Greg, I think this may be the most difficult question you have asked so far!
The trouble with Religious Philosophy is that quite ordinary words have long philosophical histories and can be used in very precise ways. Philosophers, the real articles, are a breed apart. The problem is that there is no short cut to this history you have to work through the centuries as one school reacted to the last and so on ad infinitum...
Karl Barth is a notoriously complicated and convoluted writer. In my view, he is primarily a philosopher rather than a theologian. He produced enormous amounts of material during his lifetime and has had and is having a powerful influence on many.
As an example of Karl Barth you may like to read this and this summarise it for me
[i]"If you ask about God and if I am really to tell about him, dialectic is all that can be expected from me. ... Neither my affirmation nor my denial lays claim to being God's truth. Neither one is more than a witness to that truth which stands in the center, between every Yes and No. And therefore I have never affirmed without denying and never denied without affirming, for neither affirmation nor denial can be final. If my witness to the final answer you are seeking does not satisfy you, I am sorry. It may be that my witness to it is not yet sufficiently clear, that is, that I have not limited the Yes by the No and the No by the Yes incisively enough to set aside all misunderstanding-- incisively enough to let you see that nothing is left except that upon which the Yes and the No, and the No and the Yes, depend. But it may also be that your refusal of my answer arises from your not having really asked your question, from your not having asked about God--for otherwise we should understand each other"[/i]
(Karl Barth, The Word of God and the Word of Man, Pilgrim Press, p. 209).
The great advantage of this kind of writing is that hardly anyone can argue with it. It is form of 'let your yea be yea but with a few no reservations in it, and let your nay be nay but with a few yeas in it too'. You have to wonder whether Barth actually understood this or at least his translators.
Evangelicals were originally suspicious of Barth but increasingly they are quoting him and supporting his work. Religious philosophy is a strange beast; it moves, often violently, in the opposite direction to its last step. Every fresh idea produces a counter-reaction which in turn produces a counter-reaction. Barth was reacting against the liberal modernism of the 19th century and his work is really a one-man protest movement against the catastrophic failure of the optimism of the 19th century. 19th century Europe believed that things were getting better and better. Socialism in the UK was originally Christian Socialism and a determined attempt to bring about the Kingdom of God by act of government. Let him that readeth understand
Barth felt that the solid gains of the Reformation were being lost and that a return to revelation was necessary. His views of the Bible however are a real muddle. He accepted the position of the Higher Critics who undermined the inspiration and infallibility of the Bible, but claimed that the Bible was Gods word in a specific sense. [i]the Bible was not the actual revelation of God but only the record of that revelation.[/i]. The Bible is the record of the revelation that has passed through men and what we have is their experiential testimony to the revelation not the Word of God itself. The idea lurking here is that the Bible is the authentic witness of the Christians to their genuine experience, but in some senses filtered through their experience. The Bible is interpreted by the effect it has upon the people who believe it. This is subjective, but consciously so. Conservatives evangelicals have traditionally believed that the Scripture was the testimony of God, Barth believed the Scripture was the testimony of men to the revelation of God. Consequently men's testimony can be flawed and yet still valuable; however man's testimony can never be infallible or inerrant.
The Bible was not the Word of God but the inspired witness to the Word of God in and through the experience of those who wrote it. He wrote [i]"The word which enters human ears and is uttered by human lips, is the word of God only when the miracle takes place otherwise, it is just a human word like any other. ... What stands there, in the pages of the Bible, is the witness to the Word of God ... God can be called truth only when 'truth' is understood in the sense of the Greek word 'aletheia'"[/i] (Barth, Romans).
He rejected the possibility of infallibility; [i]"The prophets and apostles as such, even in their office ... were ... actually guilty of error in their spoken and written word"[/i] (Barth, Church Dogmatics). This seems straight forward enough but the witness of those apostles and prophets is still valid and authoratitive, even if they got their facts wrong.
In some ways he is a stepping stone towards post-modernism in that only the personally interpreted word is relevant. He sees the relevance of the Word as being in the eye of the beholder; truth like beauty is in the eye of the beholder. The communication is validated by the recipients understanding and not by propositional revelation intended in the one who speaks the word. The post-modernist says what matters is not what you say but what I understand. Truth has become was has been received rather than was has been given.
At the Lausanne Conference of Evangelicals Francis Schaeffer declared that inerrancy was the watershed in evangelicalism. It often surprises younger Christians to discover that many evangelicals do not believe in the infallibility and inerrancy of the scriptures as originally given. This has had its effects on evangelical commentaries which will now use language like Paul is too strong here, he will have to modify this in Corinthians. Or the notion that he was a brilliant theologian but a 1st Century Jew whose rabbinic rhetoric has a few holes in it, or that he was a misogynist so you will need to dilute his comments about women. I have evangelical commentaries which speak of Paul becoming incoherent in Galatians as a result of his excitement. Tozer and others saw this coming and spoke strongly against these things.
Many evangelicals are now liberal evangelicals. Barth would have called himself evangelical but we need to remember that in the German European tradition evangelical now means protestant rather than bible-based. In comparison with the liberal theologians he was evangelical, but in absolute terms he was not. A growing number of modern evangelicals are impressed by Barths dialectic and feel his views should be treated with sympathy. This fits into the mood of the time with notions of Open Theology and the rest. Bonhoeffer was one of his students although, of course, Barth outlived him.
I think Barth was a protest movement which continues to appeal to evangelicals who want to stretch their wings a little and dont like being confined in the narrow nest of conservative evangelicalism. His thinking is usually called Neo-orthodoxy, but remember that is against the starting line of liberal theology. His thinking represents a philosophical attempt to move back from the excesses of liberal theology, but does not really begin with solid biblical base. There is no way back from liberal theology, you have to reject it and start again somewhere else. The somewhere else, in the Reformation, was the scripture. With Barth it is not the scripture but his reaction to the scripture. His result is not really a neo-orthodoxy it is a 'tweaked' liberal theology. Personally, I agree with Schaeffer, inerrancy is the evangelical watershed. I picked up this quote somewhere but cant trace where it came from.
NEO (NEW)-ORTHODOXY is that inconsistent and illogical contemporary movement of theological deception, also called "Crisis Theology" or "Barthianism," which is a reaction away from liberalism but which constitutes a failure to return to the historic Christian faith. It emphasizes a subjective authority of the Bible and uses an evangelical terminology while embracing the destructively critical conclusions of modernism with respect to the Bible. Neo-Orthodoxy is an old idea in a new dress whereby the Word of God is made to be subject to the ideas of man. The proponents of this view would be such men as Karl Barth, Emil Brunner and Reinhold Niebuhr.
This is the man who famously declared [i]'Christ is not the Answer; He is the Question'.[/i]
for more info try here, especially the final paragraph which shows his distinctives from the conservative evangelical position.