Principia Mathematica

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THE GREATEST SINGLE CONTRIBUTION TO LOGIC SINCE ARISTOTLE . First edition of this monumental work, one of the great rarities of modern science and mathematics, "the greatest single contribution to logic that has appeared in the two thousand years since Aristotle" (DNB). "In this monumental study of logic and set theory, Russell and Whitehead took up the task … of proving the logical basis of all mathematics by deducing the whole body of mathematical doctrine from a small number of primitive ideas and principles of logical inference. To do so, Russell and Whitehead devised a complex but precise system of symbols that enabled them to sidestep the ambiguities of ordinary language, and to give an exposition of sentential logic that has hardly been improved upon since" (Norman). Probably named after Isaac Newton s great work, Principia Mathematica "has had an influence, direct and indirect, of near Newtonian proportions upon the spheres of its chief influence: mathematical logic, set theory, the foundations of mathematics, linguistic analysis and analytical philosophy" (Grattan-Guinness (1975), p. 89). "It also served as a major impetus for research in the foundations of mathematics throughout the twentieth century. Along with Aristotle s Organon and Gottlob Frege s Grundgesetze der Arithmetik, it remains one of the most influential books on logic ever written" (Stanford Encyclopedia of Philosophy). "Whether they know it or not, all modern logicians are the heirs of Whitehead and Russell" (Palgrave, p. 20). Complete sets of the first edition are very rare. Vol. I was printed in an edition of 750 copies and, due to disappointing sales, the publishers reduced the print run of Vols. II and III to 500 copies each, so that only 500 complete sets in first edition are possible. John Slater, Emeritus Professor of Philosophy at the University of Toronto and editor of The Collected Papers of Bertrand Russell, suggests that there are probably fewer than 50 sets surviving in private hands. "Gottlob Frege (1848-1925) had attempted to demonstrate logicism about arithmetic (though not geometry) in the period from 1879, when his first book, Begriffsschrift, was published, to 1903, when the second volume of his Grundgesetze der Arithmetik appeared. However, in 1902, as that second volume was in press, Russell (1872-1970) had written to him informing him of the contradiction that he had discovered in Frege s system" (Palgrave, p. viii). This was Russell s paradox , that the set of all sets that are not members of themselves is a member of itself if and only if it is not a member of itself. "Frege had attempted to respond to the contradiction … in a hastily written appendix, but he soon realized that his response was inadequate and abandoned his logicist project. It was left to Russell to find a solution to the paradox and to reconstruct the logicist program accordingly. The final result was Russell s ramified theory of types and Principia Mathematica itself, but this theory and the logicist reconstruction in which it is embedded took a decade to develop" (ibid.). "Principia Mathematica had its origins in Russell s discovery of the work of [Giuseppe] Peano (1858-1932) at the International Congress of Philosophy held in Paris in the summer of 1900, which Peano and his supporters attended in force. To that time Russell had been working for several years attempting to develop a satisfactory philosophy of mathematics. Despite some philosophical successes … a satisfactory outcome had always eluded him. At the conference, however, he very quickly realized that the Peano school had a set of techniques of which he could make use, and on his return from the conference he immediately set about applying them. As a result, he quickly rewrote The Principles of Mathematics, which he had started in 1899, finishing the new version by the end of the year. It was published, after some delay and substantial revisions of Part I, in 1903, billed as the first of two vo. N° de ref. del artículo 5377

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