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# Inductive reasoning

Inductive reasoning, sometimes called inductive logic, is the process of reasoning in which a general rule is inferred from some set of specific observations. It is to ascribe properties or relations to types based on limited observations of particular tokens; or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is used, for example, in using specific propositions such as:

• This swan is white.
• A billiard ball moves when struck with a cue.
to infer general propositions such as:
• All swans are white.
• For every action, there is an equal and opposite re-action

Some philosophers consider the term "inductive logic" a misnomer because the validity of inductive reasoning is not dependent on the rules of formal logic which is by definition only deductive, not inductive. In contrast to deductive reasoning, conclusions arrived at by inductive reasoning do not necessarily have the same validity as the initial assumptions. In the example above, the conclusion that all swans are white is obviously wrong, but may have been thought correct in Europe until the settlement of Australia. Inductive arguments are never binding but they may be cogent. Inductive reasoning expresses the truth-value of its inferences in terms of probability rather than necessity.

The problem of induction, the search for a justification for inductive reasoning, was formally addressed first by David Hume. Hume criticised induction based on repeated experiences.

Karl Popper developed the notion of falsification as a way around the problem of induction. Popper replaced induction with deduction, making modus tollens the centrepiece of his theory. On this account, when assessing a theory one should pay greater heed to data which is in disagreement with the theory than to data which is in agreement with it.

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. (See ontological relativity.)

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