Some of our earliest experiences of the conclusive force of an argument come from school mathematics: faced with a mathematical proof, we cannot deny the conclusion once the premises have been accepted. Behind such arguments lies a more general pattern of 'demonstrative arguments' that is studied in the science of logic. Logical reasoning is applied at all levels, from everyday life to advanced sciences, and a remarkable level of complexity is achieved in everyday logical reasoning, even if the principles behind it remain intuitive. Jan von Plato provides an accessible but rigorous introduction to an important aspect of contemporary logic: its deductive machinery. He shows that when the forms of logical reasoning are analysed, it turns out that a limited set of first principles can represent any logical argument. His book will be valuable for students of logic, mathematics and computer science.
Author: Jan von Plato
Publisher: Cambridge University Press
Author: Richard Whately (abp. of Dublin.)
Author: Noah Knowles Davis
Das Buch ist die deutsche Übersetzung des Standardwerkes der Stanforder Professoren Michael R. Genesereth und Nils J. Nilsson.Im Unterschied zu deutschen Lehrbüchern der Informatik zeichnet sich das Buch dadurch aus, daß es einen gut lesbaren Überblick gibt, ohne allzu formalistisch zu werden, gleichwohl aber von hohem Niveau ist und die Ergebnisse jüngster Forschung berücksichtigt. Das Buch empfiehlt sich sowohl für Studenten und Dozenten der Inf ormatik, aber auch für Forscher aus anderen Gebieten, die von den Grundlagen der Künstlichen Intelligenz profitieren möchten.
Author: Nils J. Nilsson
Category: Technology & Engineering
Logik ist die Basis der Wissenschaft, aber auch eine Brücke zwischen Wissenschaft und Alltag, denn die Grundlagen sind einfach logisch. Doch so einfach sie auf den ersten Blick scheint, so anspruchsvoll ist sie im Detail. "Logik kompakt für Dummies" führt Sie systematisch und so einfach wie möglich in dieses Teilgebiet von Mathematik und Philosophie ein. Dabei arbeitet Mark Zegarelli mit anschaulichen Beispielen und schafft es so, dieses abstrakte Thema nicht nur verständlich zu erklären, sondern auch Wert und Nutzen der Logik aufzuzeigen.
Publisher: John Wiley & Sons
Dugald Stewart was appointed assistant professor of mathematics in the University of Edinburgh in 1772, aged only 19. He became one of the most influential academics in the eighteenth- and nineteenth-century European ‘Republic of Letters’. Both Stewart’s contemporaries and modern scholars have recognised the impact his influential figure had over many young minds. He was one of the leading figures of the Scottish Common Sense school, a name by which we are used to identifying the philosophical tradition headed by Thomas Reid. The selection given here departs in some ways from Stewart’s own division of the subject, and aims to reflect the logical priority of each discipline, a priority which Stewart himself seems to give in the internal development of his ‘system’.
Selected Philosophical Writings
Author: Emanuele Levi Mortera
Publisher: Andrews UK Limited
With Imprimatur. Introduction 1. Definition of Logic. -- Logic is the systematic study of the order to be observed in judging, reasoning, and other processes of thought in order to arrive at the knowledge of truth. This definition shows us: (1) the materials (material cause) of the logical order; (2) their elaboration (formal cause) (3) the purpose of this elaboration (final cause). 2. Materials of Logical Order. -- In some sense, these materials are acts of the mind, like apprehension, judgment, ratiocination (reasoning); but strictly speaking, only apprehensions are the material object of logical order (3). (1) By apprehension the mind represents to itself one thing or many things, without either affirming or denying anything. Concepts; the product of apprehension, are expressed by names or terms. (2) To establish a relation of identity or non-identity, of agreement or non-agreement, between the objects of two concepts, in affirming or denying one object of another is to judge. A judgment is expressed in a proposition. (3) To reason is to combine two or more judgments so as to form a new one. The complete ordinary expression of this simplest exercise of reasoning is the syllogism. 3. The Formal Cause of the Logical Order. -- The formal object of logic, or the point of view from which logic regards the acts of the mind, is their adaptability to certain processes of thought which are called either particular sciences or philosophy. These processes imply stages. The mind must grasp the numerous aspects of reality one after another before coordinating the fragmentary explications. Judgment is the first step in combining ideas; judgments in their turn become the materials of reasoning; an isolated piece of reasoning does not suffice to produce adequate knowledge of things, but several reasonings become materials of a scientific system. This rational arrangement of ideas constitutes the logical order properly so called: "the order which reason constitutes for its own acts". 4. Difference between Psychology and Logic. -- Many different sciences may be concerned with one and the same subject, if they study different properties in it, and, consequently, consider it from different points of view. They are then said to have a common (that is, undetermined) object, but each has its own formal (or determined) object. Psychology, too, has in part for its (material) object the act of human reason, but it does not study them under the same aspect (formal object) as logic does. Psychology sees in them vital acts, of which it seeks the nature and origin. Logic considers them in so far as they are cognitions of objects, objective representations, abstract and universal, furnishing the matter of the relations which reason formulates in judgments and reasonings, and arranges in a scientific system. In psychology, as in all the sciences of the real, order is the necessary condition of science; but logic has this order for its object. Its proper object is the form itself of this scientific construction.
Author: Cardinal Mercier
Publisher: Createspace Independent Publishing Platform
Der Autor hat es in bewundernswerter Weise geschafft, anhand einer Vielzahl bekannter Spiele von Schach über Poker bis Mastermind einen kleinen Einblick in mathematisch so anspruchsvolle Gebiete wie Wahrscheinlichkeitsrechnung, Optimierungstheorie, Kombinatorik und Spieltheorie zu geben. Hierbei werden so gut wie keine mathematischen Vorkenntnisse erwartet, so dass man das Buch auch interessierten Nichtmathematikern wärmstens empfehlen kann. Anspruchsvolle und unerschrockene Leserinnen und Leser werden in den sehr lesenswerten Anmerkungen am Schluss des Buches Hinweise auf weiterführende Literatur finden, anhand derer sie auch tiefer in mathematische Aspekte eindringen können. Ein schönes Buch, ohne wirkliche Konkurrenz auf dem deutschen Markt, und dies zu einem vernünftigen Preis. Zentralblatt MATH Database 1931 - 2002
Mathematik im Spiel - Methoden, Ergebnisse und Grenzen
Author: Jörg Bewersdorff
Mr. Rush Limbaugh may be our most influential media personality, but he is not the most clear-thinking. Logic and Mr. Limbaugh not only exposes the fallacies in Mr. Limbaugh's persuasive arguments - it also gives a hilarious introduction to Logic, the science of correct reasoning.
A Dittohead's Guide to Fallacious Reasoning
Author: Ray Perkins (Jr.)
Publisher: Open Court Publishing
Diagrams are widely used in reasoning about problems in physics, mathematics, and logic, but have traditionally been considered to be only heuristic tools and not valid elements of mathematical proof. This book challenges this prejudice against visualization in the history of logic and mathematics provides a formal foundation for work on natural reasoning in a visual mode. The author presents Venn diagrams as a formal system of representation and specifies rules of transformation that make this system sound and complete. The soundness of the diagrammatic system refutes the contention that graphical representation is misleading in reasoning. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems.This pathbreaking book will have important influence on research in logic, philosophy, and knowledge representation.
Author: Sun-Joo Shin
Publisher: Cambridge University Press
Increase your score on the LSAT If you're preparing for law school, your single biggest hurdleis the Law School Admission Test or LSAT. This three and a halfhour exam consisting of five multiple choice sections and one timedwriting sample can make or break your legal aspirations. Fortunately, LSAT For Dummies, Premier PLUS 2ndEdition—now with access to practice tests online preparesyou for the LSAT by giving you proven test-taking strategies andample practice opportunities. From the book you'll gain the vitaltools you need to understand the reasoning behind analyticalreasoning, get a handle on logical reasoning, flaunt your talent inthe writing section, master reading comprehension, and much more.Plus, go online and study wherever and whenever with free access toadditional LSAT practice opportunities; and the ability to createcustomized practice in the subjects you need to study the most. Includes proven strategies to help you identify common pitfallsand increase your score Lets you test your skills with practice problems for everyquestion type Premier edition offers additional test-taking opportunitiesonline If you're an aspiring lawyer and want to put your best footforward, LSAT For Dummies, Premier 2nd Edition has youcovered.
Author: Lisa Zimmer Hatch,Scott A. Hatch,Amy Hackney Blackwell
Publisher: John Wiley & Sons
Category: Study Aids
This book introduces a new form of argumentative analysis: rhetorical heuremes. The method applies the concepts of heuristic thinking, probability, and contingency in order to develop a better understanding of complex arguments in classical oratory. A new theory is required because Greek and Roman rhetoric cannot provide detailed answers to problems of strategic argumentation in the analysis of speeches. Building on scholarship in Ciceronian oratory, this book moves beyond the extant terminology and employs a concept of heuristic reasoning derived from the psychology of decision making and mathematical problem solving. The author analyses selected passages from Cicero’s forensic speeches where arguments of probability are deployed, and shows that the Sophistic concept of probability can link ancient rhetoric and modern theories of argumentation. Six groups of heuremes are identified, each of which represents a form of probabilistic reasoning by which the orator plays upon the perception of the jurors.
Author: Gábor Tahin
Publisher: Springer Science & Business Media
Background and techniques for formalizing deductive argumentation in a logic-based framework for artificial intelligence.
Author: Philippe Besnard,Anthony Hunter
Publisher: Mit Press
The core of Volume 3 consists of lecture notes for seven sets of lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and 1926. These texts make possible for the first time a detailed reconstruction of the rapid development of Hilbert’s foundational thought during this period, and show the increasing dominance of the metamathematical perspective in his logical work: the emergence of modern mathematical logic; the explicit raising of questions of completeness, consistency and decidability for logical systems; the investigation of the relative strengths of various logical calculi; the birth and evolution of proof theory, and the parallel emergence of Hilbert’s finitist standpoint. The lecture notes are accompanied by numerous supplementary documents, both published and unpublished, including a complete version of Bernays’s Habilitationschrift of 1918, the text of the first edition of Hilbert and Ackermann’s Grundzüge der theoretischen Logik (1928), and several shorter lectures by Hilbert from the later 1920s. These documents, which provide the background to Hilbert and Bernays’s monumental Grundlagen der Mathematik (1934, 1938), are essential for understanding the development of modern mathematical logic, and for reconstructing the interactions between Hilbert, Bernays, Brouwer, and Weyl in the philosophy of mathematics.
Author: William Ewald,Wilfried Sieg
adapted to the capacity of younger students : and designed for academies and the higher classes of common schools
Author: Charles Kittredge True
We succeed in business and in life when we influence how others think, feel, and act: getting them to accept our point of view, follow our lead, join our cause, feel our excitement, or buy our products and services. The act of influencing is such a part of our daily lives that we often don't even realize when we (or others) are doing it. But to succeed, we need to know how influence works...and how to use it. Influencing effectively requires adaptability, perceptiveness, and insight into other people and cultures. Based on 20 years of research, Elements of Influence shows readers how to: * Understand why people allow themselves to be influenced-and why they resist * Choose the right approach for each situation * Be influential when they have no formal authority * Succeed in every kind of organization-even in other countries Filled with exercises and practical applications, this book shows how anyone can increase his or her influence to achieve greater success.
The Art of Getting Others to Follow Your Lead
Author: Terry Bacon
Category: Business & Economics