Abstract

This paper deals with the treatment of infinity and finiteness in mereology. After an overview of some first-order mereological theories, finiteness axioms are introduced along with a mereological definition of “x is finite” in terms of which the axioms themselves are derivable in each of those theories. The finiteness axioms also provide the background for definitions of “ T makes an assumption of infinity”. In addition, extensions of mereological theories by the axioms are investigated for their own sake. In the final part, a definition of “x is finite” stated in a second-order language is also presented, followed by some concluding remarks on the motivation for the study of the extensions of mereological theories dealt with in the paper.