Precise numerical degrees of belief look artificial, so we might favour a coarser-grained system with some small number of distinct grades of belief. But whatever small number of grades we took, it is likely that our scale would seem too fine to be realistic. A better response is to continue to treat a belief system as a precise numerical probability distribution, but then to say that normally there is no fully determinate fact of the matter about exactly which belief system someone has. There are a range of belief systems that fit him equally well, though it may be that none fits perfectly; and there is no saying that his real belief system is one rather than another within this range. Then whatever coarse-graining is appropriate comes out as a spread of exact numerical values within the systems in the range. There may be more spread and there may be less; we needn’t try to settle once and for all how coarse the grain should be.

We have another reason also to acknowledge that someone may have a multiplicity of beliefs systems. To a greater or lesser extent, we are all doublethinkers: we are disposed to think differently depending on what question is put, what choice comes before us, what topics we have been attending to. Belief is compartmentalized and fragmented. Sometimes a doublethinking believer acts in a way that best fits one belief system, sometimes in a way that best fits another. And it should not be said just that his belief system changes rapidly; because, throughout, he remains simultaneously disposed towards both systems. In this way also, both systems may fit him equally well even if neither fits him perfectly.

David Kellogg Lewis

On the Plurality of Worlds, 1986