Mathematics, the Loss of CertaintyOne of the most learned men of his day and called «the philosopher» by contemporaries, George Amiroutzes (c. 1400-c. 1469) attended the Council of Florence (1438-39) as a lay scholar in the Greek delegation. As a high government official in his native Trebizond, he helped to negotiate the surrender of this last independent Greek state to Mehmed the Conqueror in 1461. He eventually entered the Sultan's household as someone with whom Mehmed enjoyed having intellectual discussions. Despite his contemporary fame, however, almost no philosophical writings of his survive. The present work offers an edition of fifteen previously unknown philosophical tractates. Although they are unpublished drafts in a fragmentary state, the tractaes reveal Amiroutzes to be an Aristotelian philosopher influenced by Thomas Aquinas and firmly intent upon refuting Platonism. He also shows himself to be an original thinker in discussing ethics and metaphysics. |
Contents
The Thesis | 3 |
The Genesis of Mathematical Truths | 9 |
The Flowering of Mathematical Truths | 31 |
Copyright | |
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19th century abstract accepted algebra analysis applied argument arithmetic assertion astronomy axiom of choice axiomatic basis believed body calculus called Cantor Cauchy Chapter classical complex numbers concepts consistency continuum hypothesis contradictions correct creation deductive definitions derivative Descartes elliptic geometry equations Euclid Euclid's Euclidean geometry Euler example excluded middle existence experience fact false finite formalists Galileo Gauss Gödel Greek Hence Hermann Weyl Hilbert ideas infinite number infinite sets infinitesimals integers intuition intuitionists irrational numbers knowledge law of excluded Leibniz logical principles mathe mathematical induction mathematical laws mathematicians maticians matics means method Moreover motion nature negative numbers Newton non-Euclidean geometry number system objects paradoxes parallel axiom phenomena philosophy physical world planets Poincaré problems proof properties proved pure mathematics Pythagoreans quantities quaternions question rational real numbers reason rigor roots Russell set theory space statement structure symbols theorems thought tion true truths universe velocity Weyl whole numbers