Science/Engineering Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz (0199299730)

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Representation and Productive Ambiguity in Mathematics and the Sciences by Emily R. Grosholz

Emily Grosholz offers an original investigation of demonstration in mathematics and science, examining how it works and why it is persuasive. Focusing on geometrical demonstration, she shows the roles that representation and ambiguity play in mathematical discovery. She presents a wide range of case studies in mechanics, topology, algebra, logic, and chemistry, from ancient Greece to the present day, but focusing particularly on the seventeenth and twentieth centuries. She argues that reductive methods are effective not because they diminish but because they multiply and juxtapose modes of representation. Such problem-solving is, she argues, best understood in terms of Leibnizian "analysis"--the search for conditions of intelligibility. Discovery and justification are then two aspects of one rational way of proceeding, which produces the mathematician's formal experience.

Grosholz defends the importance of iconic, as well as symbolic and indexical, signs in mathematical representation, and argues that pragmatic, as well as syntactic and semantic, considerations are indispensable fore mathematical reasoning. By taking a close look at the way results are presented on the page in mathematical (and biological, chemical, and mechanical) texts, she shows that when two or more traditions combine in the service of problem solving, notations and diagrams are subtly altered, multiplied, and juxtaposed, and surrounded by prose in natural language which explains the novel combination. Viewed this way, the texts yield striking examples of language and notation that are irreducibly ambiguous and productive because they are ambiguous. Grosholtz's arguments, which invoke Descartes, Locke, Hume, and Kant, will be of considerable interest to philosophers and historians of mathematics and science, and also have far-reaching consequences for epistemology and philosophy of language.

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	Science/Engineering How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics William Byers, “How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics” Princeton University Press \| 2007-05-07 \| ISBN: 0691127387 \| 425 pages \| DJVU \| 3,35 MB To many outsiders, mathematicians appe ...
	Encyclopedias Representation Theory and Noncommutative Harmonic Analysis II (Encyclopedia of Mathematical Sciences Series) Representation Theory and Noncommutative Harmonic Analysis II: Homogeneous Spaces, Representations and Special Functions (Encyclopedia of Mathematical Sciences Series)Springer \| 1995 \| ISBN: 0387547029 \| Pages: 273 \| DJVU \| 1.38 MBThis volu ...
	Encyclopedias Representation Theory and Noncommutative Harmonic Analysis I (Encyclopaedia of Mathematical Sciences) Representation Theory and Noncommutative Harmonic Analysis I: Fundamental Concepts. Representations of Virasoro and Affine Algebras (Encyclopaedia of Mathematical Sciences)Springer \| 1994 \| ISBN: 3540186980 \| Pages: 234 \| DJVU \| 1.51 MBPart ...
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	Science/Engineering From Genetics to Mathematics (Series on Advances in Mathematics for Applied Sciences) From Genetics to Mathematics (Series on Advances in Mathematics for Applied Sciences) World Scientific Publishing Company \| ISBN: 9812837248 \| edition 2009 \| PDF \| 244 pages \| 9,3 mb This volume contains pedagogical and elementary introduc ...
	Study Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics) Stuart Martin "Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics)"Cambridge University Press \| English \| 1994-01-28 \| ISBN: 0521415918 \| 252 pages \| DJVU \| 1 MBSchur algebras are an algebraic system that provide a li ...

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	Science/Engineering How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics William Byers, “How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics” Princeton University Press \| 2007-05-07 \| ISBN: 0691127387 \| 425 pages \| DJVU \| 3,35 MB To many outsiders, mathematicians appe ...
	Encyclopedias Representation Theory and Noncommutative Harmonic Analysis II (Encyclopedia of Mathematical Sciences Series) Representation Theory and Noncommutative Harmonic Analysis II: Homogeneous Spaces, Representations and Special Functions (Encyclopedia of Mathematical Sciences Series)Springer \| 1995 \| ISBN: 0387547029 \| Pages: 273 \| DJVU \| 1.38 MBThis volu ...
	Encyclopedias Representation Theory and Noncommutative Harmonic Analysis I (Encyclopaedia of Mathematical Sciences) Representation Theory and Noncommutative Harmonic Analysis I: Fundamental Concepts. Representations of Virasoro and Affine Algebras (Encyclopaedia of Mathematical Sciences)Springer \| 1994 \| ISBN: 3540186980 \| Pages: 234 \| DJVU \| 1.51 MBPart ...
	Science/Engineering Mathematical Methods for the Natural and Engineering Sciences (Series on Advances in Mathematics for Applied Sciences, Vol. 65) Mathematical Methods for the Natural and Engineering Sciences (Series on Advances in Mathematics for Applied Sciences, Vol. 65) Publisher: World Scientific Publishing Company \| ISBN: 9812387501 \| edition 2004 \| PDF \| 540 pages \| 13,4 mbThi ...
	Science/Engineering From Genetics to Mathematics (Series on Advances in Mathematics for Applied Sciences) From Genetics to Mathematics (Series on Advances in Mathematics for Applied Sciences) World Scientific Publishing Company \| ISBN: 9812837248 \| edition 2009 \| PDF \| 244 pages \| 9,3 mb This volume contains pedagogical and elementary introduc ...
	Study Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics) Stuart Martin "Schur Algebras and Representation Theory (Cambridge Tracts in Mathematics)"Cambridge University Press \| English \| 1994-01-28 \| ISBN: 0521415918 \| 252 pages \| DJVU \| 1 MBSchur algebras are an algebraic system that provide a li ...

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