Universalism entails Extensionalism

Analysis 69 (4):599 - 604 (2009)
Abstract
1. Universalism (also known as Conjunctivism, or Collectivism) is the thesis that mereological composition is unrestricted. More precisely: (U) Any non-empty collection of things has a fusion, i.e., something that has all those things as parts and has no part that is disjoint from each of them.1 Extensionalism is the thesis that sameness of composition is sufficient for identity. More precisely: (E) No two things have exactly the same proper parts (unless they are atomic, i.e., have no proper parts at all). Clearly these two theses are not equivalent. They are, however, more closely related than one might think. For while (E) does not entail (U), the converse entailment holds —or so I will argue. More precisely, the entailment holds as long as it is agreed that the following postulates are constitutive of the meaning of ‘part’: (1) Transitivity: Any part of any part of a thing is itself part of that thing. (2) Supplementation: Whenever a thing has a proper part, it has at least another part that is disjoint from the first. 2. One way to establish the entailment can be extracted from two results of Simons (1987: 29ff), which concern a set of postulates logically equivalent to (1) and (2). The first is that such postulates license the derivation of (E) from the following strengthening of (2): (3) Strong Supplementation: Whenever a thing is not part of another, the first has at least a part that is disjoint from the the second. 1 I write ‘is disjoint from’ as shorthand for ‘has no parts in common with’. I will also write ‘overlaps’ for ‘has parts in common with’ and ‘is a proper part of’ for ‘is part of, but not identical to’.
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References found in this work BETA
Paul Hovda (2009). What Is Classical Mereology? Journal of Philosophical Logic 38 (1):55 - 82.
Nicholas Rescher (1955). Axioms for the Part Relation. Philosophical Studies 6 (1):8 - 11.
Donald Smith (2009). Mereology Without Weak Supplementation. Australasian Journal of Philosophy 87 (3):505 – 511.

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