Decidability of Mereological Theories
نویسنده
چکیده
Mereology is a theory based on a binary predicate “being a part of.” Most philosophers believe that such a predicate must at least define a partial ordering: that is, it is reflexive (P1), antisymmetric (P2) and transitive (P3). In other words, three basic principles of mereology can thus be fixed. The theory axiomatized by these three basic principles is called ground mereology (GM). There are some other mereological principles which are arguably still strongly philosophically motivated, such as extensionality principle (EP), weak supplementation principle (WSP), strong supplementation principle (SSP), finite sum (FS), and finite product (FP). (We will formally make those principles precise very soon). The last two are called closure principles. Variants of mereological theories can be formed by adding one or more of the foregoing principles on top of GM. Being applicable to metaphysical analyses, mereological theories have attracted quite a few philosophers’ interest recently. In order to know those theories better, it is very natural for us to look into their meta-logical properties. However, not much has been said on this in the literature. In this paper, I shall check the decidability of some mereological theories. Why decidability? Since most of those recursively axiomatized theories have finite as well as infinite models, obviously they cannot be complete. Hence it is mainly decidability which remains to be investigated.
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