Picking an epistemology

Christians with a philosophical bent often wish to develop a Christian epistemology. A theory of knowledge which incorporates Christian distinctives, like Biblical revelation, the imago Dei, divine providence, the noetic effects of sin, &c.

They don't necessarily start from scratch. This may involve assessing extant rival theories of knowledge, like rationalism, empiricism, and variations thereof. Sometimes Christians will modify a preexisting theory of knowledge, the way Thomism modifies Aristotelian epistemology, or Augustinianism modifies Platonic epistemology. 

In this respect, Christians often take sides in traditional debates. They side with rationalism (e.g. Augustine) or empiricism (e.g. Locke). They endeavor to determine which competing position is correct, then hitch their star to that position. And it's obviously valuable to weigh the strengths and weaknesses of various positions.

That said, Reformed theism has the metaphysical resources to make different theories of knowledge work. Take the debate between internalists and externalists concerning epistemic justification:

There is considerable disagreement among epistemologists concerning what the relevant sort of justification here consists in. Internalists about justification think that whether a belief is justified depends wholly on states in some sense internal to the subject. According to one common such sense of ‘internal’, only those features of a subject's experience which are directly or introspectively available count as ‘internal’—call this ‘access internalism’. According to another, only intrinsic states of the subject are ‘internal’—call this ‘state internalism’. See Conee & Feldman 2001 for the distinction. 

Conee and Feldman present an example of an internalist view. They have it that S's belief that p is justified if and only if believing that p is the attitude towards p that best fits S's evidence, where the latter is understood to depend only on S's internal mental states. Conee and Feldman call their view ‘evidentialism’, and characterize this as the thesis that justification is wholly a matter of the subject's evidence. Given their (not unsubstantial) assumption that what evidence a subject has is an internal matter, evidentialism implies internalism.^[5^] Externalists about justification think that factors external to the subject can be relevant for justification; for example, process reliabilists think that justified beliefs are those which are formed by a cognitive process which tends to produce a high proportion of true beliefs relative to false ones.^[6^] We shall return to the question of how reliabilist approaches bear on the analysis of knowledge in §6.1. 

http://plato.stanford.edu/entries/knowledge-analysis/#JusCon 

Internalism 

Belief is a mental state, and belief-formation is a mental process. Accordingly, one might reason, whether or not a belief is justified – whether, that is, it is formed in the right way – can be determined by examining the thought-processes of the believer during its formation. Such a view, which maintains that justification depends solely on factors internal to the believer’s mind, is called internalism. (The term “internalism” has different meanings in other contexts; here, it will be used strictly to refer to this type of view about epistemic justification.) 

According to internalism, the only factors that are relevant to the determination of whether a belief is justified are the believer’s other mental states. After all, an internalist will argue, only an individual’s mental states – her beliefs about the world, her sensory inputs (for example, her sense data) and her beliefs about the relations between her various beliefs – can determine what new beliefs she will form, so only an individual’s mental states can determine whether any particular belief is justified. In particular, in order to be justified, a belief must be appropriately based upon or supported by other mental states. 

http://www.iep.utm.edu/epistemo/#SH3a 

Externalism 

According to externalism, the only way to avoid the isolation objection and ensure that knowledge does not include luck is to consider some factors other than the individual’s other beliefs. Which factors, then, should be considered? The most prominent version of externalism, called reliabilism, suggests that we consider the source of a belief. Beliefs can be formed as a result of many different sources, such as sense experience, reason, testimony, memory. More precisely, we might specify which sense was used, who provided the testimony, what sort of reasoning is used, or how recent the relevant memory is. For every belief, we can indicate the cognitive process that led to its formation. In its simplest and most straightforward form, reliabilism maintains that whether or not a belief is justified depends upon whether that process is a reliable source of true beliefs. Since we are seeking a match between our mind and the world, justified beliefs are those which result from processes which regularly achieve such a match. So, for example, using vision to determine the color of an object which is well-lit and relatively near is a reliable belief-forming process for a person with normal vision, but not for a color-blind person. Forming beliefs on the basis of the testimony of an expert is likely to yield true beliefs, but forming beliefs on the basis of the testimony of compulsive liars is not. In general, if a belief is the result of a cognitive process which reliably (most of the time – we still want to leave room for human fallibility) leads to true beliefs, then that belief is justified. 

http://www.iep.utm.edu/epistemo/#SH3b

i) Suppose justification depends on a reliable belief-producing process. Calvinism, with its doctrine of meticulous providence, could make that work. General or special providence could ground that. If God intends someone to have a justified (or warranted) belief, God can ensure a reliable chain of testimony, confirm his recollection, or make inductive samples representative.

Conversely, suppose justification depends on mental states. Since God controls our thought processes, God can ensure the suitable relationship between various mental states. 

ii) Apropos (i), suppose that after examining the pros and cons of externalism and internalism, you can't decide which is correct. Maybe both can account for the relevant facts. Or maybe each has unique advantages and disadvantages, such that neither one enjoys a decisive advantage over the other.

Indeed, it can be difficult to form a definitive assessment inasmuch as this is an ongoing debate in which both sides continue to refine their positions in response to criticisms from the other side. You don't have the luxury of comparing the final version of externalism against the final version of internalism.

If, however, both are workable given Reformed theism, then perhaps it's not necessary for you to choose which one is right. 

iii) Apropos (i-ii), if God can make either model work, then that raises the question of whether we can know which one true. Which one is true depends on whether God put us in a world where internalism is true or a world in which externalism is true. If, however, both are viable, then perhaps we can't tell which world we're in. If both are adequate to account for the relevant facts, then at that level, there doesn't seem to be any independent criterion to distinguish which one describes the real world. 

Of course, if one is clearly defective, then that's a distinguishing consideration.