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Author: Luitzen Egbertus Jan Brouwer Publisher: Cambridge University Press ISBN: 9780521177368 Category : Mathematics Languages : en Pages : 130
Book Description
Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.
Author: Luitzen Egbertus Jan Brouwer Publisher: Cambridge University Press ISBN: 9780521177368 Category : Mathematics Languages : en Pages : 130
Book Description
Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.
Author: Maria Hämeen-Anttila Publisher: Springer Nature ISBN: 3030872963 Category : Mathematics Languages : en Pages : 133
Book Description
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.
Author: Daniel C. Dennett Publisher: W. W. Norton & Company ISBN: 0393348784 Category : Philosophy Languages : en Pages : 512
Book Description
One of the world's leading philosophers offers aspiring thinkers his personal trove of mind-stretching thought experiments. Includes 77 of Dennett's most successful "imagination-extenders and focus-holders.O
Author: Joel David Hamkins Publisher: MIT Press ISBN: 0262542234 Category : Mathematics Languages : en Pages : 350
Book Description
An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Author: John Rawls Publisher: Harvard University Press ISBN: 0674042565 Category : Philosophy Languages : en Pages : 497
Book Description
Constantly revised and refined over three decades, Rawls's lectures on various historical figures reflect his developing and changing views on the history of liberalism and democracy. With its careful analyses of the doctrine of the social contract, utilitarianism, and socialism, this volume has a critical place in the traditions it expounds.
Author: Luitzen Egbertus Jan Brouwer
Author: Luitzen Egbertus Jan Brouwer
Author: Anne S. Troelstra
Author: Maria Hämeen-Anttila
Author: Anne Sjerp Troelstra
Author: Dirk Dalen
Author: 
Author: Daniel C. Dennett
Author: Joel David Hamkins
Author: Dirk van Dalen
Author: John Rawls