Rationalist foundationalism suggests that all of our beliefs are ultimately justified by truths of logic and mathematics, such as “2+2=4” and “Nothing is both red and green all over”.

Empiricist foundationalism suggests that all of our beliefs are ultimately justified by experience, such as patches of colour in our visual field, or immediate awareness of our own thoughts.

In either case, this is simply not enough of a foundation to support anything like the belief sets that most of us possess. In particular, this is not enough of a foundation to support our many empirical beliefs, our extensive account of how the external world is.

We have beliefs about the location of the Eiffel Tower, about the History of Britain, and about the structure of the atom; none of these follows from the foundationalist’s basic beliefs. The fact that I have an experience of redness and all the truths of maths and logic put together do not entail that there is anything red in the world at all.

All that can be justified by the basic beliefs of the foundationalist are the very beliefs that are said to be basic.