Falsifiability

Are all swans white?

Falsifiability or refutability of an assertion or atheory is the logical possibility that the assertion (or the theory) can be contradicted by an observation or the outcome of a physical experiment. That something is "falsifiable" does not mean it is false; rather, that if it is false, then some observation or experiment will produce a reproducible result that is in conflict with it.

For example, the assertion "all swans are white" is falsifiable, since it it conceivable to find a swan for which one may successfully argue that it is not white, and hence this would allow us to conclude that the statement "all swans are white" is false. On the other hand, the statement "all women are mortal" is not falsifiable, since there is no known way to prove that a particular person is immortal.

The concept was made popular by Karl Popper, who, in his philosophical criticism of the popular positivist view of the scientific method, concluded that a hypothesis, proposition, or theory talks about the observable only if it is falsifiable. Still, Popper stressed that unfalsifiable statements are important in science, and that, contrary to intuition, they 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 senseless 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.

Falsifiability is an important concept within the creation–evolution controversy, where proponents of both sides claim that Popper developed falsifiability to denote ideas as unscientific or pseudoscientific and use it to make arguments against the views of the respective other side. The question of what can legitimately be called science and what cannot be legitimately called science is of major importance in this debate because US law says that only science may be taught in public school science classes. Thus, the controversy raises the issue whether creationistic ideas, or at least some of them, or at least in some form, may be legitimately called science. Falsifiability has even been used in court decisions in this context as a key deciding factor to distinguish genuine science from the nonscientific.

Naïve falsification

Two types of statements: observational and categorical

In work beginning in the 1930s, Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.

Popper noticed that two types of statements are of particular value to scientists.

The first are statements of observations, such as "there is a white swan." Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They are equivalent to a propositional calculus statement of the form: There exists an x such that x is a swan, and x is white.

The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has eluded observation (and, in fact, the discovery of the Australian black swan demonstrated the deductive invalidity of this particular statement).

Inductive categorical inference

Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the problem of induction. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false—in logic this is called modus tollens. 'There is a black swan' implies 'there is a non-white swan,' which, in turn, implies 'there is something that is a swan and that is not white', hence 'all swans are white' is false, because that is the same as 'there is nothing that is a swan and that is not white'.

One notices a white swan. From this one can conclude:

At least one swan is white.

From this, one may wish to conjecture:

All swans are white.

It is impractical to observe all the swans in the world to verify that they are all white.

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single black swan, then the statement all swans are white would be falsified by the counterexample of the single black swan.

Deductive falsification

Deductive falsification is different from an absence of verification. The falsification of statements occurs through modus tollens, via some observation. Suppose some universal statement U forbids some observation O:

$U \rightarrow \neg O$

Observation O, however, is made:

$\ \ O$

So by modus tollens,

$\neg U$

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 Pierre Duhem. 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.

Falsificationism

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 evolutionary 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 evolving 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.

The criterion of demarcation

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.

The Popperian criterion excludes from the domain of science not unfalsifiable statements but only whole theories that contain no falsifiable statements; thus it leaves us with the Duhemian problem of what constitutes a 'whole theory' as well as the problem of what makes a statement 'meaningful'. Popper's own falsificationism, thus, is not only an alternative to verificationism, it is also an acknowledgement of the conceptual distinction that previous theories had ignored.

Verificationism

Main article: Verificationist

See also: Abductive reasoning

In the philosophy of science, verificationism (also known as the verifiability theory of meaning) holds that a statement must, in principle, be empirically verifiable for it to be both meaningful and scientific. This was an essential feature of the logical positivism of the so-called Vienna Circle that included such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath, the Berlin philosopher Hans Reichenbach, and the 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. 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.

Thus, Popper urged that verifiability be replaced with falsifiability as the criterion of demarcation. On the other hand, he strictly opposed the view that non-falsifiable statements are meaningless or otherwise inherently bad, and noted that falsificationism does not imply it.

Use in courts of law

Falsifiability was one of the criteria used by Judge William Overton in the McLean v. Arkansas ruling 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 conclusion related to this criterion he 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."

It was also enshrined in United States law as part of the Daubert Standard set by the Supreme Court for whether scientific evidence is admissible in a jury trial.

Criticisms

Contemporary philosophers

Many contemporary philosophers of science and analytic philosophers are strongly critical of Popper's philosophy of science^{[citation needed]} . Popper's mistrust of inductive reasoning has led to claims that he misrepresents scientific practice. Among the professional philosophers of science, the Popperian view has never been seriously preferred to probabilistic induction, which is the mainstream account of scientific reasoning. Adherents of Popper speak with disrespect of "professional philosophy", for example W. W. Bartley:

Sir Karl Popper is not really a participant in the contemporary professional philosophical dialogue; quite the contrary, he has ruined that dialogue. If he is on the right track, then the majority of professional philosophers the world over have wasted or are wasting their intellectual careers. The gulf between Popper's way of doing philosophy and that of the bulk of contemporary professional philosophers is as great as that between astronomy and astrology.

Rafe Champion:

Popper's ideas have failed to convince the majority of professional philosophers because his theory of conjectural knowledge does not even pretend to provide positively justified foundations of belief. Nobody else does better, but they keep trying, like chemists still in search of the Philosopher's Stone or physicists trying to build perpetual motion machines.

and David Miller:

What distinguishes science from all other human endeavours is that the accounts of the world that our best, mature sciences deliver are strongly supported by evidence and this evidence gives us the strongest reason to believe them.’ That anyway is what is said at the beginning of the advertisement for a recent conference on induction at a celebrated seat of learning in the UK. It shows how much critical rationalists still have to do to make known the message of Logik der Forschung concerning what empirical evidence is able to do and what it does.

Kuhn and Lakatos

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 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.

Some philosophers of science, such as Paul Feyerabend, take Kuhn's work as showing that social factors, rather than adherence to a purely rational method, decide which scientific theories gain general acceptance. Many other philosophers of science dispute such a view, such as Alan Sokal and Kuhn himself.

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 (published in the UK as Intellectual Impostures) the 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.

Sokal and Bricmont write, "When a theory successfully withstands an attempt at falsification, a scientist will, quite naturally, consider the theory to be partially confirmed and will accord it a greater likelihood or a higher subjective probability. ... But Popper will have none of this: throughout his life he was a stubborn opponent of any idea of 'confirmation' of a theory, or even of its 'probability'. ... [but] the history of science teaches us that scientific theories come to be accepted above all because of their successes." (Sokal and Bricmont 1997, 62f)

They further argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions that are sometimes incorrect.

David Miller, a contemporary philosopher of critical rationalism, has attempted to defend Popper against these claims. Miller argues that astrology does not lay itself open to falsification, while astronomy does, and this is the litmus test for science.

Examples

Claims about verifiability and falsifiability have been used to criticize various controversial views. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise a theory.

Non-falsifiable theories can be general existential statements such as there exists a green swan. It is entirely possible to verify this statement as true (by finding one green swan). But since this statement does not specify when or where the green swan must exist, it will be practically impossible to show that the swan is not out there somewhere (this is the problem of induction). The claim is therefore practically unfalsifiable. It is worth noting that scientists and philosophers often recognize instances where there is evidence of absence, however. In other words, even without demanding an absolutely certain falsification, they may grant that the claim "there exists a green swan" is almost certainly false (e.g. if the scientists decide that they have searched satisfactorily). Even unfalsifiable claims, then, can be practically rejected.

Economics

Aspects of economics have been accused of not being falsifiable, mainly by sociologists and other social scientists in general.

The most common argument is made against rational expectations theories, which work under the assumption that people act to maximize their utility. However, under this viewpoint, it is impossible to disprove the fundamental theory that people are utility-maximizers. The political scientist Graham T. Allison, in his book Essence of Decision, attempted to both quash this theory and substitute other possible models of behavior.

Another construct that has been accused of being irrefutable is the principle of comparative advantage

Karl Popper argued that Marxism shifted from falsifiable to unfalsifiable.

Ethics

Ethical statements such as "murder is evil" or "it is good to help those in need" are not usually considered to be falsifiable. This does not necessarily amount to conclusion that they are all false, or without truth-values. It mainly affects their status as scientific theories. The meta-ethical thesis that ethical statements have no truth-value is called non-cognitivism.

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 animals, such as a hippo, would suffice.

Karl Popper at first spoke against the testability of natural selection but later 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."

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.

Logic and mathematics

The question may be raised as to whether the theorems of logic and mathematics are falsifiable or not. In considering this question, it is helpful to introduce a classical distinction that is frequently emphasized in this connection by Charles Sanders Peirce. On the one hand, he defines a positive science as "an inquiry which seeks for positive knowledge", that is, for knowledge that can be expressed in a categorical proposition (Peirce, The Essential Peirce (EP) v. 2, 144). He goes on to say the following of the normative sciences, namely, logic, ethics and aesthetics:

Logic and the other normative framework ask not what is but what ought to be. They are nevertheless positive sciences since it is by asserting positive, categorical truth that they are able show that what really is so; and the right reason derived from positive categorical fact. (Peirce, EP 2, 144).

On the other hand, Peirce distinguishes mathematics proper from all positive sciences, and reckons it more fundamental than any of them, saying that any positive science "must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other" (Peirce, EP 2, 144).

In this way of looking at things, logic is a science that seeks after knowledge of how we ought to conduct our reasoning if we want to achieve the goals of reasoning. As such, the logical knowledge that we have at any given time can easily fall short of perfection. However, the laws of logic themselves (the rules of inference and logical axioms) are not subject to falsifiability per se. That is, since truth values are defined in relation to the laws of logic any "falsification" of these laws would represent a self-contradictory situation though this conclusion has been argued against by philosophers such as W.V. Quine.

Pure mathematics, on the contrary, contains no propositions that are not contingent on prior assumptions. Its apparent certainty is but a relative certainty, relative to the certainty of its axioms. One can say that its theorems are tautologies, so long as one remembers the original meaning of tautology, which is a repetition of something previously asserted. Mathematical theorems merely say more acutely what the axioms already say more obtusely.

Applied mathematics, in particular, mathematics as applied in empirical science, is still more generalized. The application of mathematical abstractions to a domain of experiential phenomena involves a critical comparison of many different mathematical models, not all of them consistent with each other, and it normally leads to a judgment that some of the hypothetical models are better analogues or more likely icons than others of the empirical domain in question. This is, of course, an extremely fallible business, and each judgment call is subject to revision as more empirical data comes in.

How well a mathematical formula applies to the physical world is a physical question, and thus testable, within certain limits. For example, the proposition that all objects follow a parabolic path when thrown into the air is falsifiable; indeed, it is false. To see this, one has but to think of a feather. A slightly better proposition is that all objects follow a parabolic path when thrown in a vacuum and acted upon by gravity, which is itself falsified in regard to paths whose lengths are not negligible in proportion to a given planet's radius (or equivalently if the path is in a non-uniform gravitational field).

The above discussion addressed the nature of mathematical theorems in and of themselves, and then took up their application to empirical phenomena. But the actual practice of mathematics involves yet another level of consideration, and it may yet involve activities that are very similar to empirical science. Many working mathematicians, from Peirce in his day to Stephen Wolfram in ours, have remarked on the active, observational, and even experimental character of mathematical work. Imre Lakatos brings the concept of falsifiability to bear on the discipline of mathematics in his Proofs and Refutations. The question of whether mathematical practice is a quasi-experimental science depends in part on whether proofs are fundamentally different from experiments. Lakatos argues that often axioms, definitions, and proofs evolve through criticism and counterexample in a manner not unlike the way that a scientific theory evolves in response to experiments.

Solipsism

Metaphysical solipsism is the view that the individual self of the solipsistic philosopher is the whole of reality and that the external world and other persons are representations of that self having no independent existence (Wood, p. 295). Metaphysical solipsism is not empirically falsifiable because once one has taken the solipsistic position, any evidence that might establish an external world is already viewed as being within (or produced by) the self. However, expressions of solipsism may be self-refuting.

Anti-solipsism—the position that an external world does exist—is similarly non-falsifiable because regardless of what evidence is produced, it is always possible that there exists an external world outside one's experiences that does not interact with them.

Theism

The existence of an deity is potentially unfalsifiable, depending on the postulated characteristics of such a being. Mono-theistic deities are often described as possessing omnipotence (power to do anything, or anything not logically contradictory) and omniscience (possesses knowledge of all things that are knowable). In this situation, there is no observation or experiment that could be used to falsify the existence of the deity, as they would possess the power and knowledge to avoid, obfuscate, or otherwise alter the outcome of any such observation or experiment.

Chance

The philosophical concept of chance is unfalsifiable, since there is no way to prove that a hypothetical independent variable does not exist^{[citation needed]}. Any observation showing true randomness could possibly have a systematic component that can not be detected by current scientific knowledge.

Quotations

• Albert Einstein is reported to have said: No amount of experimentation can ever prove me right; a single experiment can prove me wrong. (paraphrased)
• The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability. — Karl Popper, (Popper, CR, 36)

See also

• Closed circle
• Cognitive bias
• Contingency
• Defeasible reasoning
• Demarcation problem
• Duhem–Quine thesis
• Fallibilism
• Hypothetico-deductive model
• Inquiry

• Logical positivism
• Metaphysical solipsism
• Methodological solipsism
• Not even wrong
• Occam's razor
• Philosophy of mathematics
• Philosophy of science
• Pragmatic maxim

• Precambrian rabbit
• Predictive power
• Reproducibility
• Scientific method
• Superseded scientific theory
• Tautology
• Testability
• Theory-ladenness

References

• Angeles, Peter A. (1992), Harper Collins Dictionary of Philosophy, 2nd edition, Harper Perennial, New York, NY. ISBN 0-06-461026-8.
• Feyerabend, Paul K., Against Method: Outline of an Anarchistic Theory of Knowledge, Humanities Press, London, UK, 1975. Reprinted, Verso, London, UK, 1978.
• Kuhn, Thomas S., The Structure of Scientific Revolutions, University of Chicago Press, Chicago, IL, 1962. 2nd edition 1970. 3rd edition 1996.
• Peirce, C.S., "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part, Collected Papers, CP 5.14–212. Published in full with editor's introduction and commentary, Patricia Ann Turisi (ed.), Pragmatism as a Principle and Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism", State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington, IN, 1998.
• Popper, Karl, The Logic of Scientific Discovery, Basic Books, New York, NY, 1959.
• Popper, Karl, Conjectures and Refutations, Routledge, London, 1963.
• Runes, Dagobert D. (ed.), Dictionary of Philosophy, Littlefield, Adams, and Company, Totowa, NJ, 1962.
• Sokal, Alan, and Bricmont, Jean, Fashionable Nonsense, Picador, New York, NY, 1998.
• Theobald, D.L. (2006). 29+ Evidences for Macroevolution: The Scientific Case for Common Descent. The Talk.Origins Archive. Version 2.87.
• Wood, Ledger (1962), "Solipsism", p. 295 in Runes (ed.), Dictionary of Philosophy, Littlefield, Adams, and Company, Totowa, NJ.

External links

• Problems with Falsificationism at The Galilean Library