Book Title: An Introduction to Logic

Book Description

This course introduces the main types of logical reasoning. Studying logic provides brain fitness and awareness training to support life as a responsible citizen and consumer in a world where misinformation and enticing arguments are widespread. Throughout the book, interactive exercises are included for learners to check their understanding with immediate feedback. Selected topics offer non-interactive practice assignments for applying skills.

Logic Fundamentals are covered in the two initial learning modules.

• Module 1: The Basics of Logical Analysis – Arguments are the fundamental unit of logical reasoning. In this module, we learn about the components and basic structure of arguments, how to recognize arguments in ordinary language and distinguish arguments from explanations. The essential features of deductive and inductive reasoning are introduced, along with the concepts of validity, soundness, and logical strength.
• Module 2: Language and Informal Fallacies – Language is messy. In this module, we start by exploring some frailties and imprecision of ordinary language that contribute to faulty reasoning. Then we work with fallacies – arguments with defects. The distinction is made between formal and informal fallacies, with detailed focus on informal fallacies that make arguments and claims incorrect but often, nevertheless, persuasive.

Deductive Logic is the topic of the next two modules, each of which involves a unique approach for evaluating deductive arguments. In effect, we will see two different “deductive logics”. Each will have its own method for accomplishing the same goal — evaluating deductive arguments to determine whether they are valid or invalid.

• Module 3: Aristotelian Logic – Aristotelian Logic is the first of two “deductive logics” to be addressed. The four categorical proposition types are explored in depth, and Venn diagrams are used to demonstrate relationships between categories, or classes of things. The Square of Opposition and operations that can be performed on categorical propositions demonstrate how inferences can be drawn when the truth value of a particular type of categorical proposition is known. Problems that arise from categories with no members (empty classes) are explored. And finally, Venn diagrams are used to demonstrate the validity of standard-form categorical syllogisms.
• Module 4: Sentential Logic – Sentential Logic presents a second deductive logic that can be applied to a wider range of argument forms than Aristotelian logic. We learn to translate natural-language sentences and arguments to a symbolic language and use truth tables to determine the validity status of the symbolic-language argument forms.

Inductive Reasoning is covered in the final three modules, each of which examines a specific type of inductive reasoning that has its own useful applications. These reasoning patterns are common ways of thinking that many of us use routinely.

• Module 5: Analogical Reasoning – Analogies are similarities between a known set of circumstances and others that we’re seeking to understand more fully. We apply a standard pattern to ordinary-language argument-from-analogy to identify analogical components. Criteria for assessing strength and weakness of analogical arguments are presented, and the use of analogical arguments is demonstrated as a strategy for refuting bad arguments we hear. And finally, the analogical mechanisms that support legal decisions are explored.
• Module 6: Causal Reasoning – Causal arguments make claims about causes and effects. The distinction between sufficient causes and necessary causes is explored. Patterns of reasoning identified and cataloged by John Stuart Mill are presented as methods for discovering the causes of natural phenomena, and some cautionary limits are identified for using certain methods.
• Module 7: Hypothetical Reasoning and Science – Hypothetical reasoning is an essential strategy in scientific discovery. This general method is compared to the inductive method delineated by Sir Francis Bacon. We focus on the basic steps of the hypothetical method. Conditional (hypothetical) statements are used as the logical building block of hypothetical reasoning, and we refer back to both correct and fallacious deductive argument forms that are integral to the hypothetical method for testing scientific hypotheses. We consider the possibility and criteria for acceptance of hypotheses as working theories, despite lack of certainty (in the deductive sense) that is available with hypothetical (inductive!) reasoning.