 We can find numerous formally precise attempts to capture the relevant sense of a metaphysical foundation in recent work. Dixon’s (2016: 446) preferred understanding (which he calls “full foundations”) suggests that every non-fundamental fact is fully grounded by some fundamental fact(s). Rabin &amp; Rabern (2016: 363) attempt to capture the idea of a metaphysical foundation with the phrase “having a foundation”, whereby a grounding structure has a foundation if and only if there is some set of facts that (i) together ground all the derivative facts and (ii) are themselves ungrounded. Raven suggests (2016: 612) that metaphysical foundationalism could be understood in terms of ineliminability (to be discussed in  section 3).  Tahko (2014: 263) tries to analyze metaphysical foundationalism in terms of an “ontological” sense of well-foundedness, which requires that an ontologically well-founded chain terminates in a fundamental supervenience base. Trogdon (2018b) follows the recent suggestions for a weaker understanding of metaphysical foundationalism and defines it as the view that, necessarily, any non-fundamental entity is fully grounded by fundamental entities. Even though the terminology varies, it’s quite clear that there are weaker senses of metaphysical foundationalism than the one defined in terms of set-theoretic well-foundedness. We arrive at the following definition of metaphysical foundationalism: