Fundamental Methods of Logic

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Matthew Knachel, University of Wisconsin - Milwaukee

Pub Date: 2017

ISBN 13: 978-0-9961502-2-4

Publisher: Independent

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Table of Contents

Chapter 1 - The Basics of Logical Analysis

  • I. What is Logic?
  • II. Basic Notions: Propositions and Arguments
  • III. Recognizing and Explicating Arguments
  • IV. Deductive and Inductive Arguments
  • V. Diagramming Arguments

Chapter 2 - Informal Logical Fallacies

  • I. Logical Fallacies: Formal and Informal
  • II. Fallacies of Distraction
  • III. Fallacies of Weak Induction
  • IV. Fallacies of Illicit Presumption
  • V. Fallacies of Linguistic Emphasis

Chapter 3 – Deductive Logic I: Aristotelian Logic

  • I. Deductive Logics
  • II. Classes and Categorical Propositions
  • III. The Square of Opposition
  • IV. Operations on Categorical Sentences
  • V. Problems with the Square of Opposition
  • VI. Categorical Syllogisms

Chapter 4 – Deductive Logic II: Sentential Logic

  • I. Why Another Deductive Logic?
  • II. Syntax of SL
  • III. Semantics of SL
  • IV. Translating from English into SL
  • V. Testing for Validity in SL

Chapter 5 – Inductive Logic I: Analogical and Causal Arguments

  • I. Inductive Logics
  • II. Arguments from Analogy
  • III. Causal Reasoning

Chapter 6 – Inductive Logic II: Probability and Statistics

  • I. The Probability Calculus
  • II. Probability and Decision-Making: Value and Utility
  • III. Probability and Belief: Bayesian Reasoning
  • IV. Basic Statistical Concepts and Techniques
  • V. How to Lie with Statistics

About the Book

Fundamental Methods of Logic is suitable for a one-semester introduction to logic/critical reasoning course. It covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill's Methods. Chapter Six covers basic probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.

About the Contributors


Matthew Knachel is Professor in the Philosophy department at University of Wisconsin - Milwaukee, Milwaukee, WI.