Thanks George; a good question I’ve been pondering for a couple days.

First issue; I’ll try to get to a better understanding of how I use of the term belief.  I’m thinking pragmatically here about how I act in most everyday situations, not in an idealized logical theoretical way.  In this context, I use the term belief not as an ill-formed or unsubstantiated theory, but more as a gestalt of everything I know that relates to the context in which I’m about to act.  Some of that may be informed by knowing that we’re not even conscious of drawing upon at the time we’re deciding and acting.  (Thinking of JG’s reference to intuition.)  I think that well founded theories are important, and hopefully, we get them into our gestalt beliefs in a way that will influence our actions to advance whatever practice we are engaged in.

Second issue, I’ll try to get at the relativism issue implied by your question.  Even though I love discussing theory, my primary concern has always been with practice.  (You might say, Phronesis informed by Pragmatism.)  Where I think Boghossian is arguing from first principles to achieve a version of a valid philosophical theory, I’m attempting to achieve the best practice possible by combining the best of all concepts and theories, as I understand them, that can move me towards that best practice.  I need well founded theories, but I’m interested in them in instrumental ways.  Now, that does lead me toward a relativist’s path, but I don’t argue for relativist first principles.  Not all viewpoints are equal and our arguments can be substantiated, but there are limitations to our thinking and knowing that should also be acknowledged.  I favored Joseph Margolis‘ explanation in grad school and I’ll go back to that now.

(According to Wikipedia) Margolis lists 5 themes in philosophy that have been gathering momentum since the time of Kant. (Emphasis added)

1. Reality is cognitively intransparent. That is, everything we say about the world must pass through our conceptual schemes and the limits of our language, hence there is no way of knowing whether what we say “corresponds” to what there is; what the world is like independent of our investigating it;
2. The structure of reality and the structure of thought are symbiotized. That is, there is no way of knowing how much of the apparent intelligibility of the world is a contribution of the mind and how much the world itself contributes to that seeming intelligibility;
3. Thinking has a history. That is, all we take to be universal, rational, logical, necessary, right behaviour, laws of nature, and so on, are changing artifacts of the historical existence of different societies and societal groups. All are open to change and all are the sites of hegemonic struggle;
4. The structure of thinking is preformed. That is, our thinking is formed by the enculturing process by which human babies become adults. The infant begins in a holistic space which is immediately parsed according to the norms and conduct and language she is brought up in. By taking part in the process, we alter it, alter ourselves, and alter the conditions for the next generation;
5. Human culture, including human beings, are socially constructed or socially constituted. That is, they have no natures, but are (referentially) or have (predicatively) histories, narratized careers.

I don’t see this as a strong version of relativism that offers no possibility of making arguable judgements (I don’t know where he is now, but back in the 90s Margolis was willing to acknowledge that some of these, especially the social construction parts, could be open to argument).  It’s just that theories, judgements, scientific findings and the like are definitely limited by our cognitive abilities and situatedness.  As an example, one of my favorite topics is validity, which I conceive of as the degree to which evidence and theory support specific practices (I draw this from test validity, not philosophical validity).  You can make a judgement about the objectivity and correctness of a conclusion or test, but no matter how strong the evidence, validity never reaches 100%.  I must posses an openness to look at things in other ways, which also can be stated as, I expect science to progress by giving us better ways of understanding what we once thought differently about.

P.S. I generally thing of theoretical validity as how a theory is substantiated in a general sense.  Usually this will include the requirements of being predictive, descriptive, and testable, but I’ll usually judge that according to the context of my judgement, not in a prescriptive sense.