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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 10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers
§2 n5 p.4 10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized
3.1 p.8 10626 Objects just are what singular terms refer to
3.2 p.12 10627 Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions
3.2 p.17 10630 Abstracted objects are not mental creations, but depend on equivalence between given entities
3.2 p.18 10631 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 10629 If structures are relative, this undermines truth-value and objectivity
3.2 n26 p.15 10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts
2007 Logicism in the 21st Century
1 p.167 8786 One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines
1 p.169 8784 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic
1 n2 p.167 8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach
3 p.179 8787 The Julius Caesar problem asks for a criterion for the concept of a 'number'
8 p.196 8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
2009 The Metaontology of Abstraction
§3 p.182 12223 It is a fallacy to explain the obscure with the even more obscure
§4 p.184 12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist?
§4 n19 p.186 12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment
§5 p.187 12226 The identity of Pegasus with Pegasus may be true, despite the non-existence
§5 p.188 12227 Abstractionism needs existential commitment and uniform truth-conditions
§8 p.195 12228 Equivalence abstraction refers to objects otherwise beyond our grasp
§9 p.197 18443 A successful predicate guarantees the existence of a property - the way of being it expresses
§9 p.198 12229 Maybe we have abundant properties for semantics, and sparse properties for ontology
§9 p.207 12230 Singular terms refer if they make certain atomic statements true
§9 p.208 12231 Reference needs truth as well as sense