Visualization, Explanation and Reasoning Styles in MathematicsP. Mancosu, Klaus Frovin Jørgensen, S.A. Pedersen Springer Science & Business Media, 30. mars 2006 - 300 sider In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc. |
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Side 5
... focuses on Liu Hui's commentary on the measurement of the circle. The commentary, made up of two parts, reveals Liu Hui's concerns for explaining why a certain algorithm is correct and it functions as an explanation of the INTRODUCTION 5.
... focuses on Liu Hui's commentary on the measurement of the circle. The commentary, made up of two parts, reveals Liu Hui's concerns for explaining why a certain algorithm is correct and it functions as an explanation of the INTRODUCTION 5.
Side 14
... circles. Such results and many other concomitant factors, led mathematicians to formulate more rigorous approaches to mathematics that excluded the recourse to such treacherous tools as images and diagrams in favor of a linguistic ...
... circles. Such results and many other concomitant factors, led mathematicians to formulate more rigorous approaches to mathematics that excluded the recourse to such treacherous tools as images and diagrams in favor of a linguistic ...
Side 25
... circles, there is no way to go beyond 3 classes, that is the addition of a fourth circle to the diagram will not be able to represent all the possible combinations between 4 classes. In the case of Euler's diagrams there are also ...
... circles, there is no way to go beyond 3 classes, that is the addition of a fourth circle to the diagram will not be able to represent all the possible combinations between 4 classes. In the case of Euler's diagrams there are also ...
Side 56
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Innhold
13 | |
GIAQUINTO From Symmetry Perception to Basic Geometry | 31 |
A Geometrical Concept for Squares | 39 |
Is It Knowledge? | 46 |
References | 53 |
Godels Platonism | 60 |
Maddys Naturalism | 66 |
References | 72 |
On Reasoning Styles in Early Mathema | 91 |
K CHEMLA The Interplay Between Proof and Algorithm in 3rd Century | 122 |
Visual | 147 |
J HAFNER AND P MANCOSU The Varieties of Mathematical Explana | 215 |
A Study | 251 |
Index | 295 |
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Visualization, Explanation and Reasoning Styles in Mathematics P. Mancosu,Klaus Frovin Jørgensen,S.A. Pedersen Ingen forhåndsvisning tilgjengelig - 2010 |
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