First of all, we need to be aware of the distinctions between Externalism about Knowledge (KE) and Internalism about Knowledge (KI). And also, the difference between Externalism about Justification (JE) and Internalism about Justification (JI).
JE vs JI
Deciding whether to be an internalist or externalist about justification is to focus the discussion on our definition of justification and how we wish to understand it rather than what is needed to call something ‘knowledge’.
Justification-externalists about are going to be looking at justification as a way that turns true belief into knowledge. They will also consider the Gettier problem and try to find ways around it (such as Nozick’s tracking account or reliabilism) as the Gettier problem is an external matter.
Justification-internalists view justification as a way to turn true and already de-gettiered belief into knowledge because they think that internal justification is necessary for knowledge. I can be justified in my belief purely on the basis of reflective thought.
KE vs KI
Here we are talking about what it takes for one to have knowledge of something, using our externalist and internalist definitions of justification. For example:
A Knowledge-externalist would say that internal justification is not a necessary condition for knowledge. A belief being formed by an external process alone is sufficient for it to be knowledge.
A Knowledge-internalist would hold that internal justification is a necessary condition for knowledge. So a belief that has been reliably formed by itself (i.e. without internal justification) is not sufficient for knowledge.
The reason to distinguish between justification and knowledge is born out of the thought that justification and knowledge are grounded in very different ways. Justification seems to be grounded in what is internal to the subject. That is, in order to be justified in something, I seem to have to perform some sort of internal reflection. This is internalism about justification (JI).
But knowledge, on the other hand, seems to be externally grounded. We can’t know things based on introspection alone, so perhaps we are tempted to naturalise it (clarify it by scientific explanations) by appealing to external sources. This is known as externalism about knowledge (KE).
It is important to note that these two forms of internalism and externalism are compatible. For the JI, what I justifiably believe is dependent on my mental states, reason, sensory perceptions (the internal experiences I get when I sense things), memories and such. But what I know is dependent on the things outside my mind, those things that are not subject to my thinking about them. For the KE, in order to have a reliable true belief, one must have some connection to objects external to oneself.
The reason we might want to combine these two is, firstly, it matches our intuitions about what we mean when we talk about justification and knowledge. If we go purely external about knowledge and admit that internal justification is not necessary for knowledge, we get counterexamples like the Truetemp case (see Externalist views). It would seem wrong to deny that we need internal justification.
On the other hand however, going internalist about knowledge seems dangerous because we end up with Evil Demon cases where we can hold justified beliefs but not know they are utterly false (see Internalist-views). For this reason, we want some reliable external verification that our internal mental states are actually true.
So a view that holds both KE and JI (i.e. internal-justification and reliable external-connections are necessary conditions for knowledge) might be a semi-externalist view about knowledge. This is similar to saying that JI and JE are necessary conditions for knowledge, but by doing so our beliefs couldn’t only be justified internally – they would rely on external factors too, which many people who hold JI wouldn’t want to admit. This is a more technical problem about the definition of justification however. So it seems more sensible to say that KE and JI are compatible, not JI and JE.
This is perhaps why we have this debate about the fundamental differences in what makes justification and what makes knowledge. Maybe then, externalist truth-tracking accounts and such that seek to externalise justification are in danger of missing this distinction.