Index:Russell, Whitehead - Principia Mathematica, vol. I, 1910.djvu

Title	Principia Mathematica, I
Author	Bertrand Russell, Alfred North Whitehead
Editor	Cambridge, University Press
Year	1910
Location	Cambridge
Source	djvu
Progress	To be proofread
Transclusion	Index not transcluded or unreviewed
Volumes	I • II

Pages (key to Page Status)

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Contents of Volume I

		Page
Preface		v
Introduction		1
Chapter I. Preliminary Explanations of Ideas and Notations		4
Chapter II. The Theory of Logical Types		39
Chapter III. Incomplete Symbols		69
Part I. Mathematical Logic.
Summary of Part I		91
Section A. The Theory of Deduction		94
✱1.	Primitive Ideas and Propositions	95
✱2.	Immediate Consequences of the Primitive Propositions	102
✱3.	The Logical Product of two Propositions	114
✱4.	Equivalence and Formal Rules	120
✱5.	Miscellaneous Propositions	128
Section B. Theory of Apparent Variables		132
✱9.	Extension of the Theory of Deduction from Lower to Higher Types of Propositions	132
✱10.	Theory of Propositions containing one Apparent Variable	143
✱11.	Theory of two Apparent Variables	157
✱12.	The Hierarchy of Types and the Axiom of Reducibility	168
✱13.	Identity	176
✱14.	Descriptions	181
Section C. Classes and Relations		196
✱20.	General Theory of Classes	196
✱21.	General Theory of Relations	211
✱22.	Calculus of Classes	217
✱23.	Calculus of Relations	226
✱24.	The Universal Class, the Null-Class, and the Existence of Classes	229
✱25.	The Universal Relation, the Null Relation, and the Existence of Relations	241
Section D. Logic of Relations		244
✱30.	Descriptive Functions	245
✱31.	Converses of Relations	251
✱32.	Referents and Relata of a given Term with respect to a given Relation	255
✱33.	Domains, Converse Domains, and Fields of Relations	260
✱34.	The Relative Product of two Relations	269
✱35.	Relations with Limited Domains and Converse Domains	278
✱36.	Relations with Limited Fields	291
✱37.	Plural Descriptive Functions	293
✱38.	Relations and Classes derived from a Double Descriptive Function	311
	Note to Section D	314
Section E. Products and Sums of Classes		317
✱40.	Products and Sums of Classes	319
✱41.	The Product and Sum of a Class of Relations	331
✱42.	Miscellaneous Propositions	336
✱43.	The Relations of a Relative Product to its Factors	319
Part II. Prolegomena to Cardinal Arithmetic.
Summary of Part II		345
Section A. Unit Classes and Couples		347
✱50.	Identity and Diversity as Relations	349
✱51.	Unit Classes	356
✱52.	The Cardinal Number 1	363
✱53.	Miscellaneous Propositions involving Unit Classes	368
✱54.	Cardinal Couples	376
✱55.	Ordinal Couples	383
✱56.	The Ordinal Number 2	395
Section B. Sub-Classes, Sub-Relations, and Relative Types		404
✱60.	The Sub-Classes of a given Class	406
✱61.	The Sub-Relations of a given Realtion	412
✱62.	The Relation of Membership of a Class	414
✱63.	Relative Types of Classes	419
✱64.	Relative Types of Relations	429
✱65.	On the Typical Definition of Ambiguous Symbols	434
Section C. One-Many, Many-One, and One-One Relations		437
✱70.	Relations whose Classes of Referents and of Relata belong to given Classes	439
✱71.	One-Many, Many-One, and One-One Relations	446
✱72.	Miscellaneous Propositions concerning One-Many, Many-One, and One-One Relations	462
✱73.	Similarity of Classes	476
✱74.	On One-Many and Many-One Relations with Limited Fields	490
Section D. Selections		500
✱80.	Elementary Properties of Selections	505
✱81.	Selections from Many-One Relations	519
✱82.	Selections from Relative Products	524
✱83.	Selections from Classes of Classes	531
✱84.	Classes of Mutually Exclusive Classes	540
✱85.	Miscellaneous Propositions	549
✱88.	Conditions for the Existence of Selections	561
Section E. Inductive Relations		569
✱90.	On the Ancestral Relation	576
✱91.	On Powers of a Relation	585
✱92.	Powers of One-Many and Many-One Relations	601
✱93.	Inductive Analysis of the Field of a Relation	607
✱94.	On Powers of Relative Products	617
✱95.	On the Equi-factor Relation	626
✱96.	On the Posterity of a Term	637
✱97.	Analysis of the Field of a Relation into Families	654