Multilocation and Minimal Mereology do not mix well. It has been pointed out that Three-Dimensionalism, which can be construed as multilocation-friendly, runs into trouble with Weak Supplementation. 1 But in fact, regardless of one's theory of persistence, if someone posits the possibility of any one of several kinds of multilocation, he or she will not be able to maintain the necessity of any of the three axioms of Minimal Mereology: the Transitivity of Proper Parthood, the Asymmetry of Proper Parthood, and Weak Supplementation. 2 In fact, positing even the mere conceivability of cases involving multilocation will require the denial of the analyticity of Minimal Mereology. In response to this, some have claimed that we ought to relativise parthood, either to one region or to two. Unfortunately, if we replace the axioms of Minimal Mereology with region-relativised counterparts, we will not be able to capture the intuitions that supported the original axioms. In what follows I will argue for the incompatibility of this plausible picture of parthood and liberalism about location, then I will consider the region-relativising response that involves adopting an analogous logic of parts and wholes which uses region-indexed parthood, and I will argue that this analogous logic fails to capture the spirit of the original. The only adequate solution, I maintain, is to restrict multilocation to a domain outside the scope of the rules we intuitively take to govern the parthood relation. For those who take Minimal Mereology to be necessary and universal, that will mean relinquishing the possibility of multilocation.
We seem to talk about repeatable artworks, such as symphonies, plays, films, dances, and so on, all the time. We say things like, "The Moonlight Sonata has three movements" and "Duck Soup makes me laugh". But how are these sentences to be understood? On a simple treatment of these sentences, they have ordinary, subject-predicate form. The subject 2 refers to a repeatable artwork (e.g., The Moonlight Sonata, or Duck Soup) and the predicate ascribes some property to this artwork. The sentences are true just in case the individual referred to by the subject has the property ascribed to it by the predicate. Accepting this simple interpretation of the semantics of these sentences will have immediate consequences for our theory of repeatable artworks: the truth of the sentences will require that things like The Moonlight Sonata exist, that they are singular entities, and that they have the properties that the predicates in our sentences about them pick out. But perhaps the simple treatment of these sentences isn't the correct one. The surface form of a sentence isn't always a sure guide to its logical form. We are familiar with this phenomenon with respect to sentences like the following: 1. The average man has two and a half children. 2. Nothing is inside of the room. Neither of these sentences is such that the subject refers to some individual entity and the predicate tells us something about that entity. We will argue that the same is true of the following sentences: 3. The polar bear has four paws.
Some Trinitarians, such as Thomas Aquinas, wish to claim that God is mereologically simple; that is, God has no parts distinct from Himself. In this paper, I present Simple Trinitarianism, a view that takes God to be simple but, diverging from Aquinas, does not identify the Father, Son, and Holy Spirit with anything in our ontology. Nonetheless, Simple Trinitarians would like Trinitarian sentences to be true; thus, they must give a non-standard semantics for those sentences. I will focus on one possible semantics a Simple Trinitarian may give: taking Trinitarian claims to be translatable into feature-placing sentences, which posit property instantiation without requiring commitment to any objects that instantiate those properties. 2 As Dan Howard-Snyder points out, this puzzle has two readings: we could take "God" to be a count-noun (synonymous with "a god"), or as a name (Howard-Snyder, "Trinity"). I will generally treat "God" as a name, using "a God" to indicate when I wish to use it as a count-noun. But please substitute the count-noun reading as you prefer. 3 See Martinich, "Identity and Trinity," Cain, "The Doctrine of the Trinity," and Kleinschmidt, "Many-One Identity" for a sample. I will set aside such responses in this paper. 4 See van Inwagen, "And Yet They Are Not Three Gods," and Brower and Rea, "Material Constitution and the Trinity," for example. I will also set aside responses like these in this paper. 5 I am borrowing Dale Tuggy's terminology and division here. See Tuggy, "Trinity."
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