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Some properties and relations take time to be instantiated. They are not instantiated at a time, but through a temporal interval. Cognitive properties and relations such as understanding and thinking are like this, but also many biological, chemical, and microphysical properties and relations such as absorbing, freezing, radiating, and decaying. In this paper, I make a case for taking seriously such temporally extended properties (TEPs). I argue that they are ubiquitous and that our current theories of persistence would do well to make room for them in their ontology. The focus here is on fourdimensionalism and different ways it can accommodate TEPs. I explore four different ways of dealing with TEPs within a fourdimensionalist framework. These are: (a) to make the objects that bear apparent TEPs temporally more extended or “chunky,” while giving TEPs a reductive or eliminativist treatment in favor of instantaneous properties (IPs); (b) to make a series of objects the bearer of TEP predicates, while, again, holding only to IPs; (c) to endorse TEPs in their own right and take them to be temporally extended in a literal sense; and (d) to hold on to TEPs as atemporal properties and make the exemplification relation temporally extended. I discuss each of these options and highlight the types of problems that a fourdimensionalist faces in attempting to accommodate TEPs. I conclude that fourdimensionalists do not yet have a satisfactory account of TEPs in their hands.

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Vallicella’s influential work makes a case that, when formulated broadly, as a problem about unity, Bradley’s challenge to Armstrongian states of affairs is practically insurmountable. He argues that traditional relational and non-relational responses to Bradley are inadequate, and many in the current metaphysical debate on this issue have come to agree. In this paper, I argue that such a conclusion is too hasty. Firstly, the problem of unity as applied to Armstrongian states of affairs is not clearly defined; in fact, it has taken a number of different forms each of which need to be carefully distinguished and further supported. Secondly, once we formulate the problem in more neutral terms, as a request for a characterization of the way that particulars, universals, and states of affairs stand to one another, it can be adequately addressed by an Armstrongian about states of affairs. I propose the desiderata for an adequate characterization and present a neo-Armstrongian defense of states of affairs that meets those desiderata. The latter relies on an important distinction between different notions of fundamentality and existential dependence.

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