Principia Mathematica to *56

ISBN-13: 9780521626064 / Angielski / Miękka / 1997 / 460 str.

Alfred North Whitehead; Bertrand Russell; Bertrand Russell

Opis

The 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).

Spis treści

Part I. Mathematical Logic: 1. The theory of deduction; 2. Theory of apparent variables; 3. Classes and relations; 4. Logic or relations; 5. Products and sums of classes; Part II. Prolegomena to Cardinal Arithmetic: 6. Unit classes and couples; Appendix A. Type theory of dependant variables and propositions containing apparent variables; Appendix B. Truth functions and others.