Newton C.A. da Costa's Books

On Hilbert's Sixth Problem

By: Newton C. A. da Costa,Francisco Antonio Doria

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On Hilbert's Sixth Problem

By: Newton C. A. da Costa,Francisco Antonio Doria

This book explores the premise that a physical theory is an interpretation of the analytico–canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico–canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism. The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler–Lagrange equations. The theory of Suppes predicates as the main tool in the axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences. This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set–theoretically generic spacetimes.

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Page Count

191

Publisher

Springer Nature

Published Date

ISBN 10

3030838374

ISBN 13

9783030838379

Science and Partial Truth

A Unitary Approach to Models and Scientific Reasoning

By: Newton C. A. da Costa,Steven French

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Science and Partial Truth

A Unitary Approach to Models and Scientific Reasoning

By: Newton C. A. da Costa,Steven French

Explores the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. This framework describes issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

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Page Count

270

Publisher

Oxford University Press on Demand

Published Date

ISBN 10

019515651X

ISBN 13

9780195156515

Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

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Page Count

162

Publisher

CRC Press

Published Date

ISBN 10

0415690854

ISBN 13

9780415690850

Science and Partial Truth

A Unitary Approach to Models and Scientific Reasoning

By: Newton C. A. da Costa,Steven French

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Science and Partial Truth

A Unitary Approach to Models and Scientific Reasoning

By: Newton C. A. da Costa,Steven French

In the past thirty years, two fundamental issues have emerged in the philosophy of science. One concerns the appropriate attitude we should take towards scientific theories--whether we should regard them as true or merely empirically adequate, for example. The other concerns the nature of scientific theories and models and how these might best be represented. In this ambitious book, da Costa and French bring these two issues together by arguing that theories and models should be regarded as partially rather than wholly true. They adopt a framework that sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate. The new machinery of "partial structures" that they develop offers a new perspective from which to view the nature of scientific models and their heuristic development. Their conclusions will be of wide interest to philosophers and historians of science.

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Page Count

272

Publisher

Oxford University Press

Published Date

ISBN 10

0198035535

ISBN 13

9780198035534

Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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162

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CRC Press

Published Date

ISBN 10

0203169573

ISBN 13

9780203169575

On Hilbert's Sixth Problem

By: Newton C. A. da Costa,Francisco Antonio Doria

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On Hilbert's Sixth Problem

By: Newton C. A. da Costa,Francisco Antonio Doria

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191

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Springer Nature

Published Date

ISBN 10

3030838374

ISBN 13

9783030838379

Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Goedel's Way

Exploits into an undecidable world

By: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

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Page Count

160

Publisher

CRC Press

Published Date

ISBN 10

1136587594

ISBN 13

9781136587597

Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

By: Isaac Newton

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Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

By: Isaac Newton

I consider philosophy rather than arts and write not concerning manual but natural powers, and consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore I offer this work as the mathematical principles of philosophy.In the third book I give an example of this in the explication of the System of the World. I derive from celestial phenomena the forces of gravity with which bodies tend to the sun and other planets.

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Page Count

292

Publisher

Univ of California Press

Published Date

ISBN 10

0520009290

ISBN 13

9780520009295

Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

By: Isaac Newton

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Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

By: Isaac Newton

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1934.

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Page Count

714

Publisher

Univ of California Press

Published Date

ISBN 10

0520364252

ISBN 13

9780520364257

The Principia

Mathematical Principles of Natural Philosophy

By: Isaac Newton,I. Bernard Cohen

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The Principia

Mathematical Principles of Natural Philosophy

By: Isaac Newton,I. Bernard Cohen

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

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Page Count

996

Publisher

Univ of California Press

Published Date

ISBN 10

0520088174

ISBN 13

9780520088177

Book's by Newton C.A. da Costa

On Hilbert's Sixth Problem

On Hilbert's Sixth Problem

Science and Partial Truth

Science and Partial Truth

Goedel's Way

Goedel's Way

Science and Partial Truth

Science and Partial Truth

Goedel's Way

Goedel's Way

On Hilbert's Sixth Problem

On Hilbert's Sixth Problem

Goedel's Way

Goedel's Way

Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World

The Principia

The Principia

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