By Robert J. Ackermann (auth.)
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Extra resources for Belief and Knowledge
This result is compatible with intuition since this is the simplest case in which a pair of expressed beliefs represent agnosticism with respect to some assertion. •• Bn*, the reason why we add but one non-belief at a time to what the agent believes is that it is perfectly acceptable for an agent not to believe each sentence of a pair of sentences which together are contradictory. The simplest case of agnosticism is sufficient to show that if we add two sentences not believed by an agent (whose beliefs are consistent) to the set B*, we may get a contradiction.
The use of formulae like Bap to abstract sentences like "a believes that p" is perspicuous given the restriction to factual belief. There are, however, other grammatical constructions associated with belief sentences in English that require some discussion. The three important cases can be presented by these examples: (1 ) (2) (3) a believes in God. a believes the theory of evolution. a believes what his mother tells him. Philosophers are generally agreed that all such cases can be found in context to be equivalent to other sentences using the familiar "a believes that" prefixed Belief and Knowledge 52 to some factual sentence.
There is one consequence of our assignment of numbers to beliefs in the rational ordered belief set that should be explicitly noticed. By the consistency requirement, we can't have both a sentence and its negation in the set of a person's actual beliefs. 5 to any actual belief, say p. , p had a greater likelihood on the available evidence. This situation violates the intuition underlying the assignment of likelihood numbers. 5 in his rational ordered belief set. This will prevent the situation just Rational Belief 39 noted from arising.
Belief and Knowledge by Robert J. Ackermann (auth.)