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Mathematics and Philosophy of Mathematics
Philosophia Mathematica, 1994Nach den Ausführungen des Verf. führt das Studium der Ontologie zu keinen ersten Prinzipien der Mathematik, noch bestimmt die Mathematik die Ontologie. Die Begründung dieser Ansicht stützt sich auf eingehende Studien sowohl von Plato und Proklos sowie der Werke von Gödel, Brouwer, Poincaré, Lebesgue and Bernays.
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Mathematics of Philosophy or Philosophy of Mathematics?
Nonlinear Dynamics, Psychology, and Life Sciences, 2001This article examines recent attempts to gain insight into philosophical paradoxes through using NDS models employing iterated difference equations and resulting phase portraits and escape time diagrams. The temporal nature of such models is contrasted with an alternative approach based on the a-temporal and non-dynamical construct of a lattice ...
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PASCH’S PHILOSOPHY OF MATHEMATICS
The Review of Symbolic Logic, 2010Moritz Pasch (1843–1930) gave the first rigorous axiomatization of projective geometry in hisVorlesungen über neuere Geometrie(1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics,
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The Impact of the Philosophy of Mathematical Practice on the Philosophy of Mathematics
2014There are always several ways to read a paper on any topic. This paper, for instance, can be read as a two-part text, the first major part dealing with the history of the study of mathematical practice, and the second, somewhat shorter part with a proposal as to how the "traditional" philosophy of mathematics and the philosophy of mathematical practice
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Wittgenstein’s Philosophies of Mathematics
Synthese, 1991Wittgenstein's philosophy of mathematics has long been notorious. Part of the problem is that it has not been recognized that Wittgenstein, in fact, had two chief post-Tractatus conceptions of mathematics. I have labelled these the calculus conception and the language-game conception. The calculus conception forms a distinct middle period.
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The Philosophy of Mathematical Practice
International Studies in the Philosophy of Science, 2010Paolo Mancosu (Ed.) Oxford, Oxford University Press, 2008 xi + 447 pp., ISBN 9780199296453, £53.00, US$100 (hardback) From the end of the nineteenth century to this day, philosophers of mathematics...
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Meinongianism and the Philosophy of Mathematics†
Philosophia Mathematica, 2003This paper presents the view of Richard Routley (later Sylvan) that mathematical objects are non-existent. [Cf. \textit{R. Routley}, Exploring Meinong's jungle -- and beyond. Canberra: Philosophy RSSS, Australian National University (1980), Chapter 10 of which is reprinted as: \textit{R.
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