If one is going to get into semantics, as a matter of ordinary English usage "belief" does not preclude knowledge: "belief" simply connotes the state of mind in which one accepts something as a fact. It therefore encompasses accepting as a fact:
(1) that which is capable of proof
(2) that which is in that which is neither capable of being proved nor capable of being disproved; and
(3) that which is capable of being disproved.
There are specific terms for each of these belief states: (1) is "rational belief" (2) is "faith" and (3) is "delusion".
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