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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

10702

Set theory's three roles: taming the infinite, subjectmatter of mathematics, and modes of reasoning

01.1

p.8

10703

Supposing axioms (rather than accepting them) give truths, but they are conditional

01.2

p.13

10704

We can formalize secondorder formation rules, but not inference rules

02.1

p.22

13041

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

02.1

p.23

10707

Mereology elides the distinction between the cards in a pack and the suits

03.2

p.37

10708

Nowadays we derive our conception of collections from the dependence between them

03.3

p.39

10709

Priority is a modality, arising from collections and members

03.3

p.40

13042

If dependence is wellfounded, with no infinite backward chains, this implies substances

03.8

p.51

10712

If set theory didn't found mathematics, it is still needed to count infinite sets

04.3

p.59

10713

Usually the only reason given for accepting the empty set is convenience

04.7

p.65

13043

A relation is a set consisting entirely of ordered pairs

04.9

p.68

13044

Infinity: There is at least one limit level

05.2

p.92

17882

It is remarkable that all natural number arithmetic derives from just the Peano Axioms

13.5

p.227

13546

The 'limitation of size' principles say whether properties collectivise depends on the number of objects
