Occam razor (also Ockham razor or Ocham razor ; Latin: lex parsimoniae " the law stinginess ") is a problem-solving principle that, when presented with a hypothetical answer that competes for the problem, one should choose the answer that makes the least assumption. This idea is associated with William of Ockham (c 1287-1347), who was a British Franciscan friar, a scholastic philosopher, and a theologian.
In science, Occam's razor is used as a heuristic guide in the development of theoretical models, rather than as a strict referee among candidate models. In the scientific method, Occam's razor is not regarded as an indisputable principle of logic or scientific result; the preference for simplicity in the scientific method is based on falsifiability criteria. For every explanation it receives about a phenomenon, there may be an enormous number of possible alternatives, perhaps even incomprehensible. Because one can always burden a failed explanation with an ad hoc hypothesis to prevent it from being forged, the simpler theories are preferred over the more complex because they are more testable.
Video Occam's razor
History
The term Occam's razor did not appear until several centuries after the death of William of Ockham in 1347. Libert Froidmont, in his book On Christian Philosophy of the Soul , takes praise for this phrase. , talking about " novacula occami ". Ockham did not create this principle, but the "razor" - and its relationship with him - probably because of the frequency and effectiveness it uses. Ockham states the principle in various ways, but the most popular version, "Entities can not be multiplied without necessity" ( Non edit multiplicanda entia sine requires ) was formulated by the Irish Franciscan philosopher John Punch in 1639 comments on the works of Duns Scotus.
Formulation before William of Ockham
The origins of what came to be known as Occam's razors could be traced back to the works of previous philosophers such as John Duns Scotus (1265-1308), Robert Grosseteste (1175-1253), Maimonides (Moses ben-Maimon, 1138-1204), and even Aristotle (384-322 BC). Aristotle writes in his Posterior Analytics , "We can assume the superiority ceteris paribus [other things the same thing] from demonstrations derived from postulates or lesser hypotheses. "Ptolemy (AD c) AD 90 - c AD 168 states," We consider it a good principle to explain the phenomenon with Simple hypothesis possible. "
Phrases like "Nothing to do with what can be done with less" and "A plurality should not be put forward without necessity" are commonplace in 13th century scholastic writing. Robert Grosseteste, in Commentary on [Aristotle] Posterior Poster Book Commentarius in Posteriorum Analyticorum Libros ) (c 1217-1220), states: "It's better and more valuable that needs less, other circumstances are the same... Because if one thing is demonstrated from many other things than fewer known places, it's obviously better that fewer because it makes us know quickly. , as universal demonstrations are better than special because they produce less knowledge of the place, and in the natural sciences, in moral science, and in the best of metaphysics are those who do not need a place and better that require less, other circumstances become the same. "
The Summa Theologica of Thomas Aquinas (1225-1274) states that "it is useless to suppose that what some principles can account for has been generated by many." Aquinas uses this principle to build an objection to the existence of God, an objection that he in turn responds and denies in general (cf. quinque viae ), and in particular, through an argument based on causality. Therefore, Aquinas acknowledges the principle that today is known as Occam's razor, but prefers a causal explanation for other simple explanations (see Correlation also does not imply causation).
William from Ockham
William of Ockham ( circa 1287-1347) was a British Franciscan monk and theologian, an influential medieval philosopher and nominalist. His popular fame as a great logician lies primarily in the proverb associated with it and is known as Occam's razor. The term razor refers to distinguishing between two hypotheses either by "shaving" unnecessary assumptions or cutting off the same two conclusions.
Although it has been claimed that Occam's razor is not found in William's writings, one can quote statements such as Numquam ponenda est plurality requires sinus Plurality should not be dated without necessity, which occurs in his book. theological work on the 'Peter Lombard Sentence' ( Quaestiones et decision in libros quattuor Sententiarum Petri Lombardi (ed. Lugd., 1495), i, dist. 27, qu. 2, K).
However, the exact words are sometimes associated with William of Ockham, entia non sunt multiplicanda praeter necessitatem ( entity should not be multiplied beyond necessity), not in his existing works; This particular phrase is derived from John Punch, which describes the principle as the "general axiom" ( axioma vulgare ) of Scholastic. William's contribution from Ockham seems to limit the operation of this principle in matters relating to God's miracles and power; so, in the Eucharist, the plurality of miracles is possible, simply because it pleases God.
This principle is sometimes expressed as " plurality non est ponenda sine requires " ("plurality should not be confirmed without necessity" ). In his book Summa Totius Logicae , i. 12, William of Ockham cites the economic principle, Next formulation
To quote Isaac Newton, "We must admit that there are no more natural causes than they are both true and sufficient to explain their appearance, and therefore, in the same natural effect we must, as far as possible, establish the same cause."
Bertrand Russell offers a special version of Occam razor: "Whenever possible, substitute the construction of a known entity for inference to an unknown entity."
Around the year 1960, Ray Solomonoff founded the theory of universal inductive inference, the theory of prediction based on observation; for example, predicting the next symbol based on a given set of symbols. The only assumption is that the environment follows some unknown but unrecognized probability distribution. This theory is the mathematical formalization of Occam razor.
Another technical approach to Occam razor is ontological parsimonies. Parsimony means misery and is also called the Rule of Simplicity. This is considered a strong version of Occam razor. The variation used in medicine is called "Zebra": doctors should reject the exotic medical diagnosis when more general explanations are more likely, derived from Theodore Woodward's dictum "When you hear a horse's voice, think of a horse instead of a zebra".
Ernst Mach formulated a stronger version of Occam's razor into physics, which he called the Economic Principle which states: "Scientists must use the simplest way to achieve their results and remove all that the senses do not feel."
This principle goes back at least as far as Aristotle, who writes "Nature operates in the shortest possible way." The notion of parsimony or simplicity in deciding between theories, though not the intent of the original expression of Occam's razor, has been assimilated into our culture as a widespread formula that "the simplest explanation is usually the right one."
Maps Occam's razor
Justifications
Aesthetics
Before the 20th century, it was a common belief that nature itself was simple and that simple hypotheses about nature were thus more likely to become reality. This idea is firmly rooted in aesthetic value simplified by simplicity for human thought and justification presented because it is often drawn from theology. Thomas Aquinas made this argument in the 13th century, writing, "If a thing can be done adequately by using one of them, it is superfluous to do it in some way, because we observe that nature does not use two instruments [if] one is enough. "
Beginning in the 20th century, epistemological justification based on induction, logic, pragmatism, and especially probability theory has become more popular among philosophers.
Empirical
Occam's razor has gained strong empirical support in helping to unify the theory better (see the "Applications" section below for some examples).
In overfitting related concepts, models that are overly complex are influenced by statistical noise (a problem also known as trade-off bias-variance), whereas simpler models can capture better basic structures and thus can have better prediction performance. However, it is often difficult to conclude which parts of the data are noisy (see Model selection, test set, minimum description length, Bayesian inference, etc.).
Test the razor
The razor statement that "other things are equal, simpler explanations are usually better than more complicated explanations" are acceptable for empirical testing. Another interpretation of the razor's statement is that "simpler hypotheses are generally better than complex ones". The procedure for testing the previous interpretation will compare complex and complex comparative explanatory track records. If one accepts the first interpretation, the validity of Occam's razor as a tool must then be rejected if more complex explanations are more often correct than less complex (while otherwise would provide support for their use). If the latter interpretation is accepted, the validity of the Occam razor as a tool may be acceptable if a simpler hypothesis leads to a correct conclusion more often than not.
Some improvement in complexity is sometimes necessary. So there is still a general bias justified against two competing explanations. To understand why, consider that for every explanation it receives about a phenomenon, there are always a number of possibilities that are infinite, more complex, and ultimately untrue, alternate. This is because one can always burden the failed explanation with the ad hoc hypothesis. The ad hoc hypothesis is a justification that prevents the theory from being forged. Even other empirical criteria, such as consilience, can never completely eliminate such explanations as competition. Any correct explanation, then, may have many simpler and false alternatives, but also a number of infinite alternatives that are more complex and false. But if the alternative ad hoc hypothesis is justifiable, its implicit conclusions will be empirically verifiable. In a generally accepted repetition principle, these alternative theories have never been observed and continue to escape observation. In addition, one does not say a true explanation if he does not stick with this principle.
In other words, the new, and even more complex, theories may still be true. For example, if someone makes a supernatural claim that leprechaun is responsible for breaking the vase, the simpler explanation is that he is mistaken, but the ongoing ad hoc justification (eg "... and it's not me in the movie; they're tampered with it, also ") successfully prevented direct counterfeiting. The provision of this endlessly complex explanation, called storing the hypothesis, can not be excluded - except by using Occam's razor. A study of the predictive validity of Occam's razors found 32 published papers that included 97 comparison of economic forecasts from simple and complex forecasting methods. None of the papers provide a balance of evidence that the complexity of the method increases the approximate accuracy. In 25 papers with quantitative comparisons, complexity increases estimation errors by an average of 27 percent.
Practical considerations and pragmatism
Math
An Occam razor justification is a direct result of the basic probability theory. By definition, all assumptions introduce possible errors; if the assumption does not improve the accuracy of the theory, its only effect is to increase the probability that the whole theory is false.
There are also other attempts to derive Occam's razor from probability theory, including the important efforts made by Harold Jeffreys and E. T. Jaynes. The probabilistic (Bayesian) basis for the Occam razor is described by David JC MacKay in chapter 28 of his book The Information Theory, Inference and Algorithm of Learning, where he emphasizes that the earlier bias in favor of a simpler model is not required.
William H. Jefferys and James O. Berger (1991) generalize and measure the "assumption" of the original formulation concept as to what extent the proposition needs to accommodate the possibilities of observable data. They state, "A hypothesis with fewer adjustable parameters automatically will have an improved posterior probability, due to the fact that the predictions it makes are sharp." Their proposed model balances the precision of theoretical predictions to their sharpness - favoring theories that sharply make precise predictions of theories that accommodate other possible outcomes. This, again, reflects the mathematical relationship between key concepts in Bayesian inference (ie marginal probability, conditional probability, and posterior probability).
Other philosophers
Karl Popper
Karl Popper argues that preference for simple theories does not need to attract practical or aesthetic considerations. Our preference for simplicity can be justified by its falsifiability criteria: we prefer a simpler theory to a more complex "because their empirical content is greater, and because they are better tested" (Popper 1992). The idea here is that simple theory applies to more cases than is more complex, and thus more easily falsified. This once again compares simple theories with more complex theories in which both describe data equally well.
Elliott Sober
The philosopher of science Elliott Sober once argued along the same lines as Popper, binding simplicity with "informitivity": The simplest theory is more informative, in the sense that it requires less information for a question. He has rejected this report of simplicity, purportedly failing to provide epistemic justification for simplicity. He now believes that the considerations of simplicity (and especially parsimonic considerations) do not count unless they reflect something more fundamental. The philosophers, he argues, may have made the mistake of hypostatic simplicity (ie, blessing in the presence of sui generis ), when it has meaning only when embedded in a particular context (Sober 1992). If we fail to justify the consideration of simplicity based on the context in which we use it, we may have no non-circular justification: "Just as the question 'why be rational?' may not have a non-circular answer, the same may be true of the question 'why is simplicity to be considered in evaluating the plausibility of the hypothesis?'
Richard Swinburne
Richard Swinburne argues for simplicity by logical reasons:
... the simplest hypothesis proposed as an explanation of phenomena is more likely to be true than any other available hypothesis, that its predictions are more likely to be true than any other available hypothesis, and that it is of the utmost importance. the priori epistemic principle that simplicity is a proof of truth.
According to Swinburne, since our choice of theory can not be determined by data (see Underdetermination and Duhem-Quine thesis), we must rely on several criteria to determine which theory to use. Since it is absurd not to have a logical method to solve one hypothesis between an infinite number of hypotheses corresponding to the same data, we must choose the simplest theory: "Either irrational science [in the way of judging theory and possible predictions] or the principle of simplicity is the basic synthetic a priori truth "(Swinburne 1997).
Ludwig Wittgenstein
From Tractatus Logico-Philosophicus :
- 3.328 "If the mark is not needed then it means nothing, that's what Razor Occam means."
- (If everything in symbolism works as if a sign has a meaning, it has a meaning.)
- 4.04 "In that proposition there must be many things that can be distinguished because it is in the state, which it represents.They must both have the same logical (mathematical) diversity (see Hertz Mechanics, on Dynamic Model). "
- 5.47321 "Razor Occam, of course, is not an arbitrary or justified rule of practical success, he merely says that unnecessary elements in symbolism mean nothing.The signs that serve one purpose are logically equivalent unnecessary signs are logically meaningless. "
and on the concept of "simplicity":
- 6.363 "The induction procedure is accepting as the simplest law that can be reconciled with our experience."
Apps
Science and the scientific method
In science, Occam's razor is used as a heuristic to guide scientists in developing theoretical models rather than as referees between published models. In physics, parsimony is an important heuristic in the formulation of Albert Einstein's special relativity, in the development and application of the principle of action at least by Pierre Louis Maupertuis and Leonhard Euler, and in the development of quantum mechanics by Max Planck, Werner Heisenberg and Louis de Broglie.
In chemistry, Occam's razor is often an important heuristic when developing a model of reaction mechanism. Although useful as a heuristic in developing a model of reaction mechanism, it has been shown to fail as a criterion for choosing among selected published models. In this context, Einstein himself expressed caution when he formulated the Einstein Constraint: "It is almost undeniable that the main aim of all the theories is to make the basic elements irreducible as simple and as minimal as possible without having to give up adequate representation of a theory, one datum of experience ". The often quoted version of this constraint (which can not be verified as Einstein himself puts it) says "Everything must be kept as simple as possible, but not simpler."
In the scientific method, parsimony is an epistemological, metaphysical or heuristic preference, not an incontrovertible principle of logic or scientific result. As a logical principle, Occam's razor will require scientists to accept the simplest theoretical explanation for existing data. However, science has demonstrated repeatedly that future data often supports more complex theories than existing data. Science prefers the simplest explanations that are consistent with the data available at any given time, but the simplest explanation can be ruled out when new data becomes available. That is, science is open to the possibility that future experiments may support a more complex theory than is required by current data and more interested in designing experiments to distinguish between competing theories rather than favoring one above the other theories based solely on philosophical principles.
When scientists use the idea of ​​parsimony, it only has meaning in the context of a very specific inquiry. Some background assumptions are required for parsimony to connect with possibilities in a particular research problem. The feasibility of parsimony in one research context may not have anything to do with its fairness in another. It is a mistake to think that there is a global principle that includes diverse material.
It has been argued that Occam's razor is a widely accepted example of extraevidential consideration, although it is entirely a metaphysical assumption. There is little empirical evidence that the world is actually simple or that simple accounts are more likely to be true than complicated ones.
Most of the time, Occam's razor is a conservative tool, cutting out complicated and crazy constructions and ensuring that hypotheses are based on the science of the day, resulting in a "normal" science: explanation and prediction models. But there are exceptions where Occam's razor turns a conservative scientist into a reluctant revolutionary. For example, Max Planck inserts between Wien and Jeans radiation laws and uses Occam's razor logic to formulate quantum hypotheses, even rejecting the hypothesis because it becomes more clear that it is true.
The plea for simplicity is used to argue against the phenomena of meteorites, lightning balls, continental drift, and reverse transcriptase. One can debate the atomic building blocks for matter, since it provides a simpler explanation for the observed reversibility of mixing and chemical reactions as simple separation and rearrangement of atomic building blocks. At that time, however, atomic theory was considered more complex because it implies the existence of invisible particles that have not been detected directly. Ernst Mach and the logical positivists rejected John Dalton's atomic theory until the atomic reality was more evident in Brownian motion, as Albert Einstein pointed out.
In the same way, postulating ethers is more complex than transmitting light through a vacuum. At that time, however, all known waves were propagated through the physical medium, and it seemed easier to postulate the existence of the medium than to theorize about the non-media wave propagation. Likewise, Newton's notion of light particles seems simpler than Huygens's idea of ​​Christiaan waves, so many love them. In this case, as it turns out, neither wave - nor particle - explanation alone is enough, since light behaves like waves and particles like.
Three axioms presupposed by the scientific method are realism (the existence of objective reality), the existence of natural law, and the firmness of natural law. Rather than relying on the provocation of these axioms, science depends on the fact that they are not objectively counterfeited. Occam's razor and parsimony support, but do not prove, the axioms of this science. The general principle of science is that the theory (or model) of natural law must be consistent with repeated experimental observations. This main arbiter (selection criteria) lies in the axiom mentioned above.
There are instances where Occam's razor would like the wrong theory by providing the available data. The principle of simplicity is a useful philosophical preference for choosing a more probable theory of several possibilities that are all consistent with the data available. An example of Occam's razor supports the wrong theory of falsifying a razor as a general principle. Michael Lee and others provide cases where a stingy approach does not guarantee a correct conclusion and, if based on a false work hypothesis or incomplete data interpretation, may even strongly support a false conclusion.
If some models of natural law make predictions for the same predictions, they are equivalent and do not need parsimony to choose the preferred ones. For example, classical mechanics Newtonian, Hamiltonian and Lagrangian equivalent. Physicists are not interested in using Occam's razor to say that the other two are wrong. Likewise, there is no demand for the principle of simplicity to mediate between waves and mathematical formulations of quantum mechanics. Science often does not require arbitration or selection criteria between models that make the same testable predictions.
Biology
Biologists or biological philosophers use Occam razors in one of two contexts in both the evolutionary biology: the selection and systematic controversial units. 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 selection (ie, individuals) as opposed to high-level groups. selection. Altruism is defined by some evolutionary biologists (eg, R. Alexander, 1987, WD Hamilton, 1964) as behaviors that benefit others (or groups) at the expense of individuals, and many place individual elections as mechanisms that explain altruism solely in the behavior of individual organisms acting in their own interests (or for the sake of their genes, through family selection). Williams argued against the perspective of others who proposed group-level selection as an evolutionary mechanism that opted for altruistic properties (eg, D. S. Wilson & E. O. Wilson, 2007). The basis of Williams's opinion is that of both, individual selection is a more parsimonious theory. In doing so he uses Occam's razor variant known as Canon Morgan: "In any case animal activity can not be interpreted in terms of higher psychological processes, if that can be reasonably interpreted in terms of a lower process on an evolutionary scale. and psychological development. "(Morgan 1903).
However, more recent biological analyzes, such as Richard Dawkins' The Selfish Gene, argue that Canon Morgan is not the simplest and most basic explanation. Dawkins argues the way evolution works is that the genes propagated in most copies ultimately determine the development of a particular species, that is, natural selection turns out to select a particular gene, and this is really a fundamental principle that automatically provides individual and group selection. as a feature emerging from evolution.
Zoology gives an example. Muskoxen, when threatened by a wolf, forms a circle with a male outside and a female and young on the inside. This is an example of behavior by men who seem altruistic. Such behavior harms them individually but is beneficial to the group as a whole and hence is seen by some to support the theory of group selection. Another interpretation is family selection: if men protect their offspring, they protect copies of their own alleles. Engaging in this behavior will be favored by individual selection if the cost for male bulls is less than half of the benefits received by the calves - which can easily happen if the wolf has an easier time killing a calf than the adult male. It could also happen that musk bulls will be individually less likely to be killed by wolves if they stand in a circle with their horns showing, regardless of whether they protect the females and their offspring. That would be an example of ordinary natural selection - a phenomenon called "selfish herd".
Systematics is a branch of biology that seeks to establish the pattern of genealogical relationships between biological taxa. It also deals with their classification. There are three major camps in systematics: cladists, pheneticists, and taxonomists of evolution. Clinters argue that the genealogy itself must determine the classification, the pheneticists argue that the overall equality is a decisive criterion, while the evolutionary taxonomist says that both the comparison of genealogy and similarity in classification.
This is one of the clones found by Occam's razor, though their term for it is an expired parsimony. Cladistic denial (or maximum parsimony) is a phylogenetic inference method in the development of phylogenetic tree species (more specifically, cladogram). The cladogram is a branching, tree-like structure used to represent the relative relationship level hypothesis, based on the state of the shared derived character. Expired density is used to select as the preferred hypothesis of the cladogram relationship requiring the least implied character status transformation. Critics of the cladistic approach often observe that for some tree species, parsimony consistently produces false results, regardless of how much data is collected (this is called statistical inconsistency, or long branch appeal). However, this criticism is also potentially true for all types of phylogenetic inference, unless the model used to estimate the tree reflects the way evolution actually takes place. Since this information is not empirically accessible, criticism of statistical inconsistencies against parsimonies has no power. For a lengthy book-length treatment of paranitivitas, see Elliott Sober's Reconstruction of the Past: Parsimony, Evolution, and Inference (1988). For a discussion of the use of Occam razors in biology, see Sober article "Mari Razor Ockham's Razor" (1990).
Another method of concluding the evolutionary relationship is using parsimony in a more traditional way. The method of possibility for phylogeny to use parsimony as they do for all possible tests, with hypotheses requiring several different parameters (that is, the number of different levels of character change or different frequencies of the character status transitions) is treated as a null hypothesis relative to the hypothesis requires many different parameters.. Thus, the complex hypothesis must predict data much better than a simple hypothesis before the researcher rejects a simple hypothesis. Recent advances use information theory, close cousin possibilities, which use Occam razors in the same way.
Francis Crick commented on the potential limitations of Occam's razor in biology. He argues that since biological systems are the product of natural selection (in progress), the mechanism is not necessarily optimal in a clear sense. He warns: "While the Ockham razor is a useful tool in physics, it can be a very dangerous tool in biology, so it is rash to use simplicity and grace as a guide in biological research."
In biogeography, parsimony is used to infer migration of ancient species or populations by observing the geographic distribution and relationship of existing organisms. Given the phylogenetic tree, the ancestral migration is inferred into those who need the minimum amount of total movement.
Religion
In the philosophy of religion, Occam's razor is sometimes applied to the existence of God. William of Ockham himself is a Christian. He believed in God, and in the authority of Scripture; he writes that "there is nothing to think about for no reason given, unless it is self-evident (literally, known through itself) or known by experience or proven by the authority of Scripture." Ockham believes that explanations do not have a sufficient basis in reality when not in harmony with reason, experience, or the Bible. However, unlike many theologians of his time, Ockham did not believe God could be proven logically by argument. For Ockham, science is a matter of discovery, but theology is a matter of revelation and faith. He states: "only faith gives us access to theological truth God's ways are not open for reason, because God has freely chosen to create the world and set the road of salvation in it apart from the necessary law that human logic or rationality can uncover. "
St. Thomas Aquinas, in Summa Theologica, uses Occam's razor formulation to build an objection to the idea that God exists, which he denies directly with a counter argument:
Furthermore, it is excessive to suppose that what some principles can account for has been generated by many people. But it seems that everything we see in the world can be accounted for by other principles, in case God does not exist. For all natural things can be reduced to one principle of its nature; and all voluntary things can be reduced to a principle that is human reason, or will. Therefore it is not necessary to suppose the existence of God.
In turn, Aquinas answers this with quinque viae , and addresses the above specific objection with the following answer:
Since nature works for the ultimate purpose under the direction of higher agents, whatever nature does must be traced back to God, as the first cause. Thus, anything done voluntarily must also be traced back to some higher cause other than human reason or desire, as this may change or fail; for all things that can change and be capable of defects must be traced back to the first principle that can not be moved and self-required, as shown in the article content.
Rather than arguing about the need for gods, some theists base their beliefs on an independent basis, or before, the reasons, making Occam's razors irrelevant. This is the attitude of SÃÆ'¸ren Kierkegaard, who views belief in God as a leap of faith that is sometimes directly opposed to reason. It is also a preconditionary precondition doctrine of Gordon Clark, with the exception that Clark never thought a leap of faith contradicted reason (see also Fideism).
Various arguments in favor of God establish God as a useful or even necessary assumption. In contrast some anti-theists hold fast to the belief that assuming the existence of God introduces unnecessary complexity (Schmitt 2005, for example, Ultimate Boeing 747 gambit).
Another application of this principle can be found in George Berkeley's work (1685-1753). Berkeley is an idealist who believes that all reality can be explained only from his mind alone. He uses Occam's razor against materialism, arguing that matter is not needed by his metaphysics and thus can be eliminated. One potential problem with this belief is that perhaps, given Berkeley's position, to find solipsism itself more in line with the razor than the God-mediated world beyond a single thinker.
Occam's razor can also be recognized in the apocryphal story of the exchange between Pierre-Simon Laplace and Napoleon. It is said that in praising Laplace for one of his recent publications, the emperor asked how it is that the name of God, which is so often featured in Lagrange's writings, appears anywhere in Laplace. At that point, he was said to have replied, "That's because I do not need that hypothesis." Despite some points in this story as an illustration of Laplace's atheism, a more careful consideration suggests that it may mean simply to portray the power of methodological naturalism, or even simply that the fewer logical places one assumes, the stronger one's conclusions.
In his article "Sensation and Process of the Brain" (1959), J. J. C. Smart uses Occam's razor in order to justify his preference for the mind-brain identity theory of the spirit-body dualism. Dualis states that there are two kinds of matter in the universe: physical (including body) and spiritual, non-physical. Instead, the theorist of identity states that everything is physical, including consciousness, and that nothing is nonphysical. Although it is impossible to appreciate spiritually when limiting oneself to the physical, Smart maintains that identity theory explains all phenomena by assuming only physical reality. Furthermore, Smart has been criticized for its use (or abuse) of Occam's razors and ultimately withdraws its defense in this context. Paul Churchland (1984) states that in itself Occam's razor is inconclusive about duality. In the same way, Dale Jacquette (1994) argues that Occam's razor has been used in an attempt to justify eliminativism and reductionism in the philosophy of mind. Eliminativism is a thesis that folk psychology ontology including entities such as "pain", "joy", "desire", "fear", etc., can be eliminated in favor of an ontology of complete neuroscience.
Power ethics
In criminal theory and punishment philosophy, parsimony refers specifically to pay attention to the distribution of punishments to avoid excessive punishment. In a utilitarian approach to the philosophy of punishment, Jeremy Bentham's "parsimonious principle" states that any greater penalty than necessary to reach the end is unjust. This concept is related but not identical to the concept of proportionality law. Modesty is a key consideration of modern restorative justice, and is a component of the utilitarian approach to punishment, as well as the impending removal movement. Bentham believes that true parsimonies will require punishment to be individuals to take into account the sensitivity of individuals who are more sensitive to punishment should be given proportionately, because otherwise, unnecessary pain will be inflicted. The later utilitarian writers tend to abandon this idea, in large part because of the impracticality in determining any relative sensitivity of the perpetrator to a particular punishment.
Theory and possible statistics
Marcus Hutter's universal intelligence was built on the formalization of Solomonoff's mathematics from razors to calculate the expected value of an action.
There are various papers in scientific journals that take the formal version of Occam's razors of probability theory, apply them in statistical inference, and use them to generate criteria for punishing complexity in statistical inference. The paper suggests a link between Occam's razor and Kolmogorov complexity.
One of the problems with the original formulation of a razor is that it only applies to models with the same explanatory power (that is, it just tells us to choose the simplest of models equally well). The more general shape of the razor can be derived from the Bayesian model comparison, which is based on the Bayes factor and can be used to compare models that do not match the observations equally well. These methods can sometimes optimally balance the complexity and strength of a model. Generally, the exact Occam factor is difficult to solve, but estimates such as the Akaike information criteria, Bayesian information criteria, the Bayesian Variational method, the invention level are wrong, and the Laplace method is used. Many artificial intelligence researchers now use such techniques, for example through the work of Occam Learning or more generally on the principle of free Energy.
Occam's razor statistical version has a more rigorous formulation of what philosophical discussion results. In particular, they must have a specific definition of the term simplicity , and the definition may vary. For example, in Kolmogorov-Chaitin's long-range approach, subjects must choose Turing machines whose operations describe basic operations that are believed to represent "simplicity" by the subject. However, one can always choose a Turing machine with a simple operation that takes place to build the whole theory and therefore will score high under a razor. This causes two opposing camps: who believe Occam's razor is objective, and who believes it is subjective.
The objective razor
The minimum instruction set of universal Turing machines requires approximately the same length description across different formulations, and is small compared to Kolmogorov's complexity of most practical theories. Marcus Hutter has used this consistency to define a small "natural" Turing machine as the right base to exclude intricate and arbitrary sets of instructions in the formulation of a razor. Describing the program to the universal program as a "hypothesis", and the representation of the evidence as program data, has been formally proven under the Zermelo-Fraenkel set theory that "the universal log probability sum of the models plus logs of possible data given models must be minimized." Interpret this as minimizing the total length of the two-part encoding model followed by the given data model gives us the minimum message length principle (MML).
One possible conclusion from mixing Kolmogorov's complexity concept and Occam's razor is that the ideal data compressor will also be an explanatory/scientific formulation generator. Several attempts have been made to recover the known law from consideration of simplicity or compressibility.
According to JÃÆ'¼rgen Schmidhuber, the corresponding mathematical theory of Occam's razor already exists, namely Solomonoff's theory of optimal inductive inference and extension. See discussion at David L. Dowe "CS Wallace's Preface" for the subtle differences between Solomonoff's algorithmic probability work and Chris Wallace's MML work, and see "MML graphical network model, Bayesian Dowes hybrid, statistical consistency, invariance and uniqueness" that kind and for (in part 4) a discussion of MML and Occam razors. For a specific example of MML as Occam razor in the induced decision tree problem, see "Length of Dowe and Needham Messages as an Effective Ockham Shaver in Decision-Making Tree".
The controversial aspects of the razor
Occam's razor is not an embargo on the mastery of any type of entity, or a recommendation from the simplest theory can occur. Occam razors are used to judge between theories that have passed the "theoretical examination" test and are equally supported by evidence. Furthermore, it can be used to prioritize empirical testing between two testable but unequal hypotheses; thereby minimizing costs and waste while increasing the likelihood of falsifying simpler hypotheses to be tested.
Another disputed aspect of the razor is that theory can become more complex in terms of its structure (or syntax), while its ontology (or semantics) becomes simpler, or vice versa. Quine, in the discussion of definitions, refers to these two perspectives as "practical expression economy" and "economics in grammar and vocabulary", respectively.
Galileo Galilei rails abuse Occam razors in the Dialogue . This principle is represented in the dialogue by Simplicio. The point Galileo conveys ironically is that if one really wants to start from a small number of entities, one can always consider the letters of the alphabet as fundamental entities, because one can build all human knowledge from them.
Anti-razors
Occam's razor has encountered some contradictions from people who think it is too extreme or rash. Walter Chatton (c 1290-1343) is contemporary William of Ockham (c 1287-1347) who took exception to Occam's razor and Ockham's use. In response, he designed his own anti-razor: "If three things are not enough to verify affirmative propositions about things, the fourth must be added, and so on." Although there have been a number of philosophers who have formulated similar anti-rifle weapons since the Chatton days, no anti-rhetoric has been immortalized as important as the anti-Chatton torch, though this could be the case of the unknown late Renaissance Italian motto. attribution Se non ÃÆ'¨ vero, ÃÆ'¨ ben trovato ("Even if it is not true, it is conceived well") when referring to an artful explanation.
Anti-razor has also been made by Gottfried Wilhelm Leibniz (1646-1716), Immanuel Kant (1724-1804), and Karl Menger (1902-1985). The Leibniz version takes the form of the principle of abundance, as Arthur Lovejoy calls it: the idea that God created the world's most diverse and abundant. Kant found it necessary to moderate the effects of Occam's razor and thus create his own razor: "The diversity of creatures should not be reduced fast."
Karl Menger found that mathematicians were too parsimonious of variables, so he formulated his Law of Errors, which took one of two forms: "Entities should not be reduced to the point of incompetence" and "Nothing to do with less what needs more. "A less serious but (some might say) even more extreme anti-rheumatism is' Pataphysics, the" science of imaginary solutions "developed by Alfred Jarry (1873-1907). Perhaps most profoundly anti-reductionism, "Physics attempts no less than perceiving every event in the universe as something entirely unique, not subject to the law except its own law." Variations on this theme were later explored by Argentine writer Jorge Luis Borges in his story/mock-essay "TlÃÆ'¶n, Uqbar, Orbis Tertius". There is also Bludgeon Crabtree, which cynically states that "[n] an inconsistent set of observations can exist so that some human intellect can not understand a coherent explanation, however complicated it may be."
See also
Note
References
Further reading
External links
- What is Occam's Razor? This essay distinguishes Occam's Razor (used for theories with identical predictions) from the Principle of Parsimony (which can be applied to theories with different predictions).
- Skeptic's Dictionary: Occam's Razor
- Ockham's Razor, an essay at The Galilean Library about historical and philosophical implications by Paul Newall.
- Razor in Toolbox: History, usage, and abuse of Occam razors, by Robert Novella
- NIPS 2001 Workshop "Razor Occam Foundation and parsimony in learning"
- Simplicity at Stanford Encyclopedia of Philosophy
- "Occam's Razor". PlanetMath .
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Courtney, Amy; Courtney, Michael (2008). "Comment On" In Nature of Science "". Physics in Canada . 64 (3): 7-8. arXiv: 0812.4932 .
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