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Guided tour of Logic I: Tools for Thinking, with sample chapters

A selection of sample chapters is introduced below, with context provided by a brief description of the program's topic sequence.

For a more detailed topic listing, you may want to view the Table of Contents
from the teacher’s manual. (The teacher's manual has all the same chapter and section titles as the student book, so the teacher's manual table of contents shows you the topic sequence for the student book as well.)

Introduction to logic  

Many users of Logic I: Tools for Thinking are new to logic. Logic is a big field, and the sheer variety of logic topics chosen for inclusion in this or that logic textbook can be a bit bewildering. Our Introduction to Logic from the teacher's manual will be helpful for users of any logic textbook. It covers such topics as what is logic, what are the parts or branches of logic, how should Christians view logic, and why study logic. It also features an annotated bibliography of logic programs.

Reasoning and logic

How are the students of Logic I: Tools for Thinking introduced to logic? After studying Chapter 1, which gets them thinking about reasoning, they meet a definition of logic in Chapter 2. They also encounter the organizing metaphor for this book. Logic is presented as a toolbox, containing a wide variety of tools, each of which is used for a specific purpose on a specific kind of material.

Statements and logical operators  

Chapters 4 through 13 develop tools for use on two kinds of material: statements and logical operators. Logical operator may not be a term familiar to you, but actually, you know many logical operators already. For example, the conjunction operator is commonly expressed by the English word "and." The sentence "Parsnip is gray and Parsnip is fuzzy" contains a conjunction operator.

Chapter 10 presents a technique for telling whether a statement that contains logical operators is true or false. It employs a tool, introduced in Chapter 7, called a Parsnip tree (officially called a parse tree, but renamed in this book in honor of our cat Parsnip Poffle-Hoover). Chapter 10 of the Teacher's Manual comments on Chapter 10 of the student textbook, and provides exercise solutions.

Moleculan, or the sentential calculus

On the foundation laid in Chapters 4 through 13, Chapters 14 through 26 present a system of symbolic logic for use on statements that contain logical operators. Because such statements are called molecular statements, and because our other cat is named Tiger Molecule, the book refers to this system as Moleculan. (It is more commonly known as the sentential calculus, the propositional calculus, sentence logic, or propositional logic.)

In this part of the book, the students learn the grammar of the Moleculan language, and they gain experience translating from English to Moleculan and vice versa. This focus on translation into and out of Moleculan is a distinctive and important feature of Logic I: Tools for Thinking. Students also learn how to tell whether a given Moleculan sentence is true or false, using a truth table. In Chapter 19, they encounter tautologies, sentences that are always true, and learn how to determine whether a certain sentence is a tautology. (Keep in mind as you look at Chapter 19 that the student who has been working his way through all the chapters is already familiar with much in the chapter that you may find unfamiliar or perplexing at first glance.)

Arguments in Moleculan

Next the students meet arguments, a very important class of objects on which logic tools can be used. They learn what a valid argument is, and they learn to test Moleculan arguments for validity, using truth tables. They also encounter a sizable number of common argument forms, or patterns of argumentation that one meets frequently.

Informal logic

Moleculan is an example of formal logic. Formal logic is useful in such areas as mathematics and computer programming (not to mention deciphering tax instructions!) Informal logic is more useful in everyday life, and so in Chapters 27 through 31 the book shifts its focus to some important kinds of informal arguments. Chapter 27 connects this new focus to what has come before, by distinguishing among deductive, inductive and conductive arguments. Chapter 28 and Chapter 29 present the appeal to authority. (And here's Chapter 28 of the Teacher's Manual.) Chapter 30 presents the argument from analogy. In Chapter 31, students meet the inductive generalization. Then in Chapters 32-33, they begin their study of questions, which present an interesting set of logical issues all their own.

Informal arguments have a very different feel from formal arguments, and analyzing them calls upon students' wisdom in a way that formal arguments do not. But developing wisdom—rather than mere mechanical reasoning skills, as valuable as they are in their place—is what we're aiming for, and so the extra effort is abundantly repaid.

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