Paradoxes And Inconsistent Mathematics PDF Download
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| Author | : Zach Weber |
| Publisher | : Cambridge University Press |
| Total Pages | : 339 |
| Release | : 2021-10-21 |
| Genre | : Mathematics |
| ISBN | : 1108999026 |
Download Paradoxes and Inconsistent Mathematics Book in PDF, ePub and Kindle
Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
| Author | : C.E. Mortensen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 167 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 9401584532 |
Download Inconsistent Mathematics Book in PDF, ePub and Kindle
without a properly developed inconsistent calculus based on infinitesimals, then in consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories.
| Author | : Bryan Bunch |
| Publisher | : Courier Corporation |
| Total Pages | : 228 |
| Release | : 2012-10-16 |
| Genre | : Mathematics |
| ISBN | : 0486137937 |
Download Mathematical Fallacies and Paradoxes Book in PDF, ePub and Kindle
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.
| Author | : Hamza E. Alsamraee |
| Publisher | : Curious Math Publications |
| Total Pages | : 214 |
| Release | : 2020-09-10 |
| Genre | : Mathematics |
| ISBN | : 1735715603 |
Download Paradoxes Book in PDF, ePub and Kindle
Does .999?=1? Can you cut and reassemble a sphere into two identically sized spheres? Is the consistency of mathematical systems unprovable? Surprisingly, the answer to all of these questions is yes! And at the heart of each question, there lies paradox. For millennia, paradoxes have shaped mathematics and guided mathematical progress forwards. From the ancient paradoxes of Zeno to the modern paradoxes of Russell, paradoxes remind us of the constant need to revamp our mathematical understanding. It is for this reason that paradoxes are so important. Paradoxes: Guiding Forces in Mathematical Exploration provides a survey of mathematical paradoxes spanning a wide variety of topics. It delves into each paradox mathematically, philosophically, and historically, and attempts to provide a full picture of how paradoxes contributed to the progress of mathematics and guided it in many ways. In addition, it discusses how paradoxes can be useful as educational tools. All of that, plus the fact that it is written in a way that is accessible to anyone with a high school background in mathematics! Entertaining and educational, this book will appeal to any reader looking for a mathematical and philosophical challenge.
| Author | : Matt Cook |
| Publisher | : MIT Press |
| Total Pages | : 369 |
| Release | : 2021-08-03 |
| Genre | : Mathematics |
| ISBN | : 0262542293 |
Download Sleight of Mind Book in PDF, ePub and Kindle
This “fun, brain-twisting book . . . will make you think” as it explores more than 75 paradoxes in mathematics, philosophy, physics, and the social sciences (Sean Carroll, New York Times–bestselling author of Something Deeply Hidden). Paradox is a sophisticated kind of magic trick. A magician’s purpose is to create the appearance of impossibility, to pull a rabbit from an empty hat. Yet paradox doesn’t require tangibles, like rabbits or hats. Paradox works in the abstract, with words and concepts and symbols, to create the illusion of contradiction. There are no contradictions in reality, but there can appear to be. In Sleight of Mind, Matt Cook and a few collaborators dive deeply into more than 75 paradoxes in mathematics, physics, philosophy, and the social sciences. As each paradox is discussed and resolved, Cook helps readers discover the meaning of knowledge and the proper formation of concepts—and how reason can dispel the illusion of contradiction. The journey begins with “a most ingenious paradox” from Gilbert and Sullivan’s Pirates of Penzance. Readers will then travel from Ancient Greece to cutting-edge laboratories, encounter infinity and its different sizes, and discover mathematical impossibilities inherent in elections. They will tackle conundrums in probability, induction, geometry, and game theory; perform “supertasks”; build apparent perpetual motion machines; meet twins living in different millennia; explore the strange quantum world—and much more.
| Author | : Nathaniel S. Hellerstein |
| Publisher | : World Scientific |
| Total Pages | : 274 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9789812796110 |
Download Diamond Book in PDF, ePub and Kindle
This book is about OC diamondOCO, a logic of paradox. In diamond, a statement can be true yet false; an OC imaginaryOCO state, midway between being and non-being. Diamond''s imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, GAdelian meta-mathematics and dilemma games."
| Author | : Stanley J. Farlow |
| Publisher | : Courier Corporation |
| Total Pages | : 182 |
| Release | : 2014-02-20 |
| Genre | : Mathematics |
| ISBN | : 0486791734 |
Download Paradoxes in Mathematics Book in PDF, ePub and Kindle
Students and puzzle enthusiasts will get plenty of enjoyment plus some painless mathematical instruction from 28 conundrums, including The Curve That Shook the World, Space Travel in a Wineglass, and Through Cantor's Looking Glass.
| Author | : Augustus De Morgan |
| Publisher | : |
| Total Pages | : 406 |
| Release | : 1915 |
| Genre | : Circle-squaring |
| ISBN | : |
Download A Budget of Paradoxes Book in PDF, ePub and Kindle
| Author | : Agustin Rayo |
| Publisher | : MIT Press |
| Total Pages | : 321 |
| Release | : 2019-04-02 |
| Genre | : Mathematics |
| ISBN | : 0262039419 |
Download On the Brink of Paradox Book in PDF, ePub and Kindle
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.
| Author | : John Woods |
| Publisher | : Cambridge University Press |
| Total Pages | : 384 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780521009348 |
Download Paradox and Paraconsistency Book in PDF, ePub and Kindle
In a world plagued by conflict one might expect that the exact sciences of logic and mathematics would provide a safe harbor. In fact these disciplines are rife with internal divisions between different, often incompatible systems. This original book explores apparently intractable disagreements in logic and the foundations of mathematics and sets out conflict resolution strategies that evade these stalemates. This book makes an important contribution to such areas of philosophy as logic, philosophy of language and argumentation theory. It will also be of interest to mathematicians and computer scientists.
