Labeled Mereological Set Theory

TL;DR

This paper introduces a labeled mereological set theory aimed at examining and circumventing classical set-theoretic paradoxes, providing a novel approach with identified shortcomings and proposed solutions.

Contribution

It presents a new labeled mereological set theory that offers a fresh method for analyzing and avoiding well-known set-theoretic paradoxes.

Findings

The theory can analyze classical paradoxes like Russell's and Cantor's.

It highlights shortcomings in the proposed approach.

Suggestions for improving the method are discussed.

Abstract

The methodology used here might provide a neat method of examining paradoxes and ways to circumvent them. Most of the known set theoretic paradoxes (Russell's, Cantor's, Burali-Forti's,..) can be paralleled here and examined. This account will shed the light on a particular application of this method that appears to elude paradoxes; an application that have shortcomings that will be illustrated here and suggestions to solutions are proposed. First I'll present the exposition of the theory, and then speak about its background and the aims behind it and how it can extend our knowledge of overcoming paradoxes.