Universalism entails Extensionalism

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 (E) No two things have exactly the same proper parts (unless they are atomic, i.e. have no proper parts at all). 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): The second result is that the postulates license the derivation of (3) itself from the following thesis: Now, obviously (U) entails (4), for a product of any two overlapping things is just a fusion of their common parts: it has each of those parts as parts and it has no further part, hence no part that is disjoint from each of them. Thus, given (1) and (2), it follows that (U) entails (3) (by Simons's second result), hence that it entails (E) (by the first).