Epistemic foundationalism is a view about the proper architecture of one’s knowledge or justified beliefs. Some beliefs are known or justifiedly believed only because some other beliefs are known or justifiedly believed. The claim that one has heart disease is known only if some other beliefs are known—for example, that doctors have reported this and that the doctors are reliable.
This dependence among our beliefs naturally raises the question about the proper epistemic structure for our beliefs. Should all beliefs be supported by other beliefs? Are some beliefs rightly believed apart from receiving support from other beliefs? What is the nature of the proper support between beliefs? Epistemic foundationalism is one view about how to answer these questions. Foundationalists maintain that some beliefs are properly basic and that the rest of one’s beliefs inherit their epistemic status (knowledge or justification) in virtue of receiving proper support from the basic beliefs. Foundationalists have two main projects: a theory of proper basicality (that is, a theory of noninferential justification) and a theory of appropriate support (that is, a theory of inferential justification).
Foundationalism has a long history. Aristotle in the Posterior Analytics argues for foundationalism on the basis of the regress argument. Aristotle assumes that the alternatives to foundationalism must either endorse circular reasoning or land in an infinite regress of reasons. Because neither of these views is plausible, foundationalism comes out as the clear winner in an argument by elimination. Arguably, the most well known foundationalist is Descartes, who takes as the foundation the allegedly indubitable knowledge of his own existence and the content of his ideas. Every other justified belief must be grounded ultimately in this knowledge.
. . . [Debates over foundationalism] touched off a burst of activity on foundationalism in the late 1970s to early 1980s. One of the significant developments from this period is the formulation and defense of reformed epistemology, a foundationalist view that took as the foundations beliefs such as there is a God (see Plantinga (1983)). While the debate over foundationalism has abated in recent decades, new work has picked up on neglected topics about the architecture of knowledge and justification. (Continue article)
— Ted Poston, “Foundationalism,” Internet Encyclopedia of Philosophy
* Hyperlinks are mine