- Beliefs which are properly basic, in that they do not depend for their justification on other beliefs, but on something outside the realm of belief (a “non-doxastic justification”);
- Beliefs which are derivative of one or more basic beliefs, and therefore depend on the basic beliefs for their validity;
Within this basic framework of foundationalism, there are a number of views regarding which types of beliefs qualify as properly basic; that is, what sorts of beliefs can be justifiably held without the justification of other beliefs.
- In classical foundationalism, beliefs are held to be properly basic if they are either self-evident axiom, or evident to the senses (empiricism). However Anthony Kenny and others have argued that this is a self-refuting idea.
- In modern foundationalism, beliefs are held to be properly basic if they were either self-evident axiom or incorrigible. One such axiom is René Descartes’s axiom, Cogito ergo sum (“I think, therefore I am”). Incorrigible (lit. uncorrectable) beliefs are those which one can believe without possibly being wrong. Notably, the evidence of the senses is not seen as properly basic because, Descartes argued, all our sensory experience could be an illusion.
- In what Keith Lehrer has called “fallible foundationalism”, also known as “moderate foundationalism”, the division between inferential and non-inferential belief is retained, but the requirement of incorrigibility is dropped. This, it is claimed, allows the senses to resume their traditional role as the basis of non-inferential belief despite their fallibility.
- In Reformed epistemology, beliefs are held to be properly basic if they are reasonable and consistent with a sensible world view. This rather broad criterion can include faith in our senses, faith in our memory, and faith in God.