If we think of epistemic justification in inferential terms, i.e. in terms of a belief being justified by being inferred from other justified beliefs, then we face a problem: on this account, for every justified belief there must be at least one other justified belief on which it is based, which must in turn be based on at least one other justified belief, and so on. If all of our beliefs are justified in this way, therefore, then there must be an infinite regress of justified beliefs.
This implication of the idea that all of our beliefs are inferentially justified has struck many as implausible, if not incoherent. Clever though human beings may be, our intellects are finite; we do not seem to have the capacity to execute an infinite chain of inferences. The problem of avoiding this implication has become known as the regress problem of justification.
Foundationalism is a response to this problem, an attempt to halt the regress of justification.
The foundationalist seeks avoid the regress problem by positing the existence of foundational or “basic” beliefs. Basic beliefs are non-inferentially justified, i.e. they are justified without being inferred from other beliefs. As basic beliefs are justified, they are able to confer justification onto other beliefs that can be inferred from them. As basic beliefs are justified non-inferentially, however, they halt the regress of justification; we need not posit an infinite series of justified beliefs on which basic beliefs are based, because basic beliefs are self-justifying, and so need no such series.
According to foundationalism, the justification for all of our beliefs is ultimately derived from the basic beliefs that act as the foundation for all that we know.
There are a number of criticisms of foundationalism, among them that the idea of a basic belief doesn’t make sense, that basic beliefs can’t support a useful belief set, and that the choice of basic beliefs is arbitrary.