The main thesis of Alvin Plantinga's Reformed Epistemology is that belief in God is, or can be, properly basic; that is, it can be reasonable to believe in a god without any propositional evidence or arguments whatsoever. His Reformed Epistemology comes in two forms: Old School (the version he developed and defendend from the end of the 70s to the late 80s/early 90s) and New School (the version he developed and defended from the early 90s to the present).
To understand the difference between Plantinga's Old School and his New School Reformed Epistemology, we must first point out a distinction between two competing accounts of knowledge and justification: internalism and externalism. Very rougly (VERY roughly -- there are a gazillion versions of internalism and externalism out there now, and there a lots of subtle distinctions regarding them; my characterization here runs roughshod over them), internalism is the view that the factors that render a belief known or justified are internal to a person, in that such factors are mental states, such as reasons and evidence. By constrast, externalist theories assert that the factors that render a belief known or justified are at least partly external to the agent. For example, on one common view of externalism, at least part of what it is to know or justifiedly believe something is for it to be *caused* in the right way. But often, if not always, the relevant causal chain is at least partly located outside the person, in the surrounding environment. For example, if I know that a tree is in front of me, my knowledge is at least partly constituted by the fact that I'm standing in front of a tree, and the tree is causing my perceptual experience of it. And since the tree and the causal chain between us are outside of me, I can't know whether the belief is justified just by reflecting on my evidence.
I must emphasize a crucial implication of externalist theories of knowledge and justification: ***they entail that one can know or be justified in believing something without knowing *that* one knows or is justified in believing it.*** So, for example, if my belief that I see a tree in front of me is caused in the right way, then I *know* that I see a tree in front of me, even if I couldn't give you an argument to save my life that would prove that my belief wasn't caused by a hallucination, or an evil demon, or the Matrix, or whatever. This point will play a crucial role in Plantiga's defense of belief in God on New School verson of Reformed Epistemology.
In light of this distinction, we can make sense of Plantinga's Old School and New School versions of his Reformed Epistemology: his Old School version was based on an internalist theory, and his New School version is based on an externalist theory.
For an explication and defense of his internalist, Old School version, see my previous post. Here I will just point out a popular objection to it, known as "the Great Pumpkin Objection". Recall that according to the Old School version, a belief is properly basic if it's formed in the right way. What's the right way? Answer: it's formed in accordance with the criteria of proper basicality generated by your community. Now according to the Great Pumpkin objection, if belief in God is properly basic in virtue of it being formed according to a theistic community's criteria of proper basicality, then this is a game that any community can play: Wiccans, Flat-Earthers (and people who believe that the Great Pumpkin returns to the pumpkin patch every year), etc. may come up with other criteria of proper basicality that conflict with those of Christians, and thus have properly basic beliefs that conflict with theirs as a result. But, so the objection goes, this is absurd; rationality isn't relative from one community to another, at least not to this degree. Further, and relatedly, the cost of rendering belief in God rational on this account is too great; for it entails that it can be equally rational to be an atheist if one belongs to a community of atheists who form basic beliefs according to *their* criteria of proper basicality. For there just are no objective, community-independent criteria of proper basicality by which one could judge one community rational in their beliefs, and another irrational. Thus, according to the Great Pumpkin Objection, Plantinga's epistemology entails a nasty arbitrariness as to what sorts of beliefs can count as properly basic (i,.e., rational yet non-propositionally supported), and (due to their belief that non-believers are "without excuse" for their unbelief, due to the supposed obviousness of theism) this should be seen as unacceptable by Christians no less than non-Christians.
But Plantinga has an at least prima facie plausible reply to this objection. The basic idea is that Plantinga's account doesn't entail that just any old belief, or class of beliefs, can count as properly basic, for:
(i) The beliefs must have the right sorts of non-propositional/causal grounds, viz., an appropriate set of triggering-conditions (Plantinga asserts that the triggering-conditions for theistic belief are "widely-realized", but he mentions some of them, such as, e.g., looking up in the starry sky, which triggers the belief that "God made all of this"; having a contrite, repentant heart, which triggers the belief that "God forgives me for what I've done", etc.) Thus, since beliefs that lack such causal triggering-conditions can't count as properly basic, it's simply not true that Old School Reformed Epistemology entails that just any old belief can count as properly basic. Here, then, is one principled way to differentiate proper from improperly basic beliefs.
(ii) Epistemic communities generate criteria of proper basicaliy in the way that Chisholmian particularists do, viz., thinking about particular beliefs and whether they strike one as rational, and then, on this basis, framing hypotheses on as to which classes of beliefs are properly basic and which are not, etc. (See my previous post for how criteria for proper basicality are generated according to Chisholmian particularists like Plantinga). And while it's true that different epistemic communities may well generate different critieria of proper basicality, and thus may countenance a different set of beliefs as properly basic, that's just life in philosophy: philosophers hardly agree about anything, including which sorts of beliefs are rational and irrational. At any rate, each community is responsible to their own criteria of proper basicality, and so the christian will have a principled basis for not countenancing the atheist's beliefs as properly basic. Rather, they'll reject it on the grounds that it doesn't satisfy *their* community's particularistically-generated criteria of proper basicality, which in turn were generated in the appropriate Chisholmian particularist way (again, see my previous post for an explication of the way in which particularists do this).
On the basis of these points, Plantinga can remove a good deal of the force of the Great Pumpkin Objection (but see my previous post, where I discuss some remaining nasty problems for Old School Reformed Epistemology by James Sennett).
But this isn't the end of the story. For soon came what's called the "Son of Great Pumpkin" objection, which is that, while it may be that each community has their own criteria of proper basicality, and these have been generated in the proper (broadly Chisholmian particularist) way, this account of proper basicality is *itself* implausible, since it allows for this community-relative rationality. Thus, whether or not a belief can be countenanced as rational by one's epistemic community is cold comfort if such a theory of rational belif entails an implausibly radical form of community-relative rationality.
At that point, Plantinga started changing his epistemology by adding to his internalist account of justified belief an externalist account of knowledge -- or as he calls it 'warrant' (which is, as he puts it, "that quality or quantity, enough of which turns true belief into knowledge"). He developed his externalist theory of warrant in three volumes put out by Oxford University Press: (i) Warrant: The Current Debate (1993), (ii) Warrant and Proper Function (1993), and (iii) Warranted Christian Belief (2000). Roughly, Plantinga's theory of warrant says that a belief is warranted if and only if it is produced by cognitive faculties functioning properly, in accordance with a design plan aimed at truth. Thus, if I form the belief that I see a tree in front of me, then that belief is warranted if my belief was formed by my visual perceptual faculties, those faculties are functioning properly (I wasn't just hit in the head by a brick, I haven't recently taken a hit of acid, etc.), and my perceptual faculties were in turn designed (by God or evolution or both) in such a way that their goal is to get me to form true beliefs (as opposed to, say, survival, or happiness. If my cognitive faculties are *not* aimed at truth, but at one of these other goals, then my cognitive faculties might very well generate lots and lots of *false* beliefs -- and they will do so even when they're functioning *properly*; hence the clause requiring that our cognitive faculties are aimed at truth).
Now clearly this is an externalist theory of warrant. For we can't tell, just by thinking about it, whether our cognitive faculties are functioning properly (at least sometimes, anyway), and we can't tell, just by thinking about it, whether our cognitive faculties are designed in such a way that they aim at producing true beliefs. With this externalist account of warrant, though, Plantinga has found a way to respond to the Great Pumpkin Objection. For although his *internalist* theory of *rationality* and *justification* is still basically the same old one he had from the 80s, and thus still allows for community-relative rationality, his *externalist* theory of *warrant* does not. For in the final wrinkle of his theory of warrant, which is spelled out in Warranted Christian Belief, God -- the Christian God -- is the one who's designed our cognitive faculties, and he has fashioned them according to his own design plan, which is aimed at truth. And among the beliefs he has caused to be triggered under the right circumstances are specifically *Christian* beliefs, such as (what he calls) The Great Truths of the Gospel. Now Plantinga admits that he has no proof or argument to show that the Christian God exists. But -- and this is where the crucial implication of externalism comes in --*it doesn't matter*. For *if* you are a Christian, and *if* the Christian God exists, and *if* God caused you to believe the Great Truths of the Gospel in the externalist way sketched above, then your belief is warranted, even if you have no idea *that* it is. For again, his theory of warrant is an externalist theory, and as such, one can know something without knowing *that* one knows it. All that matters is that your belief was produced by a reliable process or mechanism, whether or not you know that it was.
Thus, Plantinga can respond to the Great Pumpkin Objection as follows: Only externalist theories of warrant are tenable (as he argued ably in his three-volume series on warrant), and externalism about warrant entails that a belief may be warranted as long as it arises from a reliable source, even if one has no idea whether that source *is* reliable. But if so, then as long as, say, your belief in the Great Truths of the Gospel arose from a reliable source, it's warranted. And if it did, and if the basic beliefs of *other* epistemic communities with basic beliefs that *conflict* with these are *not* generated from reliable sources, then *their* basic beliefs are *not* warranted. Now we may not be able to *tell*, via argument, which community, if any has the reliably generated, and thus warranted, basic beliefs. But that doesn't cut any ice one way or the other. All that matters is whether the Christian's basic beliefs *are* generated by a reliable source.
So here's the big picture: there are all of these communities, and they have their own appropriately-generated criteria of properly basic beliefs. And a number of the properly basic beliefs of each community clash with those of the others. But that's okay, because that's the best we can do. Each community thus may well be *rational* and *justified* in the *internalist* sense: they are faithful to form their beliefs according to their community's criteria of rational belief. However, *only one* community, at most, has all of their basic beliefs *caused* in the right way, and thus only one community (at most) has a full set of properly basic beliefs that are *warranted*. In this way, then, he can answer the Son of Great Pumpkin Objection.
Well, that's Plantinga's latest version of Reformed Epistemology, and that's how he responds to some of the most powerful objections to his view of the proper basicality of belief in God. What to make of this?
My own view is that Plantinga's proper function epistemology, upon which his account is based, admits of counterexamples, (and these are well-known in the literature). But at any rate, I'm happy to grant Plantinga all of the points above: re his replies to Great Pumpkin and Son of Great Pumpkin. But that's not very interesting. Plantinga himself admits at the very end of Warranted Christian Belief that he doesn't know, and probably *can't* know (in the internalist sense) whether basic Christian beliefs are generated by a reliable source, and thus can't know (in the internalist sense) whether Christian beliefs formed in this way are warranted. All one can know, at best, is the *conditional* claim that *if* Christianity is true, and thus the beliefs are formed from a reliable source, *then* christian beliefs formed in this way are warranted. And of course, the appropriate response to that is "big deal". The same thing goes for the Muslim and the Zoroastrian or the Jew: if *their* God exists, and he created our cognitive faculties to form beliefs about The Great Truths of (say) the Koran, then *their* beliefs are the warranted, properly basic ones, and not those of the Christian. In fact, we have no way of knowing whether *any* such account is correct.
So in the end, Plantinga has not given us reason to be Christians. He has only given a coherent account of *how it could be* that a Christian could be in their rights, and even warranted in believing in Christianity without propositional evidence.