An Investigation of the Laws of Thought

On Which Are Founded the Mathematical Theories of Logic and Probabilities

Author: George Boole

Publisher: Createspace Independent Publishing Platform

ISBN: 9781986622554


Page: 336

View: 2842

An Investigation of the Laws of Thought: On Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole. The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and, finally, to collect from the various elements of truth brought to view in the course of these inquiries some probable intimations concerning the nature and constitution of the human mind. The following work is not a republication of a former treatise by the Author, entitled, "The Mathematical Analysis of Logic." Its earlier portion is indeed devoted to the same object, and it begins by establishing the same system of fundamental laws, but its methods are more general, and its range of applications far wider. It exhibits the results, matured by some years of study and reflection, of a principle of investigation relating to the intellectual operations, the previous exposition of which was written within a few weeks after its idea had been conceived.

Induktive Logik und Wahrscheinlichkeit

Author: Rudolf Carnap

Publisher: Springer-Verlag

ISBN: 3709131421

Category: Juvenile Nonfiction

Page: 262

View: 1768

Dieses Buch stellt eine neue, von CARNAP entwickelte Theorie der Induktion und Wahrscheinlichkeit dar, die durch die folgenden grund legenden Auffassungen charakterisiert ist. 1. Jedes induktive Schließen, im weiten Sinne des nichtdeduktiven oder nichtdemonstrativen Schlu߭ folgerns, ist ein Schließen auf Grund von Wahrscheinlichkeit. 2. Daher ist die induktive Logik als Theorie von den Prinzipien des induktiven Schließens dasselbe wie Wahrscheinlichkeitslogik. 3. Der Begriff der Wahrscheinlichkeit, der als Grundbegriff der induktiven Logik dienen soll, ist eine logische Relation zwischen zwei Aussagen oder Sätzen, näm lich der Grad der Bestätigung einer Hypothese auf der Grundlage gegebe ner Prämissen. 4. Der sogenannte Häufigkeitsbegriff der Wahrschein lichkeit, wie er in statistischen Untersuchungen verwendet wird, ist zwar an und für sich ein wichtiger wissenschaftlicher Begriff, als Grundbegriff der induktiven Logik jedoch unbrauchbar. 5. Alle Prinzipien und Lehr sätze der induktiven Logik sind analytisch. 6. Daher hängt die Gültig keit des induktiven Schließens nicht von irgendwelchen synthetischen Voraussetzungen ab, wie etwa dem vielumstrittenen Prinzip der Gleich förmigkeit der Welt. Die erste Aufgabe dieses Buches ist die Erörterung der allgemeinen philosophischen Probleme betreffend die Natur der Wahrscheinlichkeit und des induktiven Schließens, die uns zu den eben erwähnten Auffassun gen führen wird. Das zweite Ziel ist der tatsächliche Aufbau eines Systems der induktiven Logik, einer Theorie, die auf den angeführten Prinzipien beruht. Ein besonderes Augenmerk wurde in diesem Buch darauf gelegt, die intuitive philosophische Grundlegung klar von dem technischen Aufbau des Systems der induktiven Logik zu trennen.

The Scientific Letters and Papers of James Clerk Maxwell:

Author: James Clerk Maxwell

Publisher: CUP Archive

ISBN: 9780521256261

Category: Science

Page: 1029

View: 4618

This is a comprehensive edition of Maxwell's manuscript papers published virtually complete and largely for the first time. Maxwell's work was of central importance in establishing and developing the major themes of the physics of the nineteenth century: his theory of the electromagnetic field and the electromagnetic theory of light and his special place in the history of physics. His fecundity of imagination and the sophistication of his examination of the foundations of physics give particular interest and importance to his writings. Volume II: 1862-1873 contains texts which illuminate Maxwell's scientific maturity. In this period he wrote the classic works on field physics and statistical molecular theory which established his unique status in the history of science. His important correspondence with Thomson and Tait provides remarkable insight into the major themes of his physics and the writing of his seminal Treatise on Electricity and Magnetism (1873).

Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 1366

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

A Boole Anthology

Recent and Classical Studies in the Logic of George Boole

Author: James Gasser

Publisher: Springer Science & Business Media

ISBN: 9780792363804

Category: History

Page: 336

View: 8694

Modern mathematical logic would not exist without the analytical tools first developed by George Boole in The Mathematical Analysis of Logic and The Laws of Thought. The influence of the Boolean school on the development of logic, always recognised but long underestimated, has recently become a major research topic. This collection is the first anthology of works on Boole. It contains two works published in 1865, the year of Boole's death, but never reprinted, as well as several classic studies of recent decades and ten original contributions appearing here for the first time. From the programme of the English Algebraic School to Boole's use of operator methods, from the problem of interpretability to that of psychologism, a full range of issues is covered. The Boole Anthology is indispensable to Boole studies and will remain so for years to come.

NMR Quantum Information Processing

Author: Ivan Oliveira,Roberto Sarthour Jr.,Tito Bonagamba,Eduardo Azevedo,Jair C. C. Freitas

Publisher: Elsevier

ISBN: 9780080497525

Category: Science

Page: 264

View: 9475

Quantum Computation and Quantum Information (QIP) deals with the identification and use of quantum resources for information processing. This includes three main branches of investigation: quantum algorithm design, quantum simulation and quantum communication, including quantum cryptography. Along the past few years, QIP has become one of the most active area of research in both, theoretical and experimental physics, attracting students and researchers fascinated, not only by the potential practical applications of quantum computers, but also by the possibility of studying fundamental physics at the deepest level of quantum phenomena. NMR Quantum Computation and Quantum Information Processing describes the fundamentals of NMR QIP, and the main developments which can lead to a large-scale quantum processor. The text starts with a general chapter on the interesting topic of the physics of computation. The very first ideas which sparkled the development of QIP came from basic considerations of the physical processes underlying computational actions. In Chapter 2 it is made an introduction to NMR, including the hardware and other experimental aspects of the technique. In Chapter 3 we revise the fundamentals of Quantum Computation and Quantum Information. The chapter is very much based on the extraordinary book of Michael A. Nielsen and Isaac L. Chuang, with an upgrade containing some of the latest developments, such as QIP in phase space, and telecloning. Chapter 4 describes how NMR generates quantum logic gates from radiofrequency pulses, upon which quantum protocols are built. It also describes the important technique of Quantum State Tomography for both, quadrupole and spin 1/2 nuclei. Chapter 5 describes some of the main experiments of quantum algorithm implementation by NMR, quantum simulation and QIP in phase space. The important issue of entanglement in NMR QIP experiments is discussed in Chapter 6. This has been a particularly exciting topic in the literature. The chapter contains a discussion on the theoretical aspects of NMR entanglement, as well as some of the main experiments where this phenomenon is reported. Finally, Chapter 7 is an attempt to address the future of NMR QIP, based in very recent developments in nanofabrication and single-spin detection experiments. Each chapter is followed by a number of problems and solutions. * Presents a large number of problems with solutions, ideal for students * Brings together topics in different areas: NMR, nanotechnology, quantum computation * Extensive references


A Hands-on Approach

Author: Michael R. W. Dawson

Publisher: John Wiley & Sons

ISBN: 1405143894

Category: Psychology

Page: 208

View: 4677

Connectionism is a “hands on” introduction toconnectionist modeling through practical exercises in differenttypes of connectionist architectures. explores three different types of connectionist architectures– distributed associative memory, perceptron, and multilayerperceptron provides a brief overview of each architecture, a detailedintroduction on how to use a program to explore this network, and aseries of practical exercises that are designed to highlight theadvantages, and disadvantages, of each accompanied by a website at that includespractice exercises and software, as well as the files and blankexercise sheets required for performing the exercises designed to be used as a stand-alone volume or alongsideMinds and Machines: Connectionism and Psychological Modeling(by Michael R.W. Dawson, Blackwell 2004)

A Transition to Advanced Mathematics

A Survey Course

Author: William Johnston,Alex McAllister

Publisher: Oxford University Press

ISBN: 9780199718665

Category: Mathematics

Page: 768

View: 857

A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.

George Boole

Selected Manuscripts on Logic and its Philosophy

Author: Ivor Grattan-Guinness,Gerard Bornet

Publisher: Springer Science & Business Media

ISBN: 9783764354565

Category: Mathematics

Page: 236

View: 1854

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day. The utility of "Boolean algebra" in computing has greatly increased curiosity in the nature and extent of his achievements. His work is most accessible in his two books on logic, "A mathematical analysis of logic" (1947) and "An investigation of the laws of thought" (1954). But at various times he wrote manuscript essays, especially after the publication of the second book; several were intended for a non-technical work, "The Philosophy of logic", which he was not able to complete. This volume contains an edited selection which not only relates them to Boole's publications and the historical context of his time, but also describes their strange history of family, followers and scholars have treid to confect an edition. The book will appeal to logicians, mathematicians and philosophers, and those interested in the histories of the corresponding subjects; and also students of the early Victorian Britain in which they were written.

The Religion of Technology

The Divinity of Man and the Spirit of Invention

Author: David F Noble

Publisher: Knopf

ISBN: 0307828530

Category: Technology & Engineering

Page: 273

View: 4809

Arguing against the widely held belief that technology and religion are at war with each other, David F. Noble's groundbreaking book reveals the religious roots and spirit of Western technology. It links the technological enthusiasms of the present day with the ancient and enduring Christian expectation of recovering humankind's lost divinity. Covering a period of a thousand years, Noble traces the evolution of the Western idea of technological development from the ninth century, when the useful arts became connected to the concept of redemption, up to the twentieth, when humans began to exercise God-like knowledge and powers. Noble describes how technological advance accelerated at the very point when it was invested with spiritual significance. By examining the imaginings of monks, explorers, magi, scientists, Freemasons, and engineers, this historical account brings to light an other-worldly inspiration behind the apparently worldly endeavors by which we habitually define Western civilization. Thus we see that Isaac Newton devoted his lifetime to the interpretation of prophecy. Joseph Priestley was the discoverer of oxygen and a founder of Unitarianism. Freemasons were early advocates of industrialization and the fathers of the engineering profession. Wernher von Braun saw spaceflight as a millenarian new beginning for humankind. The narrative moves into our own time through the technological enterprises of the last half of the twentieth century: nuclear weapons, manned space exploration, Artificial Intelligence, and genetic engineering. Here the book suggests that the convergence of technology and religion has outlived its usefulness, that though it once contributed to human well-being, it has now become a threat to our survival. Viewed at the dawn of the new millennium, the technological means upon which we have come to rely for the preservation and enlargement of our lives betray an increasing impatience with life and a disdainful disregard for mortal needs. David F. Noble thus contends that we must collectively strive to disabuse ourselves of the inherited religion of technology and begin rigorously to re-examine our enchantment with unregulated technological advance.

Statisticians of the Centuries

Author: C.C. Heyde,E. Seneta

Publisher: Springer Science & Business Media

ISBN: 9780387953298

Category: Mathematics

Page: 500

View: 5473

Written by leading statisticians and probabilists, this volume consists of 104 biographical articles on eminent contributors to statistical and probabilistic ideas born prior to the 20th Century. Among the statisticians covered are Fermat, Pascal, Huygens, Neumann, Bernoulli, Bayes, Laplace, Legendre, Gauss, Poisson, Pareto, Markov, Bachelier, Borel, and many more.

Temporal Logic

From Ancient Ideas to Artificial Intelligence

Author: Peter Øhrstrøm,Per Hasle

Publisher: Springer Science & Business Media

ISBN: 0585374635

Category: Philosophy

Page: 416

View: 6288

Temporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole.

The Age of Spiritual Machines

When Computers Exceed Human Intelligence

Author: Ray Kurzweil

Publisher: Penguin

ISBN: 9781101077887

Category: Computers

Page: 400

View: 4434

Ray Kurzweil is the inventor of the most innovative and compelling technology of our era, an international authority on artificial intelligence, and one of our greatest living visionaries. Now he offers a framework for envisioning the twenty-first century--an age in which the marriage of human sensitivity and artificial intelligence fundamentally alters and improves the way we live. Kurzweil's prophetic blueprint for the future takes us through the advances that inexorably result in computers exceeding the memory capacity and computational ability of the human brain by the year 2020 (with human-level capabilities not far behind); in relationships with automated personalities who will be our teachers, companions, and lovers; and in information fed straight into our brains along direct neural pathways. Optimistic and challenging, thought-provoking and engaging, The Age of Spiritual Machines is the ultimate guide on our road into the next century. From the Trade Paperback edition.

From Peirce to Skolem

A Neglected Chapter in the History of Logic

Author: Geraldine Brady

Publisher: Elsevier

ISBN: 9780080532028

Category: Computers

Page: 480

View: 1280

This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schröder, Leopold Löwenheim, and Thoralf Skolem. As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.

The Oxford Handbook of Process Philosophy and Organization Studies

Author: Jenny Helin,Tor Hernes,Daniel Hjorth,Robin Holt

Publisher: OUP Oxford

ISBN: 0191648108

Category: Business & Economics

Page: 648

View: 7677

Process approaches to organization studies focus on flow, activities, and evolution, understanding organizations and organizing as processes in the making. They stand in contrast to positivist approaches that see organizations and phenomena as fixed, static, and measurable. Process approaches draw on a range of ideas and philosophies. The Handbook examines 34 philosophers and social theorists, both those commonly linked to process thinking, such as Whitehead, Bergson and James, and those that are not as often addressed from a process perspective such as Dilthey and Tarde. Each chapter addresses the background and context of this thinker, their work (with a focus on the processual elements), and the potential contribution to organization and management research. For students and scholars in the field of Organization Studies this book is an entry point into the work of philosophical thinkers and social theorists for whom the world is far from being a solid place.

Rules for Reasoning

Author: Richard E. Nisbett

Publisher: Psychology Press

ISBN: 1134775539

Category: Psychology

Page: 432

View: 7856

This book examines two questions: Do people make use of abstract rules such as logical and statistical rules when making inferences in everyday life? Can such abstract rules be changed by training? Contrary to the spirit of reductionist theories from behaviorism to connectionism, there is ample evidence that people do make use of abstract rules of inference -- including rules of logic, statistics, causal deduction, and cost-benefit analysis. Such rules, moreover, are easily alterable by instruction as it occurs in classrooms and in brief laboratory training sessions. The fact that purely formal training can alter them and that those taught in one content domain can "escape" to a quite different domain for which they are also highly applicable shows that the rules are highly abstract. The major implication for cognitive science is that people are capable of operating with abstract rules even for concrete, mundane tasks; therefore, any realistic model of human inferential capacity must reflect this fact. The major implication for education is that people can be far more broadly influenced by training than is generally supposed. At high levels of formality and abstraction, relatively brief training can alter the nature of problem-solving for an infinite number of content domains.

Exzentrische Paradoxie

Sätze zum Jenseits von Differenz und Indifferenz

Author: Bernd Ternes

Publisher: Tectum Verlag DE

ISBN: 9783828884915

Category: Differentiation (Sociology)

Page: 233

View: 1819


The Britannica Guide to Algebra and Trigonometry

Author: Britannica Educational Publishing

Publisher: Britannica Educational Publishing

ISBN: 1615302190

Category: Juvenile Nonfiction

Page: 288

View: 4905

Calculating and manipulating the unknown has been the enterprise of the field of algebra since its earliest inception in Babylon and ancient Egypt. Trigonometry draws on principles presented in algebra and uses angle measurements to elaborate on geometric calculations. Essential to further mathematical and scientific study, both algebra and trigonometry provide crucial tools in managing variables and understanding the relationships between them. This volume presents the fundamentals of these fascinating areas of mathematics while chronicling their respective histories.