1 Preprint of paper in Francesco F. Calemi (ed.), Metaphysics and Scientific Realism: Essays in Honour of David Malet Armstrong, De Gruyter, Berlin. Armstrong’s Supervenience and Ontological Dependence Francesco Orilia University of Macerata ABSTRACT. In Armstrong’s mature ontology, the one in which states of affairs and truthmaking gain center stage, there is a distinctive and pervasive appeal to a certain notion of supervenience, on the basis of which he feels entitled to claim that the supervenient is not additional to the subvenient. Armstrong’s way of speaking may suggest that he does not take himself to be ontologically commi tted to supervenient entities, namely, in his opinion, mereological aggregates, sets, properties and relations of the manifest image of the world, internal relations, kinds, dispositions, and more. However, as many commentators have been quick to point out, his world view thus appears to be incoherent. It has also been suggested that Armstrong simply takes the supervenient as partially or totally overlapping with the subvenient. However, many of Armstrong’s claims about supervenient entities can hardly be interpreted in this mereological fashion. Alternatively, Correia, Schaffer and Calemi have hinted at another interpretation, according to which Armstrong presents a hierarchical ontology, wherein the supervenient is ontologically dependent on the subvenient. However, this interpretation too has its own difficulties. This paper explores it in detail, by surveying most of what Armstrong takes to be supervenient and trying to discern when it is really appropriate to view the supervenient as ontologically dependent on the subvenient. This reconstruction leads to a couple of options regarding how to conceive of the tie that brings together universals and particulars in a state of affairs, namely a brute fact approach and fact infinitism. 1. Introduction In Armstrong’s mature ontology, the one in which states of affairs and truthmaking gain center stage, there is a distinctive and pervasive appeal to a certain notion of supervenience. It is so defined: A supervenes on B iff (i) it is possible that B (the subvenient) exists and (ii) it is impossible that B exists and A (the supervenient) does not (Armstrong 1989 (CTP, hereafter), ch. 8; Armstrong 1997 (WSA, hereafter), 11). 1 The second clause can equivalently be put as follows: necessarily, if B exists, then A exists, i.e., the existence of B entails the existence of A, which suggests that supervenience is, in Armstrongian terminology, a necessitation relation: given the supervenience of A on B, we may say that A entails or necessitates B (WSA, 12, 92). Among the entities that Armstrong takes to be supervenient we find: mereological aggregates, sets, second-class properties and relations (found in the manifest image of the world), internal relations, kinds, dispositions, and more. Armstrong feels entitled to claim that supervenient entities are “no addition to the universe” (CTP, 114), “not something additional”, “no addition of being”, “nothing over and above”, or, with a most characteristic metaphor, “an ontological free lunch” (WSA, 12-13). 1 Although I have used, like Armstrong, the “s” of the third person singular in the verbs used for this definition, the variables “A” and “B” should be taken to range on both single entities and on pluralities, for Armstrong often applies supervenience to pluralities. For instance, as we shall see, he tells us that an internal relation supervenes on its relata or that an aggregate supervenes on its parts. Various notions of supervenience are often appealed to in much contemporary analytic philosophy, especially in philosophy of mind (McLaughlin and Bennett 2014), but they typically apply to properties, rather than to entities in general.