Different Theories of Parts

TL;DR

This paper explores various theories of parts, focusing on Leśniewski's mereology, examining existentially neutral and involved theories, and discussing the transitivity of the part relation in different mereological frameworks.

Contribution

It provides a comparative analysis of different mereological theories, highlighting the role of existential assumptions and the transitivity property of the part relation.

Findings

Existentially neutral theories do not assume the existence of collective sets beyond basic relations.

Some theories, like Grzegorczykian and Leśniewski's, involve existential assumptions about parts.

The transitivity of the part relation is a central issue discussed in various mereological frameworks.

Abstract

Stanis{\l}aw Le\'sniewski's mereology was formulated in a specific way, deviating from standard formalizations. Nowadays, Le\'sniewski's theory is presented in the form of an elementary theory or translated into the language of the theory of relational structures. In this article, firstly, we look at existentially neutral theories, in which we do not postulate the existence of any other collective sets than those obtained from the definition and the basic properties of the relation of being a part. We also examine some existentially involved theories of parts. Among them, there is Grzegorczykian mereology and Le\'sniewskian mereology. One of the main principles of mereology is the transitivity of the concept of being a part of. This property is often questioned in the literature on the subject. In the final part, we present problems related to the transitivity of this concept.