Let me try to make clear what it would mean for knowledge to have foundations. It is an open question whether knowledge is like a building where some beliefs are more fundamental than others and so others follow after those beliefs, or whether knowledge is like a web of beliefs, or whether it's neither a building with a foundation nor a web of belief.
Philosopher Roderick Chisholm in his paper "The Myth of the Given" wants to defend a traditional view: that knowledge has a foundation or foundations. He specifically wants to defend the view that some of the foundations of knowledge are sense-data (or the like). But he wants to reject the idea that the only foundational knowledge is the set of sense-data.
So Chisholm accepts the following traditional principles:
(A) The knowledge which a person has at any time is a structure or edifice, many parts and stages of which help to support each other, but which as a whole is supported by its own foundations.But he rejects the following principle:
(B) The foundation of one's knowledge consists (at least in part) of the apprehension of what have been called, variously, "sensations," "sense-impressions," "appearances," "sensa," "sense-qualia," and "phenomena."
(C) The only apprehension which is thus basic to the structure of knowledge is our apprehension of "appearances" (etc.)--our apprehension of the given.Let's look at his argument. He wants to arrive at this idea, ultimately: "What justifies me in thinking I know that n is true is simply the fact that n is true." He wants to arrive at some basic belief that is of this form. His argument is basically a disjunctive argument against all the other positions.
Chisholm tries to exhaust the possibilities thus:
(1) One may believe that the questions about justification which give rise to our problem are based upon false assumptions and hence that they should not be asked at all.1. One may believe that the questions about justification which give rise to our problem are based upon false assumptions and hence that they should not be asked at all.
(2) One may believe that no statement or claim is justified unless it is justified, at least in part, by some other justified statement or claim which is does not justify; this belief may suggest that one should continue the process of justifying ad infinitum, justifying each claim by reference to some additional claim.
(3) One may believe that no statement or claim... is justified unless it is justified by some other justified statement..., and that [the other justified statement] is not justified unless it is justified by [the first]; this would suggest that the process of justifying is, or should be, circular.
Chisholm addresses this objection by looking at philosophers' responses and rejecting them. He thinks that previous philosophers have used words, especially, for example 'doubt,' ambiguously. I don't know how relevant his objects are to today, so for the sake of argument let's assume that he has correctly refuted those people. Ultimately, Chisholm thinks we can ask about the justification of our beliefs, and when we do, we learn something about ourselves. We could ask, for example, why we believe we saw someone commit a crime. We could claim, for example, we noticed that that man also wore the same jacket as was revealed in the trial that the defendant wore. Etc. So he thinks this objection doesn't hold water, because we learn something when subjecting our beliefs to questions of justification and when we ask whether or not some beliefs ground other beliefs.
2. One may believe that no statement or claim is justified unless it is justified, at least in part, by some other justified statement or claim which is does not justify; this belief may suggest that one should continue the process of justifying ad infinitum, justifying each claim by reference to some additional claim.
Chisholm responds to a specific philosophical objection here by a fellow named Hans Reichenbach but perhaps his point could generate to something like this. Any statement where someone says that all beliefs are based on other beliefs before that and other beliefs before that and so on must itself be justified by the another belief, but it is essentially a claim that looks on the face of it to be a fundamental belief. But the paradox is is that if it is a fundamental belief, it is false. If it is a non-fundamental belief and so a belief that needs further and further justification all the way down, it is not clear how this belief is not either a belief which requires other beliefs so as to cohere in an overall system or some fundamental belief. Again, if we allow that is it not fundamental, then perhaps it is just a belief that needs other beliefs in an overall coherent system. Indeed, it is hard to imagine what belief could further justify it. This isn't exactly Chisholm's argument but assume he would give and assume it's true, for the sake of argument.
3. One may believe that no statement or claim... is justified unless it is justified by some other justified statement..., and that [the other justified statement] is not justified unless it is justified by [the first]; this would suggest that the process of justifying is, or should be, circular.
Chisholm wants to object to some coherence theory in the following way. He writes:
If we accept the coherence theory, we may still ask, concerning any proposition... which we think we know to be true, 'What is my justification for thinking I know that... [it] is a member of the system of propositions in which everything real and possible is coherently included, or that [it] is a member of the system of propositions which is actually adopted by mankind and by the scientists of our culture circle?" And when we ask suck a question, we are confronted, once again, with our original alternatives.So according to Chisholm, we are back to our original position. He write:
When we have made the statement "There lies a key," we can, of course, raise the question "What is my justification for thinking I know, or for believing, that there lies a key?" The answer would be "I see the key." We cannot ask "What is my justification for seeing a key?"So Chisholm basically argues that because we can always ask further what makes a set of beliefs cohere that some beliefs must be fundamental, and also because in ordinary language we just 'can't' ask what beliefs justify that we believe we see something, for example, other than that we believe we see something.
... When we reach a statement have the property just referred to--an experiential statement such that to describe its evidence "would simply mean to repeat the experiential statement itself"--we have reached a proper stopping place in the process of justification.
... We are thus led to the concept of a belief, statement, claim, proposition, or hypothesis, which justifies itself.
... A statement, belief, claim, proposition, or hypothesis may be said to be self-justifying for a person, if the person's justification for thinking he knows it to be true is simply the fact that it is true.