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David H. Sanford

Sum

From Handbook of Mereology

ISBN: 978-3-88405-674-5

Preis: €9.80 (inkl. 19 % MwSt.)


Starting with overlaps as primitive, we can define part as follows: x is part of y if and only if everything that overlaps x also overlaps y. Something that overlaps nothing, according to this definition, is part of everything. To avoid this and similar strange consequences, the domain of mereology is properly restricted to items – call them ‘overlappers’ – that overlap something. (Every overlapper overlaps itself.) Although this made-up term appears only in this paragraph, readers may assume that colorless words such as ‘thing’, ‘everything’, and so forth, refer to overlappers. Coincidence is a central notion: x and y coincide when they overlap exactly the same things. In terms of ‘part’, x and y coincide when they are parts of each other. Some definitions of ‘sum’ are in terms of ‘part’, ‘distinct’, ‘overlap’, and combinations of these. The following definition is purely in terms of ‘overlap’: x is a sum of the y’s if and only if anything that overlaps any y overlaps x and anything that overlaps x overlaps some y. Some authors put definitions in terms of set and member. ‘For a nonempty set A, x is a sum of A if and only if every member of A … &c.’




 


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