Internalist Foundationalism

I provide a construal of the epistemic regress problem and I take issue with the contention that a foundationalist solution is incompatible with an internalist account of warrant. I sketch a foundationalist solution to the regress problem that respects a plausible version of internalism. I end with the suggestion that the strategy that I have presented is not available only to the traditional versions of foundationalism that ascribe foundational status to experiential beliefs. It can also be used to generate a version of internalist foundationalism based on reliabilist principles. 0. Logical Preliminaries Let a sprouting function on a set A be a function pairing each element of A with a subset of A. Let f be a sprouting function on a set A, and let a be an element of A. Let’s refer to the elements of f(a), if it has any, as the offshoots of a. By the f-tree of a, we shall refer to the set containing the offshoots of a, if there are any, the offshoots of these, if there are any... and nothing else. And by an f-branch of a, we shall refer to any of the subsets of A that you generate by picking exactly one offshoot of a, if it has any, exactly one offshoot of this, if it has any... (See the appendix for formal definitions.) We can now define three properties that a sprouting function f on a set A might exhibit. First, let’s say that f is total if every element of A has offshoots (i.e. no element of A has the empty set as its image under f). Second, let’s say that f is non-circular if no element of A is an element of its own f-tree. Third, let’s say that f is finitary if every f-branch is finite. We end these logical preliminaries by formulating the following straightforward result about sprouting functions (see the appendix for a proof): * I am grateful to an anonymous referee for this journal. 1 Notice that an f-tree can contain infinitely many elements of A and still be finitary, if (and, by König’s Lemma, only if) any of its elements has infinitely many offshoots.