The Problem of a Logical Theory of Belief Statements
Nicholas Rescher · Philosophy of Science · 1960
It is shown that the logical theory of belief statements must be prepared to take into account relationships among statements which are subtler and more delicate than is requisite in other contexts. It is necessary here to draw distinctions (of a modal and semantical character) which the standard assertory logic can ignore with impunity. This is due to the fact that it is entirely possible to be in ignorance of various logical relationships (eg., entailment, equivalence, etc.) that in fact obtain among believed statements, and so, for example to believe the premisses of a valid deductive argument, and yet disbelieve the conclusion which follows from them. The implications of such difficulties for the logic of belief statements are examined.