Falsifiability  

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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.

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.

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!"

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

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:

<math>U \rightarrow \neg O</math>

Observation O, however, is made:

<math>\ \ O</math>

So by modus tollens,

<math>\neg U</math>

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.

See also

• Closed circle
• Cognitive bias
• Contingency
• Defeasible reasoning
• Demarcation problem
• Duhem–Quine thesis
• Fallibilism
• Fallacy (informal logic and rhetoric)
• False (logic)
• 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