Truth And Assertibility

World Scientific
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The book is a research monograph on the notions of truth and assertibility as they relate to the foundations of mathematics. It is aimed at a general mathematical and philosophical audience. The central novelty is an axiomatic treatment of the concept of assertibility. This provides us with a device that can be used to handle difficulties that have plagued philosophical logic for over a century. Two examples relate to Frege's formulation of second-order logic and Tarski's characterization of truth predicates for formal languages. Both are widely recognized as fundamental advances, but both are also seen as being seriously flawed: Frege's system, as Russell showed, is inconsistent, and Tarski's definition fails to capture the compositionality of truth. A formal assertibility predicate can be used to repair both problems. The repairs are technically interesting and conceptually compelling. The approach in this book will be of interest not only for the uses the author has put it to, but also as a flexible tool that may have many more applications in logic and the foundations of mathematics.
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About the author

Nik Weaver (Washington University in St. Louis, USA)
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Additional Information

Publisher
World Scientific
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Published on
Apr 22, 2015
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Pages
204
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ISBN
9789814619981
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Best For
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Language
English
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Genres
Mathematics / History & Philosophy
Mathematics / Logic
Mathematics / Set Theory
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Content Protection
This content is DRM protected.
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Andrew Hodges
A NEW YORK TIMES BESTSELLER

The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley

It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades--all before his suicide at age forty-one. This New York Times–bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing's royal pardon in 2013, is the definitive account of an extraordinary mind and life.

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The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution.

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The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

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Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
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