- This article is about induction in philosophy. For other article subjects named induction see induction.
- 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
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2 Bayesian inference
3 Related topics
4 External link
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.
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.