I'm not sure I see a problem with the idea that some concepts must reference themselves to be analyzable. I feel like, coming from ideas of axiomatic set theory, people view "the world" or "the set of all true statements in a system" as a tree, where there are fundamental truths (axioms) that one must start with and everything branches from there. Such a visualization does make it seem difficult to reconcile understanding those fundamental truths because nothing grounds them—they are the ground. But rather than a "tree of truth", I view the world as more of a nervous system, a graph or network (whichever you prefer) where everything is interconnected, and there aren't necessarily "undefinable" elements like the axioms. It should be noted that in such a visualization, everything would perhaps technically be circular, just more or less removed because there is no presupposed foundation.
So with respect to your example about being, I personally have a somewhat sophisticated (at least more sophisticated than "being" is "to be") understanding of it, which does rely on some circularity, but also incorporates elements of other concepts, such that a network can start to be realized. In my view, existence means "to stand in relation" to other things in an ontological sense (this is ontic structural realism). So if we're looking at the "network model" of the world, to say something exists means it is a node (or perhaps bridge between nodes) in that world. With some additional understanding, this implies a few things about existence that informs us of its nature: 1) There can be no world of just one node (one thing, because it doesn't stand in relation to anything else), 2) Something that exists in one world need not exist in another world; i.e., existence is relative, or 3) there is some barrier between that which exists actually and that which exists conceptually (concepts, like a physical unicorn, may fail to exist actually, in which case we may be said to be non-existent, although the concept exists in some sense).
Also, you also pose truth/falsehood as potential fundamental concept, but related to this definition of being, that may be explainable too: recall (1) that nothing can exist by itself, so there must at least be, say, two things that stand in relation. The most primitive relation of this nature can only be that of "something", and "not that something": this I believe, without additional structure giving weight to the meaning of "true" and "false", is the relationship that truth/falsehood describes. It's also akin to the idea of being and non-being, and harkens back to the Greek beliefs about opposites.
Don't mean to pontificate about my own beliefs, but with regards to your topic, I would say I think ultimately, not just some, but all concepts experience some level of circularity, but with some being more closely entwined, such as that of being and non-being, which is essentially self-referential, but can still be analyzed in the context of other concepts, and is not arbitrary. So I guess I disagree that they are unanalyzable, but also disagree that they must be non-circular. I thus conclude the answer is D, none of the above
:grin: