mercredi 21 novembre 2007

Le rasoir d'Occam, son histoire

Extrait de

Formulations of Occam's Razor:

by Russell Johnston, Victoria, BC, Canada

Occam's Razor/The Principle of Simplicity, or something like it, has been stated in more than one way.

Citing those with the most definite historical provenance first:

1a) “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]. []
(As we will discuss, this may be only a principle of logic or etiquette for proofs, however, and not the more modern principle.)

1b)"the more perfect a nature is the fewer means it requires for its operation"Aristotle

2) "Pluralitas non est ponenda sine neccesitate" or "plurality should not be posited without necessity." (a quote from Book II of Occam's Commentary on the Sentences of Peter Abelard) []

3)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, T. (1945) Basic Writings of St. Thomas Aquinas, trans. A.C. Pegis, New York: Random House, p. 129.

4) “One should not increase, beyond what is necessary, the number of entities required to explain anything.” which dates from 1639, from John Ponce of Cork. []

5) “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, while comparing the Ptolemaic and Copernican theories of solar system dynamics. Galileo, G. Dialogue Concerning the Two Chief World Systems, translated by Drake (1962), Berkeley, p. 397.

6a) “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's first of three ‘Rules of Reasoning in Philosophy’ (philosophy then included the sciences), Book III of Principia Mathematica.

As well as:

6b) “Nature is pleased with simplicity, and affects not the pomp of superfluous causes” - Newton, I. (1964) The Mathematical Principles of Natural Philosophy, New York: Citadel Press, p. 398). []
(6a is admirably specific, but seems more a truth of logic than a predictive principle when compared to 6b.)

7) “[T]he 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.” - Albert Einstein [Nash, L. (1963) The Nature of the Natural Sciences, Boston: Little, Brown.].

Finally, perhaps the two most common or popular formulations of the Principle:

8) Entia non sunt multiplicanda praeter necessitatem”, or "Entities should not be multiplied beyond necessity" (probably the most common formulation.)

9) “Of two equivalent theories or explanations, all other things being equal the simpler one is to be preferred.” - this is a common formulation, but also quite possibly the most ambiguous, which is to say least specific or informative.

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