Believing Conjunctions

I shall argue in this paper that it should.1 To begin with, I shall defend (CP) against several criticisms that have been launched against it. These criticisms are of two kinds, which I shall call internal and external respectively. Internal objections are that a theory that includes (CP) fails to give an account of what it is rational to believe that is satisfactory by its own standards. In particular, since almost everyone agrees that belief in a contradiction is not rational, (CP) is criticized on the grounds that it would imply that beliefs in some contradictions are rational. External objections maintain that the degree of idealization in a theory including (CP) is so great as to make it irrelevant to various real-world phenomena to which a theory of rational belief should be relevant.2 After addressing these objections I shall briefly reject one avenue of support for (CP), based on the claim that rational belief should be closed under entailment. Finally, I proceed to what I see as the right way to argue for (CP). This will involve an examination of the idea that people’s beliefs can be divided into fragments that do not rationally affect each other. I shall argue that within such fragments, people do believe the conjunctions of their beliefs. Putting this together with the claim that a rational person should not have a multiply fragmented belief system, we will arrive at an argument for (CP). Regardless of one’s final verdict on (CP) itself, I hope it will emerge uncontroversially from this paper that whether a theory of rational belief