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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, subject-matter 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 second-order 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 well-founded, 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 1879-1930
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 non-logical 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