more on this theme     |     more from this thinker

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 14 ideas from 'Set Theory and Its Philosophy'

10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
10704 We can formalize second-order formation rules, but not inference rules [Potter]
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
10709 Priority is a modality, arising from collections and members [Potter]
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
13043 A relation is a set consisting entirely of ordered pairs [Potter]
13044 Infinity: There is at least one limit level [Potter]
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]