Inductive reasoning

== Bayesian inference ==
As a logic of induction rather than a theory of belief, [[Bayesian inference]] does not determine which beliefs are ''a priori'' rational, but rather determines how we should rationally change the beliefs we have when presented with evidence. We begin by considering an exhaustive list of possibilities, a definite probabilistic characterisation of each of them (in terms of likelihoods) and precise  [[prior probability|prior probabilities]] for them (e.g. based on logic or induction from previous experience) and, when faced with evidence, we adjust the strength of our belief in the given hypotheses in a precise manner using [[conditional probability|Bayesian logic]] to yield candidate 'a posteriori probabilities', taking no account of the extent to which the new evidence may happen to give us specific reasons to doubt our assumptions. Otherwise it is advisable to review and repeat as necessary the consideration of possibilities and their characterisation until, perhaps, a stable situation is reached.<ref>{{cite book |last1=Good |first1=Irving J. |title=Good Thinking: The Foundations of Probability and Its Applications |date=1983 |publisher=University of Minneapolis Press |location=Minneapolis |pages=ix-xvii, 18, 27, 29, 36–38, 123–127 |edition=Dover, New York, 2009 replication}}</ref>