• [5][54] That is, science is open to the possibility that future experiments might support more complex theories than demanded by current data and is more interested in designing
  experiments to discriminate between competing theories than favoring one theory over another based merely on philosophical principles.

• 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.

• Another interpretation of the razor’s statement would be that “simpler hypotheses are generally better than the complex ones”.

• “[27] Justifications Aesthetic[edit] 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 true.

• 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.

• “[3] This philosophical razor advocates that when presented with competing hypotheses about the same prediction and both theories have equal explanatory power one should prefer
  the hypothesis that requires the fewest assumptions[4] and that this is not meant to be a way of choosing between hypotheses that make different predictions.

• Critics of the cladistic approach often observe that for some types of data, parsimony could produce the wrong results, regardless of how much data is collected (this is called
  statistical inconsistency, or long branch attraction).

• However, this criticism is also potentially true for any type of phylogenetic inference, unless the model used to estimate the tree reflects the way that evolution actually
  happened.

• ‘”[41] Richard Swinburne[edit] Richard Swinburne argues for simplicity on logical grounds: … the simplest hypothesis proposed as an explanation of phenomena is more likely
  to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for
  truth.

• If one accepts the first interpretation, the validity of Occam’s razor as a tool would then have to be rejected if the more complex explanations were more often correct than
  the less complex ones (while the converse would lend support to its use).

• Dawkins argues the way evolution works is that the genes propagated in most copies end up determining the development of that particular species, i.e., natural selection turns
  out to select specific genes, and this is really the fundamental underlying principle that automatically gives individual and group selection as emergent features of evolution.

• — Swinburne 1997 According to Swinburne, since our choice of theory cannot be determined by data (see Underdetermination and Duhem–Quine thesis), we must rely on some criterion
  to determine which theory to use.

• Since it is absurd to 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.

• In the related concept of overfitting, excessively complex models are affected by statistical noise (a problem also known as the bias–variance tradeoff), whereas simpler models
  may capture the underlying structure better and may thus have better predictive performance.

• [55] It has been suggested that Occam’s razor is a widely accepted example of extraevidential consideration, even though it is entirely a metaphysical assumption.

• However, science has shown repeatedly that future data often support more complex theories than do existing data.

• [53][54][55] When scientists use the idea of parsimony, it has meaning only in a very specific context of inquiry.

• [39] The idea here is that a simple theory applies to more cases than a more complex one, and is thus more easily falsifiable.

• Thus, complex hypotheses must predict data much better than do simple hypotheses before researchers reject the simple hypotheses.

• For each accepted explanation of a phenomenon, there may be an extremely large, perhaps even incomprehensible, number of possible and more complex alternatives.

• “[27] The idea of parsimony or simplicity in deciding between theories, though not the intent of the original expression of Occam’s razor, has been assimilated into common
  culture as the widespread layman’s formulation that “the simplest explanation is usually the correct one.

• In doing so he is invoking a variant of Occam’s razor known as Morgan’s Canon: “In no case is an animal activity to be interpreted in terms of higher psychological processes,
  if it can be fairly interpreted in terms of processes which stand lower in the scale of psychological evolution and development.”

• [35] Practical considerations and pragmatism[edit] See also: Pragmatism and Problem of induction Mathematical[edit] Main article: Akaike information criterion One justification
  of Occam’s razor is a direct result of basic probability theory.

• [29] Ernst Mach formulated the stronger version of Occam’s razor into physics, which he called the Principle of Economy stating: “Scientists must use the simplest means of
  arriving at their results and exclude everything not perceived by the senses.

• Even if some increases in complexity are sometimes necessary, there still remains a justified general bias toward the simpler of two competing explanations.

• Elliott Sober[edit] 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.

• [6] In this context, Einstein himself expressed caution when he formulated Einstein’s Constraint: “It can scarcely be denied that the supreme goal of all theory is to make
  the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.

• [12] Robert Grosseteste, in Commentary on [Aristotle’s] the Posterior Analytics Books (Commentarius in Posteriorum Analyticorum Libros) (c. 1217–1220), declares: “That is
  better and more valuable which requires fewer, other circumstances being equal… 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 it makes
  us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises.

• [53][54][55] As a logical principle, Occam’s razor would demand that scientists accept the simplest possible theoretical explanation for existing data.

• [54] If multiple models of natural law make exactly the same testable predictions, they are equivalent and there is no need for parsimony to choose a preferred one.

• Nevertheless, the precise words sometimes attributed to William of Ockham, (Entities must not be multiplied beyond necessity),[16] are absent in his extant works;[17] this
  particular phrasing comes from John Punch,[18] who described the principle as a “common axiom” (axioma vulgare) of the Scholastics.

• [clarification needed] Thomas Aquinas made this argument in the 13th century, writing, “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 [if] one suffices.

• “[37] The use of “sharp” here is not only a tongue-in-cheek reference to the idea of a razor, but also indicates that such predictions are more accurate than competing predictions.

• “[31] Beginning in the 20th century, epistemological justifications based on induction, logic, pragmatism, and especially probability theory have become more popular among
  philosophers.

• Testing the razor[edit] The razor’s statement that “other things being equal, simpler explanations are generally better than more complex ones” is amenable to empirical testing.

• The term razor refers to distinguishing between two hypotheses either by “shaving away” unnecessary assumptions or cutting apart two similar conclusions.

• The procedure to test the former interpretation would compare the track records of simple and comparatively complex explanations.

• Our preference for simplicity may be justified by its falsifiability criterion: we prefer simpler theories to more complex ones “because their empirical content is greater;
  and because they are better testable”.

• 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?’

• may have no non-circular answer, the same may be true of the question ‘why should simplicity be considered in evaluating the plausibility of hypotheses?

• This is again comparing a simple theory to a more complex theory where both explain the data equally well.

• [32][33][34] Any more complex theory might still possibly be true.

• George C. Williams in his book Adaptation and Natural Selection (1966) argues that the best way to explain altruism among animals is based on low-level (i.e., individual)
  selection as opposed to high-level group selection.

• “[22] Around 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observations – for example, predicting the next symbol
  based upon a given series of symbols.

• The general principle of science is that theories (or models) of natural law must be consistent with repeatable experimental observations.

• Several background assumptions are required for parsimony to connect with plausibility in a particular research problem.

• 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 fewer, other circumstances
  being equal.

• 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.

• While it has been claimed that Occam’s razor is not found in any of William’s writings,[15] one can cite statements such as (“Plurality must never be posited without necessity”),
  which occurs in his theological work on the Sentences of Peter Lombard (ed.

• Since 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 tend to be more testable.

• This notion was deeply rooted in the aesthetic value that simplicity holds for human thought and the justifications presented for it often drew from theology.

• [7] Empirical[edit] Occam’s razor has gained strong empirical support in helping to converge on better theories (see Uses section below for some examples).

• Altruism is defined by some evolutionary biologists (e.g., R. Alexander, 1987; W. D. Hamilton, 1964) as behavior that is beneficial to others (or to the group) at a cost to
  the individual, and many posit individual selection as the mechanism that explains altruism solely in terms of the behaviors of individual organisms acting in their own self-interest (or in the interest of their genes, via kin selection).

• None of the papers provided a balance of evidence that complexity of method improved forecast accuracy.

• Most of the time, however, 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.

• That would be an example of regular natural selection – a phenomenon called “the selfish herd”.

• Likelihood methods for phylogeny use parsimony as they do for all likelihood tests, with hypotheses requiring fewer differing parameters (i.e., numbers or different rates
  of character change or different frequencies of character state transitions) being treated as null hypotheses relative to hypotheses requiring more differing parameters.

• Systematics is the branch of biology that attempts to establish patterns of relationship among biological taxa, today generally thought to reflect evolutionary history.

• 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.

• It is a mistake to think that there is a single global principle that spans diverse subject matter.

• Science often does not demand arbitration or selection criteria between models that make the same testable predictions.

• Later formulations[edit] To 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.

• This endless supply of elaborate competing explanations, called saving hypotheses, cannot be technically ruled out – except by using Occam’s razor.

• The probabilistic (Bayesian) basis for Occam’s razor is elaborated by David J. C. MacKay in chapter 28 of his book Information Theory, Inference, and Learning Algorithms,[36]
  where he emphasizes that a prior bias in favor of simpler models is not required.

• Philosophers, he suggests, may have made the error of hypostatizing simplicity (i.e., endowed it with a sui generis existence), when it has meaning only when embedded in a
  specific context (Sober 1992).

• In science, Occam’s razor is used as a heuristic to guide scientists in developing theoretical models rather than as an arbiter between published models.

• The ways of God are not open to reason, for God has freely chosen to create a world and establish a way of salvation within it apart from any necessary laws that human logic
  or rationality can uncover.

• It is, however, often difficult to deduce which part of the data is noise (cf.

 

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