P. M. S. Hacker is an Emeritus Research Fellow at St John’s College, Oxford, and Professor of Philosophy at the University of Kent at Canterbury.

Acknowledgements x

Introduction to Volume 2 xii

Abbreviations xvi

ANALYTICAL COMMENTARY 1

I Two fruits upon one tree 3

1. The continuation of the Early Draft into philosophy of mathematics 3

2. Hidden isomorphism 7

3. A common methodology 12

4. The flatness of philosophical grammar 19

FOLLOWING A RULE §§185–242 23

Introduction to the exegesis 25

II Rules and grammar 41

1. The Tractatus and rules of logical syntax 41

2. From logical syntax to philosophical grammar 43

3. Rules and rule-formulations 46

4. Philosophy and grammar 55

5. The scope of grammar 59

6. Some morals 65

Exegesis §§185–8 68

III Accord with a rule 81

1. Initial compass bearings 81

2. Accord and the harmony between language and reality 83

3. Rules of inference and logical machinery 88

4. Formulations and explanations of rules by examples 90

5. Interpretations, fitting and grammar 93

6. Further misunderstandings 95

Exegesis §§189–202 98

IV Following rules, mastery of techniques, and practices 135

1. Following a rule 135

2. Practices and techniques 140

3. Doing the right thing and doing the same thing 145

4. Privacy and the community view 149

5. On not digging below bedrock 156

V Private linguists and ‘private linguists’ – Robinson Crusoe sails again 157

1. Is a language necessarily shared with a community of speakers? 157

2. Innate knowledge of a language 158

3. Robinson Crusoe sails again 160

4. Solitary cavemen and monologuists 163

5. Private languages and ‘private languages’ 165

6. Overview 166

Exegesis §§203–37 169

VI Agreement in definitions, judgements and forms of life 211

1. The scaffolding of facts 211

2. The role of our nature 215

3. Forms of life 218

4. Agreement: consensus of human beings and their actions 223

Exegesis §§238–42 231

VII Grammar and necessity 241

1. Setting the stage 241

2. Leitmotifs 245

3. External guidelines 258

4. Necessary propositions and norms of representation 262

5. Concerning the truth and falsehood of necessary propositions 270

6. What necessary truths are about 280

7. Illusions of correspondence: ideal objects, kinds of reality and ultra-physics 283

8. The psychology and epistemology of the a priori 289

(i) Knowledge 289

(ii) Belief 291

(iii) Certainty 294

(iv) Surprise 298

(v) Discoveries and conjectures 300

(vi) Compulsion 305

9. Propositions of logic and laws of thought 308

10. Alternative forms of representation 320

11. The arbitrariness of grammar 332

12. A kinship to the non-arbitrary 338

13. Proof in mathematics 345

14. Conventionalism 356

Index 371

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