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The Church of Scientology has a distinct belief system which, despite its somewhat strange cosmology – mocked by the TV show South Park and many others – is not essentially more strange than, say, the idea of a virgin birth.
The judge, Monti Belot, said, "I have the distinct belief that had she not been involved in the operation of the clinic, or had she approached her role there in a professional and responsible way, none of us would be here".
But these are clearly distinct belief states.
If distinct belief attributions indicate differences in cognitive value of the sentences in their that -clauses, then these two problems are really a single problem, presumably with a single solution.
On a holistic view, though, there need not be an identifiable distinct belief state by virtue of which the subject has that narrow content, whereas on a particularist view there will be.
Perry 1977 argues that once we accept the distinction between belief states and belief contents, we should see that rational agents can believe a proposition and its negation, so long as they do so by being in "distinct" belief states.
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But the problem with this attribution is that it fails to distinguish between the two distinct beliefs that Jane has about her ailments.
In any given case the actions and desires will fit distinct, even radically distinct, beliefs, but knowing more desires and observing more actions should, by clever design, let us narrow the candidates.
(For a response to Frege's puzzle about how two distinct beliefs can be about the same object on behalf of the theory of direct reference, see Salmon, 1986).
People with knee OA hold distinct beliefs about their illness and treatment.
Distinct beliefs allow a differentiation between males, females, khat users and abstainers when targeting preventive measures.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com