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Ideas of Michael Potter, by Text

[British, fl. 2004, Senior Lecturer at Cambridge, and Fellow of Fitzwilliam College.]

2004 Set Theory and Its Philosophy
Intro 1 p.4 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning
01.1 p.8 Supposing axioms (rather than accepting them) give truths, but they are conditional
01.2 p.13 We can formalize second-order formation rules, but not inference rules
02.1 p.22 Collections have fixed members, but fusions can be carved in innumerable ways
02.1 p.23 Mereology elides the distinction between the cards in a pack and the suits
03.2 p.37 Nowadays we derive our conception of collections from the dependence between them
03.3 p.39 Priority is a modality, arising from collections and members
03.3 p.40 If dependence is well-founded, with no infinite backward chains, this implies substances
03.6 p.43 Russell's paradox means we cannot assume that every property is collectivizing
03.8 p.51 If set theory didn't found mathematics, it is still needed to count infinite sets
04.3 p.59 Usually the only reason given for accepting the empty set is convenience
04.7 p.65 A relation is a set consisting entirely of ordered pairs
04.9 p.68 Infinity: There is at least one limit level
05.2 p.92 It is remarkable that all natural number arithmetic derives from just the Peano Axioms
13.5 p.227 The 'limitation of size' principles say whether properties collectivise depends on the number of objects