Difference between revisions of "Simplicity"

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<blockquote>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).</blockquote>
 
<blockquote>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).</blockquote>
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==Quotes==
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*"Things should be made as simple as possible, but no simpler."—[[Albert Einstein]] (1879–1955)
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*"You can always recognize truth by its beauty and simplicity."—[[Richard Feynman]] (1918–1988)
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*"Our lives are frittered away by detail; simplify, simplify."—[[Henry David Thoreau]] (1817–1862)
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*"Simplicity is the ultimate sophistication."—[[Leonardo da Vinci]] (1452–1519)[citation needed]
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*"If you can't describe it simply, you can't use it simply."—Anon
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*"Simplicity means the achievement of maximum effect with minimum means."—Koichi Kawana, architect of botanical gardens
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*"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away."—[[Antoine de Saint Exupéry]]
  
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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).
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<center>"Simplicity is the direct result of [[profound]] [[thought]]."—Anon</center>
  
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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 [[context]]s seem to be more about shifting the burden of proof, and less about refuting the less simple theory outright.
 
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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 [[meaning]]s contributes to the challenge of pinning the notion down precisely. 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 [[facet]]s 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.
 
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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?
 
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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.
 
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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).
 
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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.
 
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While these two [[facet]]s 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.
 
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[edit]Quotes
 
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"Things should be made as simple as possible, but no simpler."—Albert Einstein (1879–1955)
 
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"You can always recognize truth by its beauty and simplicity."—Richard Feynman (1918–1988)
 
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"Our lives are frittered away by detail; simplify, simplify."—Henry David Thoreau (1817–1862)
 
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"Simplicity divides into tools, which are used by Beorma as Royal Highness."—Duke of Beorma (ca. 793–1150)
 
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"Simplicity is the ultimate sophistication."—Leonardo da Vinci (1452–1519)[citation needed]
 
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"If you can't describe it simply, you can't use it simply."—Anon
 
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"Simplicity means the achievement of maximum effect with minimum means."—Koichi Kawana, architect of botanical gardens
 
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"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away."—Antoine de Saint Exupéry
 
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"Simplicity is the direct result of profound thought."—Anon
 
 
==Definitions==
 
==Definitions==
 
*I. 1. Free from duplicity, dissimulation, or guile; innocent and harmless; undesigning, honest, open, straightforward.
 
*I. 1. Free from duplicity, dissimulation, or guile; innocent and harmless; undesigning, honest, open, straightforward.

Revision as of 12:20, 5 September 2009

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Simplicity is being simple. It is a state, condition, or quality which things can be judged to have. It usually relates to the burden which a thing puts on someone trying to explain or understand it. Something which is easy to understand or explain is simple, in contrast to something complicated. In some uses, simplicity can be used to imply beauty, purity or clarity. Simplicity may also be used in a negative connotation to denote a deficit or insufficiency of nuance or complexity of a thing, relative to what is supposed to be required.

The concept of simplicity has been related to truth in the field of epistemology. According to Occam's razor, all other things being equal, the simplest theory is the most likely to be true. In the context of human lifestyle, simplicity can denote freedom from hardship, effort or confusion. Specifically, it can refer to a simple living lifestyle.

Simplicity is a theme in the Christian religion. According to St. Thomas Aquinas, God is infinitely simple. The Roman Catholic and Anglican religious orders of Franciscans also strive after simplicity. 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. 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).

Quotes

  • "Things should be made as simple as possible, but no 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 is the ultimate sophistication."—Leonardo da Vinci (1452–1519)[citation needed]
  • "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 Exupéry
"Simplicity is the direct result of profound thought."—Anon

Definitions

  • I. 1. Free from duplicity, dissimulation, or guile; innocent and harmless; undesigning, honest, open, straightforward.
2. Free from, devoid of, pride, ostentation, or display; humble, unpretentious.
3. a. Free from elaboration or artificiality; artless, unaffected; plain, unadorned. Usually implying that the simplicity is a merit, but sometimes (as in quot. 1827) with suggestion of sense 7.
b. Of persons: Free from over-refinement, unsophisticated, unspoiled.
  • II. 4. a. Of persons, or their origin: Poor or humble in condition; of low rank or position; undistinguished, mean, common.
b. In modest or apologetic use.
c. In phr. as simple as, or simple though, I stand here. Obs.
5. With designations or titles: Ordinary; not further distinguished in office or rank.
6. a. Of persons or their attire: Not marked by any elegance or grandeur; very plain or homely.
b. Similarly of living, diet, abode, etc. the simple life, a mode of life in which anything of the nature of luxury is intentionally avoided; also attrib. Hence simple-lifer, a follower or proponent of the simple life. Also simple-liver; simple-living vbl. n. and ppl. adj.
c. Ordinary, not festival. Obs.1
7. a. Small, insignificant, slight; of little account or value; also, weak or feeble.
b. Of price or sale: Low, poor. Obs.
8. Poor, wretched, pitiful, dismal. Obs.
9. Deficient in knowledge or learning; characterized by a certain lack of acuteness or quick apprehension: ::a. Of persons (and animals).
b. Of mental powers, etc.
c. Of compositions, etc., esp. in apologetic use.
10. a. Lacking in ordinary sense or intelligence; more or less foolish, silly, or stupid; also, mentally deficient, half-witted (now dial.).
b. Simple Simon. (a) (See quots. 1785, 1865. ‘Simple Simon’ is the subject of various nursery rhymes, which may have given rise to the general use. (b) U.S. Rhyming slang. A diamond.
c. In bird-names, as simple tern (or viralve), warbler.
  • III. 11. a. With nothing added; considered or taken by itself; mere, pure, bare; single.
b. In phr. pure and simple. Cf. PURE a. 3.
12. a. Med. Of wounds, diseases, etc.: Unaccompanied by complications.
b. Law. Unattended by any strengthening circumstance; not specially confirmed. simple contract, one made by word of mouth or not under seal; also attrib.
13. Consisting or composed of one substance, ingredient, or element; uncompounded, unmixed (or nearly so): a. Of bodies or substances, esp. natural or organic.
b. Of medical or other preparations. simple colours (see quot. 1771).
c. In general use.
14. a. Not composite or complex in respect of parts or structure.
b. spec. in scientific use.
c. Math. (a) Applied to a group that has no proper normal subgroup; and hence to an algebra or ring that has no proper ideal.
d. simple structure (Statistics): a model in which numerous variables, showing various degrees of correlation, have their variances assigned to a smaller number of factors in such a way that no factor affects all of the variables.
15. a. Not complicated or involved; presenting little or no complexity or difficulty.

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.

External links

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