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Full Idea
The 'general sum' of all objects satisfying a certain predicate is denoted by a variable-binding operator, expressed by 'σx(Fx)', read as 'the sum of objects satisfying F'.
Gist of Idea
General sum: the sum of objects satisfying some predicate, written σx(Fx)
Source
Peter Simons (Parts [1987], 1.1.08)
Book Ref
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.15
A Reaction
This, it seems, is introduced to restrict some infinite classes which aspire to be sums.
| 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] |