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Ideas of Crispin Wright, by Text

[British, fl. 1990, Professor at University of St Andrew's, then Stirling, and New York University.]

1983 Frege's Concept of Numbers as Objects
p.41 We derive Hume's Law from Law V, then discard the latter in deriving arithmetic
p.55 The attempt to define numbers by contextual definition has been revived
p.71 Frege has a good system if his 'number principle' replaces his basic law V
p.189 Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are
p.189 An expression refers if it is a singular term in some true sentences
p.189 Wright says Hume's Principle is analytic of cardinal numbers, like a definition
p.226 Contextually defined abstract terms genuinely refer to objects
p.354 Wright has revived Frege's discredited logicism
Intro p.-10 Number theory aims at the essence of natural numbers, giving their nature, and the epistemology
Intro p.-9 There are five Peano axioms, which can be expressed informally
Intro p.-9 Number truths are said to be the consequence of PA - but it needs semantic consequence
Intro p.-8 What facts underpin the truths of the Peano axioms?
Intro p.-1 Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms
Intro p.-1 Frege's platonism and logicism are in conflict, if logic must dictates an infinity of objects
Pref p.-12 We can only learn from philosophers of the past if we accept the risk of major misrepresentation
1.i p.2 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities
1.i p.3 A concept is only a sortal if it gives genuine identity
1.i p.3 Instances of a non-sortal concept can only be counted relative to a sortal concept
1.i p.4 Sortal concepts cannot require that things don't survive their loss, because of phase sortals
1.i p.4 Number platonism says that natural number is a sortal concept
1.i p.4 We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism
1.iii p.10 Treating numbers adjectivally is treating them as quantifiers
1.iii p.14 Singular terms in true sentences must refer to objects; there is no further question about their existence
1.iv p.17 We can accept Frege's idea of object without assuming that predicates have a reference
1.vii p.44 A milder claim is that understanding requires some evidence of that understanding
1.vii p.49 The best way to understand a philosophical idea is to defend it
2.x p.83 The idea that 'exist' has multiple senses is not coherent
2.xi p.88 If apparent reference can mislead, then so can apparent lack of reference
3.xiv p.112 If numbers are extensions, Frege must first solve the Caesar problem for extensions
3.xiv p.114 Entities fall under a sortal concept if they can be used to explain identity statements concerning them
3.xv p.118 One could grasp numbers, and name sizes with them, without grasping ordering
3.xv p.120 It is 1-1 correlation of concepts, and not progression, which distinguishes natural number
3.xv p.120 Sameness of number is fundamental, not counting, despite children learning that first
4.xix p.161 It may be possible to define induction in terms of the ancestral relation
4.xix p.168 The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals
4.xvi p.131 The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes
4.xvi p.131 The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems
4.xviii p.148 If we can establish directions from lines and parallelism, we were already committed to directions
1986 Inventing Logical Necessity
p.126 Holism cannot give a coherent account of scientific methodology
p.149 Logical necessity involves a decision about usage, and is non-realist and non-cognitive