Mathematics: The Loss of CertaintyOxford University Press, 1982 - 366 páginas This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century. |
Índice
The Thesis | 3 |
The Genesis of Mathematical Truths | 9 |
The Flowering of Mathematical Truths | 31 |
The Mathematization of Science | 50 |
The Withering of Truth | 69 |
The Illogical Development of a Logical Subject | 100 |
The Morass of Analysis | 127 |
The Predicament circa 1800 | 153 |
Logicism versus Intuitionism | 216 |
The Formalist and SetTheoretic Foundations | 245 |
Disasters | 258 |
The Isolation of Mathematics | 278 |
Whither Mathematics? | 307 |
The Authority of Nature | 328 |
355 | |
361 | |
Términos y frases comunes
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 formulas 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
Referencias a este libro
Conversational Realities: Constructing Life Through Language John Shotter Vista previa restringida - 1993 |
More Heat Than Light: Economics as Social Physics, Physics as Nature's Economics Philip Mirowski Vista previa restringida - 1991 |