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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> |
| | + | ==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]] |
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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).
| + | <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
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| | ==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. |
