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Cartesian Method and the Problem of Reduction

Author: Emily Grosholz

Publisher: Oxford University Press on Demand

Published: 1991

Total Pages: 161

ISBN-13: 9780198242505

The Cartesian method, construed as a way of organizing domains of knowledge according to the "order of reasons," was a powerful reductive tool. Descartes made significant strides in mathematics, physics, and metaphysics by relating certain complex items and problems back to more simple elements that served as starting points for his inquiries. But his reductive method also impoverished these domains in important ways, for it tended to restrict geometry to the study of straight line segments, physics to the study of ambiguously constituted bits of matter in motion, and metaphysics to the study of the isolated, incorporeal knower. This book examines in detail the negative and positive impact of Descartes's method on his scientific and philosophical enterprises, exemplified by the Geometry, the Principles, the Treatise of Man, and the Meditations.

Cartesian Method and the Problem of Reduction

Author: Emily Grosholz

Publisher:

Published: 1991-03-14

Total Pages: 176

ISBN-13: 9786610809745

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Cartesian method, construed as a way of organizing domains of knowledge according to the 'order of reason', was a powerful reductive tool. Descartes produced important results in mathematics, physics, and metaphysics by relating certain complex items and problems back to simpler elements that serve as starting points for his inquiries. However, his reductive method also impoverished these domains in important ways, for it tended to restrict geometry to the study of straight line segments, physics to the study of ambiguously constituted bits of matter in motion, and metaphysics to the study of the isolated, incorporeal knower. This book examines in detail the impact, negative and positive, of Descartes's method on his scientific and philosophical enterprises, exemplified by the Geometry, the Principles, the Treatise of Man, and the Meditations.

Cartesian Method and the Problem of Reduction

Author: Emily Grosholz

Publisher:

Published: 1991

Total Pages: 161

ISBN-13: 9780191680502

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Examines in detail the impact, negative and positive, of Descartes's method on his scientific and philosophical enterprises, exemplified by the 'Geometry', 'Principles', 'Treatise of Man', and 'Meditations'.

Descartes's Concept of Mind

Author: Lilli Alanen

Publisher: Harvard University Press

Published: 2009-07-01

Total Pages: 404

ISBN-13: 9780674020108

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Descartes's concept of the mind, as distinct from the body with which it forms a union, set the agenda for much of Western philosophy's subsequent reflection on human nature and thought. This is the first book to give an analysis of Descartes's pivotal concept that deals with all the functions of the mind, cognitive as well as volitional, theoretical as well as practical and moral. Focusing on Descartes's view of the mind as intimately united to and intermingled with the body, and exploring its implications for his philosophy of mind and moral psychology, Lilli Alanen argues that the epistemological and methodological consequences of this view have been largely misconstrued in the modern debate. Informed by both the French tradition of Descartes scholarship and recent Anglo-American research, Alanen's book combines historical-contextual analysis with a philosophical problem-oriented approach. It seeks to relate Descartes's views on mind and intentionality both to contemporary debates and to the problems Descartes confronted in their historical context. By drawing out the historical antecedents and the intellectual evolution of Descartes's thinking about the mind, the book shows how his emphasis on the embodiment of the mind has implications far more complex and interesting than the usual dualist account suggests.

Isaac Newton on Mathematical Certainty and Method

Author: Niccolo Guicciardini

Publisher: MIT Press

Published: 2011-08-19

Total Pages: 449

ISBN-13: 0262291657

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An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics. Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics. Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the “common” and “new” analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns. Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newton on Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.

The Philosophical Roots of the Ecological Crisis

Author: Joshtrom Isaac Kureethadam

Publisher: Cambridge Scholars Publishing

Published: 2018-06-11

Total Pages: 409

ISBN-13: 1527512991

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The Philosophical Roots of the Ecological Crisis: Descartes and the Modern Worldview traces the conceptual sources of the present environmental degradation within the worldview of Modernity, and particularly within the thought of René Descartes, universally acclaimed as the father of modern philosophy. The book demonstrates how the triple foundations of the Modern worldview – in terms of an exaggerated anthropocentrism, a mechanistic conception of the natural world, and the metaphysical dualism between humanity and the rest of the physical world – can all be largely traced back to Cartesian thought, with direct ecological consequences.

Descartes's Method

Author: Tarek R. Dika

Publisher: Oxford University Press

Published: 2023-02-27

Total Pages: 407

ISBN-13: 0192696947

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Descartes's Method develops an ontological interpretation of Descartes's method as a dynamic and, within limits, differentiable problem-solving cognitive disposition or habitus, which can be actualized or applied to different problems in various ways, depending on the nature of the problem. Parts I-II develop the foundations of an habitual interpretation of Descartes's method, while Parts III-V demonstrate the fruits of such an interpretation in metaphysics, natural philosophy, and mathematics. The first book to draw on the recently discovered Cambridge manuscript of Descartes's Rules for the Direction of the Mind, Descartes's Method concretely demonstrates the efficacy of Descartes's method in the sciences and the underlying unity of Descartes's method from Rules for the Direction of the Mind to Principles of Philosophy (1644).

Representation and Productive Ambiguity in Mathematics and the Sciences

Author: Emily R. Grosholz

Publisher: Clarendon Press

Published: 2007-08-30

Total Pages: 330

ISBN-13: 0191538515

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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 for 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 sublty 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.

Descartes and the Possibility of Science

Author: Peter A. Schouls

Publisher: Cornell University Press

Published: 2000

Total Pages: 202

ISBN-13: 9780801437755

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Joining these topics together within the context of Cartesian doctrine, Schouls opens up a substantially new reading of the Meditations and a more complete picture of Descartes as a scientist."--BOOK JACKET.

Descartes's Meditations

Author: Catherine Wilson

Publisher: Cambridge University Press

Published: 2003-11-20

Total Pages: 288

ISBN-13: 9780521007665

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