Papers by Alejandro Garciadiego
Historia Mathematica, Feb 1, 1992
Historia Mathematica, Feb 1, 1986
Historia Mathematica, Aug 1, 1981
Gaceta UNAM (1990-1999), May 30, 1994
Boston studies in the philosophy of science, 1995
Bertrand Russell wrote prolifically for a long period of time. He lived for almost ninety-eight y... more Bertrand Russell wrote prolifically for a long period of time. He lived for almost ninety-eight years and wrote more than seventy books, hundreds of articles and thousands of letters. This material included his personal and intellectual biographies.
The main goal of this fourth chapter is to present a plausible historical reconstruction of the a... more The main goal of this fourth chapter is to present a plausible historical reconstruction of the actual way in which Russell discovered the ‘contradiction’ of the greatest cardinal number, known today as the “Cantor paradox”; how Russell discovered his own inconsistency of the class of all classes which are not members of themselves; and how he presented the elements that would give rise to the ‘contradiction’ of the greatest ordinal number, today called the “Burali-Forti paradox”.
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas, 1999
Birkhäuser Basel eBooks, 2002
Gaceta UNAM (1990-1999), Jun 29, 1992
The Sixteenth century journal, Oct 1, 2005
Birkhäuser Basel eBooks, 1992
The popular interpretation of the origins of the set-theoretic ‘paradoxes’ is now almost a classi... more The popular interpretation of the origins of the set-theoretic ‘paradoxes’ is now almost a classic story, and it is to this account that I now turn along with some criticisms. The term popular is not used in a derogatory way: it means that this interpretation is the best known and accepted by the general public. This standard interpretation is simply a summary of the account given by mathematicians and professional historians of mathematics, among others, in general encyclopedias, philosophical and mathematical encyclopedias and dictionaries, textbooks of mathematics and textbooks on the history and philosophy of mathematics. The following quotations are representative of the prevailing chronicle: There remained logical difficulties in the theory of transfinite numbers and paradoxes appeared, such as those of Burali-Forti and Russell. This again led to different schools of thought on the foundations of mathematics. The crisis was brought about by the discovery of paradoxes or antinomies in the fringe of Cantor’s general theory of sets. Since so much of mathematics is permeated with set concepts and, for that matter, can actually be made to rest upon set theory as a foundation, the discovery of paradoxes in set theory naturally cast [sic] into doubt the validity of the whole foundational structure of mathematics.
Birkhäuser Basel eBooks, 1992
The chief purpose of this third chapter is to discuss those aspects of Russell’s philosophical an... more The chief purpose of this third chapter is to discuss those aspects of Russell’s philosophical and mathematical background which led to the ideas expressed in The Principles of Mathematics published in May, 1903. Emphasis will be given to events ocurring before July 1900, when Russell met Peano.
The Sixteenth century journal, Dec 1, 2003
... Geometrical Landscapes THE VOYAGES OF DISCOVERY AND THE TRANSFORMATION OF MATHEMATICAL PRACTI... more ... Geometrical Landscapes THE VOYAGES OF DISCOVERY AND THE TRANSFORMATION OF MATHEMATICAL PRACTICE Amir R. Alexander STANFORD UNIVERSITY ... sometimes assigned other religious tasks, such as King Arthur's knights' search for the Holy Grail.2' Some ...
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Papers by Alejandro Garciadiego