Problem of induction
The problem of induction, also: Humesches problem or Hume - problem is a basic problem of epistemology. It refers to the question of whether and when a conclusion by induction of individual cases is permitted on a general law. It was first addressed in 1740 by David Hume.
Although the problem of induction was formulated in empiricism, it is a problem of all philosophies or sciences that permit inductive inferences as proof procedures. It is a modern variant of nominalism, which denies the reasonable orders of rationalism, but also based on measurements generalizations of science, an observer-independent reality.
David Hume
The problem of induction, Hume developed in his first work, A Treatise of Human Nature (I, 3.6 ) and in its revision to Enquiry Concerning Human Understanding.
Human knowledge is gained either intuitively ( that a bachelor is unmarried, it follows from the use of the word ) or deductively ( by inference, for example:. All men are mortal Socrates is a man Therefore, Socrates is mortal. ) Or empirically ( by perception of repetitions, for example, that the sun rises every morning ).
The induction is seen as a principled justification method that takes general validity in its explanatory power. A necessary prerequisite for this method is the assumption that something will behave in the future as in the past. Thus, the induction principle can rightly lay claim to universal validity, it must be impossible that this condition is not true ( law of contradiction ). The contrary assumption of this premise that the future of the past is not the same, but carries no contradiction in terms. So is also true and is quite conceivable. However, if both assumptions are equally possible, the condition of events are predictable, necessary or impossible in general. Therefore, the claim of the induction method on a general reasoning power is necessarily false.
Thus Hume has shown that there is no rule of inference in his model of human cognition, which justifies the induction. Humans do not come from logical thought processes but from habit, to conclude from the previous experience in the future.
Immanuel Kant
From the two distinctions are four possible combinations are:
The question of whether and how experience independently valid extension judgments are possible, the task of Kant's 1781 erschienenem Critique of Pure Reason.
Kant affirms the possibility of synthetic a priori judgments. They are possible because of our experience takes place only in certain forms of intuition (space and time ) and categories (12 in total, including causality). These conditions of possibility of experience then stick to everything that can be experienced at all: It is not the objects determine the knowledge, but the knowledge determines the objects. Therefore, experience independent extension judgments are possible for the range of possible experience, the validity of which is not based on induction but on discursive a priori knowledge, such as in a philosophy of nature, as he describes in his book Metaphysical Foundations of Natural Science.
In the empirical physics laws are so general as well as rationally formed hypotheses possible, which can be tested experimentally. The formation of the general statements is based not on a psychological association, but on a rational speculation, which can be operationalized using the imagination in predictions for the experience. According to Kant, this method is since Galileo Galilei in physics in use, as was only to science (See Immanuel Kant: AA 0003III, 15-16)
Classical position of critical rationalism
The truth of the proposition " All swans are white " can not by individual observation sentences of the type " This swan is white " to be proved. For a single observed black swan is sufficient to refute such a Allsatz. It should therefore be ruled out that there could be black swans at all. Can be true existential statements against - Between existence theorems ( "It is a white swan " ), as used to describe observations and Allsätzen ( " All swans are white " ), which make up by Popper, scientific theories, there is here an asymmetry be detected, in which one they verified empirically. For scientific theories, which consist of general statements, this is not true: they can only be falsified.
Therefore Popper formulated the steps of the scientific method as follows: First new hypotheses are as answers to problems. Then an attempt is made to falsify by observations. If this fails, there is no guarantee that it will not succeed in the future, but the theory is thus far superior at least already falsified theories.
Revision and solutions
Hume's statement was generalized by the critical rationalism (Hans Albert ) pursuant to which final arguments are in principle not possible because of Munchausen's trilemma. Each proof is based on rationally unjustifiable assumptions.
There are other solutions to the problem of induction:
- Rafael Ferber sees the non- logical " legal basis " for the rationality of induction circuits in a " hypothetical demand of practical reason ": the principle of induction is "a natural and legitimate demand of practical reason ." An induction ban " would equal an invitation to suicide. "