A statement, hypothesis, or theory has falsifiability or refutability if there is the possibility of showing it to be false. It is falsifiable if it is possible to conceive an empirical observation which could refute it. For example, the universal generalization that All swans are white is falsifiable since it is logically possible to falsify it by observing a single swan that is not white.
The concern with falsifiability gained attention by way of philosopher of science Karl Popper’s scientific epistemology referred to as ‘falsificationism.’ Popper stresses the problem of ‘demarcation’—distinguishing the scientific from the unscientific—and makes falsifiability the demarcation criterion, such that what is unfalsifiable is classified as unscientific, and the practice of declaring an unfalsifiable theory to be scientifically true is pseudoscience.
The classical view of the philosophy of science is that it is the goal of science to prove hypotheses like ‘All swans are white’ or to induce them from observational data. Popper argued that this would require the inference of a general rule from a number of individual cases, which is inadmissible in deductive logic. However, if one finds one single swan that is not white, deductive logic admits the conclusion that the statement that all swans are white is false. Falsificationism thus strives for questioning of hypotheses instead of proving them.
For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come into conflict with observation. A key observation of falsificationism is thus that a criterion of demarcation is needed to distinguish those statements that can come into conflict with observation and those that cannot. Popper chose falsifiability as the name of this criterion.
Contrary to intuition, unfalsifiable statements can be embedded in—and deductively entailed by—falsifiable theories. For example, while ‘all men are mortal’ is unfalsifiable, it is a logical consequence of the falsifiable theory that ‘every man dies before he reaches the age of 150 years.’ Similarly, the ancient metaphysical and unfalsifiable idea of the existence of atoms has led to corresponding falsifiable modern theories. Popper invented the notion of metaphysical research programs to name such unfalsifiable ideas.
In contrast to Positivism, which held that statements are meaningless if they cannot be verified or falsified, Popper claimed that falsifiability is merely a special case of the more general notion of criticizability, even though he admitted that empirical refutation is one of the most effective methods by which theories can be criticized. Criticizability, in contrast to falsifiability, and thus rationality, may be comprehensive (i.e., have no logical limits), though this claim is controversial, even among proponents of Popper’s philosophy and critical rationalism.
Although the logic of naïve falsification is valid, it is rather limited. Nearly any statement can be made to fit the data, so long as one makes the requisite ‘compensatory adjustments.’ Popper drew attention to these limitations in ‘The Logic of Scientific Discovery’ in response to criticism from French philosopher of science Pierre Duhem. American logician W. V. Quine expounded this argument in detail, calling it ‘confirmation holism.’ To logically falsify a universal, one must find a true falsifying singular statement. But Popper pointed out that it is always possible to change the universal statement or the existential statement so that falsification does not occur. On hearing that a black swan has been observed in Australia, one might introduce the ad hoc hypothesis, ‘all swans are white except those found in Australia’; or one might adopt another, more cynical view about some observers, ‘Australian bird watchers are incompetent’.
Thus, naïve falsification ought to, but does not, supply a way of handling competing hypotheses for many subject controversies (for instance conspiracy theories and urban legends). People arguing that there is no support for such an observation may argue that there is nothing to see, that all is normal, or that the differences or appearances are too small to be statistically significant. On the other side are those who concede that an observation has occurred and that a universal statement has been falsified as a consequence. Therefore, naïve falsification does not enable scientists, who rely on objective criteria, to present a definitive falsification of universal statements.
Naïve falsificationism is an unsuccessful attempt to prescribe a rationally unavoidable method for science. Sophisticated methodological falsification, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice. The object of this is to arrive at an incremental process whereby theories become less bad.
Naïve falsification considers scientific statements individually. Scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypotheses. As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.
In place of naïve falsification, Popper envisioned science as progressing by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories that can account for the phenomena that falsified the prior theory, that is, with greater explanatory power. For example, Aristotelian mechanics explained observations of everyday situations, but were falsified by Galileo’s experiments, and were replaced by Newtonian mechanics, which accounted for the phenomena noted by Galileo (and others). Newtonian mechanics’ reach included the observed motion of the planets and the mechanics of gases.
The Youngian wave theory of light (i.e., waves carried by the luminiferous aether) replaced Newton’s (and many of the Classical Greeks’) particles of light but in turn was falsified by the Michelson-Morley experiment and was superseded by Maxwell’s electrodynamics and Einstein’s special relativity, which did account for the newly observed phenomena. Furthermore, Newtonian mechanics applied to the atomic scale was replaced with quantum mechanics, when the old theory could not provide an answer to the ultraviolet catastrophe, the Gibbs paradox, or how electron orbits could exist without the particles radiating away their energy and spiraling towards the centre. Thus the new theory had to posit the existence of unintuitive concepts such as energy levels, quanta and Heisenberg’s uncertainty principle.
At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found that had greater explanatory power (i.e., could account for the previously unexplained phenomena), and as a result, provided greater opportunity for its own falsification.
Popper uses falsification as a criterion of demarcation to draw a sharp line between those theories that are scientific and those that are unscientific. 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, or come to see an unfalsifiable theory as unsupportable. Popper claimed that, if a theory is falsifiable, then it is scientific.
Judge William Overton used falsifiability in the ‘McLean v. Arkansas’ ruling in 1982 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). The argument was presented by philosopher Michael Ruse, who defined the characteristics which constitute science as ‘explanatory,’ ‘testable,’ and ‘tentative’; the latter of the three being another term for falsifiability. In his conclusion related to this criterion Judge Overton stated that ‘[w]hile 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.’
The Daubert standard set forth in the United States Supreme Court decision ‘Daubert v. Merrell Dow Pharmaceuticals, Inc.’ suggests that when determining whether scientific evidence is admissible, one of five factors that the U.S. federal courts should consider is ‘whether the theory or technique in question can be and has been tested.’ Some commentators have suggested that ‘inquiring into the existence of meaningful attempts at falsification is an appropriate and crucial consideration in admissibility determinations’ but that some courts have misconstrued Daubert by accepting ‘the abstract possibility of falsifiability’ as sufficient, rather than requiring ‘actual corroboration’ through empirical testing.
Many contemporary philosophers of science and analytic philosophers are strongly critical of Popper’s philosophy of science. Popper’s mistrust of inductive reasoning has led to claims that he misrepresents scientific practice.
Whereas Popper was concerned in the main with the logic of science, Thomas Kuhn’s influential book ‘The Structure of Scientific Revolutions’ examined in detail the history of science. Kuhn argued that scientists work within a conceptual paradigm that strongly influences the way in which they see data. Scientists will go to great length to defend their paradigm against falsification, by the addition of ad hoc hypotheses to existing theories. Changing a ‘paradigm’ is difficult, as it requires an individual scientist to break with his or her peers and defend a heterodox theory.
Some falsificationists saw Kuhn’s work as a vindication, since it provided historical evidence that science progressed by rejecting inadequate theories, and that it is the decision, on the part of the scientist, to accept or reject a theory that is the crucial element of falsificationism. Foremost amongst these was Hungarian philosopher of mathematics Imre Lakatos.
Lakatos attempted to explain Kuhn’s work by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naïve falsification. In Lakatos’ approach, a scientist works within a research program that corresponds roughly with Kuhn’s ‘paradigm.’ Whereas Popper rejected the use of ad hoc hypotheses as unscientific, Lakatos accepted their place in the development of new theories.
In their book ‘Fashionable Nonsense,’ physicists Alan Sokal and Jean Bricmont criticized falsifiability on the grounds that it does not accurately describe the way science really works. They argue that theories are used because of their successes, not because of the failures of other theories. Their discussion of Popper, falsifiability and the philosophy of science comes in a chapter entitled ‘Intermezzo,’ which contains an attempt to make clear their own views of what constitutes truth, in contrast with the extreme epistemological relativism of postmodernism where every fact is subjective. They further argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions that are sometimes incorrect.
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.
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.
Many philosophers believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper. However, in the 1930s Gödel’s incompleteness theorems proved that there does not exist a set of axioms for mathematics which is both complete and consistent. Karl Popper concluded that ‘most mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently.’ Other thinkers, notably Imre Lakatos, have applied a version of falsificationism to mathematics itself.
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.’
The Daily Omnivore 
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