## Notre Dame Journal of Formal Logic

- Notre Dame J. Formal Logic
- Volume 55, Number 3 (2014), 359-381.

### A General Concept of Being a Part of a Whole

#### Abstract

The transitivity of the relation of part to whole is often questioned. But it is among the most basic principles of mereology. In this paper we present a general solution to the problem of transitivity of parthood which may be satisfactory for both its advocates and its opponents.

We will show that even without the transitivity of parthood one can define—basic in mereology—the notion of being a mereological sum of some objects. We formulate several proposals of general approaches to the concept of being a part of a whole, none of which contains any existential assumptions. By adding the transitivity of parthood we obtain an axiomatization of “existentially neutral” (or “nonexistential”) mereology.

#### Article information

**Source**

Notre Dame J. Formal Logic, Volume 55, Number 3 (2014), 359-381.

**Dates**

First available in Project Euclid: 22 July 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ndjfl/1406034052

**Digital Object Identifier**

doi:10.1215/00294527-2688069

**Mathematical Reviews number (MathSciNet)**

MR3263533

**Zentralblatt MATH identifier**

1337.03010

**Subjects**

Primary: 03B80: Other applications of logic

Secondary: 03A99: None of the above, but in this section 06A99: None of the above, but in this section

**Keywords**

parthood transitivity of parthood nonexistential theory of wholes and parts nonexistential mereology

#### Citation

Pietruszczak, Andrzej. A General Concept of Being a Part of a Whole. Notre Dame J. Formal Logic 55 (2014), no. 3, 359--381. doi:10.1215/00294527-2688069. https://projecteuclid.org/euclid.ndjfl/1406034052