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Switch to: References
Citations of:
History of geometry and the development of the form of its language
Synthese 116 (2):141–186 (1998)
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This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwrizm, Cardano, and Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form of the symbolic language of algebra. Thus the paper develops further the (...) |
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Cieľom článku je upozorniť na niektoré možnosti použitia metód formálnej epistemológie v oblasti sociálnych vied. Ide predovšetkým o teóriu objektácií a teóriu re-prezentácií a s nimi spojené metódy rekonštrukcie potencialít a formálnych aspektov jazyka. V článku sa ďalej snažíme zodpovedať niektoré kritické námietky Markéty Patákovej, ktoré sformulovala na adresu formálnej epistemológie vo svojom texte Predikce v Kvaszově formální epistemologii ve světle historické metody Michela Foucaulta. |
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The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form . Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form . If this is correct, Kant’s philosophy is a reasonable reconstruction of such theories as projective geometry; (...) |
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During the first phase of Greek mathematics a proof consisted in showing or making visible the truth of a statement. This was the epagogic method. This first phase was followed by an apagogic or deductive phase. During this phase visual evidence was rejected and Greek mathematics became a deductive system. Now epagoge and apagoge, apart from being distinguished, roughly according to the modern distinction between inductive and deductive procedures, were also identified on account of the conception of generality as continuity. (...) |
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This paper takes up a suggestion made by Floridi that the digital revolution is bringing about a profound change in our metaphysics. The paper aims to bring some older views from philosophy of mathematics to bear on this problem. The older views are concerned principally with mathematical realism—that is the claim that mathematical entities such as numbers exist. The new context for the discussion is informational realism, where the problem shifts to the question of the reality of information. Mathematical realism (...) |
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The question whether Kuhn's theory of scientific revolutions could be applied to mathematics caused many interesting problems to arise. The aim of this paper is to discuss whether there are different kinds of scientific revolution, and if so, how many. The basic idea of the paper is to discriminate between the formal and the social aspects of the development of science and to compare them. The paper has four parts. In the first introductory part we discuss some of the questions (...) |
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