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| {{multiple issues |original research=February 2011 |refimprove=November 2011}}
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| [[File:Black Swans.jpg|thumb|Are all [[swan]]s white?]]
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| '''Falsifiability''' or '''refutability''' of a [[proposition|statement]], [[hypothesis]], or [[theory]] is an inherent possibility to prove it to be false. A statement is called '''falsifiable''' if it is possible to conceive an observation or an argument which proves the statement in question to be false. In this sense, ''falsify'' is synonymous with ''nullify'', meaning not "to commit fraud" but "show to be false". Some philosophers argue that science must be falsifiable.<ref name="Popper 2005p17">{{cite book| last1 = Popper| first1 = Karl| title = The Logic of Scientific Discovery| edition = Taylor & Francis e-Library| year = 2005| publisher = Routledge / Taylor & Francis e-Library| location = London and New York| isbn = 0203994620| page = 17| url = http://books.google.com.au/books/about/The_Logic_of_Scientific_Discovery.html?id=Yq6xeupNStMC
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| | quote = The criterion of demarcation inherent in inductive logic—that is, the positivistic dogma of meaning—is equivalent to the requirement that all the statements of empirical science (or all ‘meaningful’ statements) must be capable of being finally decided, with respect to their truth and falsity; we shall say that they must be ‘conclusively decidable’. This means that their form must be such that to verify them and to falsify them must both be logically possible.}}</ref>
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| For example, by the [[problem of induction]], no number of confirming observations can verify a [[enumerative induction|universal generalization]], such as ''All swans are white'', yet it is logically possible to falsify it by observing a single black swan. Thus, the term ''falsifiability'' is sometimes synonymous to ''testability''. Some statements, such as ''It will be raining here in one million years'', are falsifiable in principle, but not in practice.<ref>{{cite book |first=K. R. |last=Popper |chapter={{lang|de|Zwei Bedeutungen von Falsifizierbarkeit}} [Two meanings of falsifiability] |editor1-first=H. |editor1-last=Seiffert |editor2-first=G. |editor2-last=Radnitzky |title=Handlexikon der Wissenschaftstheorie |publisher=Deutscher Taschenbuch Verlag |location=München |year=1994 |pages=82–85 |isbn=3-423-04586-8}}</ref> | |
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| The concern with falsifiability gained attention by way of [[philosophy of science|philosopher of science]] [[Karl Raimund Popper|Karl Popper]]'s scientific [[epistemology]] "[[falsificationism]]". Popper stresses the [[demarcation problem|problem of demarcation]]—distinguishing the scientific from the unscientific—and makes ''falsifiability'' the demarcation criterion, such that what is unfalsifiable is classified as [[unscientific]], and the practice of declaring an unfalsifiable theory to be [[scientific method|scientifically]] true is [[pseudoscience]]. This is often epitomized in [[Wolfgang Pauli]] famously saying, of an argument that fails to be scientific because it cannot be falsified by experiment, "it is not only not right, it is [[not even wrong]]!"
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| ==Overview==
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| The classical view of the philosophy of science is that it is the goal of science to prove [[hypotheses]] like "All swans are white" or to [[inductive reasoning|induce]] them from observational data. Popper argued that this would require the inference of a general rule from a number of individual cases, which is inadmissible in deductive logic.<ref>LScD p. 4</ref> However, if one finds one single black swan, deductive logic admits the conclusion that the statement that all swans are white is false. Falsificationism thus strives for questioning, for falsification, of hypotheses instead of proving them.
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| For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come in conflict with observation. A key observation of falsificiationism is thus that a criterion of demarcation is needed to distinguish those statements that can come in conflict with observation and those that cannot (Chorlton, 2012). Popper chose falsifiability as the name of this criterion.
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| {{Quote|text=My proposal is based upon an ''asymmetry'' between [[Formal verification|verifiability]] and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements.|sign=Karl Popper|source=''[[The Logic of Scientific Discovery]]'', [http://books.google.com/books?id=0a5bLBbe_dMC&pg=PA19&dq=%22is+based+upon+an+asymmetry+between+verifiability+and+falsifiability;+an+asymmetry+which+results+from+the+logical+form+of+universal+statements.%22%22For+these+are+never+derivable+from+singular+statements,+but+can+be+contradicted+by+singular+statements%22 p. 19].}}
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| Popper stressed that unfalsifiable statements are important in science.<ref>''LScD'', p. 16</ref> Contrary to intuition, unfalsifiable statements can be embedded in - and [[logical consequence|deductively entailed]] by - falsifiable theories. For example, while "all men are mortal" is unfalsifiable, it is a [[logical consequence]] of the falsifiable theory that "every man dies before he reaches the age of 150 years".<ref>Keuth: ''The philosophy of Karl Popper'', p. 45</ref> Similarly, the ancient metaphysical and unfalsifiable idea of the existence of atoms has led to corresponding falsifiable modern theories. Popper invented the notion of [[metaphysical research program]]s to name such unfalsifiable ideas.<ref>Quantum theory and the schism in physics, introductory comments</ref> In contrast to [[Positivism]], which held that statements are meaningless if they cannot be verified or falsified, Popper claimed that falsifiability is merely a special case of the more general notion of criticizability, even though he admitted that empirical refutation is one of the most effective methods by which theories can be criticized. Criticizability, in contrast to falsifiability, and thus rationality, may be comprehensive (i.e., have no logical limits), though this claim is controversial even among proponents of Popper's philosophy and critical rationalism.
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| == Naive falsification{{anchor|Na.C3.AFve}} ==<!-- see [[Karl Popper]] -->
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| {{Unreferenced section|date=May 2011}}
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| ===Two types of statements: observational and categorical===
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| In work beginning in the 1930s, Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.
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| Popper noticed that two types of statements<ref name="Popper 2005p47-50">{{cite book| last1 = Popper
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| | first1 = Karl| title = The Logic of Scientific Discovery| edition = Taylor & Francis e-Library| year = 2005
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| | publisher = Routledge / Taylor & Francis e-Library| location = London and New York| isbn = 0203994620
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| | pages = 47–50| url = http://books.google.com.au/books/about/The_Logic_of_Scientific_Discovery.html?id=Yq6xeupNStMC}}</ref> are of particular value to [[scientist]]s.
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| The first are statements of observations, such as "there is a white swan." Logicians call these statements [[existential quantification|singular existential statements]], since they assert the existence of some particular thing. They are equivalent to a predicate calculus statement of the form: ''There exists an x such that x is a swan, and x is white.''
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| The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements [[universal quantification|universal]]. They are usually parsed in the form: ''For all x, if x is a swan, then x is white''. [[Physical law|Scientific law]]s are commonly supposed to be of this type. One difficult question in the [[scientific method|methodology of science]] is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?
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| [[Inductive reasoning|Inductivist]] methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white.' This method is clearly ''deductively'' invalid, since it is always possible that there may be a non-white swan that has eluded observation (and, in fact, the discovery of the Australian [[black swan]] demonstrated the deductive invalidity of this particular statement).
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| === Inductive categorical inference ===
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| Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the [[problem of induction]]. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false—in logic this is called ''[[modus tollens]]''. 'There is a black swan' implies 'there is a non-white swan,' which, in turn, implies 'there is something that is a swan and that is not white', hence 'all swans are white' is false, because that is the same as 'there is ''nothing'' that is a swan and that is not white'.
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| One notices a white swan. From this one can conclude:
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| :At least one swan is white.
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| From this, one may wish to conjecture:
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| :All swans are white.
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| It is impractical to observe all the swans in the world to verify that they are all white.
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| Even so, the statement ''all swans are white'' is testable by being falsifiable. For, if in testing many swans, the researcher finds a single [[black swan]], then the statement ''all swans are white'' would be falsified by the counterexample of the single black swan.
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| ==== Deductive falsification ====
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| {{unreferenced section|date=November 2011}}
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| Deductive falsification is different from an absence of [[Verification theory|verification]]. The falsification of statements occurs through ''[[modus tollens]]'', via some observation. Suppose some universal statement ''U'' forbids some [[observation]] ''O'':
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| :<math>U \rightarrow \neg O</math>
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| Observation O, however, is made:
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| :<math>\ \ O</math>
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| So by ''modus tollens'',
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| :<math>\neg U</math>
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| Although the logic of naïve falsification is valid, it is rather limited. Nearly any statement can be made to fit the data, so long as one makes the requisite 'compensatory adjustments'. Popper drew attention to these limitations in ''[[The Logic of Scientific Discovery]]'' in response to criticism from [[Pierre Duhem]]. [[Willard Van Orman Quine|W. V. Quine]] expounded this argument in detail, calling it [[confirmation holism]]. To logically falsify a [[universality (philosophy)|universal]], one must find a true falsifying singular statement. But Popper pointed out that it is always possible to ''change'' the universal statement or the existential statement so that falsification does not occur. On hearing that a black swan has been observed in Australia, one might introduce the ''[[ad hoc]]'' hypothesis, 'all swans are white except those found in Australia'; or one might adopt another, more cynical view about some observers, 'Australian [[ornithology|bird watchers]] are incompetent'.
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| Thus, naïve falsification ought to, but does not, supply a way of handling competing hypotheses for many subject controversies (for instance [[conspiracy theories]] and [[urban legends]]). People arguing that there is no support for such an observation may argue that there is nothing to see, that all is normal, or that the differences or appearances are too small to be statistically significant. On the other side are those who concede that an observation has occurred and that a universal statement has been falsified as a consequence. Therefore, naïve falsification does not enable scientists, who rely on [[Objectivity (science)|objective]] criteria, to present a definitive falsification of universal statements.
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| == Falsificationism ==
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| Naïve falsificationism is an unsuccessful attempt to prescribe a rationally unavoidable method for science. Sophisticated methodological falsification, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice. The object of this is to arrive at an evolutionary process whereby theories become ''less bad''.
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| Naïve falsification considers scientific statements individually. Scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of [[ad hoc hypothesis|''ad hoc'' hypotheses]]. As Popper put it, a ''decision'' is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ''ad hoc'' hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.
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| In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories that can account for the [[phenomena]] that falsified the prior theory, that is, with greater [[explanatory power]]. For example, [[Aristotle|Aristotelian mechanics]] explained observations of everyday situations, but were falsified by [[Galileo Galilei|Galileo]]'s experiments{{citation needed|date=January 2013}}, and were replaced by Newtonian mechanics, which accounted for the phenomena noted by Galileo (and others). [[Newtonian mechanics]]' reach included the observed motion of the planets and the mechanics of gases. The Youngian wave theory of light (i.e., waves carried by the [[luminiferous aether]]) replaced Newton's (and many of the Classical Greeks') particles of light but in turn was falsified by the [[Michelson-Morley experiment]] and was superseded by [[James Clerk Maxwell|Maxwell]]'s electrodynamics and Einstein's [[special relativity]], which did account for the newly observed phenomena. Furthermore, Newtonian mechanics applied to the atomic scale was replaced with [[quantum mechanics]], when the old theory could not provide an answer to the [[ultraviolet catastrophe]], the [[Gibbs paradox]], or how [[Atomic orbital|electron orbits]] could exist without the particles radiating away their energy and spiraling towards the centre. Thus the new theory had to posit the existence of unintuitive concepts such as [[energy levels]], [[quantum|quanta]] and [[Heisenberg's uncertainty principle]].
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| At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found that had greater ''explanatory power'' (i.e., could account for the previously unexplained phenomena), and as a result, ''provided greater opportunity for its own falsification''.
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| == The criterion of demarcation ==
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| Popper uses falsification as a [[demarcation problem|criterion of demarcation]] to draw a sharp line between those theories that are scientific and those that are unscientific. It is useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable.
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| Popper claimed that, if a theory is falsifiable, then it is scientific.
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| The Popperian criterion excludes from the domain of science not unfalsifiable ''statements'' but only ''whole theories'' that ''contain no'' falsifiable statements; thus it leaves us with the [[confirmation holism|Duhemian]] problem of what constitutes a 'whole theory' as well as the problem of what makes a statement 'meaningful'. Popper's own falsificationism, thus, is not only an alternative to verificationism, it is also an acknowledgement of the conceptual distinction that previous theories had ignored.
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| ===Verificationism===
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| {{Main|Verificationist}}
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| {{See also|Abductive reasoning}}
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| In the [[philosophy of science]], verificationism (also known as the verifiability theory of meaning) holds that a statement must, in principle, be empirically verifiable in order that it be both meaningful and scientific.
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| This was an essential feature of the [[logical positivism]] of the so-called [[Vienna Circle]] that included such philosophers as [[Moritz Schlick]], [[Rudolf Carnap]], [[Otto Neurath]], the Berlin philosopher [[Hans Reichenbach]], and the [[logical empiricism]] of [[A.J. Ayer]].
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| Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, that of meaning and that of demarcation, and had proposed in verificationism a single solution to both. In opposition to this view, Popper emphasized that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.
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| Thus, Popper urged that verifiability be replaced with falsifiability as the criterion of demarcation. On the other hand, he strictly opposed the view that non-falsifiable statements are meaningless or otherwise inherently bad, and noted that falsificationism does not imply it.<ref>''Logic of Scientific Discovery'', section 6, footnote *3</ref>
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| ===Use in courts of law===
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| Judge [[William Overton (judge)|William Overton]] used falsifiability in the [[McLean v. Arkansas]] ruling in 1982 as one of the criteria to determine that "[[creation science]]" was not scientific and should not be taught in [[Arkansas]] [[Public school (government funded)|public school]]s as such (it can be taught as religion). In his conclusion related to this criterion Judge Overton stated that "[w]hile anybody is free to approach a scientific inquiry in any fashion they choose, they cannot properly describe the methodology as scientific, if they start with the conclusion and refuse to change it regardless of the evidence developed during the course of the investigation."<ref name=mclean>
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| [http://www.talkorigins.org/faqs/mclean-v-arkansas.html McLean v. Arkansas Board of Education], Decision January 5, 1982.</ref>
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| [[United States law]] also enshrined falsifiability as part of the [[Daubert Standard]] set by the [[United States Supreme Court]] for whether scientific evidence is admissible in a jury trial.
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| == Criticisms ==
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| ===Contemporary philosophers===
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| Adherents of Popper speak with disrespect of "professional philosophy", for example W. W. Bartley:
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| {{quote|Sir Karl Popper is not really a participant in the contemporary professional philosophical dialogue; quite the contrary, he has ruined that dialogue. If he is on the right track, then the majority of professional philosophers the world over have wasted or are wasting their intellectual careers. The gulf between Popper's way of doing philosophy and that of the bulk of contemporary professional philosophers is as great as that between astronomy and astrology.<ref>W. W. Bartley, III: Biology & evolutionary epistemology. ''Philosophia'' '''6''':3–4 (September–December 1976), pp. 463–494</ref>}}
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| Rafe Champion:
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| {{quote|Popper's ideas have failed to convince the majority of professional philosophers because his theory of conjectural knowledge does not even pretend to provide positively justified foundations of belief. Nobody else does better, but they keep trying, like chemists still in search of the [[Philosopher's Stone]] or physicists trying to build [[perpetual motion machines]].<ref>Rafe Champion: [http://www.the-rathouse.com/bartagree.html Agreeing to Disagree: Bartley's Critique of Reason]. ''Melbourne Age Monthly Review'' (October 1985)</ref>}}
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| and [[David Miller (philosopher)|David Miller]]:
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| {{quote|What distinguishes science from all other human endeavours is that the accounts of the world that our best, mature sciences deliver are strongly supported by evidence and this evidence gives us the strongest reason to believe them.' That anyway is what is said at the beginning of the advertisement for a recent conference on induction at a celebrated seat of learning in the UK. It shows how much critical rationalists still have to do to make known the message of ''Logik der Forschung'' concerning what empirical evidence is able to do and what it does.<ref>David Miller: Some hard questions for critical rationalism</ref>}}
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| Nevertheless, many contemporary [[philosophy of science|philosophers of science]] and [[Analytic Philosophy|analytic philosophers]] are strongly critical of Popper's philosophy of science.<ref>Martin Gardner (2001), [http://www.stephenjaygould.org/ctrl/gardner_popper.html "A Skeptical Look at Karl Popper,"] Skeptical Inquirer, 25(4): 13-14, 72.</ref> Popper's mistrust of [[inductive reasoning]] has led to claims that he misrepresents scientific practice. Among the professional philosophers of science, the Popperian view has never been seriously preferred to [[Raven paradox#Probabilistic or non probabilistic induction|probabilistic induction]], which is the mainstream account of scientific reasoning.{{citation needed|date=January 2013}}
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| === Kuhn and Lakatos ===
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| Whereas Popper was concerned in the main with the ''logic'' of science, [[Thomas Samuel Kuhn|Thomas Kuhn]]'s influential book ''[[The Structure of Scientific Revolutions]]'' examined in detail the [[history of science]]. Kuhn argued that scientists work within a conceptual [[paradigm]] that strongly influences the way in which they see data. Scientists will go to great length to defend their paradigm against falsification, by the addition of ''ad hoc'' hypotheses to existing theories. Changing a 'paradigm' is difficult, as it requires an individual scientist to break with his or her peers and defend a heterodox theory.
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| Some falsificationists saw Kuhn's work as a vindication, since it provided historical evidence that science progressed by rejecting inadequate theories, and that it is the ''decision'', on the part of the scientist, to accept or reject a theory that is the crucial element of falsificationism. Foremost amongst these was [[Imre Lakatos]].
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| Lakatos attempted to explain Kuhn's work by arguing that science progresses by the falsification of ''research programs'' rather than the more specific universal statements of naïve falsification. In Lakatos' approach, a scientist works within a research program that corresponds roughly with Kuhn's 'paradigm'. Whereas Popper rejected the use of ''ad hoc'' hypotheses as unscientific, Lakatos accepted their place in the development of new theories.<ref>{{cite book|last=Lakatos|first=Imre|title=The methodology of scientific research programmes: Philosophical Papers Volume I|year=1978|publisher=Cambridge University Press|location=Cambridge|isbn=0-521-28031 -1}}</ref>
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| === Feyerabend ===
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| [[Paul Feyerabend]] examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He rejected Lakatos' argument for ad hoc hypothesis, arguing that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method. Rather, he claimed that if one is keen to have a universally valid methodological rule, [[epistemological anarchism]] or ''anything goes'' would be the only candidate. For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method.
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| ===Sokal and Bricmont===
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| In their book ''[[Fashionable Nonsense]]'' (published in the UK as ''Intellectual Impostures'') the physicists [[Alan Sokal]] and [[Jean Bricmont]] criticized falsifiability on the grounds that it does not accurately describe the way science really works. They argue that theories are used because of their successes, not because of the failures of other theories. Their discussion of Popper, falsifiability and the philosophy of science comes in a chapter entitled "Intermezzo," which contains an attempt to make clear their own views of what constitutes truth, in contrast with the extreme epistemological relativism of postmodernism.
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| Sokal and Bricmont write, "When a theory successfully withstands an attempt at falsification, a scientist will, quite naturally, consider the theory to be partially confirmed and will accord it a greater likelihood or a higher subjective probability. ... But Popper will have none of this: throughout his life he was a stubborn opponent of any idea of 'confirmation' of a theory, or even of its 'probability'. ... [but] the history of science teaches us that scientific theories come to be accepted above all because of their successes." (Sokal and Bricmont 1997, 62f)
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| They further argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions that are sometimes incorrect.
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| [[David Miller (philosopher)|David Miller]], a contemporary philosopher of critical rationalism, has attempted to defend Popper against these claims.<ref>{{Cite journal|last=Miller|first=David|title=Sokal and Bricmont: Back to the Frying Pan|journal=Pli|volume=9|year=2000|pages=156–73|url=http://www2.warwick.ac.uk/fac/soc/philosophy/staff/miller/miller_pli_9.pdf}}, also chapter 6 of {{Cite journal|last=Miller|first=David|title=Out of Error|year=2006|publisher=Ashgate}}</ref> Miller argues that astrology does not lay itself open to falsification, while astronomy does, and this is the litmus test for science.
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| == Examples ==
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| {{Original research|section|date=September 2007}}
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| Claims about verifiability and falsifiability have been used to criticize various controversial views. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise a theory.
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| === Economics ===
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| [[Karl Popper]] argued that [[Marxism]] shifted from falsifiable to unfalsifiable.<ref>:"For Marxism, Popper believed, had been initially scientific, in that Marx had postulated a theory which was genuinely predictive. However, when these predictions were not in fact borne out, the theory was saved from falsification by the addition of ''ad hoc'' hypotheses which made it compatible with the facts. By this means, Popper asserted, a theory which was initially genuinely scientific degenerated into pseudo-scientific dogma." [http://plato.stanford.edu/entries/popper/ Karl Popper] at the Stanford Encyclopedia of Philosophy.</ref>
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| Some economists, such as those of the [[Austrian School]], believe that [[macroeconomics]] is [[Empiricism|empirically]] unfalsifiable and that thus the only appropriate means to understand economic events is by [[deductive reasoning|logically]] studying [[Subjective theory of value|the intentions]] of [[methodological individualism|individual economic decision-makers]], [[Praxeology#Austrian School approach|based on]] certain fundamental [[Action axiom|truths]].<ref name="econlib">[http://www.econlib.org/library/Enc/AustrianSchoolofEconomics.html Austrian School of Economics: The Concise Encyclopedia of Economics | Library of Economics and Liberty<!-- Bot generated title -->]</ref><ref>[http://plato.stanford.edu/entries/methodological-individualism/ Methodological Individualism at the Stanford Encyclopedia of Philosophy ]</ref><ref name="Mises_Action">Ludwig von Mises. [[Human Action]], p. 11, "r. Purposeful Action and Animal Reaction". Referenced 2011-11-23.</ref> Prominent figures within the Austrian School of economics [[Ludwig von Mises]] and [[Friedrich Hayek]] were associates of Karl Popper's, with whom they co-founded the [[Mont Pelerin Society]].
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| ===Evolution===
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| {{Main|Objections to evolution#Unfalsifiability|l1=Objections to evolution: Unfalsifiability}}
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| Numerous examples of potential (indirect) ways to falsify common descent have been proposed by its proponents. [[J.B.S. Haldane]], when asked what hypothetical evidence could disprove evolution, replied "[[precambrian rabbit|fossil rabbits in the Precambrian era]]".<ref>{{cite book |title=Evolution, Third Edition |first=M |last=Ridley |publisher=Blackwell Publishing Limited |year=2003 |isbn=1-4051-0345-0}}</ref> [[Richard Dawkins]] adds that any other modern animal, such as a hippo, would suffice.<ref name="The Evolution Wars">{{cite news |last=Wallis |first=C |title=The Evolution Wars |publisher=Time Magazine |date=2005-08-07 |page=32|url=http://www.time.com/time/archive/preview/0,10987,1090909,00.html|accessdate=2007-03-24}}</ref><ref>{{cite book |first=Richard |last=Dawkins |authorlink=Richard Dawkins |title=[[River Out of Eden]] |publisher=Basic Books |year=1995 |isbn=0-465-06990-8}}</ref><ref>{{cite book |first=Richard |last=Dawkins |authorlink=Richard Dawkins |title=[[The Blind Watchmaker]] |publisher=W. W. Norton & Company, Inc. |year=1986 |isbn=0-393-31570-3 }}</ref>
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| [[Karl Popper]] at first spoke against the testability of natural selection <ref>{{Cite news |last=Lannes |first=Sophie |last2=Alain| first2=Boyer |title=Les chemins de la verite: L'Express va plus loin avec Karl Popper |newspaper=L'Express |date=1982-02-26}}; online German translation {{Cite news |title=Die Wege der Wahrheit. Zum Tode von Karl Popper|periodical=Aufklärung und Kritik |page=38 |date=2/1994 |url=http://www.gkpn.de/popper.htm}}</ref><ref>{{cite book |last=Popper |first=K |year=1985 |title=Unended Quest: An Intellectual Autobiography |publisher=Open Court |isbn=0-08-758343-7}}</ref> but later recanted, "I have changed my mind about the testability and logical status of the theory of natural selection, and I am glad to have the opportunity to make a recantation."<ref name="popper">{{cite journal |last=Popper |first=K |year=1978 |title=Natural selection and the emergence of mind |journal=Dialectica |issue=32 |pages=339–355}}</ref>
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| === Historicism ===
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| Theories of [[history]] or politics that allegedly predict future events have a [[logical form]] that renders them neither falsifiable nor verifiable. They claim that for every historically significant event, there exists an historical or economic law that ''determines'' the way in which events proceeded. Failure to identify the law does not mean that it does not exist, yet an event that satisfies the law does not prove the general case. Evaluation of such claims is at best difficult. On this basis, Popper "fundamentally criticized historicism in the sense of any preordained prediction of history",<ref name="popperc">{{cite book
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| |title=Research training for social scientists: a handbook for postgraduate researchers
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| |first1=Dawn
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| |last1=Burton
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| |publisher=SAGE
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| |year=2000
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| |isbn=0-7619-6351-0
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| |pages=12–13
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| |url=http://books.google.com/books?id=ibePpZ-6lkgC&pg=PA12}}, [http://books.google.com/books?id=ibePpZ-6lkgC&pg=PA12 Chapter 1, p. 12]
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| </ref> and argued that neither [[Marxism]] nor [[psychoanalysis]] was science,<ref name="popperc" /> although both made such claims. Again, this does not mean that any of these types of theories is necessarily ''incorrect''. Popper considered falsifiability a test of whether theories are scientific, not of whether propositions that they contain or support are true. | |
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| === Mathematics ===
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| Many philosophers{{weasel-inline|date=January 2013}} believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of [[Karl Popper]].<ref>{{cite book | title = Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists | author = Shasha, Dennis Elliot; Lazere, Cathy A. | publisher = Springer | year = 1998 | page = 228}}</ref> However, in the 1930s [[Gödel's incompleteness theorems]] proved that there does not exist a set of [[axioms]] for mathematics which is both complete and consistent. Karl Popper concluded that "most mathematical theories are, like those of [[physics]] and [[biology]], [[hypothesis|hypothetico]]-[[deductive]]: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently."<ref>Popper 1995, p. 56</ref> Other thinkers, notably [[Imre Lakatos]], have applied a version of [[falsificationism]] to mathematics itself.
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| Like all [[formal science]]s, mathematics is not concerned with the validity of theories based on observations in the [[Empiricism|empirical]] world, but rather, mathematics is occupied with the theoretical, abstract study of such topics as [[quantity]], [[structure]], [[space]] and [[Calculus|change]]. Methods of the mathematical sciences are, however, applied in constructing and testing scientific models dealing with observable [[reality]]. [[Albert Einstein]] wrote, "One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.”<ref>{{cite book |author=Albert Einstein |authorlink=Albert Einstein |title=Sidelights on relativity |chapter=Geometry and Experience |page=27 |publisher=Courier Dover Publications |year=1923}} Reprinted by Dover (2010), ISBN 978-0-486-24511-9.</ref>
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| {{See also|Mathematical proof|Scientific method#Relationship with mathematics|l2=Scientific method and mathematics|Mathematics#Mathematics as science|l3=Mathematics as science|Philosophy of mathematics#Popper's "two senses" theory|l4=Popper's "two senses" theory}}
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| ==Quotations==
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| * Albert Einstein is reported to have said: ''No amount of experimentation can ever prove me right; a single experiment can prove me wrong.'' (paraphrased)<ref>{{cite book | last = Calaprice | first = Alice | title = The New Quotable Einstein | publisher = Princeton University Press and Hebrew University of Jerusalem | year = 2005 | location = USA | page = 291 | isbn = 0-691-12074-9 }}Calaprice denotes this not as an exact quotation, but as a paraphrase of a translation of A. Einstein's "Induction and Deduction". ''Collected Papers of Albert Einstein'' Vol. 7, Document 28. ''The Berlin Years: Writings, 1918–1921''. A. Einstein; M. Janssen, R. Schulmann, et al., eds.</ref><ref>{{cite book
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| |title=The Five Biggest Ideas in Science
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| |first1=Charles M.
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| |last1=Wynn
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| |first2=Arthur W.
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| |last2=Wiggins
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| |first3=Sidney
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| |last3=Harris
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| |publisher=John Wiley and Sons
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| |year=1997
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| |isbn=0-471-13812-6
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| |page=107
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| |url=http://books.google.com/books?id=C_O8QgAACAAJ}}
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| </ref><ref>{{cite book
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| |title=Meeting the standards in primary science: a guide to the ITT NC
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| |first1=Lynn D.
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| |last1=Newton
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| |publisher=Routledge
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| |year=2000
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| |isbn=0-7507-0991-X
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| |page=21
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| |url=http://books.google.com/books?id=JLBrL3WALTQC}}, [http://books.google.com/books?id=JLBrL3WALTQC&pg=PA21 Chapter , p. 21]
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| </ref>
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| * ''The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.'' — [[Karl Popper]], (Popper, CR, 36){{elucidate|date=November 2012}}
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| ==See also==
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| {{div col}}
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| * [[Closed circle]]
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| * [[Cognitive bias]]
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| * [[Contingency]]
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| * [[Defeasible reasoning]]
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| * [[Demarcation problem]]
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| * [[Duhem–Quine thesis]]
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| * [[Fallibilism]]
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| * [[Fallacy]] ([[informal logic]] and [[rhetoric]])
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| * [[False (logic)]]
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| * [[Hypothetico-deductive model]]
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| * [[Inquiry]]
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| * [[Logical positivism]]
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| * [[Metaphysical solipsism]]
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| * [[Methodological solipsism]]
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| * [[Not even wrong]]
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| * [[Occam's razor]]
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| * [[Philosophy of mathematics]]
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| * [[Philosophy of science]]
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| * [[Pragmatic maxim]]
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| * [[Precambrian rabbit]]
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| * [[Predictive power]]
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| * [[Reproducibility]]
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| * [[Scientific method]]
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| * [[Superseded scientific theory]]
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| * [[Tautology (logic)|Tautology]]
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| * [[Testability]]
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| * [[Theory-ladenness]]
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| {{div col end}}
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| ==Notes==
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| {{Reflist|30em}}
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| ==References==
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| {{Refbegin}}
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| * Angeles, Peter A. (1992), ''Harper Collins Dictionary of Philosophy'', 2nd edition, Harper Perennial, New York, NY. ISBN 0-06-461026-8.
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| * Feyerabend, Paul K., ''[[Against Method]]: Outline of an Anarchistic Theory of Knowledge'', Humanities Press, London, UK, 1975. Reprinted, Verso, London, UK, 1978.
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| * Kuhn, Thomas S., ''[[The Structure of Scientific Revolutions]]'', University of Chicago Press, Chicago, IL, 1962. 2nd edition 1970. 3rd edition 1996.
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| * Lakatos, Imre. (1970), "Falsification and the Methodology of Scientific Research Programmes," in [[Criticism and the Growth of Knowledge]], vol. 4. Imre Lakatos and Alan Musgrave (eds.), Cambridge University Press, Cambridge.
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| * Lakatos, Imre (1978), ''The methodology of scientific research programmes: Philosophical papers, volume I.'' Cambridge: Cambridge University Press. ISBN 0-521-28031 -1.
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| * Peirce, C.S., "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part, ''Collected Papers'', CP 5.14–212. Published in full with editor's introduction and commentary, Patricia Ann Turisi (ed.), ''Pragmatism as a Principle and Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism"'', State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), ''The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913)'', Indiana University Press, Bloomington, IN, 1998.
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| * Popper, Karl, ''[[The Logic of Scientific Discovery]]'', Basic Books, New York, NY, 1959.
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| * Popper, Karl, ''[[Conjectures and Refutations]]'', Routledge, London, 1963.
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| * [[Dagobert D. Runes|Runes, Dagobert D.]] (ed.), ''Dictionary of Philosophy'', Littlefield, Adams, and Company, Totowa, NJ, 1962.
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| * Sokal, Alan, and Bricmont, Jean, ''[[Fashionable Nonsense]]'', Picador, New York, NY, 1998.
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| * Theobald, D.L. (2006). [http://www.talkorigins.org/faqs/comdesc/default.html#evidence 29+ Evidences for Macroevolution: The Scientific Case for Common Descent.] ''The Talk.Origins Archive''. Version 2.87.
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| * Wood, Ledger (1962), "Solipsism", p. 295 in Runes (ed.), ''Dictionary of Philosophy'', Littlefield, Adams, and Company, Totowa, NJ.
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| {{Refend}}
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| == External links ==
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| {{Wiktionary}}
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| * [http://www.galilean-library.org/falsificationism.html Problems with Falsificationism] at The Galilean Library
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| {{philosophy of science}}
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| {{Karl Popper}}
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| {{Positivism}}
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| [[Category:Analytic philosophy]]
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| [[Category:Epistemology of science]]
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| [[Category:Epistemological theories]]
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| [[Category:Karl Popper]]
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| [[Category:Razors (philosophy)]]
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