Presents, a Life with a Plan. My name is Karen Anastasia Placek, I am the author of this Google Blog. This is the story of my journey, a quest to understanding more than myself. The title of my first blog delivered more than a million views!! The title is its work as "The Secret of the Universe is Choice!; know decision" will be the next global slogan. Placed on T-shirts, Jackets, Sweatshirts, it really doesn't matter, 'cause a picture with my slogan is worth more than a thousand words, it's worth??.......Know Conversation!!!
Cantore arithmetic first equation: Nine tenths is 9/10. This avenue of approach brings to letter the quantity and not the mass, not changing history in mathematics rather introducing arithmetic to the metric system? This would be a natural counting program as literary to a counting system. A smooth number to the introduction to letter faces what is man to text. Should the barrel of the cave represent the mastered to the weather than the process would develop what is a roof. The wall would remain?
Possession is nine-tenths of the law
From Wikipedia, the free encyclopedia
Possession is nine-tenths of the law is an expression meaning that ownership is easier to maintain if one has possession of something, or difficult to enforce if one does not. The expression is also stated as "possession is ten points of the law", which is credited as derived from the Scottish expression "possession is eleven points in the law, and they say there are but twelve."[1]
Although the principle is an oversimplification, it can be restated as: "In a property dispute (whether real or personal), in the absence of clear and compelling testimony or documentation to the contrary, the person in actual, custodial possession of the property is presumed to be the rightful owner. The rightful owner shall have their possession returned to them; if taken or used. The shirt or blouse you are currently wearing is presumed to be yours, unless someone can prove that it is not."[2]
The adage is not literally true, that by law the person in possession is presumed to have a nine times stronger claim than anyone else, but that "it places in a strong light the legal truth that every claimant must succeed by the strength of his own title, and not by the weakness of his antagonist's."[3] The principle bears some similarity to uti possidetis ("as you possess, so may you continue to possess"), which currently refers to the doctrine that colonial administrative boundaries become international boundaries when a political subdivision or colony achieves independence. Under Roman law, it was an interdictum ordering the parties to maintain possession of property until it was determined who owned the property.[4]
In the Hatfield-McCoy feud, with testimony evenly divided, the doctrine that possession is nine-tenths of the law caused Floyd Hatfield to retain possession of the pig that the McCoys claimed was their property.[5] It has been argued that in some situations, possession is ten-tenths of the law.[6] While the concept is older, the phrase "Possession is nine-tenths of the law" is often claimed to date from the 16th century.[7] In some countries, possession is not nine-tenths of the law, but rather the onus is on the possessor to substantiate his ownership.[8]
This concept has been applied to both tangible and intangible products.[9] In particular, "knowledge management" presents problems with regard to this principle.[10]Google's possession of a large amount of content has been the cause of some wariness due to this principle.[11] It has been said[by whom?] that there was a time in which the attitude towards rights over genetic resources was that possession is nine tenths of the law, and for the other tenth reliance could be made on the principle that biological resources were the heritage of mankind.[12]
It's Friday and Ancient Aliens on the History Channel starts a new season on May 31st so no more re-runs!! Loving all the shows that play in a row on Friday I thought about the show on Osiris and his green skin, and thought, the entire alien off-world thing doesn't fit should the green skin be from metal an alloy or simply that Osiris had an allergic reaction to gold, gold being reported to be the biggest Egyptian findings for the pharaohs and should it have been plated than the probability would have increased. So no dark horror of Osiris and his green skin, it is simply discoloration until proven differently as Occams razor applied a logical principle (pespmc1.vub.ac.be/OCCAMRAZ.html) "Occam's razor is the problem-solving principle that essentially
states that "simpler solutions are more likely to be correct than
complex ones." When presented with competing hypotheses to solve a
problem, one should select the solution with the fewest assumptions."
Pure gold is slightly reddish yellow in color, but colored gold in various other colors can be produced. Colored golds can be classified in three groups: Alloys with silver and copper in various proportions, producing white, yellow, ... The strength of gold–nickel–copper alloys is caused by formation of two phases, a gold-rich ...
Tarnish is a thin layer of corrosion that forms over copper, brass, silver, aluminum, magnesium, neodymium and other similar metals as ... and practiced silver care information on the Web. Common causes of gold tarnishing & prevention.
Copper, which also migrates into gold, does so more slowly than silver. The copper is usually further plated with nickel. A gold-plated silver article is usually a silver substrate with layers of copper, nickel, and gold deposited on top of it.
Patina is a thin layer that variously forms on the surface of copper, bronze and similar metals or ... The chemical process by which a patina forms or is deliberately induced is called ... Even a lasting gold colour is possible with copper-alloy cladding, .... LaNiece, Susan; Craddock, Paul : Metal Plating and Patination: Cultural, ...
Silver is a chemical element with symbol Ag and atomic number 47. A soft, white, lustrous ... Most silver is produced as a byproduct of copper, gold, lead, and zinc refining. .... Silver cyanide solutions are used in electroplating of silver. ... its constituent elements and is the cause of the black tarnish on some old silver objects.
Shakudō (赤銅) is a Japanese billon of gold and copper (typically 4–10% gold, 96–90% copper), one of the irogane class of colored metals,
which can be treated to develop a black, or sometimes indigo, patina,
resembling lacquer. Unpatinated shakudō visually resembles bronze; the
dark color is induced ... Amita damascene included shakudo, shibuichi, gold, silver, and bronze for ...
The conservation and restoration of silver objects is an activity dedicated to the preservation ... Tarnish is a chemical reaction on the surface of metal (copper, brass, silver, .... Over polishing is an issue with silver and can cause harm to the surface of ... The main buffing type used for silver, gold, and plated objects is Canton ...
Gold is a chemical element with symbol Au (from Latin: aurum) and atomic number 79, making it one of the higher atomic number elements that occur naturally. In its purest form, it is a bright, slightly reddish yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal and a group 11 element. ... Gold is insoluble in nitric acid, which dissolves silver ...
Sterling silver is an alloy of silver containing 92.5% by weight of silver and 7.5% by weight of other metals, usually copper .... Due to sterling silver having a special acoustic character, some brasswind instrument ... pollution: silver sulfide slowly appears as a black tarnish during exposure to airborne compounds of sulfur ...
Occam's razor (also Ockham's razor or Ocham's razor (Latin: novacula Occami); further known as the law of parsimony (Latin: lex parsimoniae)) is the problem-solving principle that essentially states that "simpler solutions are more likely to be correct than complex ones."[citation needed] When presented with competing hypotheses to solve a problem, one should select the solution with the fewest assumptions. The idea is attributed to English Franciscan friar William of Ockham (c. 1287–1347), a scholastic philosopher and theologian.
In science, Occam's razor is used as an abductiveheuristic in the development of theoretical models, rather than as a rigorous arbiter between candidate models.[1][2] In the scientific method, Occam's razor is not considered an irrefutable principle of logic or a scientific result; the preference for simplicity in the scientific method is based on the falsifiability
criterion. For each accepted explanation of a phenomenon, there may be
an extremely large, perhaps even incomprehensible, number of possible
and more complex alternatives. Since one can always burden failing
explanations with ad hoc hypotheses to prevent them from being falsified, simpler theories are preferable to more complex ones because they are more testable.[3][4][5]
The term Occam's razor did not appear until a few centuries after William of Ockham's death in 1347. Libert Froidmont, in his On Christian Philosophy of the Soul, takes credit for the phrase, speaking of "novacula occami".[6]
Ockham did not invent this principle, but the "razor"—and its
association with him—may be due to the frequency and effectiveness with
which he used it.[7]
Ockham stated the principle in various ways, but the most popular
version, "Entities are not to be multiplied without necessity" (Non sunt multiplicanda entia sine necessitate) was formulated by the Irish Franciscan philosopher John Punch in his 1639 commentary on the works of Duns Scotus.[8]
Formulations before William of Ockham
Part of a page from Duns Scotus' book Commentaria oxoniensia ad IV libros magistri Sententiarus, novis curis edidit p. Marianus Fernandez Garcia (1914, p. 211)': "Pluralitas non est ponenda sine necessitate", i.e., "Plurality is not to be posited without necessity"
The origins of what has come to be known as Occam's razor are traceable to the works of earlier philosophers such as John Duns Scotus (1265–1308), Robert Grosseteste (1175–1253), Maimonides (Moses ben-Maimon, 1138–1204), and even Aristotle (384–322 BC).[9][10] Aristotle writes in his Posterior Analytics, "We may assume the superiority ceteris paribus [other things being equal] of the demonstration which derives from fewer postulates or hypotheses." Ptolemy (c. AD 90 – c. AD 168) stated, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible."[11]
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.[11] 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. 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."[12]
The Summa Theologica of Thomas Aquinas
(1225–1274) states that "it is superfluous to suppose that what can be
accounted for by a few principles has been produced by many." Aquinas
uses this principle to construct an objection to God's existence, an objection that he in turn answers and refutes generally (cf. quinque viae), and specifically, through an argument based on causality.[13]
Hence, Aquinas acknowledges the principle that today is known as
Occam's razor, but prefers causal explanations to other simple
explanations (cf. also Correlation does not imply causation).
William of Ockham
William of Ockham (circa 1287–1347) was an English Franciscan friar and theologian, an influential medieval philosopher and a nominalist. His popular fame as a great logician rests chiefly on the maxim attributed to him and known as Occam's razor. The 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 any of William's writings,[14] one can cite statements such as Numquam ponenda est pluralitas sine necessitate[1] ("Plurality must 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. Lugd., 1495, i, dist. 27, qu. 2, K).
Nevertheless, the precise words sometimes attributed to William of Ockham, Entia non sunt multiplicanda praeter necessitatem (Entities must not be multiplied beyond necessity),[15] are absent in his extant works;[16] this particular phrasing comes from John Punch,[17] who described the principle as a "common axiom" (axioma vulgare) of the Scholastics.[8]
William of Ockham's contribution seems to restrict the operation of
this principle in matters pertaining to miracles and God's power; so, in
the Eucharist, a plurality of miracles is possible, simply because it pleases God.[11]
This principle is sometimes phrased as Pluralitas non est ponenda sine necessitate ("Plurality should not be posited without necessity").[18] In his Summa Totius Logicae, i. 12, William of Ockham cites the principle of economy, Frustra fit per plura quod potest fieri per pauciora ("It is futile to do with more things that which can be done with fewer"; Thorburn, 1918, pp. 352–53; Kneale and Kneale, 1962, p. 243.)
Later formulations
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. Therefore, to the
same natural effects we must, as far as possible, assign the same
causes."[19][20] Bertrand Russell
offers a particular version of Occam's razor: "Whenever possible,
substitute constructions out of known entities for inferences to unknown
entities."[21]
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 only
assumption is that the environment follows some unknown but computable
probability distribution. This theory is a mathematical formalization of
Occam's razor.[22][23][24]
Another technical approach to Occam's razor is ontological parsimony.[25]
Parsimony means spareness and is also referred to as the Rule of
Simplicity. This is considered a strong version of Occam's razor.[26][27] A variation used in medicine is called the "Zebra": a doctor should reject an exotic medical diagnosis when a more commonplace explanation is more likely, derived from Theodore Woodward's dictum "When you hear hoofbeats, think of horses not zebras".[28] 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."[29]
This principle goes back at least as far as Aristotle, who wrote "Nature operates in the shortest way possible."[26]
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 our culture as the widespread layman's formulation
that "the simplest explanation is usually the correct one."[26]
Justifications
Aesthetic
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. 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. 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."[30]
Beginning in the 20th century, epistemological justifications based on induction, logic, pragmatism, and especially probability theory have become more popular among philosophers.[who?]
Empirical
Occam's
razor has gained strong empirical support in helping to converge on
better theories (see "Applications" section below for some examples).
In the related concept of overfitting, excessively complex models are affected by statistical noise
(a problem also known as the bias-variance trade-off), whereas 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. model selection, test set, minimum description length, Bayesian inference, etc.).
Testing the razor
The
razor's statement that "other things being equal, simpler explanations
are generally better than more complex ones" is amenable to empirical
testing. Another interpretation of 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 simple and comparatively complex explanations. 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). 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.
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.
Some increases in complexity are sometimes necessary. So there
remains a justified 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. This 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 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. 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.[clarification needed] In addition, one does 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 the film; they tampered with that, too") successfully
prevent outright falsification. This endless supply of elaborate
competing explanations, called saving hypotheses, cannot be ruled out—except by using Occam's razor.[31][32][33]
A study of the predictive validity of Occam's razor found 32 published
papers that included 97 comparisons of economic forecasts from simple
and complex forecasting methods. 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 percent.[34]
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,[35] where he emphasizes that a prior bias in favour of simpler models is not required.
William H. Jefferys 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.[36]
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."[36] The model they propose balances the precision of a theory's predictions against their sharpness[vague]—preferring theories that sharply[vague]
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 probability, conditional probability, and posterior probability).
The bias–variance tradeoff
is a framework that incorporates the Occam's razor principal in its
balance between overfitting (i.e. variance minimization) and
underfitting (i.e. bias minimization).[37]
Other philosophers
Karl Popper
Karl Popper
argues that a preference for simple theories need not appeal to
practical or aesthetic considerations. 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" (Popper 1992). The idea here is that a simple theory applies
to more cases than a more complex one, and is thus more easily
falsifiable. This is again comparing a simple theory to a more complex
theory where both explain the data equally well.
Elliott Sober
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.[38] He has since rejected this account of simplicity, purportedly because it fails to provide an epistemic
justification for simplicity. He now believes that simplicity
considerations (and 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.e.,
endowed it with a sui generis
existence), when it has meaning only when embedded in a specific
context (Sober 1992). 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?'"[39]
... 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.
— 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." (Swinburne 1997).
3.328 "If a sign is not necessary then it is meaningless. That is the meaning of Occam's Razor."
(If everything in the symbolism works as though a sign had meaning, then it has meaning.)
4.04 "In the proposition there must be exactly as many things
distinguishable as there are in the state of affairs, which it
represents. They must both possess the same logical (mathematical)
multiplicity (cf. Hertz's Mechanics, on Dynamic Models)."
5.47321 "Occam's Razor is, of course, not an arbitrary rule nor one
justified by its practical success. It simply says that unnecessary
elements in a symbolism mean nothing. Signs which serve one purpose are
logically equivalent; signs which serve no purpose are logically
meaningless."
and on the related concept of "simplicity":
6.363 "The procedure of induction consists in accepting as true the simplest law that can be reconciled with our experiences."
Applications
Science and the scientific method
Andreas Cellarius's illustration of the Copernican system, from the Harmonia Macrocosmica (1660). Future positions of the sun, moon and other solar system bodies can be calculated using a geocentric model (the earth is at the centre) or using a heliocentric model
(the sun is at the centre). Both work, but the geocentric model arrives
at the same conclusions through a much more complex system of
calculations than the heliocentric model. This was pointed out in a
preface to Copernicus' first edition of De revolutionibus orbium coelestium.
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.[1][2] In physics, parsimony was an important heuristic in Albert Einstein's formulation of special relativity,[40][41] in the development and application of the principle of least action by Pierre Louis Maupertuis and Leonhard Euler,[42] and in the development of quantum mechanics by Max Planck, Werner Heisenberg and Louis de Broglie.[2][43]
In chemistry, Occam's razor is often an important heuristic when developing a model of a reaction mechanism.[44][45]
Although it is useful as a heuristic in developing models of reaction
mechanisms, it has been shown to fail as a criterion for selecting among
some selected published models.[2]
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". An often-quoted version of this
constraint (which cannot be verified as posited by Einstein himself)[46] says "Everything should be kept as simple as possible, but not simpler."
In the scientific method, parsimony is an epistemological, metaphysical or heuristic preference, not an irrefutable principle of logic or a scientific result.[3][4][5]
As a logical principle, Occam's razor would demand that scientists
accept the simplest possible theoretical explanation for existing data.
However, science 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.[1][4]
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.[3][4][5]
When scientists 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. The reasonableness of parsimony in one research
context may have nothing to do with its reasonableness in another. It is
a mistake to think that there is a single global principle that spans
diverse subject matter.[5]
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 more likely to be true than complex ones.[47]
Most 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.[2]
There are, however, notable exceptions where Occam's razor turns a
conservative scientist into a reluctant revolutionary. 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 it was correct.[2]
Appeals to simplicity were used to argue against the phenomena of meteorites, ball lightning, continental drift, and reverse transcriptase[citation needed].
One can argue for atomic building blocks for matter, because it
provides a simpler explanation for the observed reversibility of both
mixing and chemical reactions as simple separation and rearrangements of
atomic building blocks. At the time, however, the atomic theory was considered more complex because it implied the existence of invisible particles that had not been directly detected. Ernst Mach and the logical positivists rejected John Dalton's atomic theory until the reality of atoms was more evident in Brownian motion, as shown by Albert Einstein.[48]
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, and it seemed simpler to postulate the existence of a medium
than to theorize 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 reality), the existence of natural laws, and
the constancy of natural law. Rather than depend on provability of
these axioms, science depends on the fact that they have not been
objectively falsified. Occam's razor and parsimony support, 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 criterion)
rests upon the axioms mentioned above.[4]
There are examples where Occam's razor would have favored the
wrong theory given the available data. Simplicity principles are useful
philosophical preferences for choosing a more likely theory from among
several possibilities that are all consistent with available data. A
single instance of Occam's razor favoring a wrong theory falsifies the
razor as a general principle.[4] Michael Lee and others[49]
provide cases in which a parsimonious approach does not guarantee a
correct conclusion and, if based on incorrect working hypotheses or
interpretations of incomplete data, may even strongly support a false
conclusion.
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. For example, Newtonian, Hamiltonian and
Lagrangian classical mechanics are equivalent. Physicists have no
interest in using Occam's razor to say the other two are wrong.
Likewise, there is no demand for simplicity principles to arbitrate
between wave and matrix formulations of quantum mechanics. Science often
does not demand arbitration or selection criteria between models that
make the same testable predictions.[4]
Biology
Biologists or philosophers of biology use Occam's razor in either of two contexts both in evolutionary biology: the units of selection controversy and systematics. 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. 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). Williams was arguing against the perspective
of others who propose selection at the level of the group as an
evolutionary mechanism that selects for altruistic traits (e.g., D. S.
Wilson & E. O. Wilson, 2007). The basis for Williams' contention is
that of the two, individual selection is the more parsimonious theory.
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." (Morgan 1903).
However, more recent biological analyses, such as Richard Dawkins' The Selfish Gene,
have contended that Morgan's Canon is not the simplest and most basic
explanation. 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.
Zoology provides an example. Muskoxen, when threatened by wolves,
form a circle with the males on the outside and the females and young
on the inside. This is an example of a behavior by the males that seems
to be altruistic. The behavior is disadvantageous to them individually
but beneficial to the group as a whole and was thus seen by some to
support the group selection theory. Another interpretation is kin
selection: if the males are protecting their offspring, they are
protecting copies of their own alleles. Engaging in this behavior would
be favored by individual selection if the cost to the male musk ox is
less than half of the benefit received by his calf – which could easily
be the case if wolves have an easier time killing calves than adult
males. It could also be the case that male musk oxen would be
individually less likely to be killed by wolves if they stood in a
circle with their horns pointing out, regardless of whether they were
protecting the females and offspring. That would be an example of
regular natural selection – a phenomenon called "the selfish herd".
Systematics is the branch of biology
that attempts to establish patterns of genealogical relationship among
biological taxa. It is also concerned with their classification. There
are three primary camps in systematics: cladists, pheneticists, and
evolutionary taxonomists. The cladists hold that genealogy
alone should determine classification, pheneticists contend that
overall similarity is the determining criterion, while evolutionary
taxonomists say that both genealogy and similarity count in
classification.[50]
It is among the cladists that Occam's razor is to be found, although their term for it is cladistic parsimony. Cladistic parsimony (or maximum parsimony) is a method of phylogenetic inference in the construction of types of phylogenetic trees (more specifically, cladograms). Cladograms
are branching, tree-like structures used to represent hypotheses of
relative degree of relationship, based on shared, derived character
states. Cladistic parsimony is used to select as the preferred
hypothesis of relationships the cladogram that requires the fewest
implied character state transformations. Critics of the cladistic
approach often observe that for some types of tree, parsimony
consistently produces 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. Because this
information is not empirically accessible, the criticism of statistical
inconsistency against parsimony holds no force.[51] For a book-length treatment of cladistic parsimony, see Elliott Sober's Reconstructing the Past: Parsimony, Evolution, and Inference (1988). For a discussion of both uses of Occam's razor in biology, see Sober's article "Let's Razor Ockham's Razor" (1990).
Other methods for inferring evolutionary relationships use parsimony in a more traditional way. Likelihood
methods for phylogeny use parsimony as they do for all likelihood
tests, with hypotheses requiring few differing parameters (i.e., numbers
of different rates of character change or different frequencies of
character state transitions) being treated as null hypotheses relative
to hypotheses requiring many differing parameters. Thus, complex
hypotheses must predict data much better than do simple hypotheses
before researchers reject the simple hypotheses. Recent advances employ information theory, a close cousin of likelihood, which uses Occam's razor in the same way.
Francis Crick
has commented on potential limitations of Occam's razor in biology. He
advances the argument that because biological systems are the products
of (an ongoing) natural selection, the mechanisms are not necessarily
optimal in an obvious sense. He cautions: "While Ockham's razor is a
useful tool in the physical sciences, it can be a very dangerous
implement in biology. It is thus very rash to use simplicity and
elegance as a guide in biological research."[52]
In biogeography, parsimony is used to infer ancient migrations of species or populations by observing the geographic distribution and relationships of existing organisms. Given the phylogenetic tree, ancestral migrations are inferred to be those that require the minimum amount of total movement.
In the philosophy of religion, Occam's razor is sometimes applied to the existence of God. William of Ockham
himself was a Christian. He believed in God, and in the authority of
Scripture; he writes that "nothing ought to be posited without a reason
given, unless it is self-evident (literally, known through itself) or
known by experience or proved by the authority of Sacred Scripture."[53]
Ockham believed that an explanation has no sufficient basis in reality
when it does not harmonize with reason, experience, or the Bible.
However, unlike many theologians of his time, Ockham did not believe God
could be logically proven with arguments. To Ockham, science was a
matter of discovery, but theology was a matter of revelation and faith.
He states: "only faith gives us access to theological truths. 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."[54] St. Thomas Aquinas, in the Summa Theologica,
uses a formulation of Occam's razor to construct an objection to the
idea that God exists, which he refutes directly with a counterargument:[55]
Further, it is superfluous to suppose that what can be
accounted for by a few principles has been produced by many. But it
seems that everything we see in the world can be accounted for by other
principles, supposing God did not exist. For all natural things can be
reduced to one principle which is nature; and all voluntary things can
be reduced to one principle which is human reason, or will. Therefore
there is no need to suppose God's existence.
In turn, Aquinas answers this with the quinque viae, and addresses the particular objection above with the following answer:
Since nature works for a determinate end under the
direction of a higher agent, whatever is done by nature must needs be
traced back to God, as to its first cause. So also whatever is done
voluntarily must also be traced back to some higher cause other than
human reason or will, since these can change or fail; for all things
that are changeable and capable of defect must be traced back to an
immovable and self-necessary first principle, as was shown in the body
of the Article.
Rather than argue for the necessity of a god, some theists base their
belief upon grounds independent of, or prior to, reason, making Occam's
razor irrelevant. This was the stance of Søren Kierkegaard, who viewed belief in God as a leap of faith that sometimes directly opposed reason.[56] This is also the doctrine of Gordon Clark's presuppositional apologetics, with the exception that Clark never thought the leap of faith was contrary to reason (see also Fideism).
Various arguments in favor of God
establish God as a useful or even necessary assumption. Contrastingly
some anti-theists hold firmly to the belief that assuming the existence
of God introduces unnecessary complexity (Schmitt 2005, e.g., the Ultimate Boeing 747 gambit).
Another application of the principle is to be found in the work of George Berkeley
(1685–1753). Berkeley was an idealist who believed that all of reality
could be explained in terms of the mind alone. He invoked Occam's razor
against materialism,
stating that matter was not required by his metaphysic and was thus
eliminable. One potential problem with this belief is that it's
possible, given Berkeley's position, to find solipsism itself more in line with the razor than a God-mediated world beyond a single thinker.
Occam's razor may also be recognized in the apocryphal story about an 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 was that the name of God, which featured so
frequently in the writings of Lagrange, appeared nowhere in Laplace's. At that, he is said to have replied, "It's because I had no need of that hypothesis."[57] Though some point to this story as illustrating Laplace's atheism, more careful consideration suggests that he may instead have intended merely to illustrate the power of methodological naturalism, or even simply that the fewer logical premises one assumes, the stronger is one's conclusion.
In his article "Sensations and Brain Processes" (1959), J. J. C. Smart invoked Occam's razor with the aim to justify his preference of the mind-brain identity theory over spirit-body dualism.
Dualists state that there are two kinds of substances in the universe:
physical (including the body) and spiritual, which is non-physical. In
contrast, identity theorists state that everything is physical,
including consciousness, and that there is nothing nonphysical. Though
it is impossible to appreciate the spiritual when limiting oneself to
the physical, Smart maintained that identity theory explains all
phenomena by assuming only a physical reality. Subsequently, Smart has
been severely criticized for his use (or misuse) of Occam's razor and
ultimately retracted his advocacy of it in this context. Paul Churchland
(1984) states that by itself Occam's razor is inconclusive regarding
duality. In a similar way, Dale Jacquette (1994) stated that Occam's
razor has been used in attempts to justify eliminativism and
reductionism in the philosophy of mind. Eliminativism is the thesis that
the ontology of folk psychology
including such entities as "pain", "joy", "desire", "fear", etc., are
eliminable in favor of an ontology of a completed neuroscience.
Penal ethics
In penal theory and the philosophy of punishment, parsimony refers specifically to taking care in the distribution of punishment in order to avoid excessive punishment. In the utilitarian approach to the philosophy of punishment, Jeremy Bentham's
"parsimony principle" states that any punishment greater than is
required to achieve its end is unjust. The concept is related but not
identical to the legal concept of proportionality. Parsimony is a key consideration of the modern restorative justice, and is a component of utilitarian approaches to punishment, as well as the prison abolition movement. Bentham believed that true parsimony would require punishment to be individualised to take account of the sensibility
of the individual—an individual more sensitive to punishment should be
given a proportionately lesser one, since otherwise needless pain would
be inflicted. Later utilitarian writers have tended to abandon this
idea, in large part due to the impracticality of determining each
alleged criminal's relative sensitivity to specific punishments.[58]
Probability theory and statistics
Marcus Hutter's universal artificial intelligence builds upon Solomonoff's mathematical formalization of the razor to calculate the expected value of an action.
There are various papers in scholarly journals deriving formal
versions of Occam's razor from probability theory, applying it in statistical inference, and using it to come up with criteria for penalizing complexity in statistical inference. Papers[59][60] have suggested a connection between Occam's razor and Kolmogorov complexity.[61]
One of the problems with the original formulation of the razor is
that it only applies to models with the same explanatory power (i.e.,
it only tells us to prefer the simplest of equally good models). A more
general form of the razor can be derived from Bayesian model comparison,
which is based on Bayes factors
and can be used to compare models that don't fit the observations
equally well. These methods can sometimes optimally balance the
complexity and power of a model. Generally, the exact Occam factor is
intractable, but approximations such as Akaike information criterion, Bayesian information criterion, Variational Bayesian methods, false discovery rate, and Laplace's method are used. Many artificial intelligence researchers are now employing such techniques, for instance through work on Occam Learning or more generally on the Free energy principle.
Statistical versions of Occam's razor have a more rigorous
formulation than what philosophical discussions produce. In particular,
they must have a specific definition of the term simplicity, and that definition can vary. For example, in the Kolmogorov–Chaitinminimum description length approach, the subject must pick a Turing machine whose operations describe the basic operations believed
to represent "simplicity" by the subject. However, one could always
choose a Turing machine with a simple operation that happened to
construct one's entire theory and would hence score highly under the
razor. This has led to two opposing camps: one that believes Occam's
razor is objective, and one that believes it is subjective.
Objective razor
The minimum instruction set of a universal Turing machine requires approximately the same length description across different formulations, and is small compared to the Kolmogorov complexity of most practical theories. Marcus Hutter
has used this consistency to define a "natural" Turing machine of small
size as the proper basis for excluding arbitrarily complex instruction
sets in the formulation of razors.[62]
Describing the program for the universal program as the "hypothesis",
and the representation of the evidence as program data, it has been
formally proven under Zermelo–Fraenkel set theory
that "the sum of the log universal probability of the model plus the
log of the probability of the data given the model should be minimized."[63]
Interpreting this as minimising the total length of a two-part message
encoding model followed by data given model gives us the minimum message length (MML) principle.[59][60]
One possible conclusion from mixing the concepts of Kolmogorov
complexity and Occam's razor is that an ideal data compressor would also
be a scientific explanation/formulation generator. Some attempts have
been made to re-derive known laws from considerations of simplicity or
compressibility.[23][64]
According to Jürgen Schmidhuber, the appropriate mathematical theory of Occam's razor already exists, namely, Solomonoff'stheory of optimal inductive inference[65] and its extensions.[66] See discussions in David L. Dowe's "Foreword re C. S. Wallace"[67] for the subtle distinctions between the algorithmic probability work of Solomonoff and the MML work of Chris Wallace, and see Dowe's "MML, hybrid Bayesian network graphical models, statistical consistency, invariance and uniqueness"[68]
both for such discussions and for (in section 4) discussions of MML and
Occam's razor. For a specific example of MML as Occam's razor in the
problem of decision tree induction, see Dowe and Needham's "Message
Length as an Effective Ockham's Razor in Decision Tree Induction".[69]
Controversial aspects of the razor
Occam's
razor is not an embargo against the positing of any kind of entity, or a
recommendation of the simplest theory come what may.[a]
Occam's razor is used to adjudicate between theories that have already
passed "theoretical scrutiny" tests and are equally well-supported by
evidence.[b]
Furthermore, it may be used to prioritize empirical testing between two
equally plausible but unequally testable hypotheses; thereby minimizing
costs and wastes while increasing chances of falsification of the
simpler-to-test hypothesis.
Another contentious aspect of the razor is that a theory can become more complex in terms of its structure (or syntax), while its ontology (or semantics) becomes simpler, or vice versa.[c]
Quine, in a discussion on definition, referred to these two
perspectives as "economy of practical expression" and "economy in
grammar and vocabulary", respectively.[71] Galileo Galilei lampooned the misuse of Occam's razor in his Dialogue.
The principle is represented in the dialogue by Simplicio. The telling
point that Galileo presented ironically was that if one really wanted to
start from a small number of entities, one could always consider the
letters of the alphabet as the fundamental entities, since one could
construct the whole of human knowledge out of them.
Anti-razors
Occam's razor has met some opposition from people who have considered it too extreme or rash. Walter Chatton
(c. 1290–1343) was a contemporary of William of Ockham (c. 1287–1347)
who took exception to Occam's razor and Ockham's use of it. In response
he devised his own anti-razor: "If three things are not enough to
verify an affirmative proposition about things, a fourth must be added,
and so on." Although there have been a number of philosophers who have
formulated similar anti-razors since Chatton's time, no one anti-razor
has perpetuated in as much notability as Chatton's anti-razor, although
this could be the case of the Late Renaissance Italian motto of unknown
attribution Se non è vero, è ben trovato ("Even if it is not true, it is well conceived") when referred to a particularly artful explanation.
Anti-razors have also been created by Gottfried Wilhelm Leibniz (1646–1716), Immanuel Kant (1724–1804), and Karl Menger (1902–1985). Leibniz's version took the form of a principle of plenitude, as Arthur Lovejoy
has called it: the idea being that God created the most varied and
populous of possible worlds. Kant felt a need to moderate the effects of
Occam's razor and thus created his own counter-razor: "The variety of
beings should not rashly be diminished."[72]
Karl Menger found mathematicians to be too parsimonious with
regard to variables, so he formulated his Law Against Miserliness, which
took one of two forms: "Entities must not be reduced to the point of
inadequacy" and "It is vain to do with fewer what requires more." A less
serious but (some[who?] might say) even more extremist anti-razor is 'Pataphysics, the "science of imaginary solutions" developed by Alfred Jarry
(1873–1907). Perhaps the ultimate in anti-reductionism, "'Pataphysics
seeks no less than to view each event in the universe as completely
unique, subject to no laws but its own." Variations on this theme were
subsequently explored by the Argentine writer Jorge Luis Borges in his story/mock-essay "Tlön, Uqbar, Orbis Tertius". There is also Crabtree's Bludgeon,
which cynically states that "[n]o set of mutually inconsistent
observations can exist for which some human intellect cannot conceive a
coherent explanation, however complicated."
Spherical cow – A humorous metaphor for highly simplified scientific models of complex real life phenomena
Notes
"Ockham's razor does not say that the more simple a hypothesis, the better."[70]
"While
these two facets of simplicity are frequently conflated, it is
important to treat them as distinct. One reason for doing so is that
considerations of parsimony and of elegance typically pull in different
directions. Postulating extra entities may allow a theory to be
formulated more simply, while reducing the ontology of a theory may only
be possible at the price of making it syntactically more complex."[3]
References
Immanuel Kant (1929). Norman Kemp-Smith transl (ed.). The Critique of Pure Reason. Palgrave Macmillan. p. 92. Archived from the original on 16 May 2012. Retrieved 27 October 2012. Entium varietates non temere esse minuendas
Further reading
Ariew, Roger (1976). Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony. Champaign-Urbana, University of Illinois.
Jefferys, William H.; Berger, James O. (1991). "Ockham's Razor and Bayesian Statistics". American Scientist. 80: 64–72. (Preprint available as "Sharpening Occam's Razor on a Bayesian Strop").
Menger, Karl (1960). "A Counterpart of Ockham's Razor in Pure and Applied Mathematics: Ontological Uses". Synthese. 12 (4): 415–428. doi:10.1007/BF00485426.
Pegis, A. C., translator (1945). Basic Writings of St. Thomas Aquinas. New York: Random House. p. 129. ISBN978-0-87220-380-8.
Popper, Karl (1992) [First composed 1934 (Logik der Forschung)]. "7. Simplicity". The Logic of Scientific Discovery (2nd ed.). London: Routledge. pp. 121–132. ISBN978-84-309-0711-3.
Sober, Elliott (1990). "Let's Razor Ockham's Razor". In Dudley Knowles (ed.). Explanation and its Limits. Cambridge: Cambridge University Press. pp. 73–94.
"Today,
we think of the principle of parsimony as a heuristic device. We don't
assume that the simpler theory is correct and the more complex one
false. We know from experience that more often than not the theory that
requires more complicated machinations is wrong. Until proved otherwise,
the more complex theory competing with a simpler explanation should be
put on the back burner, but not thrown onto the trash heap of history
until proven false."[70]
Hoffman, Roald; Minkin, Vladimir I.; Carpenter, Barry K. (1997). "Ockham's Razor and Chemistry". International Journal for Philosophy of Chemistry. 3: 3–28. Retrieved 12 July 2018.
Alan Baker (2010) [2004]. "Simplicity". Stanford Encyclopedia of Philosophy. California: Stanford University. ISSN1095-5054.
Courtney, A.; Courtney, M. (2008). "Comments Regarding 'On the Nature of Science'". Physics in Canada. 64 (3): 7–8. arXiv:0812.4932. Bibcode:2008arXiv0812.4932C.
Sober, Elliott (1994). "Let's Razor Occam's Razor". In Knowles, Dudley (ed.). Explanation and Its Limits. Cambridge University Press. pp. 73–93.
Sober, Elliott (2015). Ockam's Razor: A User's Manual. Cambridge University Press. p. 4. ISBN978-1107692534.
Roger Ariew, Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony, 1976
Johannes Poncius's commentary on John Duns Scotus's Opus Oxoniense, book III, dist. 34, q. 1. in John Duns Scotus Opera Omnia, vol.15, Ed. Luke Wadding, Louvain (1639), reprinted Paris: Vives, (1894) p.483a
Aristotle, Physics 189a15, On the Heavens 271a33. See also Franklin, op cit. note 44 to chap. 9.
Charlesworth, M. J. (1956). "Aristotle's Razor". Philosophical Studies (Ireland). 6: 105–112. doi:10.5840/philstudies1956606.
Franklin, James (2001). The Science of Conjecture: Evidence and Probability before Pascal. The Johns Hopkins University Press. Chap 9. p. 241.
Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science 1100–1700 (1953) pp. 85–86
Spall, James C. (11 March 2005). Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control. John Wiley & Sons. pp. 330–331. ISBN9780471441908.
Sober, Elliot (1998). Reconstructing the Past: Parsimony, Evolution, and Inference (2nd ed.). Massachusetts Institute of Technology: The MIT Press. p. 7. ISBN978-0-262-69144-4.
Brower, AVZ. 2017. Statistical consistency and phylogenetic inference: a brief review. Cladistics. (early view: doi:10.1111/cla.12216)
Crick 1988, p. 146.
"William Ockham". Encyclopedia of Philosophy. Stanford. Retrieved 24 February 2016.
Dale T Irvin & Scott W Sunquist. History of World Christian Movement Volume, I: Earliest Christianity to 1453, p. 434. ISBN9781570753961.
Chris S. Wallace and David M. Boulton; Computer Journal, Volume 11, Issue 2, 1968 Page(s):185–194, "An information measure for classification."
Chris S. Wallace and David L. Dowe; Computer Journal, Volume 42, Issue 4, Sep 1999 Page(s):270–283, "Minimum Message Length and Kolmogorov Complexity."
Paul M. B. Vitányi and Ming Li; IEEE Transactions on Information Theory, Volume 46, Issue 2, Mar 2000 Page(s):446–464, "Minimum Description Length Induction, Bayesianism and Kolmogorov Complexity."
Schmidhuber, J. (2006). "The New AI: General & Sound & Relevant for Physics". In Goertzel, B.; Pennachin, C. (eds.). Artificial General Intelligence. pp. 177–200. arXiv:cs.AI/0302012.
Dowe, David L. (2008). "Foreword re C. S. Wallace". Computer Journal. 51 (5): 523–560. doi:10.1093/comjnl/bxm117.
Scott
Needham and David L. Dowe (2001):" Message Length as an Effective
Ockham's Razor in Decision Tree Induction." Proc. 8th International
Workshop on Artificial Intelligence and Statistics (AI+STATS 2001), Key
West, Florida, U.S.A., Jan. 2001 Page(s): 253–260 "Archived copy"(PDF). Archived(PDF) from the original on 23 September 2015. Retrieved 2 September 2015.
Robert T. Carroll. "Occam's Razor". The Skeptic's Dictionary. Archived from the original on 1 March 2016. Retrieved 24 February 2016 Last updated 18 February 2012
Quine, W V O (1961). "Two dogmas of empiricism". From a logical point of view. Cambridge: Harvard University Press. pp. 20–46. ISBN978-0-674-32351-3.
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