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Falsifiability or refutability of a 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 truthness of 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". Science must be falsifiable.
For example, by the problem of induction, no number of confirming observations can verify a 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.
The concern with falsifiability gained attention by way of philosopher of science Karl Popper's scientific epistemology "falsificationism". Popper stresses the 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 scientifically true is pseudoscience.
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 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. 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.
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.
My proposal is based upon an asymmetry between 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.
Popper stressed that unfalsifiable statements are important in science. Contrary to intuition, unfalsifiable statements can be embedded in - and 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". 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 programs to name such unfalsifiable ideas. 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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In work beginning in the 1930s, Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.
The first are statements of observations, such as "there is a white swan." Logicians call these statements 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.
The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the 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?
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).
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'.
One notices a white swan. From this one can conclude:
From this, one may wish to conjecture:
It is impractical to observe all the swans in the world to verify that they are all white.
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 is different from an absence of verification. The falsification of statements occurs through modus tollens, via some observation. Suppose some universal statement U forbids some observation O:
Observation O, however, is made:
So by modus tollens,
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. W. V. Quine expounded this argument in detail, calling it confirmation holism. To logically falsify a 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 bird watchers are incompetent'.
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 objective criteria, to present a definitive falsification of universal statements.
Falsificationism is a scientific epistemology—that is, a theory of the nature, scope, and development of scientific knowledge—developed by Karl Popper. Falsificationism uses the demarcation of falsifiability to divide the scientific from the unscientific as merely the testable. Within the domain of science, falsificationism encourages imaginative and creative and even bizarre theorizing with the aim of realist explanation of nature, but a theory must forbid some occurrences that in principle can conflict with observations. Popper claimed, thus, that a scientist ought to venture at least one prediction that the theory forbids—a prediction that, if confirmed, will falsify the theory.
Popper's falsificationism has been criticized on a number of grounds. Among the most popular are the mischaracterization of Popper as a naïve falsificationist, advising that a theory be abandoned at any seemingly incompatible data. On the contrary, Popper was a critical falsificationist, advising that a highly successful theory ought to not be abandoned lightly, but be strongly tested.
Another criticism is that scientific theories can always be saved by appendage of ad hoc hypotheses or ad hoc stipulations, such as boundary conditions narrowing the empirical content of the theory, but Popper gave no formal criteria to guide when these are suitable or are pseudoscience. Popper held that scientists must make decisions to accept or reject apparently falsifying statements, and did not intend to restrict them formally, however, as Popper felt that falsificationism was an overall approach to science, not a rigid formula. And the history of science does reveal that, although highly successful or regarded theories are not abandoned lightly, they are indeed abandoned at some point when they are held to be falsified.
Another criticism, stressed by Paul Feyerabend, is that even falsified theories might either be true or at least contain some truths and ought to be revisited in light of new knowledge or technology. Popper himself did indicate that unscientific theories, such as metaphysical theories, are called for to inspire and motivate scientific theorizing and that unscientific theories can later become scientific by evolving knowledge and technology, but Popper apparently did not resolve the dilemma, then, of how even a falsified theory is, then, actually falsified.
In any event, falsificationism holds that that aim of scientific theory is not merely predictive success, since any number of banalities and tautologies can be 100% predictively successful, but that scientific theory's ambition is explanatory power and that this attained by a process of conjectures and refutations, while conjectures have no logic but are creative, while refutations are strong attempts to falsify the theory and reveal its shortcomings so that the theory can fall to development of a theory more explanatorily successful.
For example, Aristotelian physics explained both terrestrial and celestial observations via geocentrism by positing four terrestrial elements whose intrinsic motions—earth and water intrinsically falling by their property gravitas or heaviness, air and fire intrinsically rising by heir property levitas or lightness—were straight lines relative to Earth's center, while accelerating during approach to their natural places. And yet since air does not all leave Earth and attain infinite speed, an apparent absurdity, Aristotle inferred a "pure" celestial element, the fifth element—universal essence, or quintessence, or aether—whose intrinsic motion is perpetual, perfect circles and composes the Universe beyond the sublunary sphere, held in its place by the aether, and Earth's being the motionless center of the Universe explained.
Nicholas Copernicus conjectured heliocentrism to better discover perfect circles in astronomy according to aether's intrinsic motion. Johannes Kepler, however, modified Copernican orbits to ellipses with Kepler's laws of planetary motion. Galilei made telescopic observations that suggested the moon was composed of earthlike substance, not aether, and his mechanical experimentation suggested the principle inertia—whereby any body continues in straight line motion at constant speed unless an outside force acts on it—but, by the principle of relativity or invariance, every inertial frame of reference experiences procession of physical interactions identically and cannot discern whether it is at rest or is in uniform motion.
René Descartes in his Cartesian physics formalized the principle inertia as a universal trait of matter. Descartes shared the Aristotelian aversion to a void and filled all space with an aether explaining transmission of light from Sun to Earth despite the first principle of mechanism, said Descartes, No action at distance. Cartesian cosmology embraced heliocentrism and explained mechanics as by vortex motions within a universal fluid, whereby the Universe contains substance either luminous or opaque or transparent—comprising stars, planets, and darkness, respectively—but the appearance of variances are but variations of extension, speed, and relations and motions of a universal fluid filling all space, not actual particles, the particles being illusory. To explain the mind, Descartes found that thinking substance—which does not extend onto 3D space—can move extended substance, and thereby Cartesian physics failed to include the principle conservation of momentum.
Incorporating Cartesian inertia with Galilean relativity and conserving momentum, Isaac Newton developed the law of universal gravitation, which unified both terrestrial and celestial phenomena to one phenomenon, that is, gravitation—explicitly connecting the terrestrial and celestial with a single law circumscribing motion—but at the expense of violating Cartesian principle No action at a distance. Gottfried Leibniz rejected Newton's theory as the proposal that matter exhibited an occult property, and insisted that there must be some hidden mechanism, perhaps a subtle stubstance carrying the planets through their orbits. New rejected the concept of aether, and presumed that space was normally empty, so as to not interference with the putative force gravitation traversing the entire universe at instant speed, instant interaction at a distance.
Christian Huygens, too, rejected Newton's theory, but on the ground that Huygens's wave theory of light called for a luminiferous aether—an invisible medium filling all space—whose oscillations were the mechanical basis of light. Newton himself in his Optiks, his more speculative work, introduced an aether as well, if for differing reasons, as Newton proposed a particle theory of light. Michael Faraday proposed the existence of field to explain magnetic field lines, and James Clerk Maxwell developed this theory, unifying electricity and magnetism to an electromagnetic field theory, which held visible light as a consequence. Maxwell presumed that the electromagnetic field was an aspect of the aether. The Michelson-Morley experiments of 1887 sought to measure the speed of Earth relative to aether, but apparently returned a null result, none detectable. This is popularly conceived as falsifying existence of the aether, but falsified only some of its possible traits.
In 1905, accepting both Maxwell's electromagnetic field theory and Galilean relativity as empirically accurate, Einstein discarded the aether as an empty hypothesis and, in doing so, relativized both space and time in his special theory of relativity. And yet that left Newton's gravitational theory untenable, as Newton postulated absolute space and time. To explain gravitation, Einstein reintroduced an aether—the gravitational field, space and time themselves, 4D spacetime—which receives motion from bodies and transmits it to other bodies while its gravitational waves traverse the universe at the speed of the electromagnetic field, no action at a distance. Via general relativity, perhaps its greatest advocate, Arthur Eddington, explained that the aether is simply relativistic, explaining the null data in the Michelson-Morley experiment. Aiming to improve upon falsificationism, Imre Lakatos introduced his explanation of the methodology of scientific research programs.
Popper uses falsification as a 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.
Popper claimed that, if a theory is falsifiable, then it is scientific.
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 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.
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. 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.
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.
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.
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 schools 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."
Adherents of Popper speak with disrespect of "professional philosophy", for example W. W. Bartley:
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.
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.
and David Miller:
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.
Nevertheless, many contemporary philosophers of science and analytic philosophers are strongly critical of Popper's philosophy of science. 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 probabilistic induction, which is the mainstream account of scientific reasoning.
Whereas Popper was concerned in the main with the logic of science, 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.
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.
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.
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.
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.
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)
They further argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions that are sometimes incorrect.
David Miller, a contemporary philosopher of critical rationalism, has attempted to defend Popper against these claims. 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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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.
Some economists, such as those of the Austrian School, believe that macroeconomics is empirically unfalsifiable and that thus the only appropriate means to understand economic events is by logically studying the intentions of individual economic decision-makers, based on certain fundamental truths. 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.
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 "fossil rabbits in the Precambrian era". Richard Dawkins adds that any other modern animal, such as a hippo, would suffice.
Karl Popper at first spoke against the testability of natural selection  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."
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", and argued that neither Marxism nor psychoanalysis was science, 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.
Many philosophers[weasel words] believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper. 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, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently." Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.
Like all formal sciences, mathematics is not concerned with the validity of theories based on observations in the empirical world, but rather, mathematics is occupied with the theoretical, abstract study of such topics as quantity, structure, space and 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.”
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