Foliation-Like Structure in Metaphysics

I argue that a recognisable class of metaphysical posits shares a formal structure with the postulation of a privileged global present in special relativity. In both cases one starts with a genuine invariant partial order—causal precedence for events, metaphysical dependence for entities or facts—and then selects a particular total structure (a foliation, a hierarchy of levels) from among many that are equally compatible with the invariant. By Szpilrajn’s theorem, non-trivial partial orders admit multiple linear extensions; so the selection is strictly additional information. I call a posit foliation-like when it (F1) commits to such a selection, (F2) does so within a domain whose admissible extensions form a non-singleton class, and (F3) cannot be distinguished by any further invariant or by explanatory work unavailable to its rivals. The relativistic case is not an analogy for this diagnostic but an instance of it. I argue that some contemporary uses of “priority”, “fundamentality”, and “levels of reality”—most visibly Schaffer-style priority monism and graded-fundamentality proposals—are foliation-like in precisely this sense, while local dependence relations (constitution, realisation, determinate–determinable, mereological composition) are not. The proposal is diagnostic rather than eliminativist: it identifies a specific argumentative burden that defenders of global stratification must discharge, without requiring anti-realism about grounding, explanation, or asymmetric dependence.