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Inductive reasoning

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Inductive reasoning is the process of reasoning from the specific to the general. Inductive reasoning is supported by inductive logic, for example:

From specific propositions such as:

This raven is a black bird.
A billiard ball moves when struck with a cue.

To general propositions:

All ravens are black birds.
For every action, there is an equal and opposite re-action

In contrast to deductive reasoning, conclusions arrived at by inductive reasoning do not necessarily have the same validity as the initial assumptions. Inductive logic expresses the truth-value of its inferences in terms of probability rather than necessity. The nature of inductive reasoning, with examples, is discussed further at cogency.

Philosophers since at least David Hume recognized a significant distinction between two kinds of statements, later called by Immanuel Kant "analytic" and "synthetic."

Analytic truths, such as "All bachelors are unmarried men," or "Human beings are two-legged animals" are supposed to be true by virtue of the meanings of the words alone.
Synthetic statements, such as "All ravens are black," or "All men are mortal," are true if at all only by virtue of some facts about the world. One has to discover that men die and ravens are black.

W. V. Quine debunked this distinction in his influential essay Two Dogmas of Empiricism and postulated that any empirical evidence that seems to falsify any particular theory can always be accommodated by the theory in question. Quine's observation reflects the problem of inductive logic formally addressed first by David Hume. Hume's psychological theory of inductive logic, simple enumerative induction, or induction by repetition, was challenged by Karl Popper Popper's challenge was later discredited by the Quine-Duhem thesis stated above.

Some consider that the scientific method relies on inductive reasoning. However, many researchers use hypothetico-deductive approaches derived from the work of Karl Popper. The validity of some forms of such inductive and deductive reasoning is formally described by statistics.