The more I think about it, the more I become convinced that this is a key question for the church, and the more surprised I am that there is so little being written about it (at a popular level, at least). What I'm writing is very much provisional, could doubtless be expressed better and needs thinking through more.
Epistemology is the study of how we become persuaded of things or why we believe what we believe. (πειθω / peitho is the Greek for “I persuade”, which leads to πιστυω / pistuο for “I believe”). How do Christians decide what is true about their faith and what isn't?
Note that this is a very different question from how people come to be Christians in the first place or why non-Christians believe what they believe. I don't actually think there is a solid epistemology that works for non-Christians beyond asserting some stuff and saying “this seems to work for me”.
Christian Epistemology is a huge question, and everything I write here is in one sense an oversimplification and in another sense a searching. I'm not yet convinced I've got it right – I'm still trying to articulate the question...
I guess there are three commonly articulated views, and all were present to an extent during the Reformation.
As far as I can tell, a common view before the Reformation, which is still current in places, especially in Eastern Orthodoxy, is that we are free to believe what we want to believe, within the constraints of the Church. The Church as a whole has met together several times, most famously at Nicea in AD325 and at Chalcedon in AD451 to discuss what it believed.
What it is essential to believe was decided at the Ecumenical Councils. However, our beliefs should of course be shaped by the tradition of the church, by what people who have gone before have taught us, especially in and from the Bible.
Essentially, we should believe what the Church as a whole has said it believes, and where the Church as a whole hasn't said anything, there's room for disagreement.
The reason that that broke down was partly because there were some issues that were very important that the church as a whole hadn't discussed and come to a firm conclusion on. This meant that there were some people within the church who were believing things that (in retrospect) were very clearly wrong and dangerous to believe, and doing things that were very clearly wrong, because the church had not explicitly forbidden them. The obvious example is people's attitude to how they were saved – there were lots of people in the church thinking that they were saved by buying indulgences, or paying for masses to be said for them.
It became very difficult for the church to meet to condemn some of the abuses, partly because the people in power were often the people who were profiting from the abuses of power. And when people spoke out against that, the reaction of those in power was often to try and get rid of them.
Attempted Scriptural Epistemology
The solution that the Protestants came up with was essentially a Scriptural epistemology. They said that we should believe what the Bible says, which sometimes contradicts what people within the Church said. Lots of protestants today still say this, but the big problem with it is the question of who interprets the Bible – the problem of hermeneutics. Actually, saying that we know things because the Bible says them is just shifting the epistemological problem to be a hermeneutical problem.
The most common idea among the Protestants is that it's my idea about what the Bible means that is right and other people who disagree with me are wrong. This led to a few influential teachers (e.g. Melanchton, Calvin) essentially writing books to tell people how to interpret the Bible correctly. And quite a lot of people followed them, and denominations were born. So Lutheranism was essentially people who interpreted the Bible the same way that Luther and Melanchthon did, Calvinism was people who interpreted the Bible the way that Calvin and Beza did, and so on. Yes, it's more comple than that, but that's the general idea. People like Luther and Calvin agreed on quite a lot of issues (like how to be saved), but disagreed on some (like what happens at Holy Communion).
On the other hand, there were also lots of people who didn't want to go along with what the teachers who ended up running denominations said and stuck with their own interpretation – they were the radicals, including the Anabaptists, Unitarians and so on. Because they essentially had an individualised epistemology, it was very easy for one little group to disagree with another little group and so split from them. That's the kind of thing that still seems to happen a lot in their spiritual descendants in the USA. All it takes for a split is two people with different interpretations of what the Bible says who are both sure in their own minds that they are right and the other person is wrong.
Some people go so far as to claim to interpret the Bible to mean the opposite of what a lot of people think it obviously means. The problem is that with an individualised hermeneutic, there's not much you can do about it. As a result, some people are heading back towards saying that we interpret Scripture as the Church has always interpreted it, which is essentially heading back to church-delimited epistemology.
One way out of this was the imposition of magisterial epistemology - you believe what you believe because the people who run the Church say that you should believe it. The pope (or whoever) has the power to say what is right and what isn't because he has the ability to interpret the Bible. This is the way that, for example a lot of Roman Catholics take.
Most of the Protestant denominations ended up claiming to have a Scriptural epistemology, but had an essentially magisterial hermeneutic – the Bible was their authority, but the Bible needed to be interpreted according to the rules of the denomination, whether Calvin's Institutes or the Augsburg Confession or the 39 Articles, or whatever. And there isn't actually much difference in practice between that and the Catholic magisterial epistemology.
The Problem for Protestants
The problem for protestants then is that we need a way to be able to have a definite heremeneutic without resorting to saying that the Church as a whole is right, because we've seen that the Church as a whole can be wrong with the Roman response to the Reformation.
A Way Forwards?
My suggestion of a way forwards is what I call a hermeneutic of brokenness. It's probably very unoriginal, but I don't know where I lifted it from. In practice, lots of people seem to do it anyway.
The idea is that we can only interpret the Bible correctly if we come at it completely broken and without any presuppositions. Of course, we can't do that perfectly, but the more broken we are, and the more we reject our presuppositions and let them be changed by the Bible, the closer we get to a correct interpretation. It's like in science, where we can never know if we've actually got the right interpretation – we can only know that our theories fit all the available data. But as our theories enable us to get better data, so we can re-evaluate and modify them. Just like that, we allow our views to be changed by Scripture, then re-read Scripture with our changed views and understand it slightly better.
Because all interpretations are ultimately provisional, it means that we are much more generous towards people that disagree with us – we listen and try to understand their point of view, being willing to change our mind if what they say fits better than what we say. But where they seem to be putting their pride or their cultural presuppositions first, then we can legitimately disagree with them or point out where they are doing that. And if they don't listen to dialogue, it suggests they aren't broken enough yet.
Having a hermeneutic of brokenness would mean that we were much less likely to splinter into more denominations and much more likely to be in dialogue with people of different traditions. It would mean that we wouldn't be confessionally defined, as confessions would not be necessarily true in the same sense as the Bible.
It does however make the question of defining heresy more difficult...