The regress-stopping role assigned to acquaintance requires that the grasped relation itself be epistemically self-justifying, but Fumerton's own internalism demands that justification of acquaintance claims be accessible to the subject.

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Accessible to the subject(accessible to the subject): Available for the person to mentally examine or think about; something they can be aware of or understand themselves.
Epistemically self-justifying(relation being epistemically self-justifying): Something that proves itself is true or knowable without needing any other evidence or justification to back it up.
Fumerton, Richard(in epistemology): A contemporary American philosopher who studies how we know things; he developed an 'acquaintance theory' that says we're directly aware of certain facts and relationships.
Internalism(Moral psychology; used to characterize the relationship between moral judgment and motivation): The view that it is a logical or conceptual truth that some degree of motivation is internal to a moral judgment itself — that making a genuine moral claim entails being motivated to some degree.

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