A Bayesian Solution To The Paradox Of The Ravens

A detailed argument for the famous “paradox of ravens” was first put up by American philosopher Carl G.Hempel in his 1945 essay Studies in the Logic of Confirmation,in which he illustrated the problem of confirmation by example that,when confirming a hypothesis with the form of a universal statement,such as “all ravens are black”,to which the logical equivalent statement is “all non-blacks are non-ravens”.By applying the rules of confirmation that had been widely acknowledged: Nicod’s Criterion as well as the Equivalence Condition,an intuitionally unacceptable conclusion could be derived: an instance of a green leaf would confirm the hypothesis “all ravens are black”.This confirmational paradox was therefore popularized by and named after the famous raven case.After all,an epistemological puzzle was advanced by the raven paradox,our belief towards the universal synthetic propositions of this kind,e.g.,“all ravens are black”,would be qualified as knowledge if(and only if)they are well-confirmed by empirical evidence.In fact,the discussion concerning the idea of confirmation has emerged ever since the beginning of logical empiricism movement,when debating about the meaning of universal synthetic propositions,philosophers at that time found it rather problematic: the empirical verification of these propositions is inconclusive,and it was the retreat by logical positivists to the concept of confirmation,that paved the way for discussions around the raven paradox,i.e.,the question regarding the confirmational relation between evidence and propositions of the kind.This thesis combs and discusses two kinds of proposed solutions for the raven paradox: the traditional ones made by Hempel(in his paper)and Quine,which suggested qualitative modifications of the definition of confirmation,solutions of this kind tackle confirmation as an ‘all or nothing’ concept,while the Bayesian solution elaborated a quantitative analysis by introducing probability calculus,comparisons of degrees of confirmation are made to analyze these different evidences with expected accuracy.The canonical Bayesian solution,however,is questionable for making assumptions that entails the indifference in the update of degrees of confirmation,between selecting randomly from everything and selecting randomly among nonblacks.In order to alleviate the shortcomings,a modification of the canonical Bayesian solution is made in this thesis,based on the claims that non-ravens would make an impact upon our ontological belief of ravens,thus disqualify themselves as valid evidence.