The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense, since it focuses on the lack of justification for either:
- Generalizing about the properties of a class of objects based on some number of observations of particular instances of that class (for example, the inference that "all swans we have seen are white, and therefore all swans are white", before the discovery of black swans) or
- Presupposing that a sequence of events in the future will occur as it always has in the past (for example, that the laws of physics will hold as they have always been observed to hold). Hume called this the Principle of Uniformity of Nature.
The problem calls into question all empirical claims made in everyday life or through the scientific method and for that reason the philosopher C. D. Broad said that "induction is the glory of science and the scandal of philosophy". Although the problem arguably dates back to the Pyrrhonism of ancient philosophy, David Hume introduced it in the mid-18th century, with the most notable response provided by Karl Popper two centuries later. Some philosophers believe that the "no-free-lunch in search and optimization theorem" of David Wolpert and William G. Macready is a probability-based extension of induction, yet this is misleading, as inductive logic accustomed to probabilistic arguments and the no free lunch theorem (NFL) is more a variation of economic rational choice theory.
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