Logic and Information

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Overview

Arguing that we must broaden our concept of logic to obtain a deeper understanding of intelligence and knowledge acquisition, this study outlines a new kind of logic that is capable of handling the issues involved in human communication and machine information processing.
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Editorial Reviews

From the Publisher
"A bold effort to restore logic as the science of 'reasoning, thinking, and inference'....Devlin writes with uncommon clarity for an interdisciplinary audience of linguists, computer scientists, philosophers, and mathematicians." The American Mathematical Monthly

"Mathematically oriented readers interested in artificial intelligence and human cognition should be able to get new ideas from this well-written book." P. Jouvelot, Computing Reviews

"The ideas in this fascinating, challenging, but speculative, book are set forth with clarity and wit that does them justice." D.V. Feldman, Choice

"The ideas in this fascinating, challenging, but speculative, book are set forth with clarity and wit that does them justice." D.V. Feldman, Choice

"Mathematically oriented readers interested in artificial intelligence and human cognition should be able to get new ideas from this well-written book." P. Jouvelot, Computing Reviews

"...In Keith Devlin's work, however, regardless of which of these prognoses one favours, situation theory has found an able expositor. He has written a very good book indeed, which is bound to become a standard reference in the field." Neil Tennant, Philosophia Mathematica

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Product Details

  • ISBN-13: 9780521410304
  • Publisher: Cambridge University Press
  • Publication date: 6/28/2003
  • Pages: 328
  • Product dimensions: 6.85 (w) x 9.72 (h) x 0.87 (d)

Meet the Author

Keith  Devlin
Keith Devlin
Keith Devlin -- regular National Public Radio commentator and member of the Stanford University staff -- writes about the genetic progression of mathematical thinking and the most head-scratching math problems of the day. And he somehow manages to make it fun for the lay reader.

Biography

Odds are, John Grisham doesn’t get interview questions like this: "If you could meet any mathematician, who would it be?"

But author Keith Devlin does, this time from Discover magazine as part of a January 2001 article coinciding with the publication of his book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. His answer may go a long way toward explaining why he has managed to make the world of numbers not only understandable but also enjoyable to a segment of the population that can’t balance a checkbook without a net -- or backup from MIT.

“Isaac Newton,” Devlin told the inquiring minds at Discover. “He was a quarrelsome, egotistical person, but he also invented calculus. He did it, by the way, when he was a student at Cambridge. The Great Plague was going on, so the university was closed, and young Newton found himself without studies to do. Most 20-year-olds would think, ‘Whoopee! I’ll just have a good time.’ Newton went home and invented calculus.”

It is this same kind of passion for mathematics that has enabled Devlin, now the executive director of the Center for the Study of Language and Information at Stanford University, to persuade readers that arithmetic, geometry and calculus can be a bracing addition to the stack on the bedside table. In The Math Gene, he explains the “innate sense of number” that lives inside the human mind and how the development of mathematical thinking is closely bound to the development of language. In Goodbye, Descartes: The End of Logic and the Search for a New Cosmology of the Mind, he argues against the possibility of artificial intelligence, saying that computers are simply logic machines that cannot replicate the rational thought and communication that are part of human smarts. In his newest book, The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time, he explains a historic competition announced by a Cambridge, Massachusetts foundation in 2000: Anyone who could solve any one of seven of the most perplexing math problems of the current age would win $1 million.

In a 1999 review, the Economist noted that “Devlin succeeds both in giving us a glimpse of the internal beauty of the subject and in demonstrating its usefulness in the external world. The Language of Mathematics is lucidly written and richly illustrated, and remains accessible and enthusiastic throughout.”

On NPR’s Weekend Edition, where he has become a regular guest, Devlin is referred to simply as “The Math Guy,” or as host Scott Simon once put it “our white knight of the world of mathematics.”

And, going back to that provocative subtitle in The Math Gene, just how is math like gossip? “Mathematicians deal with a collection of objects -- numbers, triangles, groups, fields -- and ask questions like: ‘What is the relationship between Objects X and Y?. If X does this to Y, what will Y do back to X?’” he told Discover. “It's got plot, it's got characters, it's got relationships between them, and it's got life and emotion and passion and love and hate, a bit of everything you can find in a soap opera. On the other hand, a soap opera isn't going to get you to the moon and back. Mathematics can.”

Just don’t forget to carry the 1.

Good To Know

Devlin was the coauthor of the television special A Mathematical Mystery Tour, broadcast as part of the Nova series in 1984.

He once offered as proof of the human brain’s intuitive math skills the ability to judge speed and distance while driving and the ability to add up bowling scores.

Devlin once managed to explain the mathematical difference between a knot and a tangle to National Public Radio’s listeners.

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    1. Hometown:
      Palo Alto, California
    1. Date of Birth:
      March 16, 1947
    2. Place of Birth:
      Hull, England
    1. Education:
      B.S., King's College, London, 1968; Ph.D., University of Bristol, 1971

Table of Contents

1. Logic; 2. Information; 3. Situation theory; 4. Meaning and constraints; 5. Some logical issues; 6. Mental states; 7. Perception and action; 8. Situation semantics; 9. Topics in situation semantics; 10. Historical perspectives and future directions.

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