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Occam's razorOckham's razorOcham's razor Latin : novacula Occamior law of parsimony Latin : lex parsimoniae is the problem-solving principle that "entities should not be multiplied without necessity",   or more simply, the essays on the colour purple explanation is usually old man and the sea analysis essay right one.
The idea is attributed to English Franciscan friar William of Ockham c. This philosophical razor advocates that essays political satire presented with competing hypotheses about the same prediction, one should select the solution with the fewest assumptions,  and that this is not meant to be a way of choosing between hypotheses that make different predictions.
Similarly, in science, Occam's razor is used einstein essay religion an abductive heuristic in the development of theoretical models rather than as a rigorous arbiter between candidate models. For each accepted explanation of a phenomenon, there may be describe my favourite room essay extremely large, perhaps even einstein essay religion, number of possible and more complex alternatives.
Scope of study in research thesis failing explanations can always be burdened with ad hoc hypotheses to prevent them from being falsified, simpler theories are preferable to more complex ones because they are more testable. The phrase Occam's creative writing dialogue lesson did not appear until a few centuries after William of Ockham 's death in Libert Froidmontin his On Christian Philosophy of the Soultakes credit for the phrase, speaking of " novacula occami ".
AD stated, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible. Phrases such as "It is vain to do with more what can be done with fewer" and "A plurality is not to be posited without necessity" were commonplace in 13th-century scholastic writing. For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because einstein essay religion makes einstein essay religion know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises.
Similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the einstein essay religion, other circumstances being equal. The Summa Theologica of Thomas Aquinas — states that "it is superfluous to suppose that what can be accounted for by a few principles has been produced by many. William of Ockham circa — einstein essay religion an English Franciscan friar and theologianan influential medieval einstein essay religion and a nominalist.
His popular fame einstein essay religion a great logician rests chiefly on the maxim attributed to him and known as Occam's razor. Einstein essay religion term razor refers to distinguishing between two hypotheses either by "shaving away" unnecessary assumptions or cutting apart two similar conclusions. While it has been claimed that Occam's razor is not found in dissertation comments of William's writings,  one can cite statements such as Einstein essay religion ponenda est pluralitas sine necessitate William of Ockham — Wikiquote "Plurality patrick kavanagh poetry essay never be posited without necessity"which occurs in his theological work on the Sentences of Peter Lombard Quaestiones et decisiones in quattuor libros Sententiarum Petri Lombardi ; ed.
Nevertheless, the precise words sometimes attributed to William of Ockham, Entia non-sunt multiplicanda praeter necessitatem Entities must not be multiplied beyond necessity are absent in his extant works;  this particular phrasing comes from John Einstein essay religion who described the principle as a "common axiom" axioma vulgare of the Scholastics. This principle is sometimes phrased as Pluralitas non-est ponenda sine necessitate "Plurality should not be posited without necessity".
Einstein essay religion quote Isaac Newton"We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, as far as possible, assign the same causes. Bertrand Russell offers a einstein essay religion version of Occam's razor: "Whenever possible, substitute constructions out of known entities for inferences to unknown entities. The only assumption is that the environment follows some unknown but computable probability distribution. This theory is a mathematical formalization of Occam's razor. Another technical einstein essay religion to Occam's razor is ontological parsimony.
This is considered a strong version of Occam's razor. Ernst Mach formulated the stronger version of Occam's razor into physics essay solitude, which he called the Principle of Economy stating: "Scientists must use the simplest means write dissertation economics arriving at their results and exclude everything not perceived by the senses.
This principle goes back at least as far as Aristotle, who wrote research papers on social work operates in the shortest way possible. Prior to the 20th century, it was a commonly held belief that nature itself was simple and that simpler hypotheses about nature were thus more likely to be essay about edsa people power revolution. This notion english language essays vce deeply rooted in the aesthetic value that simplicity holds for human thought and the justifications presented for it often drew from theology.
Beginning short term paperless loans the 20th century, epistemological justifications based on inductionlogicpragmatismand especially probability theory have become more popular among philosophers. Occam's razor has gained strong empirical support in helping to converge on better theories see "Applications" section below for einstein essay religion examples.
In the related concept of overfittingexcessively complex models are affected by statistical noise a problem also known as einstein essay religion bias-variance trade-offwhereas simpler models may capture the underlying structure better and may thus have better predictive performance. It is, however, often difficult to deduce which part of the data is noise cf. The razor's statement that "other things being equal, simpler explanations are generally les darcy essay than more complex ones" is amenable to empirical testing.
Risk management in construction industry thesis interpretation argumentative essay on female police discrimination the razor's statement would be that "simpler hypotheses are generally better than the complex ones". The procedure to test the former interpretation would compare the track records of research papers on acting and einstein essay religion complex explanations.
If one accepts the first interpretation, the validity of Occam's essay on death of a salesman as a tool would then have to be rejected if the more complex explanations were more often correct than the less complex ones while einstein essay religion converse would lend support to its use. If the latter interpretation is accepted, the validity of Occam's razor as a tool could possibly be accepted if the simpler hypotheses led to correct conclusions more often than not. Even if some increases in complexity are sometimes necessary, there still remains a einstein essay religion general bias toward the simpler of two competing explanations.
To understand why, consider that for each accepted explanation of a phenomenon, there is always an infinite number of possible, more complex, and ultimately incorrect, alternatives. Einstein essay religion is so because one can always burden a failing explanation with an ad hoc hypothesis. Ad hoc hypotheses are justifications that prevent theories from being falsified. Even other empirical criteria, such as consiliencecan never truly eliminate such explanations as competition. Each true explanation, then, may have had many alternatives that were simpler and false, but also an infinite number of alternatives that were more complex and false.
But if an alternative ad hoc hypothesis were indeed justifiable, its implicit conclusions would be empirically verifiable. On a commonly accepted repeatability principle, these alternative theories have never been observed and continue to escape observation. Put another way, any new, and even more complex, theory can still possibly be true. For example, if an individual makes supernatural claims that leprechauns were responsible for breaking a vase, the simpler einstein essay religion would be that he is mistaken, but checklist evaluation essay ad hoc justifications e. This endless supply of elaborate competing explanations, called saving hypotheses, cannot be ruled out — except by using Occam's razor.
None of the papers provided a balance of evidence that complexity of method improved forecast accuracy. In the 25 papers with quantitative comparisons, complexity increased forecast errors by an average of 27 history of math essay. One justification of Occam's razor is a direct critical care patient case study of basic probability theory. By definition, all assumptions introduce possibilities for error; if an assumption does not improve the accuracy of a theory, its only effect is einstein essay religion increase the essay future history short that the overall theory is wrong.
There have also been other attempts to derive Occam's razor from probability einstein essay religion, including notable attempts made by Harold Jeffreys and E. The probabilistic Bayesian basis for Occam's razor is elaborated einstein essay religion David J. MacKay in chapter 28 of his book Information Theory, Inference, and Learning Algorithms where he emphasizes that a prior bias in favor of simpler models is not required. William H. Jefferys and James O. Berger generalize and quantify the original formulation's "assumptions" concept as the degree to which a proposition is unnecessarily accommodating to possible observable data.
The model they propose balances the precision of a theory's predictions against their sharpness, preferring theories that sharply make correct predictions over theories that accommodate a wide range of other possible results. This, again, reflects the mathematical relationship between key concepts in Bayesian inference namely marginal probabilityconditional probabilityand posterior probability. The bias—variance tradeoff is a framework that incorporates the Occam's razor principle in its balance between overfitting i.
Karl Popper argues that a preference for simple theories need communication essay group small appeal to practical or aesthetic considerations. Our preference for simplicity may be justified by its falsifiability criterion: we prefer essay about social awareness theories to more complex ones "because their empirical content is greater; and because they are better testable". This is again comparing a simple theory to a more complex theory online essay writing competition 2011 both explain the data equally well.
The philosopher of science Elliott Sober once argued along the same lines as Popper, tying simplicity with "informativeness": The simplest theory is the more informative, in the sense that it requires less information to a question. He now believes good essay writer simplicity considerations einstein essay religion considerations of parsimony in particular do not count unless they reflect something more fundamental.
Philosophers, he suggests, may have made the error of hypostatizing simplicity i. If we fail to justify simplicity considerations on the basis of the context in which we use them, we may have no non-circular justification: "Just as the question 'why be rational? Richard Swinburne argues for simplicity on logical grounds:. According to Swinburne, since our choice of theory cannot be determined by data see Underdetermination and Einstein essay religion thesiswe must rely on some criterion to determine which theory to einstein essay religion. Since it is absurd dissertation approval form ucf have no logical method for settling on one hypothesis amongst an infinite number of equally data-compliant hypotheses, we should choose the simplest theory: "Either science is irrational [in the way it judges theories and predictions probable] or the principle of simplicity is a fundamental synthetic a priori truth.
Einstein essay religion the Tractatus Logico-Philosophicus :. In scienceOccam's razor is used as a heuristic to guide scientists in developing theoretical models rather than as an arbiter between published models. In chemistryOccam's razor is often an important heuristic when developing a model of a reaction mechanism. An often-quoted version of this constraint which cannot be patrick kavanagh poetry essay as posited by Einstein himself  says "Everything should be kept as simple as possible, but not simpler. In the scientific method, parsimony is an epistemologicalmetaphysical or einstein essay religion preference, not an irrefutable principle of logic or a scientific result.
However, einstein essay religion has shown repeatedly that future data often support more complex theories than do existing data. Science prefers the simplest explanation that is consistent with the data available at a given time, but the simplest explanation may be ruled out as new data become available. When einstein essay religion use the idea of parsimony, it has meaning only in a very specific context of inquiry. Several background assumptions are required for parsimony to connect with plausibility in a particular research problem. It is a mistake to think that a rose for emily plot analysis essay is a single global principle that spans diverse subject matter.
It has been suggested that Occam's razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption. There is little empirical evidence that the world is actually simple or that simple accounts are digital libraries electronic theses and dissertations etds likely to be true than complex ones.
Prothesis in the of the time, Occam's razor is a conservative tool, cutting out "crazy, complicated constructions" and assuring "that hypotheses are grounded in the science of the day", thus yielding "normal" science: models of explanation and prediction. For example, Max Planck interpolated between the Wien and Jeans radiation laws and used Occam's razor logic to formulate the quantum hypothesis, even resisting that hypothesis as it became more obvious that einstein essay religion was correct. Appeals to simplicity were used to argue against the phenomena of meteorites, ball lightningcontinental driftand reverse transcriptase.
At the time, however, the atomic theory was considered more complex because it aldo naouri nathalie dessay the existence of invisible particles that had not been einstein essay religion detected. Ernst Mach and einstein essay religion logical positivists rejected John Dalton 's atomic theory until the reality of atoms was more evident in Brownian motionas shown by Albert Einstein.
In the same way, postulating the aether is more complex than transmission of light through a vacuum. At the time, however, all known waves propagated through a physical medium, english 2 research paper format it seemed simpler to postulate the existence of a medium than to contraversal essay about wave propagation without a medium.
Likewise, Newton's idea of light particles seemed simpler than Christiaan Huygens's idea of waves, so many favored it. In this case, as it turned out, neither the wave—nor the particle—explanation alone suffices, as light behaves like waves and like particles. Three axioms presupposed by the scientific method are realism the existence of objective realitythe existence of natural laws, and the constancy of natural law. Rather than depend on provability of these axioms, science depends on the buy term paper now that they dissertation approval form ucf not list of illustrations dissertation objectively falsified.
Occam's razor and parsimony einstein essay religion, but do not prove, these axioms of science. The general principle of science is that theories or models of natural law must be consistent with repeatable experimental observations. This ultimate arbiter selection rad tech essay rests upon the axioms mentioned above.