A statement, hypothesis, or theory has falsifiability (or is falsifiable) if it is contradicted by a basic statement, which, in an eventual successful or failed falsification, must respectively correspond to a true or hypothetical observation. For example, the claim "all swans are white and have always been white" is falsifiable since it is contradicted by this basic statement: "In 1697, during the Dutch explorer Willem de Vlamingh expedition, there were black swans on the shore of the Swan River in Australia", which in this case is a true observation. The concept is also known by the terms refutable and refutability.
The concept was introduced by the philosopher of science Karl Popper. He saw falsifiability as the logical part and the cornerstone of his scientific epistemology, which sets the limits of scientific inquiry. He proposed that statements and theories that are not falsifiable are unscientific. Declaring an unfalsifiable theory to be scientific would then be pseudoscience.
- 1 Overview
- 2 Definition
- 3 Naïve falsification
- 4 Falsificationism
- 5 Criterion of demarcation
- 6 Unfalsifiable statistics/double evidence standards combo
- 7 Criticisms
- 8 Controversies
- 9 Quotations
- 10 See also
- 11 Notes
- 12 References
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. The Inductivist methodology supposes that one can somehow move from a series of statements such as 'here is a white swan', 'over there is a white swan', and so on, to a universal statement such as 'all swans are white'. As observed by David Hume, Immanuel Kant and later by Popper and others, 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). This is known as the problem of induction.
One solution to the problem of induction, proposed by Immanuel Kant in Critique of Pure Reason, is to consider as valid, absolutely a priori, the conclusions that we would otherwise have drawn from these dubious inferential inductions. Following Kant, Popper accepted that we have to work with unproven hypotheses, but he refused that we have to justify them in any way and he wrote (Popper 1959, p. 6): "I do not think that his ingenious attempt to provide an a priori justification for synthetic statements was successful." However, if one finds one single swan that is not white, 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 or trying to view them as valid in any way.
For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come into conflict with observation. A key observation of falsificationism is thus that a criterion of demarcation is needed to distinguish those statements that can come into conflict with observation and those that cannot, but the criterion itself concerns only the logical form of the theory:
I shall require that [the] logical form [of the theory] shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.— Karl Popper, Popper 1959. p 19
Popper always insisted on a clear distinction between the logic (of falsifiability) and its applied less precise methodology., The required logical form, the criterion, is that there must exist basic statements that contradict the theory (and also some that corroborate it because the theory must be consistent). This logical form informally implies the possibility of refutations by experience because, in its informal methodological context, a basic statement must be intersubjective and interpretable in terms of observations.
Objections can be raised against falsifiability as a criterion of demarcation similar to those which can be raised against verifiability. For example, as pointed out by many and reformulated by Colin McGinn,
[w]e have to be able to infer that if a falsifying result has been found in a given experiment it will be found in future experiments; ... this is clearly an inductive inference.— Colin McGinn, McGinn 2002, sec. 3
Very early, in anticipation of this specific objection Popper wrote,
This attack would not disturb me. 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.— Karl Popper, Popper 1959. p 19
In its simple form, the point here is that although a singular existential statement such as 'there is a white swan in Europe' cannot be used to affirm a universal statement, it can be used to show that one is false: the statement 'there is a non white swan in Australia' implies that the universal statement 'all swans are white' is false. Moreover, this singular existential statement is empirical: it is impractical to observe all the swans in the world to verify that they are all white, but one can observe one swan that is not white. This shows the fundamental difference between verifiability and falsifiability. Also, in the logical form of the theory, there is no notion of future experiments, but only a (formal) class of basic statements that contradict it.
Such a simple contradiction with a basic statement is not what Popper calls a falsification. A falsification usually entails a derivation from a system of statements, which include the universal statement and initial conditions, to a singular statement, which is contradicted by a falsifying hypothesis, but the argument can be generalized. Popper explains
... it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to universal statements.— Karl Popper, Popper 1959, p. 19
The falsifiability criterion does not imply that unfalsifiable systems such as logic, mathematics and metaphysics are not parts of 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 "all men die 150 years after their birth at the latest". 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 that guide the search for a new theory.
Thus falsificationism has two levels. At the logical level, scientists use deductive logic to attempt to falsify theories. At the non-logical level, they decide on some criteria, which use falsification and other factors, to pick which theories they will study, improve, replace, apply or (further) test. These other criteria may take into account a metaphysical research program. They are not considered in the formal falsifiability criterion, but they can give a meaning to this criterion. Needless to say, for Popper, these other criteria, the so-called rules of the game, are necessary. Some philosophers consider them as parts of Popper's demarcation criterion, but Popper viewed them only as a necessary context.
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 critical rationalism, 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.
For Popper (and others) in any scientific discussion we accept a background knowledge. Such a background knowledge is thus implicit in the definition of falsifiability and corresponds to different types of statements, their relationship and their interpretation in terms of observations and measurements.
Different types of statements
Recall that a theory is falsifiable if it is contradicted by a basic statement. It remains to define what kind of statements create theories and what are basic statements. Scientific theories are a particular kind of universal statements. Basic statements are particular kind of existential statements. Not all universal statements are theories and not all existential statements are basic statements. Theories have the form of strictly universal statements. Basic statements have the form of singular existential statements. Thus we need to distinguish between existential and universal statements and also between singular and strict statements.
Existential and universal statements are built-in concepts in logic. The first are statements such as "there is a white swan". Logicians call these statements existential statements, since they assert the existence of something. They are equivalent to a first-order logic 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.
Unlike existential and universal statements, singular and strict statements are not built-in concepts in logic, because they correspond to a specific perspective on our experience of the world. We can understand them in terms of the concepts of universal or individual names:
... ‘dictator’, ‘planet’, ‘H2O’ are universal concepts or universal names. ‘Napoleon’, ‘the earth’, ‘the Atlantic’ are singular or individual concepts or names. In these examples individual concepts or names appear to be characterized either by being proper names, or by having to be defined by means of proper names, whilst universal concepts or names can be defined without the use of proper names.— Karl Popper, Popper 1959, pp. 42–43
A statement is strict or pure, if it does not use any individual name. So, a law of nature cannot refer to particular things. The sentence "This apple is attracted by the planet earth" is not a scientific statement. Popper wrote an entire section on strictly universal and strictly existential statements, because he considers the distinction between universal and individual concepts or names to be of fundamental importance.
A statement is singular if it contains an individual name or the equivalent. So, a basic statement must make reference to a specific thing or specific location and time. The sentence "There exists a black swan" is not a basic statement, but the statement "There is a black swan on the shore of the Swan River" is a basic statement, it is a singular existential statement.
Popper arrived at these conditions through an analysis of what one expects from basic statements. In addition, a basic statement must be inter-subjective. So, "John saw a black swan on the shore of the Swan River" is not a basic statement.
Methodological rules and falsifying hypotheses
Falsifiability is defined strictly in terms of the logical form of the theory, but this criterion of demarcation can not work without being complemented by methodological rules. Thus, contemporary philosophers consider that Popper's demarcation criterion has two parts: the logical part (stated in terms of rules of inference - ways to logically infer new statements from existing statements) and the methodological part (stated in terms of rules that do not claim to prove anything). The methodological rules define falsification. They should not be confused with the (logical) rules of inferences used to define falsifiability, which is about the logical form of the theory.
In this larger picture, the fact that a single basic statement can contradict a strictly universal statement, though true logically, is in itself useless, because it cannot lead to a falsification. To support falsification, Popper requires that a class of basic statements corroborate a falsifying hypothesis. A basic statement corroborates the falsifying hypothesis, if it does not logically contradict it, but contradicts the theory to be falsified. Though it corresponds to the empirical notion of reproducible experiments, this requirement exists entirely at the formal level and must be complemented by methodological rules in a falsification process.
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 incremental process whereby theories become less bad.
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 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.
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.
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In place of naïve falsification, Popper envisioned science as progressing 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, Aristotelian mechanics explained observations of everyday situations, but were falsified by Galileo's experiments, 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 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 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, quanta and Heisenberg's uncertainty principle.
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.
Criterion of demarcation
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 is only concerned with meaningful statements.
Use in courts of law
Falsifiability has been used in the McLean v. Arkansas case (in 1982), the Daubert case (in 1993) and other cases (see below). A survey of 303 federal judges conducted in 1998 (and fully reported in Krafka 2002) revealed that "[P]roblems with the nonfalsifiable nature of an expert’s underlying theory and difficulties with an unknown or too-large error rate were cited in less than 2% of cases."
The McLean v. Arkansas case
In the ruling of the McLean v. Arkansas case, Judge William Overton used falsifiability 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 testimony, philosopher Michael Ruse defined the characteristics which constitute science as (see Pennock 2000, p. 5 and Ruse 2010):
- It is guided by natural law;
- It has to be explanatory by reference to natural law;
- It is testable against the empirical world;
- Its conclusions are tentative, i.e., are not necessarily the final word; and
- It is falsifiable.
In his conclusion related to this criterion Judge Overton stated that
While 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.— William Overton, McLean v. Arkansas 1982, at the end of section IV. (C)
The Daubert case
In the Daubert case, the majority opinion proposed the so-called five Daubert factors, which include falsifiability, to define a scientific methodology that is acceptable in courts of law. These original Daubert factors have been cited in the Kumho Tire Co. v. Carmichael case and in the U.S. v. PRIME case (United States v. Prime 2002). In the Daubert case, Associate Justice Harry Blackmun, delivering the majority opinion of the United States Supreme Court, has cited Popper and other philosophers of science:
Ordinarily, a key question to be answered in determining whether a theory or technique is scientific knowledge that will assist the trier of fact will be whether it can be (and has been) tested. Scientific methodology today is based on generating hypotheses and testing them to see if they can be falsified; indeed, this methodology is what distinguishes science from other fields of human inquiry. Green 645. See also C. Hempel, Philosophy of Natural Science 49 (1966) ([T]he statements constituting a scientific explanation must be capable of empirical test); K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge 37 (5th ed. 1989) ([T]he criterion of the scientific status of a theory is its falsifiability, or refutability, or testability) (emphasis deleted).— Harry Blackmun, Daubert v. Merrell Dow Pharmaceuticals, Inc. 1993, p. 593
I defer to no one in my confidence in federal judges; but I am at a loss to know what is meant when it is said that the scientific status of a theory depends on its falsifiability, and I suspect some of them will be, too.— William Rehnquist, Daubert v. Merrell Dow Pharmaceuticals, Inc. 1993, p. 600
Professor of Law David H. Kaye argued that references to the Daubert majority opinion confused falsifiability and falsification and that "inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations."
Unfalsifiable statistics/double evidence standards combo
There are combinations of prediction types and methodologies that, while each component is compatible with falsifiability on its own, renders falsification impossible together.
One example is the combination of statistical predictions in which individual exceptions do not falsify the theory, with different evidence standards for different data points in which one type of data point only require ordinary evidence while another require extraordinary evidence.
On one hand, the theory that there are no black swans is falsifiable even if there is a requirement of extraordinary evidence for a black swan, since it is not impossible for an individual observation of a black swan to eventually meet the requirement of extraordinary evidence. On the other hand, in a country where there are, in reality, the same number of black swans as white swans, the theory that there are more white swans than black swans at a population level with individual exceptions is falsifiable - as long as the level of evidence required to record a white swan is the same as that for recording black swans. But if the theory is that white swans are more statistically common than black swans with exceptions and a higher level of evidence is required for recording a black swan than for recording a white swan, the difference in evidence standards will cause more white swans than black swans to be recorded even in a country where the ratio is in fact 50/50. This makes the combination of statistical prediction with exceptions and differences in evidence standards incompatible with falsifiability.
This have been implicated in the replication crisis, especially in psychology in which the two methodologies are more common than in other fields and therefore more often combine to prevent falsifiability even though the two factors are not unheard of on their own in other fields. The problem of falsifiability can also be caused by the active application of methodologies, and therefore spreading issues to other fields that psychology interacts with through interdisciplines, such as evolutionary psychology spreading the problems to evolution research. One solution is to allow other fields to help falsifiability in psychology, as would have been possible had the problem been a passive lack of components for falsifiability.
Several contemporary philosophers of science and analytic philosophers are strongly critical of Popper's philosophy of science.[better source needed] Popper's mistrust of inductive reasoning has led to claims that he misrepresents scientific practice.
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.
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.
Kuhn and Lakatos
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.
Sokal and Bricmont
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.
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 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."
Much of the criticism against young-Earth creationism is based on evidence in nature that the Earth is much older than adherents believe. Confronting such evidence, some adherents make an argument (called the Omphalos hypothesis) that the world was created with the appearance of age; e.g., the sudden appearance of a mature chicken capable of laying eggs. This hypothesis is non-falsifiable since no evidence about the age of the earth (or any astronomical feature) can be shown not to be fabricated during creation.
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.
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."
- Albert Einstein is reported to have said something that can be paraphrased into, no amount of experimentation can ever prove me right; a single experiment can prove me wrong.
- Popper said in Conjectures and Refutations,
... the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.— Popper
- Black swan theory
- Critical rationalism
- Defeasible reasoning
- Duhem–Quine thesis
- Experimentum crucis
- Explanatory power
- Fallacy (informal logic and rhetoric)
- Raven paradox, or Hempel's paradox
- Hypothetico-deductive model
- Metaphysical solipsism
- Methodological solipsism
- Occam's razor
- Philosophy of mathematics
- Philosophy of science
- Pragmatic maxim
- Precambrian rabbit
- Predictive power
- Russell's teapot
- Superseded scientific theories
- Newton's Flaming Laser Sword
- Popper 1983, p. XXII: "We must distinguish two meanings of the expressions falsifiable and falsifiability:
"1) Falsifiable as a logical-technical term, in the sense of the demarcation criterion of falsifiability. This purely logical concept ��� falsifiable in principle, one might say — rests on a logical relation between the theory in question and the class of basic statements (or the potential falsifiers described by them).
"2) Falsifiable in the sense that the theory in question can definitively or conclusively or demonstrably be falsified ("demonstrably falsifiable").
"I have always stressed that even a theory which is obviously falsifiable in the first sense is never falsifiable in this second sense. (For this reason I have used the expression falsifiable as a rule only in the first, technical sense. In the second sense, I have as a rule spoken not of falsifiability but rather of falsification and of its problems)"
- For an actual falsification to occur, the basic statement must be reproducible. See Popper 1959, p. 66: "We say that a theory is falsified only if we have accepted basic statements which contradict it (cf. section 11, rule 2). This condition is necessary, but not sufficient; for we have seen that non-reproducible single occurrences are of no significance to science. Thus a few stray basic statements contradicting a theory will hardly induce us to reject it as falsified. We shall take it as falsified only if we discover a reproducible effect which refutes the theory. In other words, we only accept the falsification if a low-level empirical hypothesis which describes such an effect is proposed and corroborated. This kind of hypothesis may be called a falsifying hypothesis."
- Back in those days it was assumed that everyone (in Europe) believed that swans had to be white (Life On Perth 2007), but this changed, because this basic statement is reproducible: swans can be seen at different times and locations.
- Popper put as an example of falsifiable statement with failed falsifications Einstein's equivalence principle. See Popper 1983, p. XX: "Einstein's principle of proportionality of inert and (passively) heavy mass. This equivalence principle conflicts with many potential falsifiers: events whose observation is logically possible. Yet despite all attempts (the experiments by Eötvös, more recently refined by Rickle) to realize such a falsification experimentally, the experiments have so far corroborated the principle of equivalence."
- Popper 1989, pp. 82-85.
- Popper 1959, p. 4 : "Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusion drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white."
- In Kant 1787, sec II, B4: "If, therefore, a judgment is thought with strict universality, i.e., so that no exception at all is allowed to be possible, then it is not derived from experience, but is valid absolutely a priori."
- Popper 1959, p. 9: "According to the view that will be put forward here, the method of critically testing theories, and selecting them according to the results of tests, always proceeds on the following lines. From a new idea, put up tentatively, and not yet justified in any way—an anticipation, a hypothesis, a theoretical system, or what you will—conclusions are drawn by means of logical deduction. These conclusions are then compared with one another and with other relevant statements, so as to find what logical relations (such as equivalence, derivability, compatiblity, or incompatibility) exist between them."
- Thornton 2016, Sec. 3: "Popper has always drawn a clear distinction between the logic of falsifiability and its applied methodology."
- Popper 1959, section 23, 1er paragraphe : "The requirement of falsifiability which was a little vague to start with has now been split into two parts. The first, the methodological postulate (cf. section 20), can hardly be made quite precise. The second, the logical criterion, is quite definite as soon as it is clear which statements are to be called ‘basic’."
- Miller 2014, p. 4.
- Popper 1959, pp. 66–67: "The requirement that the falsifying hypothesis must be empirical, and so falsifiable, only means that it must stand in a certain logical relationship to possible basic statements; thus this requirement only concerns the logical form of the hypothesis."
- Popper 1959, p. 66, sec. 22: "We must clearly distinguish between falsifiability and falsification. We have introduced falsifiability solely as a criterion for the empirical character of a system of statements. As to falsification, special rules must be introduced which will determine under what conditions a system is to be regarded as falsified."
- (Popper 1959, p. 55): "We may distinguish, within a theoretical system, statements belonging to various levels of universality. The statements on the highest level of universality are the axioms; statements on the lower levels can be deduced from them. Higher level empirical statements have always the character of hypotheses relative to the lower level statements deducible from them: they can be falsified by the falsification of these less universal statements. ... The falsifying mode of inference here referred to—the way in which the falsification of a conclusion entails the falsification of the system from which it is derived—is the modus tollens of classical logic. It may be described as follows: Let p be a conclusion of a system t of statements which may consist of theories and initial conditions ..."
- Popper 1972, Chapter 1.
- Thornton 2016: "For Popper, however, to assert that a theory is unscientific, is not necessarily to hold that it is unenlightening, still less that it is meaningless, for it sometimes happens that a theory which is unscientific (because it is unfalsifiable) at a given time may become falsifiable, and thus scientific, with the development of technology, or with the further articulation and refinement of the theory. Further, even purely mythogenic explanations have performed a valuable function in the past in expediting our understanding of the nature of reality."
- Keuth 2004, p. 45.
- Popper 1982, Introductory comments.
- Popper 1963, p. 26: "The proper answer to my question 'How can we hope to detect and eliminate error?' is, I believe, 'By criticizing the theories or guesses of others and--if we can train ourselves to do so--by criticizing our own theories or guesses.' (The latter point is highly desirable, but not indispensable; for if we fail to criticize our own theories, there may be others to do it for us.) This answer sums up a position which I propose to call 'critical rationalism'."
- Popper 1963, p. 238: While discussing a problem we always accept (if only temporarily) all kinds of things as unproblematic: they constitute for the time being, and for the discussion of this particular problem, what I call our background knowledge."
- Popper 1959, p. 84: "... that is to say, basic statements must be testable, inter-subjectively, by ‘observation’. Since they are singular statements, this requirement can of course only refer to observers who are suitably placed in space and time (a point which I shall not elaborate)."
- Popper 1959, p. 37: " The empirical sciences are systems of theories. The logic of scientific knowledge can therefore be described as a theory of theories. Scientific theories are universal statements."
- Popper 1959, pp. 83–84: "A statement of the form ‘There is a so-and-so in the region k’ or ‘Such-and-such an event is occurring in the region k’ (cf. section 23) may be called a ‘singular existential statement’ or a ‘singular there-is statement’. And the statement which results from negating it, i.e. ‘There is no so-and-so in the region k’ or ‘No event of such-and-such a kind is occurring in the region k’, may be called a ‘singular non-existence statement’, or a ‘singular there-is-not statement’. We may now lay down the following rule concerning basic statements: basic statements have the form of singular existential statements."
- Popper 1959, p. 48: "The theories of natural science, and especially what we call natural laws, have the logical form of strictly universal statements; thus they can be expressed in the form of negations of strictly existential statements or, as we may say, in the form of non-existence statements (or ‘there-is-not’ statements). For example, the law of the conservation of energy can be expressed in the form: ‘There is no perpetual motion machine’, or the hypothesis of the electrical elementary charge in the form: ‘There is no electrical charge other than a multiple of the electrical elementary charge’."
- Popper 1959, p. 42.
- Popper 1959, pp. 47-50.
- Popper 1959, p. 43.
- This is Popper's definition. There is no well established definition of singular statement, singular sentence or singular proposition. For example, Stanford Encyclopedia of Philosophy says that it is a sentence without variables, free or bound. This is also the definition adopted by Alfred Tarski in Introduction to logic and to the methodology of deductive sciences. However, in the debate between Fregeans and Russellians in the philosophy of language, the definition is more restrictive: a singular sentence means a sentence with a single subject that respects a property such as "Mont Blanc is more than 4000 meters high" - see "Singular Propositions and Singular Thoughts" by Arthur Sullivan.
- Popper 1959, p. 83.
- Popper 1959, p. 84.
- Unless, of course, the theory is about people seeing black swans, in which case, we view John as a thing, just as the shore is a thing.
- Popper 1959, pp. 28–29: "If therefore we characterize empirical science merely by the formal or logical structure of its statements, we shall not be able to exclude from it that prevalent form of metaphysics which results from elevating an obsolete scientific theory into an incontrovertible truth. Such are my reasons for proposing that empirical science should be characterized by its methods: by our manner of dealing with scientific systems: by what we do with them and what we do to them. Thus I shall try to establish the rules, or if you will the norms, by which the scientist is guided when he is engaged in research or in discovery, in the sense here understood."
- Thornton 2016, sec. 3: "Popper has always drawn a clear distinction between the logic of falsifiability and its applied methodology. The logic of his theory is utterly simple: if a single ferrous metal is unaffected by a magnetic field it cannot be the case that all ferrous metals are affected by magnetic fields. Logically speaking, a scientific law is conclusively falsifiable although it is not conclusively verifiable. Methodologically, however, the situation is much more complex: no observation is free from the possibility of error—consequently we may question whether our experimental result was what it appeared to be."
- Popper 1959. p.19: "It might be said that even if the asymmetry [between universal and existential statements] is admitted, it is still impossible, for various reasons, that any theoretical system should ever be conclusively falsified. For it is always possible to find some way of evading falsification, for example by introducing ad hoc an auxiliary hypothesis, or by changing ad hoc a definition. It is even possible without logical inconsistency to adopt the position of simply refusing to acknowledge any falsifying experience whatsoever. Admittedly, scientists do not usually proceed in this way, but logically such procedure is possible; and this fact, it might be claimed, makes the logical value of my proposed criterion of demarcation dubious, to say the least."
- Popper 1959, p. 18, footnote 3: "Falsifiability separates two kinds of perfectly meaningful statements: the falsifiable and the non-falsifiable. It draws a line inside meaningful language, not around it."
- Surveys were mailed to all active U.S. district court judges in November 1998 (N = 619). Only 303 usable surveys were obtained for a response rate of 51% (see Krafka 2002).
- The Daubert case and subsequent cases that used it as a reference, including General Electric Co. v. Joiner and Kumho Tire Co. v. Carmichael, resulted in an amendment of the Federal Rules of Evidence (see Rules of Evidence 2017, p. 15, Rule 702 and Rule 702 Notes 2011). The Kumho Tire Co. v. Carmichael case and other cases considered the original Daubert factors, but the amended rule, rule 702, even though it is often referred to as the Daubert standard, does not include the original Daubert factors or mention falsifiability or testability and neither does the majority opinion delivered by William Rehnquist in the General Electric Co. v. Joiner case.
- Not to be confused with David Kaye (law professor), United Nations special rapporteur. David H. Kaye is distinguished professor of law at Penn State Law.
- Kaye 2005, p. 2: "... several courts have treated the abstract possibility of falsification as sufficient to satisfy this aspect of the screening of scientific evidence. This essay challenges these views. It first explains the distinct meanings of falsification and falsifiability. It then argues that while the Court did not embrace the views of any specific philosopher of science, inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations. Consequently, it concludes that recent opinions substituting mere falsifiability for actual empirical testing are misconstruing and misapplying Daubert."
- Critical Rationalism: A Restatement and Defence | David Miller, 2015
- A Vast Graveyard of Undead Theories: Publication Bias and Psychological Science’s Aversion to the Null | Christopher J. Ferguson, Moritz Heene, Texas A&M International University and Ludwig Maximilian University Munich, Germany, 2012
- Martin Gardner (2001), "A Skeptical Look at Karl Popper," Skeptical Inquirer, 25(4): 13–14, 72.
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- Champion, Rafe (2013). Reason and Imagination (Critical Rationalist Papers Book 2). ASIN B00CGETUCM.
Philosophers' talk about rationality is apt to soar into the stratosphere of abstractions so it must be stated that Bartley's approach has immediate and practical applications. Following his teacher, Karl Popper, the operating principle of Bartley's rationalism is the formula 'I may he wrong and you may be right, and by means of critical discussion we may get nearer to the truth of the matter'. This simple principle of rationality requires philosophical defence in depth, backed up by a wide range of improved traditions and institutions to sustain the flow of ideas and critical discussion. These vehicles already exist of course, if only in rudimentary forms, among them talk-back radio, the range of serious 'little magazines' and programs on TV which allow opposing points of view to be explored and debated. These forums are vitally important despite all their imperfections and lapses into the trivial and the banal; the important thing is that they exist, not that they should be scrupulously fair and unbiased at all times nor that they confine themselves to matters of great moral and intellectual moment. Bartley has provided philosophical air support for the footsoldiers of rationality. He offers a solution to the basic logical problem of rationality, namely how can we justify the basic premise of rationality, that is, the principle of rationality itself, the principle that we should engage in critical discussion to seek for rationally defensible beliefs?
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- Thornton 2016: "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."
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|Look up falsifiability in Wiktionary, the free dictionary.|
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