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In the philosophy of science, falsifiability or refutability is the capacity for a statement, theory or hypothesis to be contradicted by evidence. For example, the statement "All swans are white" is falsifiable because one can observe that black swans exist.[A]

Falsifiability was introduced by the philosopher of science Karl Popper in his book Logik der Forschung (1934, revised and translated into English in 1959 as The Logic of Scientific Discovery). He proposed it as the cornerstone of a solution to both the problem of induction and the problem of demarcation.

Popper argued for falsifiability and opposed this to the intuitively similar concept of verifiability. Whereas verifying the claim "All swans are white" would require assessment of all swans, which is not possible, the single observation of a black swan is sufficient to falsify it.

As a key notion in the separation of science from non-science and pseudo-science, falsifiability has featured prominently in many scientific controversies and applications, even being used as legal precedent.

## The problem of induction

One of the questions in scientific method is: how does one move from observations to scientific laws? This is the problem of induction. Suppose we want to put the theory that all swans are white to the test. We come across a white swan. We cannot validly argue (or induce) from "here is a white swan" to "all swans are white"; doing so would require a logical fallacy such as, for example, affirming the consequent.[B]Karl Popper in his book Logik der Forschung (1934, revised and translated into English in 1959 as The Logic of Scientific Discovery). He proposed it as the cornerstone of a solution to both the problem of induction and the problem of demarcation.

Popper argued for falsifiability and opposed this to the intuitively similar concept of verifiability. Whereas verifying the claim "All swans are white" would require assessment of all swans, which is not possible, the single observation of a black swan is sufficient to falsify it.

As a key notion in the separation of science from non-science and pseudo-science, falsifiability has featured prominently in many scientific controversies and applications, even being used as legal precedent.

One of the questions in scientific method is: how does one move from observations to scientific laws? This is the problem of induction. Suppose we want to put the theory that all swans are white to the test. We come across a white swan. We cannot validly argue (or induce) from "here is a white swan" to "all swans are white"; doing so would require a logical fallacy such as, for example, affirming the consequent.[B][1]

Popper's idea to solve this problem is that while it is impossible to verify that every swan is white, finding a single black swan shows that not every swan is white. We might tentatively accept the proposal that every swan is white, while looking out for examples of non-white swans that would show our conjecture to be false. Falsification uses the valid inference modus tollens: if from a statement ${\displaystyle P}$ (say some law with some initial condition) we logically deduce ${\displaystyle Q}$, but what is observed is ${\displaystyle \neg Q}$, we infer that ${\displaystyle P}$ is false. For example, given the statement "all swans are white" and the initial condition "there is a swan here", we can deduce "the swan here is white", but if what is observed is "the swan here is not white" (say black), then "all swans are white" is false, or it was not a swan.

Popper's response to the problem of induction is simply that induction is actually never used in science.[C] Instead, laws are conjectured, tested and the results are considered together with other aspects to decide which of these laws are applied in practice.[2] In contrast, the logical empiricism movement, which included such philosophers as Moritz Schlick, Rudolf Carnap, Otto Neurath and A.J. Ayer wanted to formalize the idea that, for a law to be scientific, it must be possible to argue on the basis of observations either in favor of its truth or its falsity. There was no consensus among these philosophers about how to achieve that, but the thought expressed by Mach's dictum that "where neither confirmation nor refutation is possible, science is not concerned" was accepted as a basic precept of critical reflection about science.[3][4]

Popper said that a demarcation criterion was possible, but we have to use the logical possibility of falsifications, which is falsifiability. He cited his encounter with psychoanalysis in the 1910s. It did not matter what observation was presented, psychoanalysis could explain it. Unfortunately, the reason why it could explain everything is that it did not exclude anything also.[D] For Popper, this was a failure, because it meant that it could not make any prediction. From a logical standpoint, if one finds an observation that does not contradict a law, it does not mean that the law is true. A verification has no value in itself. But, if the law makes risky predictions and these are corroborated, Popper says, there is a reason to prefer this law over another law that makes less risky predictions or no predictions at all.[E][F] In the definition of falsifiability, contradictions with observations are not used for actual falsifications, but for logical "falsifications" that show that the law makes risky predictions, which is completely different.

On the basic philosophical side of this issue, Popper said that some 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: a statement that could not be verified was considered meaningless. In opposition to this view, Popper said that there are meaningful theories that are not scientific, and that, accordingly, a criterion of meaningfulness does not coincide with a criterion of demarcation.[G]