Theories of meaning that rely upon central aspects that remain in existence by directly or indirectly referring to themselves are seldom as simple as Hoffstadter's notion of a strange loop. But you can see Lacan's version of signification theory as being the same thing writ large.
The central concepts around which everything is organized are not fixed, but are maintained by continual usage, because the definitions of the less central concepts are all in terms of those central concepts.
Take the notion of 'Father'. It can be seen as the source of a concept of hierarchy. We cannot shake our social notion of male superiority because our notions of hierarchy are so embedded in our related notions of Father, Name, Deserving etc. are tied up through circular references back to their source in our experience of realizing we are in some way 'owned' by something of which we are not and have never really been a part (to our mind as an infant). But, in fact, it is a legal fiction maintained only by usage. One need to be the biological offspring of one's father. You will make others into a father if you are born without one, (If you are deeply gifted you might invent a transcendental father that shapes several cultures for the next two millennia ;) etc. Paternity suits can be based on genetics, but also on established obligation to the mother unrelated to genetics.
It is all part of one big multilayered strange loop: I am a father because I own this child, and the assignment of this ownership and its concomitant duties is a legal feature of my nationality which is defined in terms of bloodline and negotiated obligation, the former is directly related to fatherhood, the latter is an aspect of being partially owned, ownership is modeled on fatherhood, so both, I ultimately understand most basically in terms of my relationship to this child.
Even if you reject all this psychoanalysis, the theory of meaning remains compelling. Ultimate references are empty, and are refined by their dependent notions which are nailed down by their daily uses, which are identified by filling the roles in relation to other notions, which are defined in terms of the ultimate references.
One can continually 'descend' because containment and reference are dual ways of anchoring meaning, each is more basic than the other in different ways. Moves that feel 'down' can really move you 'up', and moves that feel 'lateral' are almost always really moves 'up' or 'down'. And if you try to consistently move 'up' or 'down' you end up at the same heavily-referenced points over and over again.