The problem of induction is the philosophical issue involved in deciding the place of induction in determining empirical truth. The problem of induction is whether inductive reason works. That is, what is the justification for either:
Francis Bacon, Isaac Newton, and numerous others up until at least the late 19th Century have considered inductive reasoning the basis of scientific method—indeed inductive reasoning is used today, though in a more balanced interaction with deductive reasoning and abductive reasoning. By the inductive approach to scientific method, one makes a series of observations and forms a universal generalization. If correct and stated in a sufficiently accurate way, an inductively arrived at statement relieves others of the need for making so many observations and allows them to instead use the generalization to predict what will happen in specific circumstances in the future. So, for instance, from any series of observations that water freezes at 0°C at sea-level it is valid to infer that the next sample of water will do the same--but only if induction works. That such a prediction comes true when tried merely adds to the series; it does not establish the reliability of induction, except inductively. The problem is, then, what justification can there be for making such an inference?
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Machine Learning :: Artificial Intelligence

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A Constructivist Approach to the Problem of Induction - Article by Olaf Diettrich which appeared in Evolution and Cognition in 1995.
Confirmation Theory - Article by Michael Huemer defending inductive inference against Hume's argument by appeal to `inference to the best explanation', contrasting his approach to those of Goodman and Hempel.
Conjectures - PhD thesis of Peter Flach, investigating the `logic of induction' from philosophical and machine-learning perspectives.
Mathematical Induction - Lecture notes by Peter Suber, explaining the difference between inductive inference and mathematical induction (which is a species of deductive inference).
Presuppositions and the Paradoxes of Confirmation - Discussion by Michael Beaney in Disputatio of a paradox of confirmation due to Mark Sainsbury.
The Problem of Induction - Essay by Karl Popper, arguing that there is no such thing as inductive inference.
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