The Growth of Mathematical Knowledge

Capa
Emily Grosholz, Herbert Breger
Springer Science & Business Media, 17/04/2013 - 416 páginas
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.
 

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Índice

Mathematical Knowledge
17
2
25
DONALD GILLIES An Empiricist Philosophy of Mathematics
59
MICHAEL LISTON Mathematical Empiricism
76
CRAIG FRASER HamiltonJacobi Methods and Weierstrassian
93
PAOLO MANCOSU On Mathematical Explanation 103
102
FRANCOIS DE GANDT Mathematics and the Reelaboration of Truths
121
MARK STEINER Penrose and Platonism
133
MUNTERSBJORN The Quadrature
231
Ariadnes Thread
257
COLIN MCLARTY VoirDire in the Case of Mathematical Progress
269
EBERHARD KNOBLOCHAnalogy and the Growth
294
ALEXEIBARABASHEV Evolution of the Modes of Systematization
315
ISABELLA BASHMAKOVA AND G S SMIRNOVA Geometry
331
PENELOPE MADDY Mathematical Progress
341
RESNIKSome Remarks on Mathematical Progress
353

MARK WILSON On the Mathematics of Spilt Milk 143
142
THE ROLE OF ABSTRACTION ANALYSIS AND AXIOMATIZATION IN
153
DETLEF LAUGWITZ Controversies about Numbers and Functions
177
CARL POSY Epistemology Ontology and the Continuum
199
2
218
VOLKER PECKHAUS Scientific Progress and Changes
363
SERGEIDEMIDOVOn the Progress of Mathematics
377
CHRISTIAN THIEL On Some Determinants of Mathematical Progress
407
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