The Growth of Mathematical KnowledgeEmily Grosholz, Herbert Breger Springer Science & Business Media, 17 d’abr. 2013 - 416 pàgines Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics. |
Continguts
JAAKKO HINTIKKA Knowledge of Functions in the Growth | 1 |
From Device | 17 |
DONALD GILLIES An Empiricist Philosophy of Mathematics | 40 |
IVO SCHNEIDER The Mathematization of Chance in the Middle | 59 |
MICHAEL LISTONMathematical Empiricism | 76 |
CRAIG FRASER HamiltonJacobi Methods and Weierstrassian | 93 |
PAOLO MANCOSU On Mathematical Explanation 103 | 102 |
FRANÇOIS DE GANDT Mathematics and the Reelaboration of Truths | 121 |
MUNTERSBJORN The Quadrature | 231 |
Ariadnes Thread | 257 |
COLIN MCLARTY VoirDire in the Case of Mathematical Progress | 269 |
EBERHARD KNOBLOCHAnalogy and the Growth | 294 |
ALEXEI BARABASHEV Evolution of the Modes of Systematization | 315 |
ISABELLA BASHMAKOVA AND G S SMIRNOVA Geometry | 331 |
PENELOPE MADDY Mathematical Progress | 341 |
RESNIK Some Remarks on Mathematical Progress | 353 |
MARK STEINER Penrose and Platonism | 133 |
MARK WILSON On the Mathematics of Spilt Milk 143 | 142 |
DETLEF LAUGWITZ Controversies about Numbers and Functions | 177 |
CARL POSYEpistemology Ontology and the Continuum | 199 |
HERBERT BREGER Tacit Knowledge and Mathematical Progress | 221 |
VOLKER PECKHAUS Scientific Progress and Changes | 363 |
SERGEI DEMIDOVOn the Progress of Mathematics | 377 |
CHRISTIAN THIEL On Some Determinants of Mathematical Progress | 407 |
Altres edicions - Mostra-ho tot
The Growth of Mathematical Knowledge Emily Grosholz,Herbert Breger Previsualització no disponible - 2010 |
The Growth of Mathematical Knowledge Emily Grosholz,Herbert Breger Previsualització no disponible - 2014 |
The Growth of Mathematical Knowledge Emily Grosholz,Herbert Breger Previsualització no disponible - 2000 |
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algebraic analogy analysis applied argues arithmetic axiomatic method axioms Breger Brouwer calculus calculus of variations Cauchy Cavalieri century Christiaan Huygens claim closed world view complex numbers concept construction continuum curve cycloid defined demonstration derived Descartes development of mathematics differential equations discipline divergent series domains dynamics empirical Essays Euler example existence explanation explanatory fact Fermat field Figure finite formal Foundations Frege function geometry Gillies given goal Gödel Grosholz growth of mathematical Hilbert Hintikka history of mathematics Huygens hypotheses infinite infinitesimal integration intuition ISBN Kant Kepler Kitcher Leibniz mathematical knowledge mathematical logic mathematical objects mathematical progress mathematicians means metaphysical modern natural notion parabola Pascal philosophy of mathematics Philosophy of Science physical Poincaré principle problem proof properties proposition quadrature question real numbers relation rigor scientific sense sequence set theory solution solve space structure systematization tacit knowledge theorem University Press values variable