 Using the technical notion of being bounded from below or having a lower bound introduced in  section 2,  we can start with the simple idea that, for a given notion of dependence, a chain has a lower bound only if there is an element that every element in the chain depends on (Rabin &amp; Rabern 2016: 366). As we saw earlier, infinitely descending chains of dependence may have a lower bound, that is, terminate in an independent element that may or may not be part of the chain itself, yet fail to be set-theoretically well-founded. But there is an even weaker condition than having a lower bound that can satisfy  (MF),  namely, Rabin &amp; Rabern’s (2016: 363) “having a foundation” or Dixon’s (2016: 446) equivalent “full foundations”. Both of these are based on the idea of having an infinitely large foundation. An example of this type of foundation can be constructed with the help of infinitary disjunctions, as both Rabin &amp; Rabern and Dixon demonstrate (Litland 2016b discusses the problems associated with this and constructs further examples). In such a case, (MF) is satisfied because every element depends on some independent element, despite there being no lower bound. There is no lower bound because the chain does not terminate if the foundation is infinitely large. In contrast, if the foundation is finite, then the there is a lower bound and hence the weaker requirement of (MF) is also entailed. In decreasing order of strength, we have the requirement of set-theoretical well-foundedness, having a lower bound, and having a foundation or full foundations. We defined (MF) in terms of the weakest of these three requirements in  section 2,  but a proponent of metaphysical foundationalism may of course make a stronger requirement as well, such as having a lower bound.