“Someone who acts as if Bayesianism were correct will be said to be a Bayesianite.
It is important to distinguish a Bayesian like myself—someone convinced by Savage’s arguments that Bayesian decision theory makes sense in small worlds—from a Bayesianite. In particular, a Bayesian need not join the more extreme Bayesianites in proceeding as though:
All worlds are small.
Rationality endows agents with prior probabilities.
Rational learning consists simply in using Bayes’ rule to convert a set of prior probabilities into posterior probabilities after registering some new data.
Bayesianites are often understandably reluctant to make an explicit commitment to these principles when they are stated so baldly, because it then becomes evident that they are implicitly claiming that David Hume was wrong to argue that the principle of scientific induction cannot be justified by rational argument.”
Here’s how Binmore puts it:
“Someone who acts as if Bayesianism were correct will be said to be a Bayesianite.
It is important to distinguish a Bayesian like myself—someone convinced by Savage’s arguments that Bayesian decision theory makes sense in small worlds—from a Bayesianite. In particular, a Bayesian need not join the more extreme Bayesianites in proceeding as though:
All worlds are small.
Rationality endows agents with prior probabilities.
Rational learning consists simply in using Bayes’ rule to convert a set of prior probabilities into posterior probabilities after registering some new data.
Bayesianites are often understandably reluctant to make an explicit commitment to these principles when they are stated so baldly, because it then becomes evident that they are implicitly claiming that David Hume was wrong to argue that the principle of scientific induction cannot be justified by rational argument.”
http://www.carloalberto.org/files/binmore.pdf
Re: “A totally rational agent who denied the validity of induction would be unable to think.”
No, they would be a perfectly rational agent, quite capable of logical thought.