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Full Idea
For two overlapping individuals their 'product' is the individual which is part of both and such that any common part of both is part of it, expressed by 'x · y', read as 'the product of x and y'.
Clarification
Aka 'binary product'
Gist of Idea
Product: the product of two individuals is the sum of all of their overlaps, written 'x · y'
Source
Peter Simons (Parts [1987], 1.1.05)
Book Ref
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.13
A Reaction
That is, the 'product' is the sum of any common parts between two individuals. In set theory all sets intersect at the null set, but mereology usually avoids the 'null individual'.
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] |