When Jones believes that Horatio planted petunias in the garden yesterday, and Smith shares this belief, then there is something which both Smith and Jones believe. The most convenient name I can think of for the thing which both believe is 'proposition'. And since I think all of us have many beliefs, I also think there are many propositions, at least some of which are believed by at least one of us. Of course, it is nothing philosophically new to cast propositions in the role of objects of belief, disbelief, and various other socalled 'propositional attitudes'. Moreover, if Jones, or anyone else for that matter, believes that Horatio planted petunias in the garden yesterday, it would be unreasonable for Jones to deny that Horatio planted petunias. It would be unreasonable because obviously Jones' belief logically implies that Horatio planted petunias, even though logicians may dispute about the formalities of this implication. This illustrates the point that the propositions which can serve as the objects of belief (or of propositional attitudes in general) have logical implications, and also are implied by propositions which in turn can be the objects of propositional attitudes. Thus, the very same propositions which serve as the objects for propositional attitudes also serve as subject matter for logic, although the preceding considerations leave open the possibility that the class of propositions dealt with in logic is wider than the class of possible objects for propositional attitudes of people. (Some propositions included in the subject matter of logic, for example, may be too complex to be believed by any person.) Logic, then, has at least the task of providing an account of the implications of and the various other logical relations between our beliefs, our disbeliefs, and the objects of our other propositional attitudes. (In addition, if there are propositions not subject to being objects of such attitudes, logic will also deal with them.) Because the set of propositions which logic must handle includes those propositions which real people actually believe in their day-to-day lives, logic must be prepared to deal with vague propositions, for people often have vague beliefs. This is not to say that in order to fulfill its mission to handle vague propositions logic itself must become vague. (The
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