Falsifiability: Encyclopedia II - Falsifiability - Naïve falsification

Falsifiability - Naïve falsification

Falsifiability was first developed by Karl Popper in the 1930s. Popper noticed that two types of statements are of particular value to scientists. The first are statements of observations, such as 'this is a white swan'. Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x which is a swan and x is white.

The second type of statement of interest to scientists categorizes all instances of something, for example "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 the second type. Perhaps the most 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 logically invalid, since it is always possible that there may be a non-white swan that has somehow avoided observation. Yet some philosophers of science claim that science is based on such an inductive method.

Popper held that science could not be grounded on such an invalid inference. 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 which is a swan and which is not white', hence 'all swans are white' is false, because that is the same as 'there is nothing which is a swan and which is not white'.

Although the logic of naïve falsification is valid, it is rather limited. Popper drew attention to these limitations in The Logic of Scientific Discovery, in response to anticipated criticism from Duhem and Carnap. W. V. Quine is also well-known for his observation in his influential essay, "Two Dogmas of Empiricism" (which is reprinted in From a Logical Point of View), that nearly any statement can be made to fit with the data, so long as one makes the requisite "compensatory adjustments". In order 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 ornithologists are incompetent'. 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.

Adapted from the Wikipedia article "Naïve falsification", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki