Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

    With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of "Logical Dilemmas: The Life and Work of Kurt G del

    this is one of those rare books that will change your beliefs - and in doing so will change your life. tHE ANt AND tHE FERRARI offers readers a clear, navigable path through the big questions that confront us all today. What is the meaning of life? Can we be ethical beings in today's world? Can we know if there is life after death? Is there such a thing as Absolute truth? What caused the Big Bang and why should you care?

    The price we paid for becoming intelligent was to become painfully ignorant of the difference between good and evil.Adi, a 10-year-old boy, works together with two old philosophers as they try to unravel the prophecy of a promised King. With insatiable curiosity, Adi must work with the wise men as they rationalize with each other on why and how humans became intelligent. Together they attempt to answer some of the most profound questions related to existence. Does evolution end with human beings or is there an ‘Overman’ who can reach evolution’s pinnacle? Will this Overman be able to define values for humankind?Centuries later a young boy promises his mother that he will always uphold the love that she has taught him. It is a promise that drowns him in the nectar of the gods. Krish grows up to be an engineer and joins a team of scientists as they try to create artificial consciousness in a machine.Krish soon realizes that he has a bigger fight on his hands. A fight to preserve love in a desolate world. His quest for true love ultimately leads him down a path where he comes face to face with a fearsome snake delivering a kiss of death.Humans have come a long way by questioning the nature of objects around us and pushing the limits of our intelligence, but it’s now time that we ask the greatest question yet: when does intelligence transcend to become consciousness?

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    Before his success as an author Goodkind worked primarily as a painter, as well as doing carpentry and woodworking. Goodkind is a proponent of Ayn Rand's philosophical approach of Objectivism, with references to Rand's ideas and novels referenced in his works.The Sword of Truth series sold twenty-five million copies worldwide and was translated into more than twenty languages. It was adapted into a television series called Legend of the Seeker, premiering November 1, 2008 but canceled after two seasons in May, 2010.

    Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

    Quality assurance was conducted on each of these books in an attempt to remove books with imperfections introduced by the digitization process. Though we have made best efforts - the books may have occasional errors that do not impede the reading experience. We believe this work is culturally important and have elected to bring the book back into print as part of our continuing commitment to the preservation of printed works worldwide.

    His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art—and the sheer beauty—in the science of math.

    Just turn on cable news. Philosophy is for people who want to understand the deep questions. The goal of political philosophy is to determine the standards by which we judge different institutions good or bad, just or unjust.Some people might think they don’t have much need of political philosophy: “Who cares about wishy-washy obtuse notions of justice? I’m a pragmatist. I just want to know what works.” But this isn’t a way of avoiding political philosophy; it’s a way of being dogmatic about it. Before we can just do “what works,” we have to know what counts as working.This book serves as an introduction to some of the major theories of justice, to the arguments philosophers have made for and against these theories, and, ultimately, to how to be more thoughtful and rigorous in your own thinking.

    A System of Logic is the first major installment of his comprehensive restatement of an empiricist and utilitarian position. It begins the attack on ""intuitionism"" which Mill carried on throughout his life, and makes plain his belief that social planning and political action should rely primarily on scientific knowledge, not on authority, custom, revelation, or prescription.Contents Include: OF NAMES AND PROPOSITIONS Of the Necessity of commencing with an Analysis of Language Of Names Of the Things denoted by Names Of Proposition Of the Import of Propositions Of Propositions merely Verbal Of the nature of Classification and the five Predicables Of Definition OF REASONING Of Inference, or Reasoning in General Of Ratiocination, or Syllogism Of the Functions, and logical Values of Syllogism Of trains of Reasoning and Deductive Sciences Of Demonstration and Necessary truths OF INDUCTION Observations on Induction in General On the Ground of Induction Of the Laws of Nature Of The Law of Universal Causation Of The Composition of Causes Of Observation and Experiment, Four Methods of Experimental Enquiry Miscellaneous Examples Plurality of Causes Of the Deductive Method Explanation of Laws of Nature. Keywords: Knowledge, Theory of Logic Science Methodology

    To understand the universe in the far future, we must first describe its present state and structure on the grand scale, and how its present properties arose. Dr Islam explains these topics in an accessible way in the first part of the book. From this background he speculates about the future evolution of the universe and predicts the major changes that will occur. The author has largely avoided mathematical formalism and therefore the book is well suited to general readers with a modest background knowledge of physics and astronomy.