The Induction (philosophy) reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

# Induction (philosophy)

Induction or 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

## Validity

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 is deductively invalid.

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.

## Bayesian inference

Bayesianism uses Bayesian inference in an attempt to rationally justify induction. Bayes theorem is used to calculate how much the strength of oneÒs belief in a hypothesis should change, given some evidence.

There is debate around what it is that informs the original degree of belief. Objective Bayesians seek an objective value for the degree of probability of a hypothesis being correct, and so do not avoid the philosophical criticisms of objectivism. Subjective Bayesians hold the that the prior probabilities represent subjective degrees of belief, but that repeated application of BayesÒ theorem leads to a high degree of agreement on the posterior probability. They therefore fail to provide an objective standard for choosing between conflicting hypotheses. The theorem can be used to rationally justify belief in some hypothesis, but at the expense of rejecting objectivism. Such a scheme cannot be used, for instance, to objectively decide between conflicting scientific paradigms.