Principia Mathematica to *56, Volume 2The 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). |
Contents
INTRODUCTION | 1 |
PART I MATHEMATICAL LOGIC | 85 |
PART II PROLEGOMENA TO CARDINAL ARITHMETIC | 327 |
APPENDIX A | 385 |
APPENDIX C | 401 |
LIST OF DEFINITIONS | 409 |
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Common terms and phrases
ambiguity analogues apparent variables apply asserted proposition asymmetrical relations axiom of reducibility âŷ called cardinal class of classes concerned converse domain defined definition denote descriptive function disjunction dots ê pz elementary function elementary propositions exists extensional function fact false falsehood first-order functions following propositions formally equivalent ƒ ê given Hence Hp.Ɔ hypothesis identical implies q individuals inference logical matrix mathematical induction mathematics matrix means negation notation object occurs ordinal number Ɔ F pƆq predicative function present number primitive ideas primitive propositions principle Prop Prop This proposition properties propositional function proved R¹y real variable satisfied scope second-order significant Similar proof Similarly Socrates Syll theory Transp true truth truth-functions truth-value unit classes vicious-circle φα