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.
- All swans are white.
- For every action, there is an equal and opposite re-action
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.
- 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.
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.