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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 31 ideas from Michael Potter

22273 Traditionally there are twelve categories of judgement, in groups of three [Potter]
22279 Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
22281 A material conditional cannot capture counterfactual reasoning [Potter]
22283 Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter]
22282 'Direct compositonality' says the components wholly explain a sentence meaning [Potter]
22284 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter]
22285 Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter]
22291 Deductivism can't explain how the world supports unconditional conclusions [Potter]
22287 If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter]
22290 The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter]
22295 Modern logical truths are true under all interpretations of the non-logical words [Potter]
22296 Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter]
22298 Why is fictional arithmetic applicable to the real world? [Potter]
22301 The Identity Theory says a proposition is true if it coincides with what makes it true [Potter]
22310 The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
22324 It has been unfortunate that externalism about truth is equated with correspondence [Potter]
22327 Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter]
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]