How belief-type probability can be applied to the problem of induction using the idea of learning from experience by Bayes' Rule.
The idea is already present in Chapters 13–15.
▪ We can represent degrees of belief by numbers between 0 and 1.
▪ Degrees of belief represented by these numbers should satisfy the basic laws of probability, on pain of being “incoherent” if they don't.
▪ If they do satisfy these laws, then Bayes' Rule follows.
▪ Hence we can update earlier degrees of belief by new evidence in a coherent, “rational” way.
This evasion of the problem of induction is called Bayesian.
The Bayesian does not claim to be able to justify any given set of degrees of belief as being uniquely rational. He does claim that he can tell you how it is reasonable to change your beliefs in the light of experience.
The Bayesian says to Hume:
Hume, you're right. Given a set of premises, supposed to be all the reasons bearing on a conclusion, you can form any opinion you like.
But you're not addressing the issue that concerns us!
At any point in our grown-up lives (let's leave babies out of this), we have a lot of opinions and various degrees of belief about our opinions. The question is not whether these opinions are “rational.” The question is whether we are reasonable in modifying these opinions in the light of new experience, new evidence.
Review the options below to login to check your access.
Log in with your Cambridge Aspire website account to check access.
If you believe you should have access to this content, please contact your institutional librarian or consult our FAQ page for further information about accessing our content.