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Full Idea
Formally, the part-relation is transitive and asymmetric (and thus irreflexive). Hence nothing is a proper part of itself, things aren't proper parts of one another, and if one is part of two which is part of three then one is part of three.
Gist of Idea
The part-relation is transitive and asymmetric (and thus irreflexive)
Source
Peter Simons (Parts [1987], 1.1.1)
Book Ref
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.10
| 17245 | A part of a part is a part of a whole [Hobbes] |
| 18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| 14984 | Which should be primitive in mereology - part, or overlap? [Sider] |
| 12813 | Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology [Simons] |
| 12816 | Classical mereology doesn't handle temporal or modal notions very well [Simons] |
| 12821 | The part-relation is transitive and asymmetric (and thus irreflexive) [Simons] |
| 18847 | Each wheel is part of a car, but the four wheels are not a further part [Simons] |
| 10677 | Extensional mereology needs two definitions and two axioms [Hossack] |