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Single Idea 13041

[filed under theme 9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts ]

Full Idea

A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways.

Gist of Idea

Collections have fixed members, but fusions can be carved in innumerable ways

Source

Michael Potter (Set Theory and Its Philosophy [2004], 02.1)

Book Ref

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.22

A Reaction

This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go.

The 22 ideas with the same theme [the concept of parts treated as one concept]:

15852 A 'whole' (rather than a mere 'sum') requires an internal order which distinguishes it [Aristotle]
15840 If a syllable is more than its elements, is the extra bit also an element? [Aristotle]
16790 A body is always the same, whether the parts are together or dispersed [Hobbes]
17014 The place of a thing is the sum of the places of its parts [Newton]
12852 If x is ever part of y, then y is necessarily such that x is part of y at any time that y exists [Chisholm, by Simons]
15512 In mereology no two things consist of the same atoms [Lewis]
15519 Trout-turkeys exist, despite lacking cohesion, natural joints and united causal power [Lewis]
15521 Given cats, a fusion of cats adds nothing further to reality [Lewis]
15522 The one has different truths from the many; it is one rather than many, one rather than six [Lewis]
14210 A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis]
13329 An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
13330 An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
15839 If something is 'more than' the sum of its parts, is the extra thing another part, or not? [Harte,V]
15837 What exactly is a 'sum', and what exactly is 'composition'? [Harte,V]
15838 The problem with the term 'sum' is that it is singular [Harte,V]
12814 Classical mereology says there are 'sums', for whose existence there is no other evidence [Simons]
12817 'Mereological extensionality' says objects with the same parts are identical [Simons]
12833 If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals [Simons]
12849 Sums are more plausible for pluralities and masses than they are for individuals [Simons]
12877 Sums of things in different categories are found within philosophy. [Simons]
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
14198 Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA]