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Full Idea
Two parts 'overlap' mereologically if and only if they have a part in common, expressed by 'x o y', read as 'x overlaps y'. Overlapping is reflexive and symmetric but not transitive.
Gist of Idea
Overlap: two parts overlap iff they have a part in common, expressed as 'x o y'
Source
Peter Simons (Parts [1987], 1.1.03)
Book Ref
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.11
A Reaction
Simons points out that we are uncomfortable with overlapping (as in overlapping national boundaries), because we seem to like conceptual boundaries. We avoid overlap even in ordering primary colour terms, by having a no-man's-land.
| 12822 | Proper or improper part: x < y, 'x is (a) part of y' [Simons] |
| 12823 | Overlap: two parts overlap iff they have a part in common, expressed as 'x o y' [Simons] |
| 12824 | Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y' [Simons] |
| 12825 | Product: the product of two individuals is the sum of all of their overlaps, written 'x · y' [Simons] |
| 12826 | Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y' [Simons] |
| 12827 | Difference: the difference of individuals is the remainder of an overlap, written 'x - y' [Simons] |
| 12828 | General sum: the sum of objects satisfying some predicate, written σx(Fx) [Simons] |
| 12829 | General product: the nucleus of all objects satisfying a predicate, written πx(Fx) [Simons] |
| 12830 | Universe: the mereological sum of all objects whatever, written 'U' [Simons] |
| 12831 | Atom: an individual with no proper parts, written 'At x' [Simons] |
| 12844 | Dissective: stuff is dissective if parts of the stuff are always the stuff [Simons] |