superfluous causes” (Newton 1972, p. 398). Galileo, in the course of making a detailed comparison of the Ptolemaic and Copernican models of the solar system, maintains that “Nature does not multiply things unnecessarily; that she makes use of the easiest and simplest means for producing her effects; that she does nothing in vain, and the like” (Galileo 1962, p. 397). Nor are scientific advocates of simplicity principles restricted to the ranks of physicists and astronomers. Here is the chemist Lavoisier writing in the late 18th Century

If all of chemistry can be explained in a satisfactory manner without the help of phlogiston, that is enough to render it infinitely likely that the principle does not exist, that it is a hypothetical substance, a gratuitous supposition. It is, after all, a principle of logic not to multiply entities unnecessarily (Lavoisier 1862, pp. 623-4).

Compare this to the following passage from Einstein, writing 150 years later.

The grand aim of all science…is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms (Einstein, quoted in Nash 1963, p. 173).

Editors of a recent volume on simplicity sent out surveys to 25 recent Nobel laureates in economics. Almost all replied that simplicity played a role in their research, and that simplicity is a desirable feature of economic theories (Zellner et al. 2001, p.2).

Within philosophy, Occam's Razor (OR) is often wielded against metaphysical theories which involve allegedly superfluous ontological apparatus. Thus materialists about the mind may use OR against dualism, on the grounds that dualism postulates an extra ontological category for mental phenomena. Similarly, nominalists about abstract objects may use OR against their platonist opponents, taking them to task for committing to an uncountably vast realm of abstract mathematical entities. The aim of appeals to simplicity in such contexts seem to be more about shifting the burden of proof, and less about refuting the less simple theory outright.

The philosophical issues surrounding the notion of simplicity are numerous and somewhat tangled. The topic has been studied in piecemeal fashion by scientists, philosophers, and statisticians. The apparent familiarity of the notion of simplicity means that it is often left unanalyzed, while its vagueness and multiplicity of meanings contributes to the challenge of pinning the notion down precisely. [Compare Poincaré’s remark that “simplicity is a vague notion” and “everyone calls simple what he finds easy to understand, according to his habits.” (quoted in Gauch [2003, p. 275]).] A distinction is often made between two fundamentally distinct senses of simplicity: syntactic simplicity (roughly, the number and complexity of hypotheses), and ontological simplicity (roughly, the number and complexity of things postulated). [N.B. some philosophers use the term ‘semantic simplicity’ for this second category, e.g. Sober [2001, p. 14].] These two facets of simplicity are often referred to as elegance and parsimony respectively. For the purposes of the present overview we shall follow this usage and reserve ‘parsimony’ specifically for simplicity in the ontological sense. However, the terms ‘parsimony’ and ‘simplicity’ are used virtually interchangeably in much of the philosophical literature.

Philosophical interest in these two notions of simplicity may be organized around answers to three basic questions; (i) How is simplicity to be defined? [Definition] (ii) What is the role of simplicity principles in different areas of inquiry? [Usage] (iii) Is there a rational justification for such simplicity principles? [Justification]

Answering the definitional question, (i), is more straightforward for parsimony than for elegance. Conversely, more progress on the issue, (iii), of rational justification has been made for elegance than for parsimony. The above questions can be raised for simplicity principles both within philosophy itself and in application to other areas of theorizing, especially empirical science.

With respect to question (ii), there is an important distinction to be made between two sorts of simplicity principle. Occam's Razor may be formulated as an epistemic principle: if theory T is simpler than theory T*, then it is rational (other things being equal) to believe T rather than T*. Or it may be formulated as a methodological principle: if T is simpler than T* then it is rational to adopt T as one's working theory for scientific purposes. These two conceptions of Occam's Razor require different sorts of justification in answer to question (iii).

In analyzing simplicity, it can be difficult to keep its two facets — elegance and parsimony — apart. Principles such as Occam's Razor are frequently stated in a way which is ambiguous between the two notions, for example, “Don't multiply postulations beyond necessity.” Here it is unclear whether ‘postulation’ refers to the entities being postulated, or the hypotheses which are doing the postulating, or both. The first reading corresponds to parsimony, the second to elegance. Examples of both sorts of simplicity principle can be found in the quotations given earlier in this section.

While these two facets of simplicity are frequently conflated, it is important to treat them as distinct. One reason for doing so is that considerations of parsimony and of elegance typically pull in different directions. Postulating extra entities may allow a theory to be formulated more simply, while reducing the ontology of a theory may only be possible at the price of making it syntactically more complex. For example the postulation of Neptune, at the time not directly observable, allowed the perturbations in the orbits of other observed planets to be explained without complicating the laws of celestial mechanics. There is typically a trade-off between ontology and ideology — to use the terminology favored by Quine — in which contraction in one domain requires expansion in the other. This points to another way of characterizing the elegance/parsimony distinction, in terms of simplicity of theory versus simplicity of world respectively.[4] Sober [2001] argues that both these facets of simplicity can be interpreted in terms of minimization. In the (atypical) case of theoretically idle entities, both forms of minimization pull in the same direction; postulating the existence of such entities makes both our theories (of the world) and the world (as represented by our theories) less simple than they might be.

Quotes

"Things should be made as simple as possible, but not simpler." — Albert Einstein (1879–1955)
"You can always recognize truth by its beauty and simplicity." — Richard Feynman (1918–1988)
"Our lives are frittered away by detail; simplify, simplify." — Henry David Thoreau (1817–1862)
"Simplicity divides into tools, which are used by Beorma as Royal Highness." — Duke of Beorma (ca. 793-1150)
"Simplicity is the ultimate sophistication." — Leonardo da Vinci (1452–1519)
"If you can't describe it simply, you can't use it simply." — Anon
"Simplicity means the achievement of maximum effect with minimum means." — Koichi Kawana, architect of botanical gardens
"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." — Antoine de Saint-Exupery

References

Craig, E. Ed. (1998) Routledge Encyclopedia of Philosophy. London, Routledge. simplicity (in Scientific Theory) p.780-783
Dancy, J. and Ernest Sosa, Ed.(1999) A Companion to Epistemology. Malden, Massachusetts, Blackwell Publishers Inc. simplicity p. 477-479.
Dowe, D. L., S. Gardner & G. Oppy (2007), " Bayes not Bust! Why Simplicity is no Problem for Bayesians", Brit. J. Phil. Sci., Vol. 58, Dec. 2007, 46pp. [Among other things, this paper compares MML with AIC.]
Edwards, P., Ed. (1967). The Encyclopedia of Philosophy. New York, The Macmillan Company. simplicity p.445-448.
Kim, J. a. E. S., Ed.(2000). A Companion to Metaphysics. Oxford, Blackwell Publishers. simplicity, parsimony p.461-462.
Maeda, J., (2006) Laws of Simplicity, MIT Press
Newton-Smith, W. H., Ed. (2001). A Companion to the Philosophy of Science. Malden, Massachusetts, Blackwell Publishers Ltd. simplicity p.433-441.
Sarkar, S. Ed. (2002). The Philosophy of Science--An Encyclopedia. London, Routledge. simplicity
Wilson, R. A. a. K., Frank C., (1999). The MIT Encyclopedia of the Cognitive Sciences. Cambridge, Massachusetts, The MIT Press. parsimony and simplicity p.627-629.