In this essay, beliefs about particular, spatiotemporally limited, states of affairs have been compared to maps (in many cases, inaccurate ones) which, taken together, form one great map of the world, with the believer as central reference point. General beliefs, however, are not part of the map. They are dispositions to extend the map according to certain principles, or, where there is no extension possible because the belief in question is already held, dispositions to create sustaining relations between one portion of the map and another.

It remains only to consider beliefs in the truth of unrestricted existentially quantified propositions (‘existential beliefs’). Genuinely unrestricted existential beliefs about contingent matters of fact are not common. For instance, one who is said to believe ‘that flying saucers exist’ will normally believe that they exist in the vicinity of the earth. His belief is therefore not an ‘existential belief’. But it is clearly possible that somebody should believe that something exists without relating the thing in question in any way to himself or to his spatio-temporal framework. In any case, such propositions are entailments of propositions that he does believe. Over and above existential beliefs of this sort, there are beliefs in the existence of mathematical entities, for instance, the true belief that there is a prime number between seven and thirteen, or that the number of the natural numbers is infinite.

This brief chapter will therefore consider the class of existential beliefs, beginning with those which are contingently true or false.