logic mathematical paradoxes

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One Hundred Years Of Russell S Paradox

Author : Godehard Link
ISBN : 3110174383
Genre : Mathematics
File Size : 26. 18 MB
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The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes thereby to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

Diamond

Author : N. S. Hellerstein
ISBN : 9789814287142
Genre : Electronic books
File Size : 52. 47 MB
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This book is about ''diamond'', a logic of paradox. In diamond, a statement can be true yet false; an ''imaginary'' state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book has three sections: Paradox Logic, which covers the classic paradoxes of mathematical logic, shows how they can be resolved in this new system; The Second Paradox, which relates diamond to Boolean logic and the Spencer-Brown modulator; and Metamathematical Dilemma, which relates diamond to Godelian meta-mathematics and dilemma games.

Mathematical Fallacies And Paradoxes

Author : Bryan Bunch
ISBN : 9780486296647
Genre : Mathematics
File Size : 79. 84 MB
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Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.

Paradoxes In Mathematics

Author : Stanley J. Farlow
ISBN : 9780486497167
Genre : Mathematics
File Size : 60. 58 MB
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Compiled by a prominent educator and author, this volume presents an intriguing mix of mathematical paradoxes — phenomena with surprising outcomes that can be resolved mathematically. Students and puzzle enthusiasts will get plenty of enjoyment mixed with a bit of painless mathematical instruction from 30 conundrums, including The Birthday Paradox, Aristotle's Magic Wheel, and A Greek Tragedy.

Mathematical Logic And Formalized Theories

Author : Robert L. Rogers
ISBN : 9781483257976
Genre : Mathematics
File Size : 78. 11 MB
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Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.

Impossible Folding Puzzles And Other Mathematical Paradoxes

Author : Gianni A. Sarcone
ISBN : 9780486493510
Genre : Games
File Size : 41. 56 MB
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Do all problems have solutions? Is complexity synonymous with difficulty? This original collection of mathematical puzzles and paradoxes proves that things aren't always what they seem! Readers will discover that nothing is as easy or as difficult as it looks and that puzzles can have one, several, or no solutions. The fun-filled puzzles begin with The Tricky Hole, a challenge that involves pushing a large coin through a small hole in a sheet of paper without ripping or making any cuts in the paper. Advance to the Elastic Playing Card, in which it's possible to cut a hole into a playing card big enough for someone to climb through. Other incredible puzzles include Elephants and Castles, Trianglized Kangaroo, Honest Dice and Logic Dice, Mind-reading Powers, and dozens more. Complete solutions explain the mathematical realities behind the fantastic-sounding challenges.

Perspectives On The History Of Mathematical Logic

Author : Thomas Drucker
ISBN : 9780817647698
Genre : Mathematics
File Size : 27. 4 MB
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This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.

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