TheInfoList

Falsifiability is a standard of evaluation of scientific theories and hypotheses that was introduced by the philosopher of science
Karl Popper Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian-British , and . One of the 20th century's most influential , Popper is known for his rejection of the classical views on the in favour of . According to Popper, a ...

in his book ''Logik der Forschung'' (1934). He proposed it as the cornerstone of a solution to both the
problem of induction The problem of induction is the philosophy, philosophical question of what are the Argument, justifications, if any, for any growth of knowledge understood in the Justified true belief, classic philosophical sense—knowledge that goes beyond ...
and the problem of demarcation. A theory or hypothesis is falsifiable (or refutable) if it can be logically contradicted by an empirical test with existing technologies. The purpose of falsifiability even as a ''logical'' criterion is to make the theory
predictive A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecasting, forecast, is a statement about a future event (probability theory), event or data. They are often, but not always, based upon experience or knowledge. There i ...
and
testable Testability, a property applying to an empirical hypothesis, involves two components: #Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. #The practical feasibility of observing a reproducibi ...
thus useful in practice. Popper opposed falsifiability to the intuitively similar concept of
verifiability Verify or verification may refer to: General * Verification and validation, in engineering or quality management systems, is the act of reviewing, inspecting or testing, in order to establish and document that a product, service or system meets ...
. Verifying the claim "All swans are white" would ''logically'' require observing all swans, which is not technologically possible. In contrast, the observation of a single black swan is technologically reasonable and sufficient to ''logically'' falsify the claim. On the other hand, and others said that definitive experimental falsifications are impossible. In that context, Popper insisted that there is a clean asymmetry on the logical side and falsifiability does not have the Duhem problem because it is a logical criterion, as distinct from the related concept "capacity to be proven wrong" discussed in Lakatos's falsificationism. The experimental side and the associated methodology do have the Duhem problem and other problems such as the problem of induction, but, for Popper, statistical tests and other mathematical tools, which are possible when a theory is falsifiable, remain useful in science within a critical discussion. As a key notion in the separation of science from
non-science A non-science is an area of study that is not scientific, especially one that is not a natural science or a social science that is an object of scientific inquiry. In this model, history, art, and religion are all examples of non-sciences. Class ...
and
pseudo-science Pseudoscience consists of statements, belief A belief is an Attitude (psychology), attitude that something is the case, or that some proposition about the world is truth, true. In epistemology, philosophers use the term "belief" to refer to ...
, falsifiability has featured prominently in many scientific controversies and applications, even being used as legal precedent.

# The problem of induction and demarcation

One of the questions in
scientific method The scientific method is an empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence ...

is: how does one move from
observation Observation is the active acquisition of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature of its characteristics. Th ...

s to
scientific law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
s? This is the problem of induction. Suppose we want to put the hypothesis that all swans are white to the test. We come across a white swan. We cannot validly argue (or '' induce'') from "here is a white swan" to "all swans are white"; doing so would require a
logical fallacy In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, lang ...

such as, for example,
affirming the consequent Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy In philosophy Philosophy (from , ) is the study of general and fundamental questions, such ...
. Popper's idea to solve this problem is 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. Falsification uses the valid inference ''
modus tollens In propositional calculus, propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo wiktionary:tollens, tollens'' (Latin language, Latin for "method of removing by taking away") and denying the consequent, is a Deductive r ...
'': if from a statement $P$ (say some law with some initial condition) we logically deduce but what is observed is we infer that $P$ is false. For example, given the statement "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. For Popper, induction is actually never needed in science. Instead, in Popper's view, laws are conjectured in a non-logical manner on the basis of expectations and predispositions. This has led David Miller, a student and collaborator of Popper, to write "the mission is to classify truths, not to certify them". In contrast, the
logical empiricism Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, was a movement in Western philosophy Western philosophy refers to the philosophy, philosophical thought and work of the Western worl ...
movement, which included such philosophers as
Moritz Schlick Friedrich Albert Moritz Schlick (; ; 14 April 1882 – 22 June 1936) was a Germany, German philosopher, physicist, and the founding father of logical positivism and the Vienna Circle. Early life and works Schlick was born in Berlin to a wealthy f ...
,
Rudolf Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle The Vienna Circle (german: Wiener Krei ...
,
Otto Neurath Otto Karl Wilhelm Neurath (; 10 December 1882 – 22 December 1945) was an Austria Austria (, ; german: Österreich ), officially the Republic of Austria (german: Republik Österreich, links=no, ), is a landlocked Eastern Alps, East Alp ...

and
A.J. Ayer Sir Alfred Jules "Freddie" Ayer (; 29 October 1910 – 27 June 1989), usually cited as A. J. Ayer, was an English philosopher known for his promotion of logical positivism, particularly in his books ''Language, Truth, and Logic'' (1936) an ...
wanted to formalize the idea that, for a law to be scientific, it must be possible to argue on the basis of observations either in favor of its truth or its falsity. There was no consensus among these philosophers about how to achieve that, but the thought expressed by Mach's dictum that "where neither confirmation nor refutation is possible, science is not concerned" was accepted as a basic precept of critical reflection about science. Popper said that a demarcation criterion was possible, but we have to use the ''logical possibility'' of falsifications, which is falsifiability. He cited his encounter with
psychoanalysis Psychoanalysis (from Greek language, Greek: + ) is a set of Theory, theories and Therapy, therapeutic techniques"What is psychoanalysis? Of course, one is supposed to answer that it is many things — a theory, a research method, a therapy, a bo ...

in the 1910s. It did not matter what observation was presented, psychoanalysis could explain it. Unfortunately, the reason why it could explain everything is that it did not exclude anything also. For Popper, this was a failure, because it meant that it could not make any prediction. From a logical standpoint, if one finds an observation that does not contradict a law, it does not mean that the law is true. A verification has no value in itself. But, if the law makes risky predictions and these are corroborated, Popper says, there is a reason to prefer this law over another law that makes less risky predictions or no predictions at all. In the definition of falsifiability, contradictions with observations are not used for actual falsifications, but for ''logical'' "falsifications" that show that the law makes risky predictions, which is completely different. On the basic philosophical side of this issue, Popper said that some philosophers of the
Vienna Circle The Vienna Circle (german: Wiener Kreis) of Logical Empiricism was a group of philosophers and scientists drawn from the Natural science, natural and Social Sciences, social sciences, logic and mathematics who met regularly from 1924 to 1936 at th ...
had mixed two different problems, that of meaning and that of demarcation, and had proposed in
verificationism Verificationism, also known as the verification principle or the verifiability criterion of meaning, is the philosophical doctrine which maintains that only statements that are empirically verifiable (i.e. verifiable through the sense Sense relate ...
a single solution to both: a statement that could not be verified was considered meaningless. In opposition to this view, Popper said that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.

## From Hume's problem to non problematic induction

The problem of induction is often called Hume's problem.
David Hume David Hume (; born David Home; 7 May 1711 NS (26 April 1711 OS) – 25 August 1776) Cranston, Maurice, and Thomas Edmund Jessop. 2020 999999 or triple nine most often refers to: * 999 (emergency telephone number) 250px, A sign on a beach ...

studied how human beings obtain new knowledge that goes beyond known laws and observations, including how we can discover new laws. He understood that deductive logic could not explain this learning process and argued in favour of a mental or psychological process of learning that would not require deductive logic. He even argued that this learning process can not be justified by any general rules, deductive or not. Popper accepted Hume's argument and therefore viewed progress in science as the result of quasi-induction, which does the same as induction, but has no inference rules to justify it. Philip N. Johnson-Laird, professor of psychology, also accepted Hume's conclusion that induction has no justification. For him induction does not require justification and therefore can exist in the same manner as Popper's quasi-induction does. When Johnson-Laird says that no justification is needed, he does not refer to a general method of justification that, to avoid a circular reasoning, would not itself require any justification. On the contrary, in agreement with Hume, he refers to the fact that there is no general method of justification for induction and that's ok, because the induction steps do not require justification. Instead, these steps use patterns of induction that may or may not be applicable depending on the background knowledge. Johnson-Laird wrote: " ilosophers have worried about which properties of objects warrant inductive inferences. The answer rests on knowledge: we don’t infer that all the passengers on a plane are male because the first ten off the plane are men. We know that this observation doesn’t rule out the possibility of a woman passenger." The reasoning pattern that was not applied here is
enumerative induction Inductive reasoning is a method of reasoning in which the premise A premise or premiss is a statement that an argument claims will induce or justify a Logical consequence, conclusion. It is an assumption that something is true. Explanation ...
. Popper was interested in the overall learning process in science, to quasi-induction, which he also called the "path of science". However, Popper did not show much interest in these reasoning patterns, which he globally referred to as psychologism. He did not deny the possibility of some kind of psychological explanation for the learning process, especially when psychology is seen as an extension of biology, but he felt that these biological explanations were not within the scope of epistemology. Popper proposed an evolutionary mechanism to explain the success of science, which is much in line with Johnson-Laird's view that "induction is just something that animals, including human beings, do to make life possible", but Popper did not consider it a part of his epistemology. He wrote that his interest was mainly in the ''logic'' of science and that epistemology should be concerned with logical aspects only. Instead of asking why science succeeds he considered the pragmatic problem of induction. This problem is not how to justify a theory or what is the global mechanism for the success of science but only what methodology do we use to pick one theory among theories that are already conjectured. His methodological answer to the latter question is that we pick the theory that is the most tested with the available technology: "the one, which in the light of our ''critical discussion'', appears to be the best so far". By his own account, because only a negative approach was supported by logic, Popper adopted a negative methodology.: "The fundamental difference between my approach and the approach for which I long ago introduced the label ‘inductivist’ is that I lay stress on negative arguments, such as negative instances or counter-examples, refutations, and attempted refutations—in short, criticism .. The purpose of his methodology is to prevent "the policy of immunizing our theories against refutation". It also supports some "dogmatic attitude" in defending theories against criticism, because this allows the process to be more complete. This negative view of science was much criticized and not only by Johnson-Laird. In practice, some steps based on observations can be justified under assumptions, which can be very natural. For example, Bayesian inductive logic is justified by theorems that make explicit assumptions. These theorems are obtained with deductive logic, not inductive logic. They are sometimes presented as steps of induction, because they refer to laws of probability, even though they do not go beyond deductive logic. This is yet a third notion of induction, which overlap with deductive logic in the following sense that it is supported by it. These deductive steps are not really inductive, but the overall process that includes the creation of assumptions is inductive in the usual sense. In a fallibilism perspective, a perspective that is widely accepted by philosophers, including Popper, every learning step only creates or reinforces an assumption—that is all what science does.

# Basic statements and the definition of falsifiability

Popper distinguished between the logic of science and its applied ''methodology''. For example, Newton's law of gravitation is falsifiable—it is falsified by "The brick fell upwards when released". An explanation for this imaginary state of affairs such as some hidden force other than gravity acting on the brick would make it more intuitive, but is not needed for falsifiability, because it is a logical criterion. The empirical requirement on the potential falsifier, also called the ''material requirement'', is only that it is observable inter-subjectively with existing technologies. The logical part consists of theories, statements and their purely logical relationship together with this material requirement, which is needed for a connection with the methodological part. The methodological part consists, in Popper's view, of informal rules, which are used to guess theories, accept observation statements as factual, etc. These include statistical tests: Popper is aware that observation statements are accepted with the help of statistical methods and that these involve methodological decisions. When this distinction is applied to the term "falsifiability", it corresponds to a distinction between two completely different meanings of the term. The same is true for the term "falsifiable". Popper said that he only uses "falsifiability" or "falsifiable" in reference to the logical side and that, when he refers to the methodological side, he speaks instead of "falsification" and its problems. Popper said that methodological problems require proposing methodological rules. For example, one such rule is that, if one refuses to go along with falsifications, then one has retired oneself from the game of science. The logical side does not have such methodological problems, in particular with regard to the falsifiability of a theory, because basic statements are not required to be possible. Methodological rules are only needed in the context of actual falsifications. So observations have two purposes in Popper's view. On the methodological side, observations can be used to show that a law is false, which Popper calls falsification. On the logical side, observations, which are purely logical constructions, do not show a law to be false, but contradict a law to show its falsifiability. Unlike falsifications and ''free from the problems of falsification'', these contradictions establish the value of the law, which may eventually be corroborated. He wrote that an entire literature exists because this distinction was not observed.

## Basic statements

In Popper's view of science, statements of observation can be analyzed within a logical structure independently of any factual observations. The set of all purely logical observations that are considered 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 says that basic statements do not have to be possible in practice. It is sufficient that they are accepted by convention as belonging to the empirical language, a language that allows
intersubjective verifiabilityIntersubjective verifiability is the capacity of a concept to be readily and accurately communicated between different individuals (" intersubjectively"), and to be reproduced under varying circumstances for the purposes of verification. It is a cor ...
: "they must be testable by intersubjective observation (the material requirement)". See the examples in section . In more than twelve pages of ''The Logic of Scientific Discovery'', Popper discusses informally which statements among those that are considered 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.

## The definition of falsifiability

Thornton says that basic statements are statements that correspond to particular "observation-reports". He then gives Popper's definition of falsifiability: 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. 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 detail and, as described in section , an actual agreement is needed. This may require using a deeper empirical basis, hidden within the current empirical basis, to make sure that the properties or values used in the falsifier were obtained correctly ( gives some examples). Popper says that despite the fact that the empirical basis can be shaky, more comparable to a swamp than to solid ground, the definition that is given above is simply the formalization of a natural requirement on scientific theories, without which the whole logical process of science would not be possible.

## Initial condition and prediction in falsifiers of laws

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 a universal law. A falsifier of a law has always two parts: the initial condition and the singular statement that contradicts the prediction. However, there is no need to require that falsifiers have two parts in the definition itself. This removes the requirement that a falsifiable statement must make prediction. In this way, the definition is more general and allows the basic statements themselves to be falsifiable. Criteria that require that ''a law'' must be predictive, just as is required by falsifiability (when applied to laws), 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 my book, even by critics who pooh-poohed my criterion of falsifiability."

## Falsifiability in model theory

Scientists such as the
Nobel laureate Nobel laureates of 2012 Alvin E. Roth, Brian Kobilka, Robert J. Lefkowitz">Brian_Kobilka.html" ;"title="Alvin E. Roth, Brian Kobilka">Alvin E. Roth, Brian Kobilka, Robert J. Lefkowitz, David J. Wineland, and Serge Haroche during the ceremony Th ...
Herbert A. Simon have studied the semantic aspects of the logical side of falsifiability. These studies were done in the perspective that a logic is a relation between formal sentences in languages and a collection of mathematical structures. The relation, usually denoted $\models \phi$, says the formal sentence $\phi$ is true when interpreted in the structure —it provides the semantic of the languages.This perspective can be found in any text on model theory. For example, see . According to Rynasiewicz, in this semantic perspective, falsifiability as defined by Popper means that in some observation structure (in the collection) there exists a set of observations which refutes the theory. An even stronger notion of falsifiability was considered, which requires, not only that there exists one structure with a contradicting set of observations, but also that all structures in the collection that cannot be expanded to a structure that satisfies $\phi$ contain such a contradicting set of observations.

# Examples of demarcation and applications

## Newton's theory

In response to Lakatos who suggested that Newton's theory was as hard to show falsifiable as 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. 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.

## Einstein's equivalence principle

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 described by Popper, a valid falsifier for Einstein's equivalence principle.

## Evolution

### Industrial melanism

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 The peppered moth (''Biston betularia'') is a temperate species of night-flying moth Moths are a paraphyletic group of insects that includes all members of the Order (biology), order Lepidoptera that are not Butterfly, butterflies, with mot ...
is high." Here "fitness" means "reproductive success over the next generation".For example, see , or 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 (due to a better camouflage)" is a famous example of a falsifiable statement that illustrates the effect of natural selection.

### Precambrian rabbit

A famous example of a basic statement from is " hese arefossil 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, some times wrongly attributed to Popper, 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 Richard Dawkins (born 26 March 1941) is a British evolutionary biology, evolutionary biologist and author. He is an Oxford fellow, emeritus fellow of New College, Oxford and was Simonyi Professor for the Public Understanding of Science, Prof ...

adds that any other modern animal, such as a hippo, would suffice.

## Simple examples of unfalsifiable statements

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) 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. Because no basic statement falsifies it, the statement that "All human actions are egotistic, motivated by self-interest" is thus not falsifiable.

## Omphalos hypothesis

young-Earth creationism Young Earth creationism (YEC) is a form of creationism which holds as a central wikt:tenet, tenet that the Earth and its lifeforms were created in their present forms by supernatural acts of a deity between approximately 6,000 and 10,000 years ag ...
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 is unfalsifiable 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. Moreover, if the ad hoc hypothesis says that the word was created as we observe it today without stating further laws, by definition it cannot be contradicted by observations and thus is not falsifiable. This is discussed 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.

## Useful metaphysical statements

discussed statements such as "All men are mortal". This is not falsifiable, because it does not matter how old a man is, maybe he will die next year. Maxwell said that this statement 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. This kind of non-falsifiable statements in science was noticed by Carnap as early as 1937. Maxwell also used the example "All solids have a melting point." This is not falsifiable, because maybe the melting point will be reached at a higher temperature. The law is falsifiable and more useful if we specify an upper bound on melting points or a way to calculate this upper bound. Another example from Maxwell is "All
beta decay In , beta decay (''β''-decay) is a type of in which a (fast energetic or ) is emitted from an , transforming the original to an of that nuclide. For example, beta decay of a transforms it into a by the emission of an electron accompanie ...

s 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. Maxwell said that most scientific laws are metaphysical statements of this kind, which, Popper said, need to be made more precise before they can be indirectly corroborated. In other words, specific technologies must be provided to make the statements inter-subjectively-verifiable, i.e., so that scientists know what the falsification or its failure actually means. In his critique of the falsifiability criterion, Maxwell considered the requirement for decisions in the falsification of, both, the emission of neutrinos (see ) and the existence of the melting point. For example, he pointed out that had no neutrino been detected, it could have been because some conservation law is false. Popper did not argue against the problems of falsification per se. He always acknowledged these problems. Popper's response was at the logical level. For example, he pointed out that, if a specific way is given to trap the neutrino, then, at the level of the language, the statement is falsifiable, because "no neutrino was detected after using this specific way" formally contradicts it (and it is inter-subjectively-verifiable—people can repeat the experiment). Another example, 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 maybe 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.

## Natural selection

In the 5th and 6th editions of ''
On the Origin of Species ''On the Origin of Species'' (or, more completely, ''On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life''),The book's full original title was ''On the Origin of Species by Me ...
'', following a suggestion of
Alfred Russel Wallace Alfred Russel Wallace (8 January 18237 November 1913) was a British natural history, naturalist, explorer, geographer, anthropologist, biologist and illustrator. He is best known for independently conceiving the theory of evolution throug ...
, Darwin used "Survival of the fittest", an expression first coined by
Herbert Spencer Herbert Spencer (27 April 1820 – 8 December 1903) was an English philosopher, biologist Francesco Redi, the founder of biology, is recognized to be one of the greatest biologists of all time A biologist is a professional who has speciali ...

, as a synonym for "Natural Selection". Popper and others said that, if one uses the most widely accepted definition of "fitness" in modern biology (see subsection ), namely reproductive success itself, the expression "survival of the fittest" is a tautology. In practice, as illustrated by the peppered moth example of section , 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 Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a subs ...
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. Instead, for Popper, the work of Fisher and others on Natural Selection is part of an important metaphysical research program.

## Mathematics

Popper said that not all unfalsifiable statements are useless in science. Mathematical statements are good examples. Like all
formal science Formal science is a branch of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of Testability, testable ...
s, mathematics is not concerned with the validity of theories based on observations in the
empirical Empirical evidence for a proposition In logic and linguistics, a proposition is the meaning of a declarative sentence (linguistics), sentence. In philosophy, "Meaning (philosophy), meaning" is understood to be a non-linguistic entity which is s ...
world, but rather, mathematics is occupied with the theoretical, abstract study of such topics as
quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value in terms of a unit of measu ...
,
structure A structure is an arrangement and organization of interrelated elements in a material object or system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. ...

,
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gre ...

and
change Change or Changing may refer to: Alteration * Impermanence Impermanence, also known as the philosophical problem This is a list of the major unsolved problems in philosophy Philosophy (from , ) is the study of general and fundam ...

. Methods of the mathematical sciences are, however, applied in constructing and testing scientific models dealing with observable
reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary Imaginary may refer to: * Imaginary (sociology), a concept in sociology * The Imaginary (psychoanalysis), a concept by ...

.
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

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."

## Historicism

Popper made a clear distinction between the original theory of Marx and what came to be known as Marxism later on. 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". 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." Popper's attacks was not directed toward Marxism, or Marx's theories, which were falsifiable, but toward Marxists who ignored the falsifications which had happened. Popper more fundamentally criticized 'historicism' in the sense of any preordained prediction of history, given what he saw as our right, ability and responsibility to control our own destiny.

## 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 found that " oblems 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."

### ''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 Creation science or scientific creationism is a pseudoscientific Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is o ...
" was not scientific and should not be taught in
Arkansas Arkansas () is a U.S. state, state in the South Central United States, South Central region of the United States, home to more than three million people as of 2018. Its name is from the Osage language, a Dhegihan languages, Dhegiha Siouan la ...

public schools as such (it can be taught as religion). In his testimony, philosopher
Michael Ruse Michael Ruse (born 21 June 1940) is a British-born Canadian philosopher of science who specializes in the philosophy of biology and works on the relationship between science and religion, the creation–evolution controversy, and the demarca ...
defined the characteristics which constitute science as (see and ): * 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

### Daubert standard

In several cases of the
United States Supreme Court The Supreme Court of the United States (SCOTUS) is the highest court in the Federal judiciary of the United States, federal judiciary of the United States of America. It has ultimate and largely Procedures of the Supreme Court of the United ...

, the court described scientific methodology using the five Daubert factors, which include falsifiability. The Daubert result cited Popper and other philosophers of science: David H. Kaye said 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."

# Connections between statistical theories and falsifiability

Considering the specific detection procedure that was used in the neutrino experiment, without mentioning its probabilistic aspect, Popper wrote "it provided a test of the much more significant ''falsifiable'' theory that such emitted neutrinos could be trapped in a certain way". In this manner, in his discussion of the neutrino experiment, Popper did not raise at all the probabilistic aspect of the experiment. Together with Maxwell, who raised the problems of falsification in the experiment, he was aware that some convention must be adopted to fix what it means to detect or not a neutrino in this probabilistic context. This is the third kind of decisions mentioned by Lakatos. For Popper and most philosophers, observations are theory impregnated. In this example, the theory that impregnates observations (and justifies that we conventionally accept the potential falsifier "no neutrino was detected") is statistical. In statistical language, the potential falsifier that can be statistically accepted (not rejected to say it more correctly) is typically the null hypothesis, as understood even in popular accounts on falsifiability. Different ways are used by statisticians to draw conclusions about hypotheses on the basis of available evidence.
Fisher Fisher is an archaic term for a fisherman, revived as gender-neutral. Fisher, Fishers or The Fisher may also refer to: Places Australia * Division of Fisher, an electoral district in the Australian House of Representatives, in Queensland * Elec ...

, and Pearson proposed approaches that require no prior probabilities on the hypotheses that are being studied. In contrast,
Bayesian inference Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and e ...
emphasizes the importance of prior probabilities. But, as far as falsification as a yes/no procedure in Popper's methodology is concerned, any approach that provides a way to accept or not a potential falsifier can be used, including approaches that use Bayes's theorem and estimations of prior probabilities that are made using critical discussions and reasonable assumptions taken from the background knowledge. There is no general rule that considers has falsified an hypothesis with small Bayesian revised probability, because as pointed out by Mayo and argued before by Popper, the individual outcomes described in detail will easily have very small probabilities under available evidence without being genuine anomalies. Nevertheless, Mayo adds, "they can indirectly falsify hypotheses by adding a methodological falsification rule". In general, Bayesian statistic can play a role in critical rationalism in the context of inductive logic, which is said to be inductive because implications are generalized to conditional probabilities. According to Popper and other philosophers such as Colin Howson, Hume's argument precludes inductive logic, but only when the logic makes no use "of additional assumptions: in particular, about what is to be assigned positive prior probability". Inductive logic itself is not precluded, especially not when it is a deductively valid application of Bayes' theorem that is used to evaluate the probabilities of the hypotheses using the observed data and what is assumed about the priors. Gelman and Shalizi mentioned that Bayes' statisticians do not have to disagree with the non-inductivists. Because statisticians often associate statistical inference with induction, Popper's philosophy is often said to have an hidden form of induction. For example, Mayo wrote "The falsifying hypotheses .. necessitate an evidence-transcending (inductive) statistical inference. This is hugely problematic for Popper". Yet, also according to Mayo, Popper s a non-inductivistacknowledged the useful role of statistical inference in the falsification problems: she mentioned that Popper wrote her (in the context of falsification based on evidence) "I regret not studying statistics" and that her thought was then "not as much as I do".

# The bucket and the searchlight

For Popper, the problems of falsification belong to the inductive perspective, which he also calls the bucket view of science, and the correct application of falsifiability, i.e., his methodology, is as free from the problems of falsification as falsifiability itself, because it relies on a different perspective, the searchlight view of science. Both views incorporate some unknown aspect in its explanation of progress in science. In the inductive or bucket view of science, this unknown aspect takes the form of uncertainty or lack of universality in the inductive logic. In the searchlight view of science, what is unknown is the influence of biological expectations and predispositions on the conjectures. Popper describes these biological expectations and predispositions as knowledge that has not taken (and perhaps cannot fully take) an objective form and in as such cannot participate in any logic that scientists can use.

## The bucket view of science

In the bucket view of science, observations are the basis to justify laws or theories. In this view, observation statements accumulate in a bucket through observations and various procedures are used to make sure that they are valid, so that they can fulfill their purpose. These observation statements are used as evidence to justify new laws through inference rules. This justificational picture was criticized by
Hume Hume most commonly refers to: * David Hume (1711–1776), Scottish philosopher Hume may also refer to: People * Hume (surname) * Hume (given name) * James Hume Nisbet (1849–1923), Scottish-born novelist and artist In fiction * Hume, the ...

on the basis of 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. Popper argued that an even greater weakness of this view is the level of certainty that it expects from the observation statements as falsifiers (and even as verifiers) in a logical inductive process. The potential falsifiers, which play perfectly their role to show falsifiability or to steer creativity and critical discussions in the case of falsifications, are much less useful in this justificational perspective, because of all the problems of falsifications. 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 said that the processes in the bucket are better seen as physical processes and the laws that govern these processes are biological. 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.

## The searchlight view of science

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. If one wants 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. 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. 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. 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." 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. As described in , every rule to determine or choose theories must rely on the good judgement of the scientists. 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 , this is exactly what we should expect from a scientific theory. In , it is seen that Lakatos reached the same conclusion in the following sense that he said that his methodology did not offer any "firm heuristic advice about what to do". Before Popper's time, in 1906, being aware of the problems of falsification,
Pierre Duhem Pierre Maurice Marie Duhem (; 9 June 1861 – 14 September 1916) was a French theoretical physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, ...

reached the same conclusion. Popper reemphasized non-justificationism, which was a good match for his added falsifiability criterion and associated critical methodology.

# Lakatos' falsificationism

Imre Lakatos Imre Lakatos (, ; hu, Lakatos Imre ; November 9, 1922 – February 2, 1974) was a HungarianHungarian may refer to: * Hungary, a country in Central Europe * Kingdom of Hungary, state of Hungary, existing between 1000 and 1946 * Hungarians, ethn ...
divided the problems of falsification in two categories. The first category corresponds to decisions that must be agreed upon by scientists before they can falsify a theory. The other category emerges when one tries to use falsifications and corroborations to explain progress in science. Lakatos said that there were two incorrect approaches, which he called dogmatic falsificationism and naive falsificationism. Dogmatic falsificationism ignores both types of problems, whereas naive falsificationism considers the first type only. Lakatos contrasted them with sophisticated falsificationism, his own improvement on Popper's solution. Popper's methodology is not (and has never been) based on one of the two incorrect approaches. On the terminological side of this issue, Popper said that he never referred to his methodology as "falsificationism", tended to avoid this term and proposed instead the term "
critical rationalism Critical rationalism is an epistemological Epistemology (; ) is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, kn ...
".

## Dogmatic falsificationism

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? This is sometimes called the ' Duhem–Quine problem'. An example is Galileo's refutation of the 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. Another example is the theory that neutrinos are emitted in
beta decay In , beta decay (''β''-decay) is a type of in which a (fast energetic or ) is emitted from an , transforming the original to an of that nuclide. For example, beta decay of a transforms it into a by the emission of an electron accompanie ...

s. Had they not been observed in the
Cowan–Reines neutrino experimentThe Cowan–Reines neutrino experiment was conducted by Washington University in St. Louis alumnus Clyde L. Cowan and Stevens Institute of Technology and New York University alumnus Frederick Reines in 1956. The experiment confirmed the existence ...
, many would have considered that the strength of the beta-inverse reaction used to detect the neutrinos was not sufficiently high. At the time, wrote, the possibility that this strength was sufficiently high was a "pious hope". A dogmatic falsificationist ignores the role of auxiliary hypotheses, which could explain the contradicting observation. For the falsification to logically occur, a
ceteris paribus ' or ' () is a Latin phrase meaning "other things equal"; English translations of the phrase include "all other things being equal" or "other things held constant" or "all else unchanged". A prediction or a statement about a ontic, causal, epist ...
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, though he clearly distinguished falsifiable theories such as Newton theory and unfalsifiable theories on this respect. Lakatos says that Popper's solution to these criticisms requires that one relaxes the assumption that an observation can show a theory to be false: Methodological falsificationism replaces the contradicting observation in a falsification with a "contradicting observation" accepted by convention among scientists, a convention that implies four kinds of decisions that have these respective goals: the selection of all ''basic statements'' (statements that correspond to logically possible observations), selection of the ''accepted basic statements'' among the basic statements, making statistical laws falsifiable and applying the refutation to the specific theory (instead of the ceteris paribus clause). The falsifiers and falsifications 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". He also says (see section ) that it's not an obstacle to the definition of an empirical basis and of falsifiability.

## Naive falsificationism

According to Lakatos, naive falsificationism is the claim that methodological falsifications can by themselves explain how scientific knowledge progresses. Very often a theory is still useful and used even after it is found in contradiction with some observations. Also, when scientists 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. 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. How corroborations and falsifications can explain progress in science was a subject of disagreement between many philosophers, especially between Lakatos and Popper. Popper 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. The main issue is whether the decision to select a theory among competing theories in the light of falsifications and corroborations could be justified using some kind of formal logic. It is a delicate question, because this logic would be inductive: it justifies a universal law in view of instances. Also, falsifications, because they are based on methodological decisions, are useless in a strict justification perspective. The answer of Lakatos and many others to that question is that it should. In contradistinction, for Popper, the creative and informal part is guided by methodological rules, which naturally say to favour theories that are corroborated over those that are falsified, but this methodology can hardly be made rigorous. Popper's way to analyze progress in science was through the concept of
verisimilitude In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, l ...
, a way to define how close a theory is to the truth, which he did not consider very significant, except (as an attempt) to describe 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. Today, there is still on going research on the general concept of verisimilitude.

## From the problem of induction to falsificationism

Hume explained induction with a theory of the mind that was in part inspired by Newton's theory of gravitation.: Hume explicitly models his account of the fundamental principles of the mind’s operations—the principles of association—on the idea of gravitational attraction. Popper rejected Hume's explanation of induction and proposed his own mechanism: science progresses by trial and error within an evolutionary epistemology. Hume believed that his psychological induction process follows laws of nature, but, for him, this does not imply the existence of a method of justification based on logical rules. In fact, he argued that any induction mechanism, including the mechanism described by his theory, could not be justified logically. Similarly, Popper adopted an evolutionary epistemology, which implies that some laws explain progress in science, but yet insists that the process of trial and error is hardly rigorous and that there is always an element of irrationality in the creative process of science. The absence of a method of justification is a built-in aspect of Popper's trial and error explanation. As rational as they can be, these explanations that refer to laws, but cannot be turned into methods of justification (and thus do not contradict Hume's argument or its premises), were not sufficient for some philosophers. In particular, Russell once expressed the view that if Hume's problem cannot be solved, “there is no intellectual difference between sanity and insanity” and actually proposed a method of justification. He rejected Hume's premise that there is a need to justify any principle that is itself used to justify induction. It might seem that this premise is hard to reject, but to avoid circular reasoning we do reject it in the case of deductive logic. It makes sense to also reject this premise in the case of principles to justify induction. Lakatos' proposal of sophisticated falsificationism was very natural in that context. Therefore, Lakatos urged Popper to find an inductive principle behind the trial and error learning process and sophisticated falsificationism was his own approach to address this challenge. Kuhn, Feyerabend, Musgrave and others mentioned and Lakatos himself acknowledged that, as a method of justification, this attempt failed, because there was no normative methodology to justify—Lakatos' methodology was anarchy in disguise.

## Falsificationism in Popper's philosophy

Popper's philosophy is sometimes said to fail to recognize the Quine-Duhem thesis, which would make it a form of dogmatic falsificationism. For example, Watkins wrote "apparently forgetting that he had once said 'Duhem is right ..', Popper set out to devise potential falsifiers just for Newton's fundamental assumptions". But, Popper's philosophy is not always qualified of falsificationism in the pejorative manner associated with dogmatic or naive falsificationism. The problems of falsification are acknowledged by the falsificationists. For example, Chalmer points out that falsificationists freely admit that observation is theory impregnated. Thornton, referring to Popper's methodology, says that the predictions inferred from conjectures are not directly compared with the facts simply because all observation-statements are theory-laden. For the critical rationalists, the problems of falsification are not an issue, because they do not try to make experimental falsifications logical or to logically justify them, nor to use them to logically explain progress in science. Instead, their faith rests on critical discussions around these experimental falsifications. Lakatos made a distinction between a "falsification" (with quotation marks) in Popper's philosophy and a falsification (without quotation marks) that can be used in a systematic methodology where rejections are justified. He knew that Popper's philosophy is not and has never been about this kind of justifications, but he felt that it should have been. Sometimes, Popper and other falsificationists say that when a theory is falsified it is rejected, which appears as dogmatic falsificationism, but the general context is always critical rationalism in which all decisions are open to critical discussions and can be revised.

# Controversies

## Methodless creativity versus inductive methodology

As described in section , Lakatos and Popper agreed that universal laws cannot be logically deduced (except from laws that say even more). But unlike Popper, Lakatos 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 and sets himself the task to find an inductive methodology. However, the methodology that he found did not offer any exact inductive rules. In a response to Kuhn, Feyerabend and Musgrave, Lakatos acknowledged that the methodology depends on the good judgment of the scientists. Feyerabend wrote in "Against Method" that Lakatos' methodology of scientific research programmes is epistemological anarchism in disguise and Musgrave made a similar comment. In more recent work, Feyerabend says that Lakatos uses rules, but whether or not to follow any of these rules is left to the judgment of the scientists. This is also discussed elsewhere. 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. 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.

## Ahistorical versus historiographical

Section 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?". 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."

## Normal science versus revolutionary science

Thomas Kuhn Thomas Samuel Kuhn (; July 18, 1922 – June 17, 1996) was an American whose 1962 book ' was influential in both academic and popular circles, introducing the term ', which has since become an English-language idiom. Kuhn made several cla ...
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 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 ). 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.

## Unfalsifiability versus falsity of astrology

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. Kuhn, 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 said that astrologers themselves acknowledged these falsifications.

## Anything goes versus scientific method

Paul Feyerabend Paul Karl Feyerabend (; ; January 13, 1924 – February 11, 1994) was an Austria Austria, officially the Republic of Austria, is a landlocked country in the southern part of Central Europe, located on the Eastern Alps. It is compose ...
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. He said 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 ''Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science'' (1998; UK: ''Intellectual Impostures''), first published in French in 1997 as french: Impostures intellectuelles, label=none, is a book by physicists Alan Sokal and Jean Bricmont ...
'' (from 1997, published in the UK as ''Intellectual Impostures'') the physicists
Alan Sokal Alan David Sokal (; born January 24, 1955) is a professor of mathematics at University College London and professor of physics at New York University. He works in statistical mechanics and combinatorics. He is a critic of postmodernism, and caused ...

and
Jean Bricmont Jean Bricmont (; born 12 April 1952) is a Belgian theoretical physicist and philosopher of science. Professor at the Catholic University of Louvain (UCLouvain), he works on renormalization group and nonlinear differential equation In math ...
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 description of falsifiability, and more generally, to his theory of science.

* * * * - claim that a ciphertext decrypts to a particular plaintext can be falsified by possible decryption to another potential plaintext * * * * ** ** * * * * * * * ** ** ** ** ** ** ** ** ** ** * * *

# References

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Excerpt
Science as Falsification
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *