Mereology

Anil Mitra, Friday, January 1, 2021

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Sources Mereology - Wikipedia | Mereology (Stanford Encyclopedia of Philosophy)

Introduction

The primary function of the document is as resource for the metaphysics of The Way of Being.

It may serve that function since the concepts of universe, the void, and beings correspond to the mereological concepts of universe, null part, and part. The mereological concept of ‘atom’ may also be useful to the way.

Partial order

A partial order on a set is a relation, ≤, such that for all a, b, and c, in the set

a ≤ a (reflexivity, every element is related to itself).

If a ≤ b and b ≤ a, then a = b (antisymmetry, two different elements cannot be related in the same direction).

If a ≤ b and b ≤c, then a ≤ c (transitivity).

Parthood

Pxy means x is a part of y.

Axioms for P

Pxx (reflexivity)

Pxy Pyz Pxz (transivity)

Pxy Pyx x = y (antisymmetry)

Note—all initial universal quantifiers are dropped.

Some definitions

EQxy Pxy Pxy (equality)

PPxy Pxy x=y (proper parthood)

PExy Pyx x=y (proper extension)

Oxy z (Pzx Pzy) (overlap)

Uxy z (Pxz Pyz) (underlap)

Wx Pyx (world or universe, w = x such that Wx)

Nx y (PPyx) (null part, n = x such that Nx)

Ax y (Pyx) Nx (atom, a = x such that Ax)