# Falsifiability

Are all swans white?

Falsifiability or refutability of a statement, hypothesis, or theory is an inherent possibility to prove it to be false. A statement is called falsifiable if it is possible to conceive an observation or an argument which proves the statement in question to be false. In this sense, falsify is synonymous with nullify, meaning not "to commit fraud" but "show to be false". Some philosophers argue that science must be falsifiable.[1]

For example, by the problem of induction, no number of confirming observations can verify a universal generalization, such as All swans are white, yet it is logically possible to falsify it by observing a single black swan. Thus, the term falsifiability is sometimes synonymous to testability. Some statements, such as It will be raining here in one million years, are falsifiable in principle, but not in practice.[2]

The concern with falsifiability gained attention by way of philosopher of science Karl Popper's scientific epistemology "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. This is often epitomized in Wolfgang Pauli famously saying, of an argument that fails to be scientific because it cannot be falsified by experiment, "it is not only not right, it is not even wrong!"

## Overview

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.[3] However, if one finds one single black swan, deductive logic admits the conclusion that the statement that all swans are white is false. Falsificationism thus strives for questioning, for falsification, 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 in conflict with observation. A key observation of falsificiationism is thus that a criterion of demarcation is needed to distinguish those statements that can come in conflict with observation and those that cannot (Chorlton, 2012). Popper chose falsifiability as the name of this criterion.

My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements.

Popper stressed that unfalsifiable statements are important in science.[4] 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".[5] 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.[6] 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.

## Naive falsification{{safesubst:#invoke:anchor|main}}

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### 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[7] 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 predicate 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 inferential basis. 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

{{ safesubst:#invoke:Unsubst||$N=Unreferenced section |date=__DATE__ |$B= {{ safesubst:#invoke:Unsubst||$N=Unreferenced |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} }} 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:

${\displaystyle U\rightarrow \neg O}$

${\displaystyle \ \ O}$

So by modus tollens,

${\displaystyle \neg U}$

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 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.

### 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.[15]

### 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.[16] Miller argues that astrology does not lay itself open to falsification, while astronomy does, and this is the litmus test for science.

## Examples

{{ safesubst:#invoke:Unsubst||$N=Original research |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} 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.

### Economics

Karl Popper argued that Marxism shifted from falsifiable to unfalsifiable.[17]

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.[18][19][20] Prominent figures within the Austrian School of economics Ludwig von Mises and Friedrich Hayek were associates of Karl Popper's, with whom they co-founded the Mont Pelerin Society.

### Evolution

{{#invoke:main|main}} 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".[21] Richard Dawkins adds that any other modern animal, such as a hippo, would suffice.[22][23][24]

Karl Popper at first spoke against the testability of natural selection [25][26] 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."[27][28]

### 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",[29] and argued that neither Marxism nor psychoanalysis was science,[29] 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

Many philosophersTemplate:Weasel-inline believe that mathematics is not experimentally falsifiable, and thus not a science according to the definition of Karl Popper.[30] 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."[31] 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."[32]

## 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)[33][34][35]
• The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability. — Karl Popper, (Popper, Conjectures and Refutations, 36)[36]

## Notes

1. {{#invoke:citation/CS1|citation |CitationClass=book }}
2. {{#invoke:citation/CS1|citation |CitationClass=book }}
3. LScD p. 4
4. LScD, p. 16
5. Keuth: The philosophy of Karl Popper, p. 45
6. Quantum theory and the schism in physics, introductory comments
7. {{#invoke:citation/CS1|citation |CitationClass=book }}
8. Logic of Scientific Discovery, section 6, footnote *3
9. Ruse, Michael. Science and Spirituality : Making Room for Faith in the Age of Science. ;New York: Cambridge University Press, 2010. Print.
10. McLean v. Arkansas Board of Education, Decision January 5, 1982.
11. W. W. Bartley, III: Biology & evolutionary epistemology. Philosophia 6:3–4 (September–December 1976), pp. 463–494
12. Rafe Champion: Agreeing to Disagree: Bartley's Critique of Reason. Melbourne Age Monthly Review (October 1985)
13. David Miller: Some hard questions for critical rationalism
14. Martin Gardner (2001), "A Skeptical Look at Karl Popper," Skeptical Inquirer, 25(4): 13-14, 72.
15. {{#invoke:citation/CS1|citation |CitationClass=book }}
16. {{#invoke:Citation/CS1|citation |CitationClass=journal }}, also chapter 6 of {{#invoke:Citation/CS1|citation |CitationClass=journal }}
17. :"For Marxism, Popper believed, had been initially scientific, in that Marx had postulated a theory which was genuinely predictive. However, when these predictions were not in fact borne out, the theory was saved from falsification by the addition of ad hoc hypotheses which made it compatible with the facts. By this means, Popper asserted, a theory which was initially genuinely scientific degenerated into pseudo-scientific dogma." Karl Popper at the Stanford Encyclopedia of Philosophy.
18. Austrian School of Economics: The Concise Encyclopedia of Economics | Library of Economics and Liberty
19. Methodological Individualism at the Stanford Encyclopedia of Philosophy
20. Ludwig von Mises. Human Action, p. 11, "r. Purposeful Action and Animal Reaction". Referenced 2011-11-23.
21. {{#invoke:citation/CS1|citation |CitationClass=book }}
22. Template:Cite news
23. {{#invoke:citation/CS1|citation |CitationClass=book }}
24. {{#invoke:citation/CS1|citation |CitationClass=book }}
25. Template:Cite news; online German translation Template:Cite news
26. {{#invoke:citation/CS1|citation |CitationClass=book }}
27. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
28. http://www.informationphilosopher.com/solutions/philosophers/popper/natural_selection_and_the_emergence_of_mind.html
29. {{#invoke:citation/CS1|citation |CitationClass=book }}, Chapter 1, p. 12
30. {{#invoke:citation/CS1|citation |CitationClass=book }}
31. Popper 1995, p. 56
32. {{#invoke:citation/CS1|citation |CitationClass=book }} Reprinted by Dover (2010), ISBN 978-0-486-24511-9.
33. {{#invoke:citation/CS1|citation |CitationClass=book }}Calaprice denotes this not as an exact quotation, but as a paraphrase of a translation of A. Einstein's "Induction and Deduction". Collected Papers of Albert Einstein Vol. 7, Document 28. The Berlin Years: Writings, 1918–1921. A. Einstein; M. Janssen, R. Schulmann, et al., eds.
34. {{#invoke:citation/CS1|citation |CitationClass=book }}
35. {{#invoke:citation/CS1|citation |CitationClass=book }}, Chapter , p. 21
36. http://cla.calpoly.edu/~fotoole/321.1/popper.html

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• 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.
• Lakatos, Imre. (1970), "Falsification and the Methodology of Scientific Research Programmes," in Criticism and the Growth of Knowledge, vol. 4. Imre Lakatos and Alan Musgrave (eds.), Cambridge University Press, Cambridge.
• Lakatos, Imre (1978), The methodology of scientific research programmes: Philosophical papers, volume I. Cambridge: Cambridge University Press. ISBN 0-521-28031 -1.
• 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.