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Since forming beliefs on the basis of superstition is not an epistemically appropriate way of forming beliefs, Ingrid's belief is not doxastically justified; nevertheless, she does have good reason to believe as she does, so she does have propositional justification for the proposition that the neighborhood is dangerous.
Roughly, a subject s has propositional justification for believing a proposition p just in case, whether or not s actually believes p, it would be epistemically appropriate for s to believe p. On the other hand s is doxastically justified in believing p just in case s has propositional justification for believing p and s actually believes p in virtue of that justification.
First, propositional justification does not entail belief.
(See however the supplement on Transmission of Propositional Justification versus Transmission of Doxastic Justification).
3. It is standard practice to distinguish propositional justification from doxastic justification.
Colour shows that non-transmissive arguments of propositional justification instantiating indirectness can transmit doxastic justification.
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This talk of 'sufficient reason' is intended to be consistent with the idea that in some cases, no reasons are needed to suffice for propositional justification that some justification comes 'for free', not dependent on the possession of any reasons at all.
Is the awareness or acquaintance that is the alleged source of noninferential justification propositional or conceptual?
The precise relation between propositional and doxastic justification is subject to controversy, but it is uncontroversial that the two notions can come apart.
Epistemologists typically concentrate on transmission of (propositional or doxastic) justification across deductively valid arguments (or arguments deductively valid given background information).
(While the distinction between propositional and doxastic justification is important, to simplify discussion, we do not distinguish carefully between these below).
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