Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not entail it; i.e. they do not ensure its truth. Induction is a form of reasoning that makes generalizations based on individual instances. It is used to ascribe properties or relations to types based on tokens (i.e., on a number of observations or experiences); or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is employed, for example, in using specific propositions such as:
This ice is cold.
A billiard ball moves when struck with a cue.
...to infer general propositions such as:
All ice is cold.
All billiard balls move when struck with a cue.
Inductive reasoning has been attacked several times. Historically, David Hume denied its logical admissibility. During the twentieth century, thinkers such as Karl Popper and David Miller have disputed the existence, necessity and validity of any inductive reasoning, including probabilistic (Bayesian) reasoning.
Note that Mathematical induction is not a form of inductive reasoning. Mathematical induction is a form of deductive reasoning.
Reference:
http://en.wikipedia.org/wiki/Inductive_reasoning
