The outline, if not the detail, of the conclusions reached in this essay may be summed up quite briefly.

Beliefs about particular matters of fact (including beliefs whose content is an unrestricted existentially quantified proposition) are structures in the mind of the believer which represent or ‘map’ reality, including the believer's own mind and belief-states. The fundamental representing elements and relations of the map represent the sorts of thing they represent because they spring from capacities of the believer to act selectively towards things of that sort. General beliefs, however, that is, beliefs in the truth of unrestricted universally quantified propositions, are dispositions, in the precise sense that brittleness is a disposition, to extend the ‘map’, or introduce relations of causal sustenance between portions of the map, according to general rules. It was argued that all propositions of logic and pure mathematics, whether true or false, and including apparently ‘existential’ claims in these fields, may be reduced to general propositions. If so, belief in the truth of such propositions reduces to general beliefs.

The truth of propositions, and so the truth of what is believed, is determined by the correspondence of actual or possible, belief-states, thoughts or assertions to reality. But, unlike the classical correspondence theory, it is not demanded that the relation be one-one in every case.

Knowledge of the truth of particular matters of fact is a belief which must be true, where the ‘must’ is a matter of law-like necessity. Such knowledge is a reliable representation or ‘mapping’ of reality.