A statement, hypothesis, or theory
has falsifiability (or is falsifiable) if it is contradicted by a
basic statement, which, in an eventual successful or failed falsification, must
respectively correspond to a true or hypothetical observation. For example, the
claim "all swans are white and have always been white" is falsifiable
since it is contradicted by this basic statement: "In 1697, during the Dutch
explorer Willem de Vlamingh expedition, there were black swans on the shore of
the Swan River in Australia", which in this case is a true observation.
The concept is also known by the terms refutable and refutability.
black swans
The concept was introduced by the philosopher of science Karl Popper. He saw falsifiability as the logical part and the cornerstone of his scientific epistemology, which sets the limits of scientific inquiry. He proposed that statements and theories that are not falsifiable are unscientific. Declaring an unfalsifiable theory to be scientific would then be pseudoscience.
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. The Inductivist methodology supposes that one can somehow move from a series of statements such as 'here is a white swan', 'over there is a white swan', and so on, to a universal statement such as 'all swans are white'. As observed by David Hume, Immanuel Kant and later by Popper and others, 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). This is known as the problem of induction.
One solution to the problem of induction, proposed by Immanuel Kant in Critique of Pure Reason, is to consider as valid absolutely a priori the conclusions that we would otherwise have drawn from these dubious inferential inductions. Following Kant, Popper accepted that we have to work with unproven hypotheses, but he refused that we have to justify them in any way and he wrote (Popper 1959, p. 6): "I do not think that his ingenious attempt to provide an a priori justification for synthetic statements was successful." However, if one finds one single swan that is not white, 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 or trying to view them as valid in any way.
For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come into conflict with observation. A key observation of falsificationism is thus that a criterion of demarcation is needed to distinguish those statements that can come into conflict with observation and those that cannot, but the criterion itself concerns only the logical form of the theory:
Popper always insisted on a clear distinction between the logic (of falsifiability) and its applied less precise methodology. The required logical form, the criterion, is that there must exist basic statements that contradict the theory (and also some that corroborate it because the theory must be consistent). This logical form informally implies the possibility of refutations by experience because, in its informal methodological context, a basic statement must be intersubjective and interpretable in terms of observations.
Objections can be raised against falsifiability as a criterion of demarcation similar to those which can be raised against verifiability. For example, as pointed out by many and reformulated by Colin McGinn,
Very early, in anticipation of this specific objection Popper wrote,
In its simple form, the point here is that although a singular existential statement such as 'there is a white swan in Europe' cannot be used to affirm a universal statement, it can be used to show that one is false: the statement 'there is a non white swan in Australia' implies that the universal statement 'all swans are white' is false. Moreover, this singular existential statement is empirical: it is impractical to observe all the swans in the world to verify that they are all white, but one can observe one swan that is not white. This shows the fundamental difference between verifiability and falsifiability. Also, in the logical form of the theory, there is no notion of future experiments, but only a (formal) class of basic statements that contradict it.
Such a simple contradiction with a basic statement is not what Popper calls a falsification. A falsification usually entails a derivation from a system of statements, which include the universal statement and initial conditions, to a singular statement, which is contradicted by a falsifying hypothesis, but the argument can be generalized. Popper explains
Contemporary philosopher David Miller mentions that other similar objections have been anticipated and answered by Popper.
The falsifiability criterion does not imply that unfalsifiable systems such as logic, mathematics and metaphysics are not parts of science. 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 "all men die 150 years after their birth at the latest". 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 that guide the search for a new theory.
Thus falsificationism has two levels. At the logical level, scientists use deductive logic to attempt to falsify theories. At the non-logical level, they decide on some criteria, which use falsification and other factors, to pick which theories they will study, improve, replace, apply or (further) test. These other criteria may take into account a metaphysical research program. They are not considered in the formal falsifiability criterion, but they can give a meaning to this criterion. Needless to say, for Popper, these other criteria, the so called rules of the game, are necessary. Some philosophers consider them as parts of Popper's demarcation criterion, but Popper viewed them only as a necessary context.
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 critical rationalism, 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.
black swans
The concept was introduced by the philosopher of science Karl Popper. He saw falsifiability as the logical part and the cornerstone of his scientific epistemology, which sets the limits of scientific inquiry. He proposed that statements and theories that are not falsifiable are unscientific. Declaring an unfalsifiable theory to be scientific would then be pseudoscience.
Overview of Falsifiability
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. The Inductivist methodology supposes that one can somehow move from a series of statements such as 'here is a white swan', 'over there is a white swan', and so on, to a universal statement such as 'all swans are white'. As observed by David Hume, Immanuel Kant and later by Popper and others, 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). This is known as the problem of induction.
One solution to the problem of induction, proposed by Immanuel Kant in Critique of Pure Reason, is to consider as valid absolutely a priori the conclusions that we would otherwise have drawn from these dubious inferential inductions. Following Kant, Popper accepted that we have to work with unproven hypotheses, but he refused that we have to justify them in any way and he wrote (Popper 1959, p. 6): "I do not think that his ingenious attempt to provide an a priori justification for synthetic statements was successful." However, if one finds one single swan that is not white, 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 or trying to view them as valid in any way.
For a statement to be questioned using observation, it needs to be at least theoretically possible that it can come into conflict with observation. A key observation of falsificationism is thus that a criterion of demarcation is needed to distinguish those statements that can come into conflict with observation and those that cannot, but the criterion itself concerns only the logical form of the theory:
I shall require that [the]
logical form [of the theory] shall be such that it can be singled out, by means
of empirical tests, in a negative sense: it must be possible for an empirical
scientific system to be refuted by experience.
— Karl Popper, Popper 1959. p 19
Popper always insisted on a clear distinction between the logic (of falsifiability) and its applied less precise methodology. The required logical form, the criterion, is that there must exist basic statements that contradict the theory (and also some that corroborate it because the theory must be consistent). This logical form informally implies the possibility of refutations by experience because, in its informal methodological context, a basic statement must be intersubjective and interpretable in terms of observations.
Objections can be raised against falsifiability as a criterion of demarcation similar to those which can be raised against verifiability. For example, as pointed out by many and reformulated by Colin McGinn,
[w]e have to be able to infer
that if a falsifying result has been found in a given experiment it will be
found in future experiments; ... this is clearly an inductive inference.
— Colin McGinn, McGinn 2002, sec. 3
Very early, in anticipation of this specific objection Popper wrote,
This attack would not disturb
me. 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.
— Karl Popper, Popper 1959. p 19
In its simple form, the point here is that although a singular existential statement such as 'there is a white swan in Europe' cannot be used to affirm a universal statement, it can be used to show that one is false: the statement 'there is a non white swan in Australia' implies that the universal statement 'all swans are white' is false. Moreover, this singular existential statement is empirical: it is impractical to observe all the swans in the world to verify that they are all white, but one can observe one swan that is not white. This shows the fundamental difference between verifiability and falsifiability. Also, in the logical form of the theory, there is no notion of future experiments, but only a (formal) class of basic statements that contradict it.
Such a simple contradiction with a basic statement is not what Popper calls a falsification. A falsification usually entails a derivation from a system of statements, which include the universal statement and initial conditions, to a singular statement, which is contradicted by a falsifying hypothesis, but the argument can be generalized. Popper explains
"... it is possible by
means of purely deductive inferences (with the help of the modus tollens of
classical logic) to argue from the truth of singular statements to the falsity
of universal statements. Such an argument to the falsity of universal
statements is the only strictly deductive kind of inference that proceeds, as
it were, in the ‘inductive direction’; that is, from singular to universal
statements."
— Karl Popper, Popper 1959, p. 19
Contemporary philosopher David Miller mentions that other similar objections have been anticipated and answered by Popper.
The falsifiability criterion does not imply that unfalsifiable systems such as logic, mathematics and metaphysics are not parts of science. 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 "all men die 150 years after their birth at the latest". 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 that guide the search for a new theory.
Thus falsificationism has two levels. At the logical level, scientists use deductive logic to attempt to falsify theories. At the non-logical level, they decide on some criteria, which use falsification and other factors, to pick which theories they will study, improve, replace, apply or (further) test. These other criteria may take into account a metaphysical research program. They are not considered in the formal falsifiability criterion, but they can give a meaning to this criterion. Needless to say, for Popper, these other criteria, the so called rules of the game, are necessary. Some philosophers consider them as parts of Popper's demarcation criterion, but Popper viewed them only as a necessary context.
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 critical rationalism, 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.
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