Thursday, May 31, 2012

Icons From The Age of Anxiety: The Genius of Logic Kurt Gödel

Kurt Friedrich Gödel (1906-1978): Celebrated for Gödel's incompleteness theorems, Gödel's completeness theorem, the consistency of the Continuum hypothesis with ZFC, Gödel metric, Gödel's ontological proof. Gödel, “established, beyond comparison, as the most important logician of our times,” in the words of Solomon Feferman, founded the modern, metamathematical era in mathematical logic. His Incompleteness Theorems, among the most significant achievements in logic since, perhaps, those of Aristotle, are among the handful of landmark theorems in twentieth century mathematics. His work touched every field of mathematical logic, if it was not in most cases their original stimulus. In his philosophical work Gödel formulated and defended mathematical Platonism, involving the view that mathematics is a descriptive science, and that the concept of mathematical truth is an objective one. On the basis of that viewpoint he laid the foundation for the program of conceptual analysis within set theory. He adhered to Hilbert'soriginal rationalistic conception” in mathematics (as he called it);  he was prophetic in anticipating and emphasizing the importance of large cardinals in set theory before their importance became clear.

Logic failed in later life, as Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, Adele was hospitalized for six months and could no longer prepare Gödel's food. In her absence, he refused to eat, eventually starving to death. He weighed 65 pounds when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978.

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