Russell_towrad PM 1905-08 - Contents

8/11/2019 Russell_towrad PM 1905-08 - Contents

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BERTRAND RUSSELL

Toward "Principia

Mathematica"

1905-08

Edited by

Gregory H. Moore

London and New York


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Contents

Illustrations x

Abbreviations xii

Introduction xiii

Acknowledgements xciii

Chronology xcv

PART I. NO-CLASSES THEORIES AND

SUBSTITUTIONAL THEORIES, 1905-06

General Headnote to Part I 3

1 The Theory of Implication [1905-06] 14

2 On Some Difficulties in the Theory of Transfinite

Numbers and Order Types [1905-06] 62

3 EarlyWork on the SubstitutionalTheory [1905] 90

a A Letter to Hardy on Substitution 93

b On Substitution 97

4 Developing the Substitutional Theory [1906-07] 104

a Substitution 106

b A Theory of Determination 113

c *20ff. 119

d Verbal Definitions 124

e A Paradox of the Substitutional

Theory 1255 Two Drafts on Substitution [1906] 126

a On Substitution 129

b A Partial Draft 233

6 A PaperWithdrawn from Publication [1906] 236

a On the Substitutional Theory of Classes

and Relations: Abstract 241

b On the Substitutional Theory of Classes

and Relations 243

7 Logic in Which Propositions Are Not Entities [1906] 2628 On the Functional Theory of Propositions, Classes

and Relations [1906] 268

9 The Paradoxes of Logic [1906] 273

10 Multiplicative Axiom [1906] 297

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viii CONTENTS

11 The Paradox ofthe Liar [1906] 3J7

a The Paradox of the Liar 320

b A Partial Draft 3^9

12 List ofPropositions [1906] 375

PART II. THEORIES OF TRUTH, 1906-08

General Headnote to Part II 4X7

13 Two Reviews of Joachim [1906] 419

a What IsTruth? 423

b Review of Joachim, The Nature of Truth 427

14 On the Nature of Truth [1907] 433

15 The Nature of Truth [1907] 455

16 WilliamJames's Conception of Truth [1908] 465

PART III. FROM SUBSTITUTIONAL THEORIES TO THE

RAMIFIED THEORY OF TYPES, 1906-08

General Headnote to Part III 489

17 Corrections Required in Present Work [1906] 492

18 Early Drafts on theTheory of Types [1906-08] 495

a Types 498

b On Types 515

c Notes on Types 520

d FourthTheory 525e Individuals 529

19 Fundamentals [1907] 53620 The Regressive Method of Discovering the Premises

of Mathematics [1907] 57121 "If" and "Imply", A Reply to Mr. MacColl [1908] 58122 Mathematical Logic as Based on the Theory of

Types [1908] 58523 Partial Drafts of Principia Mathematica [c.1908] 626

a * 10.Theory of One Apparent Variable 629b Deduction of Theory of Propositions of HigherType

from That of Those ofLower Type 632c *27. The Hierarchy of Types 635d *92. The Schroder-Bernstein Theorem 641e *130. Selections from Relations 645

PART IV. REVIEWS ON FOUNDATIONS OF MATHEMATICS

24 M. Poincare's Science et hypothese [1906] 65925 Two Reviews of MacColl [1906] 66X


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35

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I

CONTENTS ix

a Review of MacColl, Symbolic Logic and

ItsApplications, in the Athenaeum 666

b Review of MacColl, Symbolic Logic and

ItsApplications, in Mind 670

Review of Pastore, Logicaformale dedotta dalla

considerazione di modelli meccanici [1906] 676

The Study of Logic [1906] 678

Two Reviews of Meinong [1906-07] 680

a Review of Meinong, Uber die Erfahrungsgrundlagen

unseres Wissens [1906] 685

b Review of Meinong, Uber die Stellung der Gegenstands-

theorie im System der Wissenschaften [1907] 689

Mr.Haldane on Infinity [1908] 693

PART V. OTHER PHILOSOPHICAL REVIEWS AND WRITINGS

Is Reason Irrational? [1906]

Metaphysics for the Man of Action [1907]

Spinoza's Moral Code [1907]

Newton's Philosophy [1908]

Determinism and Morals [1908]

Review ofEssays, Philosophical and

Psychological, in Honorof William James [1908]

A Reply to Dr. Schiller [1908]

APPENDICES

Les Paradoxes de la logique [1906] 743

Comments on Definitions ofPhilosophical Terms [1905-06] 762

Notes on Ward's Comments on ThePrinciples of

Mathematics

[1905] 765

Berry's Letters to Russell [1904-10] 770

MISSING AND UNPRINTED TEXTS 783

ANNOTATION 785

TEXTUAL NOTES 839

BIBLIOGRAPHICAL INDEX 883

SYMBOLS INDEX 907

GENERAL INDEX 923

701

705

713

716

719

729

735


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Illustrations

frontispiece

Bertrand Russell: Campaign photograph for the Wimbledon By-

Election, 1907.

between pages c and 1

Verso of folio 31 of Paper 19 (ra 230.030760). The notation $ | x used

in this verso shows that the verso dates from 1903 (see Russell 1994,

49j 53)3 almost four years before Paper 19 was written. The verso is

unusual indating so longbefore the text on the recto (January 1907).

Verso of folio

35 ofPaper 19. The notations

(f>'x and ~

'fi'x used in

this verso indicate that it dates from between February 1904 and July

1905; see pp. lxiv, 17. The marginal note to replace the notation

{(f>lxYy with ) shows the verso to have been commented on later

than July 1905. The last two formulas onthe verso, unlike the rest, are

in Whitehead's handwriting.

Part of Paper 4b (verso 16 of Paper 10, ra 230.030750), showing

some of the notation for the substitutional theory, in particular the

notation (f>Q ... ?).

Folio 6, from Paper 10, showing the quantifiedvariable directly under

the implication sign, rather than after it.

Folio 26, from Paper 10,illustrating four quantified variables directlyunder one implication sign on two occasions.

Third leaf of Paper 12, showing his use of the notations (x,y) respectively. The notations

(?) and 0(??) are found in Russell's letter of 22 November 1905 to

Couturat and in Whitehead's letter of 21 February 1906 to Russell.

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ILLUSTRATIONS xi

vii Verso of folio 3 of Paper 17 (ra 230.030740). It deals with an attempt

to rule out the existence of what are now called Dedekind cardinals

(i.e. the cardinal of a set which is, in Russell's terminology, not induc

tive and not reflexive; that is, in modern terminology, a set that is

infinite but Dedekind-finite). See p. 492. Russell's use

of Cantor'snotation K0 shows that this folio dates from 1906; see A772:12.

viii Verso (ra 230.031240-Fi) about Likeness and *151 of Principia. By

the time of Paper 22 (p. 622), "likeness" has been replaced by

"Smor" or "similar ordinally", and so this verso dates from before

that, but not long before. This verso also has 1>Cls, which is a rela

tively late notation found first at 521: 7.

ix First page of letter of 11 January 1908 from Russell to Whitehead on

types (ra 710.057503). See pp. lxxix-lxxx. Very few letters from

Russell to Whitehead survive since Whitehead had all letters to him

destroyed on his death.

x Verso of folio 39 of Paper 19. This was presumably part of a draft by

Whitehead of a section ofPrincipia. It is one of a very few extant parts

of such a draft in Whitehead's handwriting.

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Russell_towrad PM 1905-08 - Contents