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Internalists hold that the factors that determine whether a belief is justified must be internally accessible to the believer through reflection — roughly, the believer must be able to tell whether their belief is justified. Externalists (like reliabilists) allow that justificatory factors can be external to the believer's perspective: a reliable process justifies a belief even if the believer cannot verify that the process is reliable. The debate is driven by competing intuitions: internalists appeal to cases where an agent does everything right by their own lights but relies on an accidentally reliable process; externalists point to animals and children who cannot reflect on their epistemic standing but surely have justified beliefs.
Work through the 'new evil demon' thought experiment: an agent whose cognitive processes are systematically fed false information by a demon seems to have the same epistemic status as a normal agent, suggesting justification is internal. Then consider why externalists dispute this intuition.
From your study of reliabilism, you know that one influential view ties epistemic justification to the reliability of the cognitive process that produced a belief — a belief is justified if it was formed by a generally truth-tracking process, like normal perception in good conditions. From your study of foundationalism and coherentism, you know that other theories locate justification in relations between beliefs — in basic beliefs or in coherent networks. The internalism vs. externalism debate cuts across all these theories: it asks whether the factors that make a belief justified must be *accessible* to the believer through reflection.
An internalist says yes. The classic motivation is this: justification is what makes belief *rational*, and rationality is an evaluation of an agent's epistemic conduct. If the factors that determine whether your belief is justified are completely hidden from you — outside your awareness, inaccessible even in principle — then it seems unfair to evaluate you by them. You can't be expected to reason well by standards you cannot access. The deontological version of this goes further: justification involves epistemic *obligation*, and obligations only apply when you can know whether you're meeting them. Internalists typically require that justificatory factors be accessible through introspection or a priori reflection.
An externalist says no. The chief externalist argument is that internalism proves too much. Very young children form accurate perceptual beliefs, and sophisticated animals navigate their environments reliably — but neither can reflect on whether their cognitive processes are reliable. If only reflectively accessible factors can justify, then animals and children have no justified beliefs at all. That seems wrong. More pointedly: what makes perception a justification-conferring process is not the fact that we can reflect on it, but the fact that it reliably produces true beliefs. The reliabilist externalism you already know makes this explicit: a reliably-formed belief is justified whether or not the believer can verify the process's reliability.
The new evil demon thought experiment is the strongest tool for internalists. Imagine a person whose cognitive faculties are normal in every introspective respect — she reasons carefully, consults her perceptions, considers evidence — but she's actually deceived by a malicious demon who feeds her false information. Intuitively, this person seems *epistemically blameless* even though her beliefs are all false. She is doing everything right by her own lights. The externalist must say her beliefs are unjustified (because her processes are unreliable), but that seems like blaming someone for bad luck. Externalists typically respond by distinguishing different senses of justification or by biting the bullet: perhaps this person's beliefs are *excusable* or *blameless* but still not genuinely justified in the knowledge-tracking sense. The debate continues because both sides are tracking real epistemic values — the connection to truth on the externalist side, and the connection to rational conduct on the internalist side.
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