The problem of induction and demarcation
One of the questions in theFrom Hume's problem to non problematic induction
The problem of induction is often called Hume's problem.The elusive distinction between the logic of science and its applied methodology
Popper distinguished between the logic of science and its applied ''methodology''. For example, the falsifiability of Newton's law of gravitation, as defined by Popper, depends purely on the logical relation it has with a statement such as "The brick fell upwards when released". A brick that falls upwards would not alone falsify Newton's law of gravitation. The capacity to verify the absence of conditions such as a hidden string attached to the brick is also needed for this state of affairs to eventually falsify Newton's law of gravitation. However, these applied methodological considerations are irrelevant in 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. There is no requirement that the potential falsifier can actually show the law to be false. The purely logical contradiction, together with the material requirement, are sufficient. 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. Popper wrote that an entire literature exists because this distinction between the logical aspect and the methodological aspect was not observed. This is still seen in a more recent literature. For example, in their 2019 article ''Evidence based medicine as science'', Vere and Gibson wrote " alsifiability hasbeen considered problematic because theories are not simply tested through falsification but in conjunction with auxiliary assumptions and background knowledge."Basic statements and the definition of falsifiability
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 verifiability: "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 cannot 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 theExamples 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. Popper thought that it was a basic statement that was a potential falsifier for Newton's theory, because the position of the apple at different times can be measured. Popper's claims on this point are controversial, since Newtonian physics does not deny that there could be forces acting on the apple that are stronger than Earth's gravity.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
Precambrian rabbit
A famous example of a basic statement from J. B. S. Haldane 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, sometimes 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 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
Some adherents of young-Earth creationism 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 world 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, because Popper considers that metaphysical statements can be useful, but also 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 falsifiable law exists, then the metaphysical law is less useful, because it is not indirectly corroborated. This kind of non-falsifiable statements in science was noticed by Carnap as early as 1937.Natural selection
In the 5th and 6th editions of '' On the Origin of Species'', following a suggestion of Alfred Russel Wallace, Darwin used "Survival of the fittest", an expression first coined byMathematics
Popper said that not all unfalsifiable statements are useless in science. Mathematical statements are good examples. Like all formal sciences, mathematics is not concerned with the validity of theories based on observations in theHistoricism
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". In Popper's view, this was both testable and subsequently 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 were not directed toward Marxism, or Marx's theories, which were falsifiable, but toward Marxists who he considered to have 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" was not scientific and should not be taught inDaubert standard
In several cases of theConnections 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, Neyman and Pearson proposed approaches that require no prior probabilities on the hypotheses that are being studied. In contrast, Bayesian inference 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' 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 as 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 a 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".Lakatos's falsificationism
Imre Lakatos 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 described four kind of falsificationisms in view of how they address these problems. Dogmatic falsificationism ignores both types of problems. Methodological falsificationism addresses the first type of problems by accepting that decisions must be taken by scientists. Naive methodological falsificationism or naive falsificationism does not do anything to address the second type of problems. Lakatos used dogmatic and naive falsificationism to explain how Popper's philosophy changed over time and viewed sophisticated falsificationism as his own improvement on Popper's philosophy, but also said that Popper some times appears as a sophisticated falsificationist. Popper responded that Lakatos misrepresented his intellectual history with these terminological distinctions.Dogmatic falsificationism
A dogmatic falsificationist ignores that every observation is theory-impregnated. Being theory-impregnated means that it goes beyond direct experience. For example, the statement "Here is a glass of water" goes beyond experience, because the concepts of glass and water "denote physical bodies which exhibit a certain law-like behaviour" (Popper). 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 inNaive 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 is 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 ofFrom 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's 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's 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, Chalmers 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 justification, 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 cannot 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's 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." According to David Stove, Lakatos succeeded, since Lakatos showed there is no such thing as a "non-Newtonian" behaviour of an observable object. Stove argued that Popper's counterexamples to Lakatos were either instances of begging the question, such as Popper's example of missiles moving in a "non-Newtonian track", or consistent with Newtonian physics, such as objects not falling to the ground without "obvious" countervailing forces against Earth's gravity.Normal science versus revolutionary science
Unfalsifiability versus falsity of astrology
Popper often uses astrology as an example of a pseudoscience. He says that it is not falsifiable because both the theory itself and its predictions are too imprecise. Kuhn, as a 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.Epistemological anarchism vs the scientific method
Paul Feyerabend rejected any prescriptive methodology at all. He rejected Lakatos's 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'' (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 description of falsifiability, and more generally, to his theory of science.See also
* * * * - claim that a ciphertext decrypts to a particular plaintext can be falsified by possible decryption to another potential plaintext * * * * ** ** * * * * * * * ** ** ** ** ** ** ** ** ** ** * * * *Notes
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* {{Authority control Analytic philosophy Epistemology of science Epistemological theories Karl Popper Razors (philosophy)