Mereological theories are theories based on a binary predicate ‘being a part of’. It is believed that such a predicate must at least define a partial ordering. A mereological theory can be obtained by adding on top of the basic axioms of partial orderings some of the other axioms posited based on pertinent philosophical insights. Though mereological theories have aroused quite a few philosophers’ interest recently, not much has been said about their meta-logical properties. In this paper, I will look (...) into whether those theories are decidable or not. Besides, since theories of Boolean algebras are in some sense upper bounds of mereological theories which can be found in the literature, I shall also make some observations about the possibility of getting mereological theories beyond Boolean algebras. (shrink)

It is customary practice to define ‘x is composed of the ys’ as ‘x is a sum of the ys and the ys are pairwise disjoint ’. This predicate has played a central role in the debate on the special composition question and on related metaphysical issues concerning the mereological structure of objects. In this note we show that the customary characterization is nonetheless inadequate. We do so by constructing a mereological model where everything qualifies as composed of atoms even (...) though some elements in the domain are gunky, i.e., can be divided indefinitely into smaller and smaller proper parts. (shrink)

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists (...) z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way. (shrink)