
Contents
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I: Formal Techniques I: Formal Techniques
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II: Stretching the Fabric of the Aristotelian Framework II: Stretching the Fabric of the Aristotelian Framework
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III: Proportions: From the Universal Lyre to a Science of Extension III: Proportions: From the Universal Lyre to a Science of Extension
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IV: Notation and new Numbers IV: Notation and new Numbers
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V: Geometry, the Science of Extension V: Geometry, the Science of Extension
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VI: Formal Causes Versus Formal Methods VI: Formal Causes Versus Formal Methods
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References References
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14 Form, Reason, and Method
Get accessMary Tiles is Professor (emeritus) of Philosophy at the University of Hawaii, Mānoa. She is the author of Bachelard: Science and Objectivity (1984), Introduction to the Philosophy of Set Theory (1989), Mathematics and the Image of Reason (1991), co‐author with James Tiles of The Authority of Knowledge: An Introduction to Historical Epistemology (1993) and with Hans Oberdiek of Living in a Technological Culture: Human Tools and Human Values (1995). Recent research interests include the role of technology in the development of global environmental science.
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Published:02 May 2011
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Abstract
This article traces the development of an ideal of method that was inspired by Ramon Lull and subsequently found new expressions in many of the proponents of a new science in early modern Europe. It investigates the unravelling of the link between scientific reason and logic and their reweaving in a pattern that integrated scientific reason with mathematics and the discovery of mathematically formulated relationships. It discusses how the transformations of one family of concepts that include proportion, ratio, and measure are implicated in the transition from natural magic to rational mechanics.
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