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Full Idea
It seems obvious that 'part' stands for a partial ordering, a reflexive ('everything is part of itself'), antisymmetic ('two things cannot be part of each other'), and transitive (a part of a part of a thing is part of that thing) relation.
Gist of Idea
'Part' stands for a reflexive, antisymmetric and transitive relation
Source
Achille Varzi (Mereology [2003], 2.1)
Book Ref
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.4
A Reaction
I'm never clear why the reflexive bit of the relation should be taken as 'obvious', since it seems to defy normal usage and common sense. It would be absurd to say 'I'll give you part of the cake' and hand you the whole of it. See Idea 10651.
Related Idea
Idea 10651 If 'part' is reflexive, then identity is a limit case of parthood [Varzi]
| 10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
| 10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
| 10653 | Maybe set theory need not be well-founded [Varzi] |
| 10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
| 10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
| 10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
| 10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
| 10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
| 10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
| 10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
| 10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |