Falsifiability

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

Falsifiability is the assertion that any hypothesis must be inherently disprovable before it can become accepted as a scientific hypothesis or theory. It was introduced by the philosopher of science Karl Popper in his book The Logic of Scientific Discovery (1934), as an answer to both the Problem of Induction and the Demarcation Problem. He saw falsifiability as the cornerstone of critical rationalism, his theory of science. As a key notion in the separation of science from non-science, it has featured prominently in many scientific controversies and applications, even being used as legal precedent.

Informally, a statement is falsifiable if some observation might show it to be false. For example, "All swans are white" is falsifiable because the discovery of a non-white swan shows it to be false. Many arguments can become unfalsifiable due to an endless stream of ad hoc theories which attempt to explain anomalous results. Young Earth Creationism is generally accepted to be unfalsifiable for this reason.

Importantly, falsifiability does not imply that there are currently arguments against a theory, only that it is possible to imagine an argument which would invalidate it. It says nothing about an argument's inherent validity.

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

Critical rationalism as a solution to the problem of induction

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

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

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

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

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

Away from dogmatic falsificationism

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

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

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

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. These observation or basic statements constitute the empirical "basis". The empirical basis thus depends on decisions made by scientists in view of the currently accepted technology and its associated theory. So, Popper says that "Science does not rest upon solid bedrock".

Away from naive falsificationism

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

Popper clearly distinguished between the creative and informal process from which theories emerge and the logical and formal process where theories are falsified or corroborated. 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. It is a delicate question, because this logic could be considered as inductive: it selects a universal law in view of instances. The answer of Lakatos and many others to that question is that it should. In contradistinction, for Popper, the creative and informal part is guided by methodological rules, which naturally say to favor theories that are corroborated, but this methodology can hardly be made rigorous. Popper does not mention corroborations when he describes the purely logical part.

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. Today, there is still on going research on the general concept of verisimilitude.

Demarcation problem

Main article: Demarcation problem

Given an empirical basis, the criterion of demarcation draws a sharp line between those theories that are scientific, and those that are un-scientific. It is useful to know if a statement or theory is falsifiable, if, for no other reason, than that it provides us with an understanding of the ways in which one might assess the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory. Popper claimed that, if a theory is falsifiable, then it is scientific.

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

Historical context : logical positivism

In the philosophy of science, verificationism holds that a statement must, in principle, be empirically verifiable in order that it be scientific. This was an essential feature of the logical positivism of the so-called Vienna Circle, which included such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath, and logical empiricism of A.J. Ayer. Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, that of meaning and that of demarcation, and had proposed in verificationism a single solution to both: a statement that could not be verified was considered meaningless and thus useless. In opposition to this view, Popper emphasized that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.

Demarcation and growth of knowledge

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

Controversies

Kuhn

Main article: Thomas Kuhn

Thomas Kuhn emphasized aspects of science that were not much considered by Popper. In particular, he analyzed what he calls periods of normal science as well as revolutions from one period of normal science to another, whereas Popper's view is that only revolutions are relevant. For Popper, the role of science, mathematics and metaphysics, actually the role of any knowledge, is to solve puzzles. In the same line of thought, Kuhn observes that in periods of normal science the scientific theories, which are created under 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 #Away_from_naive_falsificationism). In the big picture presented by Kuhn, the routinely solved puzzles are corroborations. Falsifications or otherwise unexplained observations are unsolved puzzles. All of these are used in the informal process that generates a new kind of theory. Kuhn says that Popper emphasizes formal or logical falsifications and fails to explain how the social and informal process works.

Feyerabend

Main article: Paul Feyerabend

Paul Feyerabend examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He rejected Lakatos' argument for ad hoc hypothesis, arguing that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method. Rather, he claimed that if one is keen to have a universally valid methodological rule, epistemological anarchism or anything goes would be the only candidate. For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method.

Sokal and Bricmont

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

Applications

Use in courts of law

Falsifiability has been used in the McLean v. Arkansas case (in 1982), the Daubert case (in 1993) and other cases. A survey of 303 federal judges conducted in 1998 revealed that "[P]roblems with the nonfalsifiable nature of an expert’s underlying theory and difficulties with an unknown or too-large error rate were cited in less than 2% of cases."

McLean v. Arkansas case

In the ruling of the McLean v. Arkansas case, Judge William Overton used falsifiability as one of the criteria to determine that "creation science" was not scientific and should not be taught in Arkansas public schools as such (it can be taught as religion). In his testimony, philosopher Michael Ruse defined the characteristics which constitute science as (see Pennock 2000, p. 5 and Ruse 2010):

• It is guided by natural law;
• It has to be explanatory by reference to natural law;
• It is testable against the empirical world;
• Its conclusions are tentative, i.e., are not necessarily the final word; and
• It is falsifiable.

In his conclusion related to this criterion Judge Overton stated that

While anybody is free to approach a scientific inquiry in any fashion they choose, they cannot properly describe the methodology as scientific, if they start with the conclusion and refuse to change it regardless of the evidence developed during the course of the investigation.

— William Overton, McLean v. Arkansas 1982, at the end of section IV. (C)

Daubert v. Merrell Dow Pharmaceuticals case

In the Daubert case, the majority opinion proposed the so-called five Daubert factors, which include falsifiability, to define a scientific methodology that is acceptable in courts of law. 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 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."

Economics

Karl Popper argued that Marxism shifted from scientific to unscientific.

Some economists, such as those of the Austrian School, believe that macroeconomics is empirically unfalsifiable and that thus the only appropriate means to understand economic events is by logically studying the intentions of individual economic decision-makers, based on certain fundamental truths. Prominent figures within the Austrian School of economics, Ludwig von Mises and Friedrich Hayek were associates of Karl Popper, with whom they co-founded the Mont Pelerin Society.

Evolution

Main article: Objections to evolution: Unfalsifiability

Numerous examples of potential (indirect) ways to falsify common descent have been proposed by its proponents. J.B.S. Haldane, when asked what hypothetical evidence could disprove evolution, replied "fossil rabbits in the Precambrian era". Richard Dawkins adds that any other modern animal, such as a hippo, would suffice. Karl Popper at first spoke against the testability of natural selection but recanted, "I have changed my mind about the testability and logical status of the theory of natural selection, and I am glad to have the opportunity to make a recantation."

Young-earth creationism

Main article: Omphalos hypothesis

Much of the criticism against young-Earth creationism is based on evidence in nature that the Earth is much older than adherents believe. Confronting such evidence, some adherents make an argument (called the Omphalos hypothesis) that the world was created with the appearance of age; e.g., the sudden appearance of a mature chicken capable of laying eggs. This hypothesis is non-falsifiable since no evidence about the age of the earth (or any astronomical feature) can be shown not to be fabricated during creation.

Historicism

Theories of history or politics that allegedly predict future events have a logical form that renders them neither falsifiable nor verifiable. They claim that for every historically significant event, there exists an historical or economic law that determines the way in which events proceeded. Failure to identify the law does not mean that it does not exist, yet an event that satisfies the law does not prove the general case. Evaluation of such claims is at best difficult. On this basis, Popper "fundamentally criticized historicism in the sense of any preordained prediction of history" and argued that neither Marxism nor psychoanalysis was science, although both made such claims. Again, this does not mean that any of these types of theories is necessarily incorrect. Popper considered falsifiability a test of whether theories are scientific, not of whether propositions that they contain or support are true.

Mathematics

Like all formal sciences, mathematics is not concerned with the validity of theories based on observations in the empirical world, but rather, mathematics is occupied with the theoretical, abstract study of such topics as quantity, structure, space and change. Methods of the mathematical sciences are, however, applied in constructing and testing scientific models dealing with observable reality. Albert Einstein wrote, "One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts."

See also: Mathematical proof, Scientific method and mathematics, Mathematics as science, and Popper's "two senses" theory

See also

• Black swan theory – Theory of response to surprise events
• Contingency – Possible truths which are not necessary
• Critical rationalism – Epistemological philosophy advanced by Karl Popper
• Defeasible reasoning – Reasoning that is rationally compelling, though not deductively valid
• Duhem–Quine thesis – Principle in the philosophy of science
• Experimentum crucis – Critical experiment
• Explanatory power – Ability of a theory to explain a subject
• Fallibilism – Philosophical principle
• Fallacy – Argument that uses faulty reasoning (informal logic and rhetoric)
• Raven paradox – Paradox arising from the question of what constitutes evidence for a statement, or Hempel's paradox
• Hitchens's razor – General rule rejecting claims made without evidence
• Hypothetico-deductive model – Proposed description of the scientific method
• Inquiry – Any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem
• Metaphysical solipsism – Variety of philosophical idealism
• Methodological solipsism
• Newton's Flaming Laser Sword – Australian mathematician and philosopher
• Occam's razor – Philosophical problem-solving principle
• Philosophy of mathematics
• Philosophy of science
• Pragmatic maxim
• Precambrian rabbit – Evolutionary biology hypothetical posed by J. B. S. Haldane
• Predictive power – Ability of a scientific theory to generate testable predictions
• Reproducibility – Aspect of scientific research
• Russell's teapot – Analogy devised by Bertrand Russell
• Superseded scientific theories – Obsolete theories in natural philosophy and natural historyPages displaying short descriptions of redirect targets
• Tautology – In logic, a statement which is always true
• Theory-ladenness – Degree to which an observation is affected by one's presuppositions
• Trial and error – Method of problem-solving

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• Rosende, Diego L. (2009). "Popper on Refutability : Some Philosophical and Historical Questions". In Parusnikova, Zuzana; Cohen, Robert S. (eds.). Rethinking Popper. Boston Studies in the Philosophy of Science. Springer. {{cite book}}: Invalid |ref=harv (help)
• Ruse, Michael (2010). Science and Spirituality: Making Room for Faith in the Age of Science (1st ed.). New York: Cambridge university press. ISBN 978-0-521-75594-8. {{cite book}}: Invalid |ref=harv (help)
• Sokal, Alan, and Bricmont, Jean, Fashionable Nonsense, Picador, New York, NY, 1998.
• Soler, Léna (2001). "Certitudes, incertitudes et enjeux de la philosophie des sciences contemporaine". Le Portique. 7. Archived from the original on 2017-12-16. {{cite journal}}: Invalid |ref=harv (help)
• Theobald, D.L. (2006). 29+ Evidences for Macroevolution: The Scientific Case for Common Descent. The Talk.Origins Archive. Version 2.87.
• Thornton, Stephen (2016) [original publication 1997]. "Karl Popper". In Zalta, Edward N. (ed.). The Stanford Encyclopedia of Philosophy (Summer 2017 ed.). {{cite book}}: Invalid |ref=harv (help)
• United States v. Prime, 220 F. Supp. 2d 1203 (W.D.Wash.).
• Wallis, C (2005-08-07). "The Evolution Wars". Time Magazine. {{cite magazine}}: Invalid |ref=harv (help)
• Watkins, John (1970). "Against 'Normal Science'". In Lakatos, Imre; Musgrave, Alan (eds.). Criticism and the growth of knowledge. Cambridge University Press. pp. 25–37. {{cite book}}: Invalid |ref=harv (help)