A Philosophical Research On The Logic Of The Bayesian Inference

Bayesianism has already gained a prominent. role as a theory for probability interpretation. Keynes’formal inductive system helped it to evolve into a new era: Bayesian reasoning is now remodeling statistics, economics, psychology and artificial intelligence, and its influence is still expanding.Such a trend can be traced back into the renewal of Bayesian method inside statistics. The revolutionary view Bayesianism took successfully eliminated the problem of ignore-to-prior, as well any doubt against subjective factor in induction. By solving the problem of deciding test statistic it averted the problem stopping rule has generated. When it comes to estimation, Bayesianism has replaced confidence interval with credible interval in order to obtain the prediction of the true value of a parameter. It also employs the a priori information through Bayes theorem on conditional probability.Despite its popularity, several challenges were raised against Bayesianism, specifically on its subjectivity, simplicity and on the problem of old-evidence. And as such, more space has been left for the further development of Bayesianism. The debate of subjectivity is focused on a priori-constraint, while the simplicity question is echoed by the inconsistency between probability axiom and the simplicity postulate. Forster and Sober remarked that the postulate itself is an ad hoc method; Howson argued that it should not be taken as an essential guideline. Additionally, an old-evidence in the Bayesian framework could not serve as affirming the current hypothesis, which contradicts with our instinct. Howson insightfully revealed that "evidence support" machanism is actually a ternary relation between data e, hypothesis h and background knowledge k, and the problem of old-evidence only become evident when e was decided as evidence and e was included in k. It shows that the further improvement and development were needed in Bayesian reasoning.Recent developments on the application of Bayesianism in cognitive psychology have invoked a possible cognitive turn in Bayesianism, and it reveals that the various possible approaches of Bayesian reasoning:the integration between Frequentism and Bayesianism; to conjoin the intentional factor with its logical indicative nature, it makes an attempt on the combination of extensionality and non-extensionality. Gigerenzer and Hoffrage has already offered a Bayesian model with frequency representation of information; Tversky, etc. proposed their non-extention logic for the support theory for subjective probability. This seems to be a prospective path for inductive reasoning and Bayesianism that worth further exploring.