The Scope and Limits of Mathematical Knowledge
Author: Leon Horsten,Philip Welch
Publisher: Oxford University Press
ISBN: 0198759592
Category:
Page: 288
View: 3868
The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
Gödel's Disjunction
The scope and limits of mathematical knowledge
Author: Leon Horsten,Philip Welch
Publisher: Oxford University Press
ISBN: 0191077690
Category: Mathematics
Page: 288
View: 9138
The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is not equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Gödel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field.
Author: Leon Horsten,Philip Welch
Publisher: Oxford University Press
ISBN: 0191077690
Category: Mathematics
Page: 288
View: 9138
Physical Perspectives on Computation, Computational Perspectives on Physics
Author: Michael E. Cuffaro,Samuel C. Fletcher
Publisher: Cambridge University Press
ISBN: 1316767396
Category: Science
Page: N.A
View: 8813
Interpreting Godel
Critical Essays
Author: Juliette Kennedy
Publisher: Cambridge University Press
ISBN: 1107002664
Category: Science
Page: 288
View: 2101
In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.
Author: Juliette Kennedy
Publisher: Cambridge University Press
ISBN: 1107002664
Category: Science
Page: 288
View: 2101
The Mathematical Analysis of Logic
Being an Essay Towards a Calculus of Deductive Reasoning
Author: George Boole
Publisher: N.A
ISBN: N.A
Category: Analysis (Philosophy).
Page: 82
View: 9757
Author: George Boole
Publisher: N.A
ISBN: N.A
Category: Analysis (Philosophy).
Page: 82
View: 9757
The Principles of Mathematics
Author: Bertrand Russell
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 8879
Model Building in Mathematical Programming
Author: H. Paul Williams
Publisher: John Wiley & Sons
ISBN: 1118506189
Category: Business & Economics
Page: 432
View: 3539
Mathematics for Computer Science
Author: Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher: N.A
ISBN: 9789888407064
Category:
Page: 979
View: 5979
The Influence of Computers and Informatics on Mathematics and Its Teaching
Proceedings From a Symposium Held in Strasbourg, France in March 1985 and Sponsored by the International Commission on Mathematical Instruction
Author: R. F. Churchhouse
Publisher: CUP Archive
ISBN: 9780521311892
Category: Computers
Page: 155
View: 4475
First published in 1986, the first ICMI study is concerned with the influence of computers and computer science on mathematics and its teaching in the last years of school and at tertiary level. In particular, it explores the way the computer has influenced mathematics itself and the way in which mathematicians work, likely influences on the curriculum of high-school and undergraduate students, and the way in which the computer can be used to improve mathematics teaching and learning. The book comprises a report of the meeting held in Strasbourg in March 1985, plus several papers contributed to that meeting.
Author: R. F. Churchhouse
Publisher: CUP Archive
ISBN: 9780521311892
Category: Computers
Page: 155
View: 4475
An Investigation of the Laws of Thought
On which are Founded the Mathematical Theories of Logic and Probabilities
Author: George Boole
Publisher: N.A
ISBN: N.A
Category: Logic
Page: 424
View: 6701
Author: George Boole
Publisher: N.A
ISBN: N.A
Category: Logic
Page: 424
View: 6701
The Century Dictionary
An Encyclopedic Lexicon of the English Language
Author: William Dwight Whitney
Publisher: N.A
ISBN: N.A
Category: Encyclopedias and dictionaries
Page: 7076
View: 7322
Author: William Dwight Whitney
Publisher: N.A
ISBN: N.A
Category: Encyclopedias and dictionaries
Page: 7076
View: 7322
Logic and Structure
Author: Dirk van Dalen
Publisher: Springer Science & Business Media
ISBN: 3662029626
Category: Mathematics
Page: 220
View: 6729
Probability Theory
The Logic of Science
Author: E. T. Jaynes
Publisher: Cambridge University Press
ISBN: 1139435167
Category: Science
Page: N.A
View: 4559
The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.
Author: E. T. Jaynes
Publisher: Cambridge University Press
ISBN: 1139435167
Category: Science
Page: N.A
View: 4559
Six Septembers: Mathematics for the Humanist
Author: Patrick Juola,Stephen Ramsay
Publisher: Lulu.com
ISBN: 1609621115
Category: Mathematics
Page: 422
View: 4303
Webster's New International Dictionary of the English Language
Based on the International Dictionary of 1890 and 1900
Author: William Torrey Harris,Frederic Sturges Allen
Publisher: N.A
ISBN: N.A
Category: English language
Page: 2620
View: 6442
Author: William Torrey Harris,Frederic Sturges Allen
Publisher: N.A
ISBN: N.A
Category: English language
Page: 2620
View: 6442
Introduction to Mathematical Logic, Sixth Edition
Author: Elliott Mendelson
Publisher: CRC Press
ISBN: 1482237784
Category: Mathematics
Page: 513
View: 2283
The Limitations of the Open Mind
Author: Jeremy Fantl
Publisher: Oxford University Press
ISBN: 0198807953
Category: Philosophy
Page: 256
View: 7000
How to Prove It
A Structured Approach
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 1139450972
Category: Mathematics
Page: N.A
View: 6588
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 1139450972
Category: Mathematics
Page: N.A
View: 6588
Principia Mathematica
Author: Alfred North Whitehead,Bertrand Russell
Publisher: N.A
ISBN: N.A
Category: Logic, Symbolic and mathematical
Page: N.A
View: 1209
Understanding Machine Learning
From Theory to Algorithms
Author: Shai Shalev-Shwartz,Shai Ben-David
Publisher: Cambridge University Press
ISBN: 1107057132
Category: Computers
Page: 409
View: 4222
Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.
Author: Shai Shalev-Shwartz,Shai Ben-David
Publisher: Cambridge University Press
ISBN: 1107057132
Category: Computers
Page: 409
View: 4222