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Early Analytic Philosophy - New Perspectives on the TraditionFrege and the Aristotelian Model of Science

Early Analytic Philosophy - New Perspectives on the Tradition: Frege and the Aristotelian Model... [Although profoundly influential for essentially the whole of philosophy’s twenty-five hundred year history, the model of a science that is outlined in Aristotle’sAristotlePosterior Analytics has recently been abandoned on grounds that developments in mathematicsMathematics and logic over the last century or so have rendered it obsolete. Nor has anything emerged to take its place. As things stand we have not even the outlines of an adequate understanding of the rationality of mathematics as a scientific practice. It seems reasonable, in light of this lacuna, to return again to Frege—who was at once one of the last great defenders of the model and a key figure in the very developments that have been taken to spell its demise—in hopes of finding a way forward. What we find when we do is that although Frege remains true to the spirit of the model, he also modifies it in very fundamental ways. So modified, I will suggest, the model continues to provide a viable and compelling image of scientific rationalityScientific rationality by showing, in broad outline, how we achieve, and maintain, cognitive control in our mathematical investigations.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Early Analytic Philosophy - New Perspectives on the TraditionFrege and the Aristotelian Model of Science

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References (24)

Publisher
Springer International Publishing
Copyright
© Springer International Publishing Switzerland 2016
ISBN
978-3-319-24212-5
Pages
31 –48
DOI
10.1007/978-3-319-24214-9_3
Publisher site
See Chapter on Publisher Site

Abstract

[Although profoundly influential for essentially the whole of philosophy’s twenty-five hundred year history, the model of a science that is outlined in Aristotle’sAristotlePosterior Analytics has recently been abandoned on grounds that developments in mathematicsMathematics and logic over the last century or so have rendered it obsolete. Nor has anything emerged to take its place. As things stand we have not even the outlines of an adequate understanding of the rationality of mathematics as a scientific practice. It seems reasonable, in light of this lacuna, to return again to Frege—who was at once one of the last great defenders of the model and a key figure in the very developments that have been taken to spell its demise—in hopes of finding a way forward. What we find when we do is that although Frege remains true to the spirit of the model, he also modifies it in very fundamental ways. So modified, I will suggest, the model continues to provide a viable and compelling image of scientific rationalityScientific rationality by showing, in broad outline, how we achieve, and maintain, cognitive control in our mathematical investigations.]

Published: Jan 22, 2016

Keywords: Mathematical Practice; Implicit Definition; Hypothetical Syllogism; Concept Word; Concrete Interpretation

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