By Robert J. Ackermann (auth.)
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The same fact that we can believe what we cannot know is important to the constructions in (2) and (3). Although believes can be replaced by knows, it seems here that the underlying grammar of the sentences is quite different. Consider the result of such substitution: (7) (8) a knows the theory of evolution. a knows what his mother tells him. 54 Belief and Knowledge To be said to know a theory is to be said to know how to describe the theory, to know what it will explain, and so forth. It is thus difficult if not impossible to tum (7) into a knowing that construction in many cases.
Various strategies for avoiding the difficulties hinted at in the lottery paradox amount to relaxing one or more of these assumptions. We will describe briefly how various philosophers have relaxed one or two of these assumptions and produced consistent accounts of rational belief that seem at the same time to violate some of the intuitions of other philosophers who have chosen to weaken some other assumption. At the present time, the situation is this. One can avoid the lottery paradox by producing an account of belief that seems only partial and satisfies only some of the intuitions that were invoked in leading to the paradox.
21)-(23) supply a cluster of difficulties for the naive strategy whenever beliefs are iterated in the manner that they represent. Beliefs are said to be iterated when a person has a belief that he does or does not have some other belief. If we apply the first strategy, it only enables us to drop off the outermost belief assertion. Applying the strategy to (21)-(23), for example, we would get these sentences: (24) p. (25) I believe that not p. (26) I don't believe that p. By the test of Standard Logic, either (24) and (25) or (24) and (26) are consistent.
Belief and Knowledge by Robert J. Ackermann (auth.)