In the philosophy of science, a theory is falsifiable (or refutable) if it is contradicted by an observation that is logically possible, i.e., expressible in the language of the theory, and this language has a conventional empirical interpretation. Thus there must exist a state of affairs that obtains or not and can be used as a scientific evidence against the theory, in particular, it must be observable with existing technologies. For example, "All swans are white" is falsifiable, because "Here is a black swan" contradicts it. To make falsifiability more intuitive, one can assume that the state of affairs is allowed by some other law than the one that is falsified. For example, Newton's law of gravitation is also falsifiable—it is falsified by "The brick fell upwards when released", which is a state of affairs that can be observed if some hidden force other than gravity acts on the brick. On the other hand, "All men are mortal" is not falsifiable, because, unlike a swan being black, a man being immortal is not an inter-subjective property—there is no shared procedure to systematically conclude to immortality.
Falsifiability was introduced by the philosopher of science Karl Popper in his book Logik der Forschung (1934), faithfully translated into English by himself and two other translators 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.
The role of falsifiability in Popper's philosophy is to make a deductive testing and a rational critic of the theory possible. This logical part is used within a methodology that, in Popper's own account, is hardly rigorous, because it involves irrational creative processes and, as pointed out by Duhem and others, definitive experimental falsifications are impossible. In response to the impossibility of a technologically reasonable verification and to avoid the problems of falsification, Popper argued for falsifiability and opposed this to the intuitively similar concept of verifiability. Verifying the claim "All swans are white" would require observing all swans, which is not technologically possible under reasonable assumptions in any theory that has a conventional empirical interpretation. In contrast, the observation of a single black swan is technologically reasonable and sufficient to logically falsify it and steer a critical discussion. Moreover, even if a black swan was in principle impossible due to a fundamental law of biology, it would still be a potential falsifier—i.e., an observation that is logically possible in the empirical language and in contradiction with the claim.
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.