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Ideas of B Hale / C Wright, by Text

[British, fl. 1995, two professors based in Scotland.]

2001 Intro to 'The Reason's Proper Study'
1 p.1 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers
2 n5 p.4 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized
3.1 p.8 Objects just are what singular terms refer to
3.2 p.12 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions
3.2 p.17 Abstracted objects are not mental creations, but depend on equivalence between given entities
3.2 p.18 If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological
3.2 n26 p.15 The structural view of numbers doesn't fit their usage outside arithmetical contexts
3.2 n26 p.15 If structures are relative, this undermines truth-value and objectivity
2007 Logicism in the 21st Century
1 p.167 One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines
1 p.169 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic
1 n2 p.167 Logicism might also be revived with a quantificational approach, or an abstraction-free approach
3 p.179 The Julius Caesar problem asks for a criterion for the concept of a 'number'
8 p.196 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
8 p.197 Various strategies try to deal with the ontological commitments of second-order logic
2009 The Metaontology of Abstraction
3 p.182 It is a fallacy to explain the obscure with the even more obscure
4 p.184 Are neo-Fregeans 'maximalists' - that everything which can exist does exist?
4 n19 p.186 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment
5 p.187 The identity of Pegasus with Pegasus may be true, despite the non-existence
5 p.188 Abstractionism needs existential commitment and uniform truth-conditions
8 p.195 Equivalence abstraction refers to objects otherwise beyond our grasp
9 p.197 A successful predicate guarantees the existence of a property - the way of being it expresses
9 p.198 Maybe we have abundant properties for semantics, and sparse properties for ontology
9 p.207 Singular terms refer if they make certain atomic statements true
9 p.208 Reference needs truth as well as sense