Ok. You probably won't read this, but my working definition of epistemic circularity is currently as follows:
An argument A is epistemically circular for S just in case (i) the conclusion c of A asserts that a belief, class of beliefs, or belief forming way is epistemically successful; (ii) if A is to be a cogent argument, one or more of the premises of A must enjoy, for S, the kind of positive epistemic status c ascribes to the belief, class of beliefs or belief forming way AND/OR the premises of A have positive epistemic status for S in virtue of being formed in the belief forming way mentioned as epistemically successful in c; (iii) S has no (and therefore could not rely upon) c-independent evidence for the satisfied consequent(s) of (ii), and finally (iv) if S were to have c-independent evidence for the satisfied consequent(s) of (ii), this evidence would probabilistically confirm the conclusion c of A.
This definition combines the right features of the accounts out there without succumbing to any counterexamples (that I have thought of). I'm fairly confident that it's pretty good, and of course, since epistemic circularity is a somewhat technical notion, there is room for me to stipulate the definition.
If you're familiar with inductive track record arguments, the most famous example of which is the inductive track record argument for the reliability of sense perception, then you might be interested to know that my definition of an ec-argument has it that inductive track record arguments need not be epistemically circular. Here's one inductive track record argument:
1.1 S formed the belief that p1 using a RBFM.
1.2 S is justified in believing p1.
2.1 S formed the belief that p2 using a RBFM.
2.2 S is justified in believing p2.
.
.
n.1 S formed the belief that pn using a RBFM.
n.2 S is justified in believing pn.
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Probably, S is justified in believing propositions formed using a RBFM.
ITRAs such as these are commonly considered to be epistemically circular. But I claim that they are only epistemically circular if we place a reliability constraint (As Alston has been wont to do) on justification. Such a reliability constraint is a constraint to the effect that an epistemic subject S cannot be justified in believing any proposition p unless S formed the belief that p in a reliable way. Suppose (per impossible!) such a reliability constraint is true. In this case, I take it that conditions (i) - (iv) of my definition are satisfied, and the argument will turn out to be epistemically circular for all cognizers.
But suppose that a subject was foundationally justified in believing all pairs of premises n.1 and n.2. Further suppose that (correctly) the internalist is right about justification. Then condition (iii) of my definition is not satisfied, for it is possible to have c-independent evidence that the premises have positive epistemic status (i.e., are foundationally justified) which makes no reference to a RBFM. If this is the case, the argument merely demonstrates an interesting correlation between being justified and beliefs being formed in a reliable way, but since the obtaining of the latter is not a condition for the possibility of the former, the argument fails to be epistemically circular.
If I am right, then discussions of epistemic circularity that have taken ITRAs as paradigmatic examples of epistemic circularity are a bit misguided, at least in so far as ITRAs need not always be epistemically circular.
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