Occam's razor

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William of Ockham. Sketch from a Summa-logicae manuscript from 1341 with the inscription frater Occham iste

Occam's razor - also the principle of parsimony , lex parsimoniae or thrift principle - is a heuristic research principle from scholasticism that requires the greatest possible thrift in the formation of explanatory hypotheses and theories. The principle named after Wilhelm von Ockham (1288–1347) is used in the theory of science and scientific methodology . In simple terms it says:

  1. Of several sufficient possible explanations for one and the same state of affairs, the simplest theory is preferable to all others.
  2. A theory is simple if it contains as few variables and hypotheses as possible and if these are in clear logical relationships to one another, from which the facts to be explained logically follow.

Linked to the O'ckham rule is the requirement to recognize only one single adequate explanation for each object of investigation . According to current scientific practice, this explanation does not have to be monocausal . It can consist of several related sentences. The metaphorical designation of a razor comes from the fact that all other explanations of a phenomenon can be removed easily and at once, like with a razor.

The practical advantage of this principle for the theory development is that theories with few and simple assumptions are easier to falsify than those with many and complicated assumptions. Occam's razor is only one of several criteria for the quality of theories . It cannot be used to judge the validity of explanatory models, but unnecessary assumptions can be excluded. A modern reductionist approach is the KISS principle . A development of the scientific principle of economy is the principle of permanence in mathematics .

Historical formulation and terms

The best-known formulation of the Ockham principle comes from the philosopher Johannes Clauberg (1622–1665). In 1654 he wrote: “ Entia non sunt multiplicanda praeter necessitatem [or: sine necessitate] ” (German: “ Beings may not be increased beyond what is necessary.”) The sentence can already be found in the form “ non sunt multiplicanda entia sine necessitate ” 1639 with the Scotist Johannes Poncius , who quotes it as a scholastic maxim .

The term Occam's Razor for this thrifty principle did not appear until the 19th century with the British philosopher Sir William Hamilton and became popular in the discussion led by John Stuart Mill about his philosophy of science . Wilhelm von Ockham never formulated the principle explicitly, but applied it implicitly in his writings. He demanded: "Nothing can be accepted without justification, unless it is evident or known from experience or secured by the authority of the Holy Scriptures." (In I. Sent d 30, q 1)

In addition to Occam's Razor , the phrase law of parsimony is also common in English . The Latin name is novacula Occami , the traditional German Ockhams scalpel . In French, in 1746, Étienne Bonnot de Condillac found the phrase rasoir des nominaux .

history

The idea of ​​preferring the simplest explanation goes back to Aristotle . Mostly it was justified with the fact that nature always chooses the easiest way. Ockham rejected this justification, however, because it limited the omnipotence of God. He does not accept such a limitation of the divine will. According to Ockham, God might as well choose the most complicated path. Not nature itself, but theories should satisfy the principle of economy. In the construction of theories, superfluous elements should be eliminated and the simpler of two possible theories that can both explain the same phenomenon should be chosen. In Ockham's work, an originally ontological law becomes a practical rule for epistemology .

In modern philosophy of science there are various new interpretations of "Ockham's razor", which are intended to justify this principle as a rational research maxim. Among other things, simplicity was associated with a higher degree of confirmation or with the best explanation . A higher a priori probability within the Bayesian concept of probability also justifies the preference for simpler theories. In addition, the following applies: The more independent assumptions are made to the requirement of the declaration, the higher the probability that one of them could be wrong. The objection to such justifications is that they become circular if they do not have an independent criterion for the simplicity of theories. In addition, due to the induction problem, it is not possible to mark one of several theories, which are equally compatible with all given facts, as true or more likely, regardless of how complex it is.

Current justifications that try to avoid circularity and the induction problem therefore interpret Ockham's principle as a “search strategy” or heuristic : By repeatedly applying the principle of choosing between different explanations compatible with the data, an approximation of a true general theory is to be made. In addition, Occam's razor is robust , insofar as individual deviations from the rule still lead to convergence against the true theory if one reverts to Occam's rule after a violation. This robustness is important because the rule is apparently not strictly applied in scientific practice, and what is meant by “simple” is rarely clearly defined in individual cases. However, it can also be shown that the strict application of Occam's razor among all alternative rules, which would also lead to convergence against the true theory, is distinguished by the fact that it is the most efficient rule.

Another non-circular justification of O'ckham's principle is based on the observation that if the correct theory is not known, predictions with a high probability of success can be made even with wrong theories, and that the complexity of the theory selected for the prediction plays a role in the accuracy of the predictions. Using simple models when there is statistical noise in the data can lead to even more accurate predictions.

Finally, the maxim corresponds to the motivation of reductionist approaches in science: the variety of phenomena should be derived from the smallest possible number of basic assumptions and principles and explained in this sense. A justification for the O'ckham principle is strictly linked to a justification for a large part of the scientific activities of the last centuries, in particular with the endeavor to achieve a unified science .

The principle of thrift instead of the principle of diversity

Walter Chatton , a contemporary of Wilhelm von Ockham, took a counter position to Ockham's thrift: "If three things are not enough to make a clear statement about something, a fourth must be added, and so on." Although various other philosophers in Having formulated similar “counter-principles” at that time, this did not change the meaning of the ontological principle of economy.

Gottfried Wilhelm Leibniz (1646–1716) formulated a principle of diversity : According to Leibniz, we live in the best of all possible worlds precisely because it produces the greatest possible diversity of life, and not because it is as free as possible from evil, sin and suffering ; it is therefore a matter of a principle of optimum completeness (see also theodicy ). For definitions and explanations, Leibniz nevertheless took the view that the simplest explanation is the best.

Immanuel Kant (1724–1804) formulated a principle according to which the diversity of natural species should be prematurely reduced by a reductionist explanation (Immanuel Kant: AA III, 428–441), but at the same time recognized the attempt at such a reduction through the focus imaginarius of the ideas of reason as the interest of reason (see Transcendental Dialectic ). Karl Menger (1902–1985) called mathematicians too stingy in dealing with variables and formulated his law against poverty in two variants: “ Thus what is needed is a counterpart to the Law of Parsimony - so to speak, a Law against Miserliness - stipulating that entities must not be reduced to the point of inadequacy and, more generally, that it is vain to try to do with fewer what requires more . ”( Karl Menger , German:“ Entities must not be reduced to the point of inappropriateness [and] it is pointless to do with less what requires more ”).

In fact, Occam's razor cannot be used until there are several theories that can provide the desired explanation in equal depth. A complex theory that explains the subject better can therefore be preferred to a simple theory. The theory of relativity is more complicated than classical mechanics because it considers different forces in complex mathematical relationships, but it can also explain a larger range of phenomena.

One of the applications of the diversity principle was the Ptolemaic view of the world : the more precise the astronomical observation data , the more clearly stars and planets deviated from the predicted positions. In order to be able to explain the deviations, apparent returns and other things with the classical metaphysics of Aristotle , which the church had made the binding doctrine, further epicycles had to be constantly included in the model. After that, the earth lay in the center of concentric celestial spheres on which the celestial bodies moved. The worldview of Nicolaus Copernicus represents an attempt to eliminate these epicycles and to model the planetary movements more evenly. To do this, he puts the celestial spheres around the sun , rearranges the planets and puts the earth in the order of the planets. Copernicus no longer had to look for reasons for the epicycles. Initially, however, this model agreed less well with the observational data than the improvement in the geocentric worldview developed by Tycho Brahe . The replacement of circular orbits by ellipses in Kepler's laws brought comparable agreement . But only with the introduction of gravitation as a construct by Isaac Newton could the heliocentric worldview claim to be the simpler theory, because Kepler's laws could now be derived from the general physical laws that Galileo Galilei had established and experimentally confirmed. The geocentric view of the world described the positions of the stars and planets just as precisely, but it was difficult to substantiate the movements of the celestial bodies postulated by it physically or metaphysically.

Trivia

Frank Zappa released the song Occam's Razor .

See also

literature

  • Wolfgang Hübener : Ockham's Razor not Mysterious . In: Archive for the history of concepts. Volume 27, 1983, pp. 73-92 (fundamental conceptual historical study; proves the 'invention' of the term in early modern philosophical historiography)
  • HJ Cloeren: Ockham's razor. In: J. Ritter, K. Founder, G. Gabriel (Hrsg.): Historical dictionary of philosophy. Volume 6, 1984, pp. 1094-1096 (but does not take into account the substantial early modern references in Hübener 1983).
  • Armand A. Maurer: Ockham's razor and Chatton's anti-razor. In: Medieval studies . 46/1984. Pp. 463-475.
  • Armand A. Maurer: Ockham's razor and dialectical reasoning . In: Medieval studies . 58/1996. Pp. 49-56.
  • Phil Mole: Ockham's Razor cuts both ways: The Uses and Abuses of Simplicity in Scientific Theories. In: Skeptic , Volume 1, No. 10, 2003, pp. 40-47.

Web links

Individual evidence

  1. ↑ Logica vetus et nova. (1654), p. 320.
  2. ^ William Hamilton, Discussions on Philosophy and Literature , 1852, app. I, p. 580 online
  3. ↑ in An Examination of Sir William Hamilton's Philosophy (1865), pp. 465ff. He emphasizes that an ontological reading of the principle is completely wrong in his eyes, and refers to Newton's unifying foundation of physics, where he finds its use correct.
  4. ↑ quoted from Richard Heinzmann: Philosophy of the Middle Ages. 2nd edition Kohlhammer, Stuttgart 1998, p. 249
  5. ↑ Robert Grosseteste argues in this way when he comes to the wrong conclusion in a treatise that for all rays of light that penetrate an optically denser medium, the angle of refraction corresponds to half the angle of incidence (see also the principle of the smallest effect ) .
  6. ^ John Losee: A historical introduction to philosophy of science. Oxford University Press, 1977.
  7. ↑ C. Glymour: Theory and Evidence. Princeton University Press, 1980.
  8. ^ G. Harman: The Inference to the Best Explanation. Philosophical Review 74, 88-95, 1965
  9. ^ W. Salmon: The Logic of Scientific Inference. University of Pittsburgh Press, 1967.
  10. ↑ Kevin Kelly: Efficient Convergence Implies Ockham's Razor . In: Claudio Delrieux (Ed.): Proceedings of the 2002 International Workshop on Computational Models of Scientific Reasoning and Applications . Bogart, GA: CSREA.
  11. ↑ Kevin Kelly: A New Solution to the Puzzle of Simplicity. In: Philosophy of Science. Volume 74, 2007, pp. 561-573
  12. ^ H. Akaike: Information Theory and an Extension of the Maximum Likelihood Principle . In: BN Petrov, F. Csaki (Eds.): The Second International Symposium on Information Theory . Akadémiai Kiadó, Budapest 1973, pp. 267-281.
  13. ↑ M. Forster, E. Ober: How to Tell When Simpler, More Unified, or Less Ad Hoc Theories Will Provide More Accurate Predictions. In: British Journal for the Philosophy of Science 45: 1-35, 1994
  14. ↑ So named by Arthur O. Lovejoy .
  15. ↑ Immanuel Kant, Collected Writings. Ed .: Vol. 1-22 Prussian Academy of Sciences, Vol. 23 German Academy of Sciences in Berlin, from Vol. 24 Academy of Sciences in Göttingen, Berlin 1900ff., AA III, 428–441 .
  16. ↑ A counterpart of Occam's razor in pure and applied mathematics ontological uses, in: Synthesis 12 (1960), No. 4, pp. 415-428, here: p. 415., doi: 10.1007 / BF00485426
  17. ^ Frank Zappa - Occam's Razor. Retrieved May 13, 2020 .
This version was added to the list of articles worth reading on June 3, 2005 .