Introduction to Logic

Harry Gensler

• Publisher: Routledge
• Year: 2002
• ISBN:
  9781134588800
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Introduction to Logic offers one of the most clear, interesting and accessible introductions to what has long been considered one of the most challenging subjects in philosophy. Harry Gensler engages students with the basics of logic through practical examples and important arguments both in the history of philosophy and from contemporary philosophy. Using simple and manageable methods for testing arguments, students are led step-by-step to master the complexities of logic.
The companion LogiCola instructional program and various teaching aids (including a teacher's manual) are available from the book's website: www.routledge.com/textbooks/gensler_logic

CHAPTER 1
Introduction

Logic is about reasoning—about going from premises to a conclusion. As we begin our study of logic, we need to get clearer on what logic is and why it’s important. We also need to learn some concepts (like “valid” and “argument”) that are central to the study of logic.

1.1 Logic

Logic¹ can be defined as the analysis and appraisal of arguments. When you do logic, you try to clarify reasoning and separate good from bad reasoning. As you work through this book, you’ll examine philosophical reasoning on topics like free will and determinism, the existence of God, and the nature of morality. You’ll also study reasoning on backpacking, water pollution, football, Supreme Court decisions, and the Bible. You’ll come to see logic not as an irrelevant game with funny symbols, but rather as a useful tool to clarify and evaluate our reasoning—whether on everyday topics or on life’s deeper questions.

Why study logic? I can think of three main reasons. First, logic can be fun. Doing logic is like playing a game or doing puzzles; logic will challenge your thinking processes in new ways. The rigor of logical systems will likely fascinate you. Most people find logic enjoyable.

Second, logic can deepen your understanding of philosophy. Philosophy can be defined as reasoning about the ultimate questions of life. Philosophers ask questions like “Why accept or reject free will?,” “Can one prove or disprove God’s existence?,” and “How can one justify a moral belief?” If you don’t know any logic, you’ll have only a vague grasp of such issues; and you’ll lack the tools needed to understand and evaluate philosophical reasoning. If you’ve studied philosophy, you’ll likely recognize many of the pieces of philosophical reasoning in this book. If you haven’t studied philosophy, you’ll find this book a good introduction to the subject. In either case, you should get better at recognizing, understanding, and appraising philosophical reasoning.

Finally, logic can improve your analytical skills. While you’ve been reasoning about things all your life, this may be the first time that you focus on what reasoning is and try to become better at it. In most areas, it’s a big advantage to be able to reason clearly; logic promotes intellectual skills that are important in law, business, medicine, and any other area that involves thinking and reasoning. This book is crammed with exercises; look at these as puzzles designed to help you think more clearly and logically.

1.2 Valid arguments

I begin my basic logic course with a multiple-choice test. The test has ten problems, each giving information (premises) and asking what conclusion necessarily follows. The problems are easy, but most students get almost half of them wrong.¹ Here are two of the problems—with the right answers boxed:

If you overslept, you’ll be late

You aren’t late.

Therefore:

(a) You did over sleep.

(b) You didn’t oversleep.

(c) You’re late.

(d) None of these follows.

If you overslept, you’ll be late. You didn’t oversleep.

Therefore:

(a) You’re late.

(b) You aren’t late.

(c) You did oversleep.

(d) None of these follows.

While almost everyone gets the first problem right, many students wrongly pick “(b)” for the second problem. Here “You aren’t late” doesn’t necessary follow, since you might be late for some other reason; maybe your car didn’t start. Most students, once they grasp this point, will see that (b) is wrong.²

Untrained logical intuitions are often unreliable. But logical intuitions can be developed; yours will likely improve as you work through this book. You’ll also learn special techniques for testing arguments.

An argument, in the sense used in logic, is a set of statements consisting of premises and a conclusion; normally the premises give evidence for the conclusion. Arguments put into words a possible act of reasoning. Here’s an example of a valid argument (“∴” is for therefore):

Valid argument

If you overslept, you’ll be late. ➔ You aren’t late. ∴ You didn’t oversleep.

An argument is valid if it would be contradictory (impossible) to have the premises all true and conclusion false. In calling an argument valid, we aren’t saying whether the premises are true. We’re just saying that the conclusion follows from the premises—that if the premises were all true, then the conclusion also would have to be true. In saying this, we implicitly assume that there’s no shift in the meaning or reference of the terms; hence we must use “overslept,” “late,” and “you” in the same way throughout the argument.

Our argument is valid because of its logical form—its arrangement of logical notions (like “if-then” and “not”) and content phrases (like “You overslept” and “You’re late”). We can display an argument’s form by using words or symbols for logical notions, and letters for content phrases:

If you overslept, you’ll be late.	If A then B Valid
You aren’t late.	Not-B
∴ You didn’t oversleep.	∴ Not-A

Our argument is valid because its form is correct. If we take another argument of the same form, but substituting other ideas for “A” and “B,” then this second argument also will be valid. Here’s an example:

If you’re in France, you’re in Europe.	If A then B Valid
You aren’t in Europe.	Not-B
∴ You aren’t in France.	∴ Not-A

Logic studies forms of reasoning. The content can deal with anything—back-packing, mathematics, cooking, physics, ethics, or whatever. When you learn logic, you’re learning tools of reasoning that can be applied to any subject.

In our invalid example, the second premise denies the first part of the if-then (instead of the second); this small change makes all the difference:

If you overslept, you’ll be late.	If A then B Valid
You didn’t oversleep.	Not-A
∴ You aren’t late..	∴ Not-B

Intuitively, you might be late for some other reason—just as, in the following similar argument, you might be in Europe because you’re in Italy:

If you’re in France, you’re in Europe.	If A then B Valid
You aren’t in France.	Not-A
∴ You aren’t late..	∴ Not-B

1.3 Sound arguments

Logicians distinguish valid arguments from sound arguments:

An argument is valid if it would be contradictory to ha...