## Principia Mathematica to *56The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions). |

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### Contents

Preface | v |

Contents | ix |

ALPHABETICAL LIST OF PROPOSITIONS REFERRED TO BY NAMES | xii |

INTRODUCTION TO T H E SECOND EDITION | xiii |

INTRODUCTION | 1 |

PART I MATHEMATICAL LOGIC | 85 |

PART II PROLEGOMENA TO CARDINAL ARITHMETIC | 327 |

APPENDIX A | 385 |

APPENDIX C | 401 |

LIST OF DEFINITIONS | 409 |

### Common terms and phrases

a:Ry ambiguity analogues apply asserted proposition asymmetrical relations axiom of reducibility called cardinal cardinal arithmetic class of classes class of relations concerned containing apparent variables converse domain deﬁned deﬁnition denote descriptive function DI-.Prop disjunction dots elementary function elementary propositions exists extensional function fact false falsehood ﬁeld ﬁnd ﬁnite ﬁrst ﬁrst-order functions ﬂy following propositions formally equivalent given Hence hypothesis identical implies q individuals inference logical matrix logical product mathematical induction mathematical logic mathematics matrix means mortal namely negation notation object occurs ordinal couples ordinal number possible arguments predicative function preﬁx premisses present number primitive ideas primitive propositions principle Prop This proposition properties propositional function propositions containing proved real variable result satisﬁed scope second-order signiﬁcant signiﬁcantly Similar proof Similarly Socrates statement substitute Syll Transp truth truth-functions truth-value unit classes vicious-circle