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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

2020

The Rise of Analytic Philosophy 18791930

02 'Trans'

p.15

22273

Traditionally there are twelve categories of judgement, in groups of three

03 'Axioms'

p.28

22279

Frege's sign  meant judgements, but the modern  turnstile means inference, with intecedents

04 'Sem'

p.34

22281

A material conditional cannot capture counterfactual reasoning

05 'Sem'

p.41

22283

Compositionality should rely on the parsing tree, which may contain more than sentence components

05 'Sem'

p.41

22282

'Direct compositonality' says the components wholly explain a sentence meaning

07 'Def'

p.49

22284

'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers

07 'Impred'

p.50

22285

Impredicative definitions are circular, but fine for picking out, rather than creating something

12 'Deduc'

p.127

22291

Deductivism can't explain how the world supports unconditional conclusions

12 'Numb'

p.82

22287

If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete

16 'Conc'

p.109

22290

The phrase 'the concept "horse"' can't refer to a concept, because it is saturated

19 'Frege's'

p.131

22295

Modern logical truths are true under all interpretations of the nonlogical words

21 'Lang'

p.142

22296

Compositionality is more welcome in logic than in linguistics (which is more contextual)

21 'Math'

p.143

22298

Why is fictional arithmetic applicable to the real world?

23 'Abs'

p.152

22301

The Identity Theory says a proposition is true if it coincides with what makes it true

45 'Log'

p.305

22310

The formalist defence against Gödel is to reject his metalinguistic concept of truth

65 'Truth'

p.426

22324

It has been unfortunate that externalism about truth is equated with correspondence

66 'Rel'

p.432

22327

Knowledge from a drunken schoolteacher is from a reliable and unreliable process
