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Ideas of Crispin Wright, by Text
[British, b.1942, Professor at University of St Andrew's, then Stirling, and New York University.]
1983

Frege's Concept of Numbers as Objects


p.41

10140

We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Fine,K]


p.55

10142

The attempt to define numbers by contextual definition has been revived [Fine,K]


p.71

8692

Frege has a good system if his 'number principle' replaces his basic law V [Friend]


p.189

17440

Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Heck]


p.189

9868

An expression refers if it is a singular term in some true sentences [Dummett]


p.189

17441

Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Heck]


p.226

9878

Contextually defined abstract terms genuinely refer to objects [Dummett]


p.354

7804

Wright has revived Frege's discredited logicism [Benardete,JA]

Intro

p.10

13861

Number theory aims at the essence of natural numbers, giving their nature, and the epistemology

Intro

p.9

17853

Number truths are said to be the consequence of PA  but it needs semantic consequence

Intro

p.9

13862

There are five Peano axioms, which can be expressed informally

Intro

p.8

17854

What facts underpin the truths of the Peano axioms?

Intro

p.1

13863

Logicism seemed to fail by Russell's paradox, Gödel's theorems, and nonlogical axioms

Pref

p.12

13860

We can only learn from philosophers of the past if we accept the risk of major misrepresentation

1.i

p.2

13865

'Sortal' concepts show kinds, use indefinite articles, and require grasping identities

1.i

p.3

13866

A concept is only a sortal if it gives genuine identity

1.i

p.3

13867

Instances of a nonsortal concept can only be counted relative to a sortal concept

1.i

p.4

13868

Sortal concepts cannot require that things don't survive their loss, because of phase sortals

1.i

p.4

13869

Number platonism says that natural number is a sortal concept

1.i

p.4

13870

We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism

1.iii

p.10

13873

Treating numbers adjectivally is treating them as quantifiers

1.iii

p.14

13877

Singular terms in true sentences must refer to objects; there is no further question about their existence

1.iv

p.17

17857

We can accept Frege's idea of object without assuming that predicates have a reference

1.vii

p.44

13882

A milder claim is that understanding requires some evidence of that understanding

1.vii

p.49

13883

The best way to understand a philosophical idea is to defend it

2.x

p.83

13884

The idea that 'exist' has multiple senses is not coherent

2.xi

p.88

13885

If apparent reference can mislead, then so can apparent lack of reference

3.xiv

p.112

13888

If numbers are extensions, Frege must first solve the Caesar problem for extensions

3.xiv

p.114

13890

Entities fall under a sortal concept if they can be used to explain identity statements concerning them

3.xv

p.118

13892

One could grasp numbers, and name sizes with them, without grasping ordering

3.xv

p.120

13894

Sameness of number is fundamental, not counting, despite children learning that first

3.xv

p.120

13893

It is 11 correlation of concepts, and not progression, which distinguishes natural number

4.xix

p.168

13899

The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals

4.xvi

p.131

13896

The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes

4.xvi

p.131

13895

The standard objections are Russell's Paradox, nonlogical axioms, and Gödel's theorems

4.xviii

p.148

13898

If we can establish directions from lines and parallelism, we were already committed to directions

1986

Inventing Logical Necessity


p.126

7320

Holism cannot give a coherent account of scientific methodology [Miller,A]


p.149

12189

Logical necessity involves a decision about usage, and is nonrealist and noncognitive [McFetridge]
