# Falsifiability

The observation of these black swans contradicts the law "All swans are white", but even if there were no black swans, the law would still be falsifiable, because identifying a swan and observing the color black would remain possible.

Informally, a statement is falsifiable if some observation might show it to be false. For example, "All swans are white" is falsifiable because "Here is a black swan" shows it to be false. The apparent contradiction[A] seen in the case of a true but falsifiable statement disappears once we know the technical definition.[B]

Falsifiability differs from verifiability, which was held as fundamental by many philosophers such as those of the Vienna Circle. In order to verify the claim "All swans are white" one would have to observe every swan, which is not possible, whereas the single observation "Here is a black swan" is sufficient to falsify it.

It was introduced by the philosopher of science Karl Popper in his book The Logic of Scientific Discovery (1934), as an answer to both the Problem of Induction and the Demarcation Problem. He saw falsifiability as the cornerstone of critical rationalism, his theory of science.[1]

As a key notion in the separation of science from non-science, it has featured prominently in many scientific controversies and applications, even being used as legal precedent.

## Critical rationalism as a solution to the problem of induction

Popper noticed that two types of statements are of particular value to scientists. The first are statements of observations, such as 'this is a white swan'. Logicians describe such statements in terms of existential quantification, since they assert the existence of some particular thing. For Popper, such statements form the empirical basis of scientific theory.[2] The second type of statement of interest to scientists categorises all instances of something, for example "All swans are white". Logicians describe these in terms of universal quantification.

One of the questions in Scientific method is: how does one move from observations to laws? From an existential statement to a universal statement? This is the problem of induction. Suppose we want to put the theory that all swans are white to the test. We come across a white swan. We cannot validly argue from "here is a white swan" to "all swans are white"; doing so would be to affirm the consequent[3].

Popper's solution to this problem is to flip it upside down. He noticed that while it is impossible to verify that every swan is white, finding a single black swan shows that not every swan is white. We might tentatively accept the proposal that every swan is white, while looking out for examples of non-white swans that would show our conjecture to be false. This is the basis of critical rationalism.

Falsification uses the valid inference modus tollens: if from a statement ${\displaystyle P}$ (say some law with some initial condition) we logically deduce ${\displaystyle Q}$, but what is observed is ${\displaystyle \neg Q}$, ${\displaystyle P}$ is false. For example, given the law "all swans are white" and the initial condition "there is a swan here", we can deduce "the swan here is white", but if what is observed is "the swan here is not white" (say black), then "all swans are white" is false, or it was not a swan[C].

Popper was aware that a too simplistic view on critical rationalism would be subject to valid criticisms. Lakatos, realizing that Popper's critical rationalism was misundertood, contrasted it with weaker versions, which he called dogmatic falsificationism and naive falsificationism.[4] Popper's critical rationalism is not (and never has been) one of these two weak versions.[D] Also, on the terminological side of this issue, Popper nerver used the term "falsificationism"[E] and proposed instead the term "critical rationalism".[F]

### Away from dogmatic falsificationism

A dogmatic falsificationist ignores that every observation is theory impregnated. This leads to the critique that we cannot tell which theory is falsified. Is it the one that is being studied or the one behind the observation?[G] This is sometimes called the 'Duhem–Quine problem'. An example is Galileo's refutation of the time-honoured theory that celestial bodies are faultless crystal balls. Many considered that it was the optical theory of the telescope that was false, not the theory of celestial bodies. A dogmatic falsificationist ignores a more subtle fact: only statements can contradict statements. So, it is fundamentally incorrect to say that an observation contradicts a theory.

A dogmatic falsificationist further ignores the role of auxiliary hypotheses, which could explain the contradicting observation. For the falsification to logically occur, we need a ceteris paribus clause, which says that no auxiliary hypothesis is responsible for the contradicting observation. Again, this leads to the critique that we cannot tell if it is the theory or the ceteris paribus clause that is false. Lakatos gives the example of the path of a planet. If the path contradicts Newton's law, we will not know if it is Newton's law that is false or the assumption that no other body influenced the path. Popper was aware that one can always find another auxiliary hypothesis[H], though he clearly distinguished falsifiable theories such as Newton theory and non falsifiable theories on this respect.[I]

Lakatos explains that Popper's solution to these valid criticisms against dogmatic falsificationism requires that we relax the dogmatic assumption that an observation can show a theory to be false[J] :

If a theory is falsified [in the usual sense], it is proven false; if it is falsified [in the technical sense], it may still be true.

— Imre Lakatos, Lakatos 1978, p. 24

Methodological falsificationism replaces the contradicting observation in a falsification with a "contradicting observation" accepted by convention among scientists, a convention that implies three decisions: the theory underlying the observation is correct, no auxiliary hypotheses explain this observation and the written form of the observation matches with an actual observation.[K] These observation or basic statements constitute the empirical "basis". The empirical basis thus depends on decisions made by scientists in view of the currently accepted technology and its associated theory. So, Popper says that "Science does not rest upon solid bedrock".[L]

### Away from naive falsificationism

Naive falsificationism is the claim that methodological falsifications can by themselves explain how we gain scientific knowledge. Very often we must deal with two or more competing theories which can both be non-falsified (say by not making the proper decisions). Considering only falsifications, we can not explain why we pick one theory above the other. We can not explain why often a corroborating experiment is seen as a sign of progress. Popper's falsificationism or critical rationalism use both falsifications and corroborations to explain progress in science.[M] How corroborations and falsifications can explain progress in science was a subject of disagreement between many philosophers, especially between Lakatos and Popper.[N]

Popper clearly distinguished between the creative and informal process from which theories emerge and the logical and formal process where theories are falsified or corroborated.[O][P][Q] The main issue is whether the decision to select a theory among competing theories in the light of falsifications and corroborations should be moved in the logical part as some kind of formal logic.[R] It is a delicate question, because this logic could be considered as inductive: it selects a universal law in view of instances. The answer of Lakatos and many others to that question is that it should.[S][T] In contradistinction, for Popper, the creative and informal part is guided by methodological rules, which naturally say to favor theories that are corroborated[U], but this methodology can hardly be made rigorous.[V] Popper does not mention corroborations when he describes the purely logical part.[W]

Popper's way to analyze progress in science was through the concept of verisimilitude, a way to define how close a theory is to the truth, which he did not consider very significant, except (as an attempt) to clarify a concept already clear in practice. Later, it was shown that the specific definition proposed by Popper cannot distinguish between two theories that are false, which is the case for all theories in the history of science.[X] Today, there is still on going research on the general concept of verisimilitude.[5]

## Demarcation problem

Given an empirical basis, the criterion of demarcation draws a sharp line between those theories that are scientific, and those that are un-scientific. 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. Popper claimed that, if a theory is falsifiable, then it is scientific.

The demarcation criterion excludes theories that we cannot declare scientific, but it does not say which scientific theories we must keep. For Popper, no methodology rigorously describes the choices made by scientists and he never tried to prescribe such a methodology: he always insisted that the methodology can hardly made rigorous. In particular, a scientific theory that is falsified remains scientific and can still be used in science. This view was in contradistinction to the claimed rigor of the inductive methodology of the logical positivists.

### Historical context : logical positivism

In the philosophy of science, verificationism holds that a statement must, in principle, be empirically verifiable in order that it be scientific. This was an essential feature of the logical positivism of the so-called Vienna Circle, which included such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath, and 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: a statement that could not be verified was considered meaningless and thus useless. 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.

### Demarcation and growth of knowledge

In contradistinction with the verificationists, Popper never meant that science grows by applying rules to scientific statements or theories only. In Popper's view, unfalsifiable systems such as logic, mathematics and metaphysics play a role in the growth of science. He wrote that important metaphysical research programmes have influenced the development of physics since the days of Pythagoras and Heraclitus.[6] Thornton explains[7] that science, like virtually every other human, and indeed organic, activity, Popper believes, consists largely of problem-solving. Science, in Popper’s view, starts with problems rather than with observations. Problems emerge from internal conflicts in the theory, between the theory and the metaphysical program or between the theory and observations.[Y] In the latter case, these observations do not come first. Thornton writes that, for Popper, "it is in the context of grappling with a problem that the scientist makes observations in the first instance: his observations are selectively designed to test the extent to which a given theory functions as a satisfactory solution to a given problem."

## Controversies

### Kuhn

Thomas Kuhn emphasized aspects of science that were not much considered by Popper. In particular, he analyzed what he calls periods of normal science as well as revolutions from one period of normal science to another, whereas Popper's view is that only revolutions are relevant. For Popper, the role of science, mathematics and metaphysics, actually the role of any knowledge, is to solve puzzles. In the same line of thought, Kuhn observes that in periods of normal science the accepted scientific theory is used to routinely solve puzzles and its validity is hardly in question. It's only when important new puzzles emerge that cannot be solved by the accepted theory that a revolution might occur. This can be seen as a viewpoint on the distinction made by Popper between the informal and formal process in science (see #Away_from_naive_falsificationism). In the big picture presented by Kuhn, the routinely solved puzzles are corroborations. Falsifications or otherwise unexplained observations are unsolved puzzles. All of these are used in the informal process that generates a new theory. Kuhn says that Popper emphasizes formal or logical falsifications and fails to explain how the social and informal process works.

### Feyerabend

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.[8] 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.[9]

### Sokal and Bricmont

In their book Fashionable Nonsense (from 1997, published in the UK as Intellectual Impostures) the physicists Alan Sokal and Jean Bricmont criticised falsifiability. They include this critique in the "Intermezzo" chapter, where they expose their own views on truth in contrast to the extreme epistemological relativism of postmodernism. Even though Popper is clearly not a relativist, Sokal and Bricmont discuss falsifiability because they see postmodernist epistemological relativism as a reaction to Popper's insistence on falsifiability, and more generally, to his theory of science.

## Applications

### 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. A survey of 303 federal judges conducted in 1998 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."[Z]

#### 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)

#### Daubert v. Merrell Dow Pharmaceuticals 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.[AA] 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 1993, p. 593

In a partially dissident opinion, Chief Justice William Rehnquist supported by Associate Justice John Paul Stevens, responded that:

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 1993, p. 600

Professor of Law David H. Kaye[AB] 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."[AC]

### Economics

Karl Popper argued that Marxism shifted from scientific to unscientific.[AD]

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.[10][11] 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.

### Evolution

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".[12] Richard Dawkins adds that any other modern animal, such as a hippo, would suffice.[13][14][15] Karl Popper at first spoke against the testability of natural selection[16][17] 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."[18]

### Young-earth creationism

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.

### Historicism

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"[19] and argued that neither Marxism nor psychoanalysis was science,[19] 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.

### Mathematics

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."[20]

## Notes

1. ^ The criterion must be able to accept a statement that is "definitively true", which contradicts the requirement that some observation might show it to be false. Informally, we understand with the help of examples such as "This duck weigh 2000 tons" contradicts the law "All duck weigh less than 1000 tons", which is definitively true. Formally, this is easily taken care of with the flexibility of mathematical logic augmented with some empirical interpretation. Besides this obvious contradiction, Popper mentions more important problems created when we do not distinguish between falsifiability in the logical sense and falsifiability in the sense that a conclusive falsification might be possible (see Popper 1983, Introduction, 1982) : "Although the first sense refers to the logical possibility of a falsification in principle, the second sense refers to a conclusive practical experimental proof of falsity. But anything like conclusive proof to settle an empirical question does not exist. An entire literature rests on the failure to observe this distinction."
2. ^ Thornton 2016, sec. 3 : "Formally, then, Popper’s theory of demarcation may be articulated as follows: where a ‘basic statement’ is to be understood as a particular observation-report, then we may say that a theory is scientific if and only if it divides the class of basic statements into the following two non-empty sub-classes: (a) the class of all those basic statements with which it is inconsistent, or which it prohibits—this is the class of its potential falsifiers (i.e., those statements which, if true, falsify the whole theory), and (b) the class of those basic statements with which it is consistent, or which it permits (i.e., those statements which, if true, corroborate it, or bear it out)."
3. ^ We cannot really falsify "all swans are white," because one can always allude to initial conditions that explain the contradicting observation. In this case, perhaps the observer confused a black raven for a swan. This is one of many issues with dogmatic falsificationism.
4. ^ Lakatos refers to Popper 1959 when he credits Popper for sophisticated falsificationism. See Lakatos 1978, pp. 33 and 35.
5. ^ Popper 1983, Introduction, IV : "This may be the place to mention, and to refute, the legend that Thomas S. Kuhn, in his capacity as a historian of science, is the one who has shown that my views on science (sometimes, but not by me, called ‘falsificationismism‘) can be refuted by the facts; that is to say, by the history of science."
6. ^ 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'."
7. ^ Popper 1963, p. 111 : "Against the view here developed one might be tempted to object (following Duhem 28 ) that in every test it is not only the theory under investigation which is involved, but also the whole system of our theories and assumptions--in fact, more or less the whole of our knowledge--so that we can never be certain which of all these assumptions is refuted. But this criticism overlooks the fact that if we take each of the two theories (between which the crucial experiment is to decide) together with all this background knowledge, as indeed we must, then we decide between two systems which differ only over the two theories which are at stake. It further overlooks the fact that we do not assert the refutation of the theory as such, but of the theory together with that background knowledge; parts of which, if other crucial experiments can be designed, may indeed one day be rejected as responsible for the failure. (Thus we may even characterize a theory under investigation as that part of a vast system for which we have, if vaguely, an alternative in mind, and for which we try to design crucial tests.)"
8. ^ 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."
9. ^ Lakatos explains that, if the ceteris paribus clause is false, both Newton theory and Freud theory can avoid a logical falsification, but he fails to say that for many falsifiers of Newton theory, the clause is true under normal assumptions and thus is not really required as a separate clause. Popper was concerned that Lakatos meant that Newton theory could be put in the same category as Freud theory and wrote a response of 5 pages in Popper 1974, pp. 1004-1009 to clarify this issue. See also Popper 2009, Introduction, 1978 : "[S]ome of my former students ... believe that any putative falsification of Newtonian theory may be turned into a victory by assuming the existence of an unknown (and perhaps invisible) mass. However, this is simply a physical (or mathematical) error. First, there are many motions that in principle are observable but that cannot be explained by any such auxiliary hypothesis (for instance, a sudden reversal of motions)."
10. ^ 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 a discussions of problems created by a lack of distinction, see Rosende 2009, p. 142.
11. ^ Lakatos add two other decisions. One of them is needed to accept statistical statements as falsifiable. The other allows even more falsifiable theories.
12. ^ Popper 1959, p. 94 : "Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or ‘given’ base; and if we stop driving the piles deeper, it is not because we have reached firm ground. We simply stop when we are satisfied that the piles are firm enough to carry the structure, at least for the time being."
13. ^ Popper 1959, p. 91 : "It may now be possible for us to answer the question: How and why do we accept one theory in preference to others? The preference is certainly not due to anything like a experiential justification of the statements composing the theory; it is not due to a logical reduction of the theory to experience. We choose the theory which best holds its own in competition with other theories; the one which, by natural selection, proves itself the fittest to survive. This will be the one which not only has hitherto stood up to the severest tests, but the one which is also testable in the most rigorous way. A theory is a tool which we test by applying it, and which we judge as to its fitness by the results of its applications."
14. ^ Lakatos explains that Popper is not the sophisticated falsificationist that he describes, but, of course, not the naive falsificationist either. (see Lakatos 1978) : "In an earlier paper,' I distinguished three Poppers: Popper0, Popper1, and Popper2. Popper0 is the dogmatic falsificationist ... Popper1 is the naive falsificationist, Popper2 the sophisticated falsificationist. ... The real Popper has never explained in detail the appeal procedure by which some 'accepted basic statements', may be eliminated. Thus the real Popper consists of Popper1 together with some elements of Popper2."
15. ^ 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."
16. ^ Popper clearly distinguishes between the methodological rules and the rules of pure logic (see Popper 1959, p. 32 ) : "Methodological rules are here regarded as conventions. They might be described as the rules of the game of empirical science. They differ from the rules of pure logic..."
17. ^ Popper 1959, p. 27 : "The theory of method, in so far as it goes beyond the purely logical analysis of the relations between scientific statements, is concerned with the choice of methods—with decisions about the way in which scientific statements are to be dealt with."
18. ^ Zahar wrote a brief summary of Lakatos’s position regarding Popper's philosophy. He explains (see Zahar 1983, p. 149) : "The important question of the possibility of a genuine logic of [scientific] discovery" is the main divergence between Lakatos and Popper. About Popper's view, Zahar wrote (see Zahar 1983, p. 169) : "To repeat: Popper offers a Darwinian account of the progress of knowledge. Progress is supposed to result negatively from the elimination by natural selection of defective alternatives. ... There is no genuine logic of discovery, only a psychology of invention juxtaposed to a methodology which appraises fully fledged theories."
19. ^ In Lakatos terminology, the term "falsified" has a different meaning for a naive falsificationist than for a sophisticated falsificationist. Putting aside this confusing terminological aspect, the key point is that Lakatos wanted a formal logical procedure to determine which theories we must keep. (see Lakatos 1978, p. 32) : "For the naive falsificationist a theory is falsified by a ('fortified') 'observational' statement which conflicts with it (or which he decides to interpret as conflicting with it). For the sophisticated falsificationist a scientific theory T is falsified if and only if another theory T' has been proposed with the following characteristics: ( 1 ) T' has excess empirical content over T: that is, it predicts novel facts, that is, facts improbable in the light of, or even forbidden, by (2) T' explains the previous success of T, that is, all the unrefuted content of T is included (within the limits of observational error) in the content of T'; and (3) some of the excess content of T' is corroborated."
20. ^ In his critic of Popper (see Kuhn 1965, p. 15), Kuhn says that the methodological rules are not sufficient to provide a logic of discovery : "... rules or conventions like the following: 'Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without ‘good reason’. A ‘good reason’ may be, for instance: replacement of the hypothesis by another which is better testable; or the falsification of one of the consequences of the hypothesis.'
Rules like these, and with them the entire logical enterprise described above, are no longer simply syntactic in their import. They require that both the epistemological investigator and the research scientist be able to relate sentences derived from a theory not to other sentences but to actual observations and experiments. This is the context in which Sir Karl’s term ‘falsification’ must function, and Sir Karl is entirely silent about how it can do so."
21. ^ Popper gives an example of a methodological rule that uses corroborations (see Popper 1959, p. 32 ) : "Once a hypothesis has been proposed and tested, and has proved its mettle, it may not be allowed to drop out without ‘good reason’. A ‘good reason’ may be, for instance: replacement of the hypothesis by another which is better testable; or the falsification of one of the consequences of the hypothesis."
22. ^ 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’."
23. ^ 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."
24. ^ Popper 1983, Introduction, V : "The hope further to strengthen this theory of the aims of science by the definition of verisimilitude in terms of truth and of content was, unfortunately, vain. But the widely held view that scrapping this definition weakens my theory is completely baseless."
25. ^ Popper 1982, p. 161 : "In science, problem situations are the result, as a rule, of three factors. One is the discovery of an inconsistency within the ruling theory. A second is the discovery of an inconsistency between theory and experiment— the experimental falsification of the theory. The third, and perhaps the most important one, is the relation between the theory and what may be called the ‘metaphysical research programme’."
26. ^ Surveys were mailed to all active U.S. district court judges in November 1998 (N = 619). 303 usable surveys were obtained for a response rate of 51%.
27. ^ 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.
28. ^ 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.
29. ^ 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."
30. ^ 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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## Abbreviated references

1. ^ Popper 1989, pp. 82-85.
2. ^ Popper 1959, p. 43.
3. ^ A.C.Grayling (2019). The history of philosophy. Penguin. p. 397. ISBN 9780241304556.
4. ^ Lakatos 1978, pp. 12-30.
5. ^
6. ^ Popper 1982, p. 162.
7. ^ Thornton 2016, sec. 3.
8. ^
9. ^
10. ^
11. ^ Mises 1998, p. 11.
12. ^
13. ^
14. ^
15. ^
16. ^
17. ^
18. ^
19. ^ a b Burton 2000, p. 12-13.
20. ^