Occam's razor - Wikipedia, the free encyclopedia



 The motions of the sun, moon and other solar system planets can be calculated using a geocentric model (the earth is at the center) or using a heliocentric model (the sun is at the center). Both work, but the geocentric system requires many more assumptions than the heliocentric

system, which has only seven.

This was pointed out in a preface to Copernicus' first edition of De revolutionibus orbium coelestium

 

Occam's razor - Wikipedia, the free encyclopedia: Occam's razor (also written as Ockham's razor and in Latin lex parsimoniae) is a problem-solving principle devised by William of Ockham (c. 1287–1347). It states that among competing hypotheses, the one with the fewest assumptions should be selected. Other, more complicated solutions may ultimately prove correct, but—in the absence of certainty—the fewer assumptions that are made, the better.

Mathematical

One justification of Occam's Razor is a direct result 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 to increase the probability that the overall theory is wrong.

There have also been other attempts to derive Occam's Razor from probability theory, including notable attempts made by Harold Jeffreys and E. T. Jaynes. 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,[33] where he emphasises that a prior bias in favour of simpler models is not required.

William H. Jefferys (no relation to Harold Jeffreys) and James O. Berger (1991) generalize and quantify the original formulation's "assumptions" concept as the degree to which a proposition is unnecessarily accommodating to possible observable data.[34] They state "a hypothesis with fewer adjustable parameters will automatically have an enhanced posterior probability, due to the fact that the predictions it makes are sharp".[34] The model they propose balances the precision of a theory's predictions against their sharpness; theories which sharply made their correct predictions are preferred over theories which would have accommodated a wide range of other possible results. This, again, reflects the mathematical relationship between key concepts in Bayesian inference (namely marginal probability, conditional probability, and posterior probability).

Practical considerations and pragmatism

See also: pragmatism and problem of induction

 

The common form of the razor, used to distinguish between equally explanatory hypotheses, may be supported by the practical fact that simpler theories are easier to understand.

Some argue that Occam's Razor is not an inference-driven model, but a heuristic maxim for choosing among other models and instead underlies induction.

Alternatively, if we want to have reasonable discussion we may be practically forced to accept Occam's Razor in the same way we are simply forced to accept the laws of thought and inductive reasoning (given the problem of induction). Philosopher Elliott Sober states that not even reason itself can be justified on any reasonable grounds, and that we must start with first principles of some kind (otherwise an infinite regress occurs).

The pragmatist may go on, as David Hume did on the topic induction, that there is no satisfying alternative to granting this premise. Though one may claim that Occam's Razor is invalid as a premise helping to regulate theories, putting this doubt into practice would mean doubting whether every step forward will result in locomotion or a nuclear explosion. In other words still: "What's the alternative?"

Possible explanations can become needlessly complex. It is coherent, for instance, to add the involvement of leprechauns to any explanation, but Occam's Razor would prevent such additions, unless they were necessary.

 

 Testing the razor

In the history of competing hypotheses, it is the case that the simpler hypotheses have led to mathematically rigorous and empirically verifiable theories. In the history of competing explanations this is not the case. At least, not generally (some increases in complexity are sometimes necessary), and so there remains a justified general bias towards 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. This is so because one can always burden failing explanations with ad hoc hypothesis. Ad hoc hypotheses are justifications that prevent theories from being falsified. Even other empirical criteria like consilience can 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. However, if an alternate ad hoc hypothesis were indeed justifiable, its implicit conclusions would be empirically verifiable. On a commonly accepted repeatability principle, these alternate theories have never been observed and continue to not be observed. In addition, we do not say an explanation is true if it has not withstood this principle.

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 explanation would be that he is mistaken, but ongoing ad hoc justifications (e.g. "And, that's not me on film, they tampered with that too") successfully prevent outright falsification. This endless supply of elaborate competing explanations, called saving hypotheses, cannot be ruled out—but by using Occam's Razor.^[30][31][32