Foundationalism
From Neoredemptive
Foundationalism is a flavor of epistemology (a system for thinking about what we know and how we know it) asserting that some truths are knowable simply because they are self-evident or self-justifying ("I think, therefore I am" being the most famous example).
What this means, practically, is that if you repeatedly ask a foundationalist "Why?", he will eventually say "because what I have just said is true; it has no need to be explained or justified."
Emerging Church Conversations
Many in the Emergent camp have aligned themselves with the philosophers of post-modernity and rejected foundationalism, particularly as it pertains to the knowing of God (i.e., theology). Foundationalism is "dead" both philosophically and culturally, a passing delusion of modernist thinking. However, the alternatives are not terribly appealing, as they tend to relegate all truth claims (like, say, "Jesus is Lord") to total subjectivity, relativity, and meaninglessness apart from the "language games" of individual sub-cultures. (See anti-foundationalism and the attempts to find a "third position" in post-foundationalism).
It also bears mentioning that the rumors of foundationalism's death, in both high philosophy and popular culture, have been greatly exagerated (see Reclaiming the Center, Truth and the New Kind of Christian (pg. 76 and /TODO/), and the writings of Michael DePaul).
Emerging conversants in the Evangelical stream generally holds to a kind of chastened foundationalism, in which God has revealed Himself truly (albeit not comprehensively) through the Scriptures. It thus holds that we are able to actually and accurately know much about a God who actually does exist, and what we come to know is can be a true representation which remains true regardless of our language, culture, or consciousness.
Why Doc thinks Christian Foundationalism Misses the Point
I (User:Doc) have come to believe that the epistemology debate within theology largely misses the point by running down anthropocentric rabbit holes -- see epistemology for my notes.
Particularly with respect to foundationalism, I think the evangelical insistence upon it, while well-intended, is also misguided. The essence of foundationalism is the "self-evidence" of certain true propositions. Consider for a moment the notion of "self evidence"; if I say X is self-evident, what I want to mean is that X contains in itself the evidence of its own truth; what I actually mean is that I contain within myself a sufficient set of observations and assumptions for X to appear evident to my self.
Ultimately, Karl Barth got this right where most epistemologists (Christian or otherwise) go astray. It is meaningless to think of any being, existence, or truth as self-evident because doing so presumes that it makes sense for them to be self-existent; for the Christian, self-existence is reserved exclusively to God, and everything else must be understood as His creation and creature, thoroughly contingent in its being, essence, definition, nature, and evidence upon its Creator.

