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The thesis of Weak Unrestricted Composition says that every pair of objects has a fusion. This thesis has been argued by Contessa (Analysis 72(3):455–457, 2012) and Smith (Erkenntnis 84(1):41–55, 2019) to be compatible with the world being junky and hence to evade an argument against the necessity of Strong Unrestricted Composition proposed by Bohn (Analysis 69(1):27–31, 2009a, Philos Q 59(235):193–201, 2009b). However, neither Weak Unrestricted Composition alone nor the different variants of it that have been proposed in the literature can provide us with a satisfying answer to the special composition question, or so we will argue. We will then go on to explore an alternative family of purely mereological rules in the vicinity of Weak Unrestricted Composition, Cardinal Composition: A plurality of pairwise non-overlapping objects composes an object iff the objects in the plurality are of cardinality smaller than κ . As we will show, all the instances for infinite κ s determine fusion and are compatible with junk, and every instance for a κ > ℵ 0 is furthermore compatible with gunk and dense chains of parthood. [ABSTRACT FROM AUTHOR]

This note defends the reduction of ordinals to pure sets against an argument put forward by Beau Madison Mount. In the first part I will defend the claim that dependence simpliciter can be reduced to immediate dependence and define a notion of predecessor dependence. In the second part I will provide and defend a way to model the dependence profile of ordinals akin to Mount's proposal in terms of immediate dependence and predecessor dependence. I furthermore show that my alternative dependence profile allows us to single out the reduction of ordinals to von Neumann ordinals as the only viable set-theoretic reduction. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that some truths or facts don't have a minimal full ground [see e.g. Fine (Metaphysical grounding, Cambridge University Press, Cambridge, p 57, 2012a)]. Every full ground of them contains a smaller full ground. In this paper I'll propose a minimality constraint on immediate grounding and I'll show that it doesn't fall prey to the arguments that tell against an unqualified minimality constraint. Furthermore, the assumption that all cases of grounding can be understood in terms of immediate grounding will be defended. This assumption guarantees that the proposed minimality constraint is significant for all cases of grounding. With its help one can get a clear grip on the relevance of grounding, a feature that will be put to use in the penultimate section. [ABSTRACT FROM AUTHOR]