Falsifiability

A dogmatic falsificationist ignores that every observation is theory impregnated. This leads to the critique that it is unclear which theory is falsified. Is it the one that is being studied or the one behind the observation?[upper-alpha 13] 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, a ceteris paribus clause must say that no auxiliary hypothesis is responsible for the contradicting observation. Again, this leads to the critique that it cannot be told 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,[upper-alpha 14] though he clearly distinguished falsifiable theories such as Newton theory and non-falsifiable theories on this respect.[upper-alpha 15]

Lakatos explains that Popper's solution to these valid criticisms against dogmatic falsificationism requires that one relaxes the dogmatic assumption that an observation can show a theory to be false[upper-alpha 16]:

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.[upper-alpha 17] The falsifiers thus depend 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".[upper-alpha 18] He also says (see section § Basic statements and the definition of falsifiability) that it's not an obstacle to the definition of an empirical basis and of falsifiability.

Naive falsificationism is the claim that methodological falsifications can by themselves explain how scientific knowledge progresses. Very often one must deal with two or more competing theories which are both corroborated. Considering only falsifications, it is not clear why one theory is chosen above the other, even when one is corroborated more often than the other. In fact, a stronger version of the Quine-Duhem thesis says that it's not always possible to rationally pick one theory over the other using falsifications.[7] Considering only falsifications, it is not clear why often a corroborating experiment is seen as a sign of progress. Popper's critical rationalism uses both falsifications and corroborations to explain progress in science.[upper-alpha 19] How corroborations and falsifications can explain progress in science was a subject of disagreement between many philosophers, especially between Lakatos and Popper.[upper-alpha 20]

Popper clearly distinguished between the creative and informal process from which theories and accepted basic statements emerge and the logical and formal process where theories are falsified or corroborated.[upper-alpha 21][upper-alpha 22][upper-alpha 23] 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.[upper-alpha 24] It is a delicate question, because this logic would be inductive: it selects a universal law in view of instances. The answer of Lakatos and many others to that question is that it should.[upper-alpha 25][upper-alpha 26] In contradistinction, for Popper, the creative and informal part is guided by methodological rules, which naturally say to favor theories that are corroborated,[upper-alpha 27] but this methodology can hardly be made rigorous.[upper-alpha 28] Popper does not mention corroborations when he describes the purely logical part.[upper-alpha 29]

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.[upper-alpha 30] Today, there is still on going research on the general concept of verisimilitude.[8]

In Popper's view of science, statements of observation can be constructed within a logical structure independently of any factual observations.[upper-alpha 32][9] The set of all purely logical observations that can be created constitutes the empirical basis. Popper calls them the basic statements or test statements. They are the statements that can be used to show the falsifiability of a theory. Popper insists that a basic statement does not have to be possible in practice. It is sufficient that the values or properties that appear in the observations are associated with technologies.[upper-alpha 33] See the examples in section § Examples of demarcation and applications.

In more than twelve pages of The Logic of Scientific Discovery (Popper 1959, sec. 13–15, 28), Popper discusses informally which statements among those that can be constructed in the logical structure are basic statements. A logical structure uses universal classes to define laws. For example, in the law "all swans are white" the concept of swans is a universal class. It corresponds to a set of properties that every swan must have. It is not restricted to the swans that exist, existed or will exist. Informally, a basic statement is simply a statement that concerns only a finite number of specific instances in universal classes. In particular, an existential statement such as "there exists a black swan" is not a basic statement, because it is not specific about the instance. On the other hand, "this swan here is black" is a basic statement. Popper says that it is a singular existential statement or simply a singular statement. So, basic statements are singular (existential) statements.

Thornton says that basic statements are statements that correspond to particular "observation-reports". He then gives Popper's definition of falsifiability:

"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)."

— Thornton, Stephen, Thornton 2016, at the end of section 3

As in the case of actual falsifiers, decisions must be taken by scientists to accept a logical structure and its associated empirical basis, but these are usually part of a background knowledge that scientists have in common and, often, no discussion is even necessary.[upper-alpha 34] The first decision described by Lakatos is implicit in this agreement, but the other decisions are not needed. This agreement, if one can speak of agreement when there is not even a discussion, exists only in principle. This is where the distinction between the logical and methodological sides of science becomes important. When an actual falsifier is proposed, the technology used is considered in details and, as mentioned in section § Dogmatic falsificationism, an actual agreement is needed. This may require using a deeper empirical basis,[upper-alpha 35] hidden within the current empirical basis, to make sure that the properties or values used in the falsifier were obtained correctly (Andersson 2016 gives some examples).

Despite the fact that the empirical basis can be shaky, more comparable to a swamp than to a solid ground, the definition that is given above is simply the formalization of a natural requirement on scientific theories, without which, Popper says, the whole logical process of science[upper-alpha 32] would not be possible.

This article starts by stating that a falsifier must have parts that are separately technologically possible. Yet § The definition of falsifiability don't mention a word about multiple parts in a potential falsifier. This requires some explanation. In his analysis of the scientific nature of universal laws, Popper arrived at the conclusion that laws must "allow us to deduce, roughly speaking, more empirical singular statements than we can deduce from the initial conditions alone." A singular statement that has one part only can not contradict an universal law. It can only contradict a prediction that is obtained from the law together with another singular statement, the initial condition. A falsifier of a law has always two parts: the initial condition and the singular statement that contradicts the prediction. There was no need to require that falsifiers have two parts in the definition itself. This made the definition more general and allowed the basic statements themselves to be falsifiable.[10]

Interestingly, criteria that require that a law must be predictive, just as is required by falsifiability, Popper wrote, "have been put forward as criteria of the meaningfulness of sentences (rather than as criteria of demarcation applicable to theoretical systems) again and again after the publication of [his] book, even by critics who pooh-poohed [his] criterion of falsifiability."[11]

In response to Lakatos who suggested that Newton's theory was as hard to show falsifiable than Freud's psychoanalytic theory, Popper gave the example of an apple that moves from the ground up to a branch and then starts to dance from one branch to another.[upper-alpha 36] It is clearly impossible, yet a basic statement that is a valid potential falsifier for Newton's theory, because the position of the apple at different times can be measured.

Another example of a basic statement is "The inert mass of this object is ten times larger than its gravitational mass." This is a basic statement because the inert mass and the gravitational mass can both be measured separately, even though it never happens that they are different. It is, as mentioned by Popper, a valid falsifier for Einstein's equivalence principle.[upper-alpha 37]

A black-bodied and white-bodied peppered moth.

An example of a basic statement in the theory of evolution is "In this industrial area, the relative fitness of the white-bodied peppered moth is high." Here "fitness" means "reproductive success over the next generation", which is the definition used as early as 1930 by Ronald Fisher[upper-alpha 38] and still the most widely accepted definition in modern biology.[upper-alpha 39] This is an example of a basic statement, because it is possible to separately determine the kind of environment, industrial vs natural, and the relative fitness of the white-bodied form (relative to the black-bodied form) in an area, even though it never happens that the white-bodied form has a high relative fitness in an industrial area. "In industrial areas, the black form of the peppered moth has higher relative fitness" is indeed a famous example of a falsifiable statement that illustrates the effect of natural selection.[12]

A famous example of a basic statement from J.B.S. Haldane is "[These are] fossil rabbits in the Precambrian era." This is a basic statement because it is possible to find a fossil rabbit and to determine that the date of a fossil is in the Precambrian era, even though it never happens that the date of a rabbit fossil is in the Precambrian era. Despite opinions to the contrary,[13] some times wrongly attributed to Popper,[upper-alpha 40] this shows the scientific character of paleontology or the history of the evolution of life on Earth, because it contradicts the hypothesis in paleontology that all mammals existed in a much more recent era. Richard Dawkins adds that any other modern animal, such as a hippo, would suffice.[14][15][16]

Even if it is accepted that angels exist, the sentence "All angels have large wings" is not falsifiable, because though it is possible to observe the absence of large wings, no technology (independent of the presence of wings) exists to identify these angels.

A simple example of a non-basic statement is "this angel does not have large wings". It is not a basic statement, because though the absence of large wings can be observed, no technology (independent of the presence of wings[upper-alpha 41]) exists to identify angels. Even if it is accepted that angels exist, the sentence "All angels have large wings" is not falsifiable.

Another example from Popper of a non-basic statement is "This human action is altruistic." It is not a basic statement, because no accepted technology allows us to determine whether or not an action is motivated by self-interest. Indeed, the theory "All human actions are egotistic, motivated by self-interest", with all its variants in behaviorism, psychoanalysis, individual psychology, utilitarianism, vulgar-marxism, religion, and sociology of knowledge, Popper wrote, is not falsifiable.[upper-alpha 42]

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 after the Greek word for navel) that the world was created with the appearance of age; e.g., the sudden appearance of a mature chicken capable of laying eggs. This ad hoc hypothesis introduced into young-Earth creationism makes it non-falsifiable because it says that the time of creation (of a species) measured by the accepted technology is illusory and no accepted technology is proposed to measure the claimed "actual" time of creation. Popper says that it's fine to modify a theory by the introduction of an auxiliary hypothesis, but the new theory must at the least remain falsifiable, which is not the case here. One can also present the Omphalos hypothesis as an auxiliary hypothesis that is introduced into the accepted theory. In this view, the new theory remains falsifiable, but its falsifiability does not increase, because no additional observations are predicted. In both views, the ad hoc hypothesis, seen by itself, is not falsifiable because there is no way to measure the claimed "actual" time of creation that is proposed by this hypothesis. This is discussed in details by Dienes in the case of a variation on the Omphalos hypothesis, which, in addition, specifies that God made the creation in this way to test our faith.[17]

Grover Maxwell called attention on an important class of metaphysical statements such as "All men are mortal".[18] This is not falsifiable, because it does not matter how old is a man, maybe it will die next year.[19] Maxwell's view is that this statement, which is not falsfiable, is nevertheless useful, because it is often corroborated. He coined the term "corroboration without demarcation". Popper's view is that it is indeed useful, but only because it is indirectly corroborated by the corroboration of the falsifiable law "All men die before the age of 150." For Popper, if no such a falsifiable law exists, then the metaphysical law is not useful, because it's not indirectly corroborated.[upper-alpha 43]

Clyde Cowan conducting the neutrino experiment (circa 1956)

A more practical example from Maxwell is "All solids have a melting point." This is not falsifiable, because maybe the melting point will be reached at a higher temperature.[20][19] The law is falsifiable and more useful if we specify an upper bound on melting points or a way to calculate this upper bound.[upper-alpha 44]

Another example from Maxwell is "All beta decays are accompanied with a neutrino emission from the same nucleus." This is also not falsifiable, because maybe the neutrino can be detected in a different manner. The law is falsifiable and much more useful from a scientific point of view, if the method to detect the neutrino is specified.[21]

Maxwell pointed out that most scientific laws are metaphysical statements of this kind,[20] which, Popper said, need to be made more precise before they can be indirectly corroborated.[upper-alpha 43] In his critique of the falsifiability criterion, Maxwell also considered the requirement for decisions in the detection of the neutrino and the determination of the melting point, but these issues have already been discussed in section § Dogmatic falsificationism.

Another example, easily built from the pepper moth example, is "In all areas, the white vs black trait of the pepper moth affects its fitness." This is also not falsifiable, because may be the right environmental factor was not yet considered. When it is specified, namely, fitness in polluted industrial areas vs non polluted areas, then the law is falsifiable and it says which environmental factor should be considered to actually see an effect.[upper-alpha 45]

In the 5th and 6th editions of On the origin of species, following a suggestion of Alfred Russel Wallace, Darwin used "Survival of the fittest", an expression first coined by Herbert Spencer, as a synonym for "Natural Selection".[upper-alpha 46] Popper and others noted that, if one uses the most widely accepted definition of "fitness" in modern biology (see subsection § Evolution), namely reproductive success itself, the expression "survival of the fittest" is a tautology.[upper-alpha 47][upper-alpha 48][upper-alpha 49] In practice, as illustrated by the peppered moth example of section § Evolution, the questions asked are of the kind how specific traits affect the survival rate or fitness of a species when confronted by an environmental factor such as industrial pollution. Great Darwinist Ronald Fisher worked out mathematical theorems to help answer this kind of questions. But, for Popper and others, there is no (falsifiable) law of Natural Selection in this, because it only applies to some rare traits.[upper-alpha 50][upper-alpha 51] Instead, for Popper, the work of Fisher and others on Natural Selection is part of an important metaphysical research program.

Popper insisted that not all non-falsifiable statements are useless in science. Mathematical statements are good examples. 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."[22]

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"[23] and argued that neither Marxism nor psychoanalysis was science,[23] 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.

Popper made a clear distinction between the original theory of Marx and what came to be known as Marxism later on.[24] For Popper, the original theory of Marx contained genuine scientific laws. Though they could not make preordained predictions, these laws constrained how changes can occur in society. One of them was that changes in society cannot "be achieved by the use of legal or political means".[upper-alpha 52] For Popper, this was testable, and in fact falsified. "Yet instead of accepting the refutations", Popper wrote, "the followers of Marx re-interpreted both the theory and the evidence in order to make them agree. ... They thus gave a 'conventionalist twist' to the theory; and by this stratagem they destroyed its much advertised claim to scientific status."[upper-alpha 53][upper-alpha 54]

Falsifiability has been used in the McLean v. Arkansas case (in 1982),[25] the Daubert case (in 1993)[26] and other cases. A survey of 303 federal judges conducted in 1998[upper-alpha 55] 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."[27]

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)

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.[upper-alpha 56] 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[upper-alpha 57] 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."[upper-alpha 58]

Bucket view: Observations enter into the bucket and turn into valid statements. Next, (not shown) inference rules generate valid laws.

Some tentative explanations for the growth of scientific knowledge are based on what Popper calls the bucket view of science. In this view, observation statements accumulate in a bucket through observations and various procedures are used to make sure that they are valid.[upper-alpha 59] Next, new laws are obtained in a way that can be justified using inference rules that are allowed to process all the knowledge that is available in the bucket.[upper-alpha 60] In this justificational picture, Hume argued that we cannot obtain new universal laws (except what can be obtained through deductive rules). Hume's argument is based on reasonable premises: non-deductive rules are in need of justification, circular arguments are not valid, etc. If we accept Hume's premises, even probabilistic attempts to explain the growth of knowledge in terms of the bucket view of science, Popper stated, are doomed to fail.[30]

Popper's solution to this problem is simply to reject the bucket view of science. His main argument is basically that he accepts Hume's argument, which shows that the bucket view fails to explain the growth of objective knowledge. Popper noted that the processes in the bucket are better seen as physical processes and the laws that govern these processes are biological.[upper-alpha 61] To help people get rid of the limitations associated with the bucket view, Popper brought out the main issue with this view: it ignores the organismic aspect of knowledge.[upper-alpha 62] Given that the bucket view is a dead end, it is natural to accept that biological predispositions and expectations play an important role in these processes.[upper-alpha 63]

Searchlight view: Expectations and predispositions turn into conjectures that act like a searchlight and lead to observations (not shown).

Popper proposed to replace the bucket view of science with what he called the searchlight view of science. In that view, Popper wrote, there is no reason why any methodology should work. It is easy, Popper said, to imagine universes where no methodology can work or even only exist.[upper-alpha 64] If you want to believe that the methodology will work, it must be postulated as an axiom. In Popper's case, the axiom is that the methodology of conjectures and refutations is going to work.[upper-alpha 65] The conjectures are the searchlight, because they lead to observational results. But this axiom will not help any objective rule in the justification of scientific knowledge.[upper-alpha 66] There is no point in attempting any justification in the searchlight view. For a popperian, the absence of these objective rules is expected. It is not a failure. In this line of thought, Einstein wrote that there is no logical path to science.[upper-alpha 67][upper-alpha 68]

Popper's scientific methodology that accompanies falsifiability contains rules such as "He who decides one day that scientific statements do not call for any further test, and that they can be regarded as finally verified, retires from the game."[31] In general, the rules of Popper's methodology influence which theories will be chosen or rejected, but these rules do that only through decisions taken by the scientists.[upper-alpha 69] As explained in § Methodless creativity versus inductive methodology, every rule to determine or choose theories must rely on the good judgement of the scientists.

Back to the original question: why should falsifiability be the criterion? It is not that falsification directly leads to the rejection of a theory. That would be a rule of the bucket view of science. It is not that we must always look for theories that are more falsifiable. That would also be a rule of the bucket view of science. Popper's main methodological rule is that scientists must try to guess and corroborate (or equivalently falsify) bold and useful conjectures and take any falsification as a problem that can be used to start a critical discussion. In other words, the usefulness of falsifiability is that falsifiable conjectures say more, because they prohibit more and, in the case of their falsification, they lead to useful problems, which steer the creative process of science. For Popper, who knew most of section § Examples of demarcation and applications, this is exactly what we should expect from a scientific theory.

The original answer provided, which is the possibility to actually falsify a theory as if there was a rule to eliminate laws, missed the whole point: No rule can supersede the hidden organic aspect of knowledge in the processing of the available objective knowledge. If there is any inference rule, the final decision must still be left to the organic aspect or, more simply, to the scientists. For Popper, inference rules are tantamount to a "quest for certainty", which he saw as the main weakness of the bucket view of science.[32]

In § #Methodless creativity versus inductive methodology, it is seen that Lakatos reached the same conclusion in the following sense that he admitted that his methodology did not offer any "firm heuristic advice about what to do".[upper-alpha 70] Before Popper's time, in 1906, being aware of the problems of falsification, Pierre Duhem reached the same conclusion.[upper-alpha 71] Popper reemphasized non-justificationism, which was a good match for his added falsifiability criterion and associated critical methodology.

As briefly mentioned in section § Naive falsificationism, Lakatos accepted, as did Popper, that universal laws cannot be logically deduced (except from laws that say even more), but he felt that, if the explanation for new laws can not be deductive, it must be inductive. He urged Popper explicitly to adopt some inductive principle[upper-alpha 72] and sets himself the task to find an inductive methodology.[upper-alpha 73] However, the methodology that he found did not offer any exact inductive rules. Indeed, in a response to Kuhn, Feyerabend and Musgrave, Lakatos acknowledged that the methodology depends on the good judgment of the scientists.[upper-alpha 70] Feyerabend wrote in "Against Method" that Lakatos' methodology of scientific research programmes is epistemological anarchism in disguise[upper-alpha 74] and Musgrave made a similar comment.[upper-alpha 75] In more recent work, Feyerabend explains that Lakatos uses rules, but whether or not to follow any of these rules is left to the judgment of the scientists.[upper-alpha 76] This is also discussed elsewhere.[upper-alpha 77]

Popper also offered a methodology with rules, but these rules are also not inductive rules, because they are not by themselves used to accept laws or establish their validity. They do that through the creativity or "good judgment" of the scientists only. For Popper, the required non deductive component of science never had to be an inductive methodology. He always viewed this component as a creative process beyond the explanatory reach of any rational methodology, but yet used to decide which theories should be studied and applied, find good problems and guess useful conjectures.[upper-alpha 78] Quoting Einstein to support his view, Popper said that this renders obsolete the need for an inductive methodology or logical path to the laws. For Popper, no inductive methodology was ever proposed to satisfactorily explain science.

Section § Methodless creativity versus inductive methodology says that both Lakatos's and Popper's methodology are not inductive. Yet Lakatos's methodology extended importantly Popper's methodology: it added a historiographical component to it. This allowed Lakatos to find corroborations for his methodology in the history of science. The basic units in his methodology, which can be abandoned or pursued, are research programmes. Research programmes can be degenerative or progressive and only degenerative research programmes must be abandoned at some point. For Lakatos, this is mostly corroborated by facts in history.

In contradistinction, Popper did not propose his methodology as a tool to reconstruct the history of science. Yet, some times, he did refer to history to corroborate his methodology. For example, he remarked that theories that were considered great successes were also the most likely to be falsified. Zahar's view was that, with regard to corroborations found in the history of science, there was only a difference of emphasis between Popper and Lakatos.

As an anecdotal example, in one of his articles Lakatos challenged Popper to show that his theory was falsifiable: he asked "Under what conditions would you give up your demarcation criterion?".[33] Popper always viewed his philosophy as metaphysical, but in the context of Lakatos's challenge, which contained an emphasis on history, Popper replied "I shall give up my theory if Professor Lakatos succeeds in showing that Newton's theory is no more falsifiable by 'observable states of affairs' than is Freud's."[34]

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,[35] whereas Popper's view is that only revolutions are relevant.[upper-alpha 79][upper-alpha 80] For Popper, the role of science, mathematics and metaphysics, actually the role of any knowledge, is to solve puzzles.[upper-alpha 81] In the same line of thought, Kuhn observes that in periods of normal science the scientific theories, which represent some paradigm, are used to routinely solve puzzles and the validity of the paradigm is hardly in question. It's only when important new puzzles emerge that cannot be solved by accepted theories 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 section § 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 kind of theory. Kuhn says that Popper emphasizes formal or logical falsifications and fails to explain how the social and informal process works.

Popper often uses astrology as an example of a pseudo-science. He says that it is not falsifiable because both the theory itself and its predictions are too imprecise.[upper-alpha 82] Khun, as an historian of science, remarked that many predictions made by astrologers in the past were quite precise and they were very often falsified. He also noted that astrologers themselves acknowledged these falsifications.[upper-alpha 83]

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.[36] 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.[37] 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.[38]

In their book Fashionable Nonsense (from 1997, published in the UK as Intellectual Impostures) the physicists Alan Sokal and Jean Bricmont criticised falsifiability.[39] 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.[40]