How Do We Reason?

An Introduction to Logic

Forrest E. Baird

• Publisher: IVP Academic
• Year: 2021
• ISBN:
  9780830855162
• Topic: Theology & Religion
• Subtopic: Philosophy of Religion

How do we think? What does a faithful use of logic look like?Without even pausing to think about it, we exercise our capacity for rational thought. But how exactly does logic work? What makes some arguments valid and others not?In this Questions in Christian Philosophy volume, philosopher Forrest Baird offers an introduction to logic. He considers the basic building blocks of human reason, including types of arguments, fallacies, syllogisms, symbols, and proofs, all of which are demonstrated with exercises for students throughout. In addition, he reflects on the relationship between the use of reason and the Christian faith.With this academic but accessible primer, readers will be introduced to the basics of logic—and encouraged to reason better.The Questions in Christian Philosophy Series features introductory textbooks that offer students a Christian perspective on the various branches of philosophy, enabling them as they seek to understand all facets of life including existence, knowledge, ethics, art, and more.

What is logic? In the broad sense, it is the study of the correct method of reasoning. But in a narrow sense, it is the study of the correct form of arguments. As a subject, logic is not nearly as difficult as many people think—and most people use it all the time. The problem is that language is so vague and serves so many functions that it is often difficult to find the form of an argument embedded within it. One of the chief tasks of logic is to find that form, examine it closely, and determine whether the argument is properly structured.

This book will begin by defining arguments: the parts of arguments, the kinds of arguments, and what makes for a good argument. After this brief introduction, we will look at “full-bodied” language as expressed in everyday sentences and the many ways it is used. We will examine the difference between form and function, between denotation and connotation, and learn to find the arguments embedded within the common uses of language. We will also take time to look at a number of common “informal fallacies.”

Next, we will start to look below the surface of everyday language by examining one very formal way of arguing: categorical syllogisms. These formal arguments will begin to show us the underlying logical structure of arguments as expressed in language. We will also learn how to determine whether these stylized arguments are correct, and we will learn to take ordinary language and turn it into these formal arguments.

In the final unit, we will examine the underlying form of arguments by using symbols. We will develop a set of rules for constructing a logic of sentences and find ways to evaluate these arguments. This will give us the skeleton, as it were, of the argument. We will conclude by going back to arguments in language and translating them into symbols to see how well they are constructed.

1.1 TERMS

Arguments. So what is an argument? In a famous Monty Python skit, Michael Palin goes into an “Argument Clinic.” There, he pays John Cleese to have an argument with him. After some typical Monty Python silliness, the two men get down to arguing:

Palin: I came here for a good argument.

Cleese: No you didn’t; no, you came here for an argument.

Palin: An argument isn’t just contradiction.

Cleese: It can be.

Palin: No it can’t. An argument is a connected series of statements to establish a proposition.

Cleese: No it isn’t.

Palin: Yes it is! It’s not just contradiction.

Cleese: Look, if I argue with you, I must take up a contrary position.

Palin: Yes, but that’s not just saying “No it isn’t.”

Cleese: Yes it is!

Palin: No it isn’t! An argument is an intellectual process. Contradiction is just the automatic gainsaying of any statement the other person makes.

Cleese: No it isn’t.

Palin: It is.

Cleese: Not at all.1

In the middle of this short excerpt from the interminable exchange, Palin gives a very good definition of an argument: “a connected series of statements to establish a proposition.” Notice there are three parts to this definition:

• 1. “statements”

These statements that are given as a reason to accept a certain proposition are called “premises.” All arguments have at least one premise or reason given for why one should accept something else.

• 2. “a proposition”

The proposition that the argument is attempting to establish is called the “conclusion.” This is what the speaker wants to prove.

• 3. “a connected series . . . to establish”

It is not enough to just have statements and propositions in order to have an argument—they must be connected in a certain way. Consider the following:

P₁ I am hungry

P₂ This is a pen

C Tomorrow is Tuesday2

While we have two statements and a proposition, this is clearly not an argument. What is missing? There is no connection here to establish the proposition “Tomorrow is Tuesday” on the basis of the previous two statements. The “connected series . . . to establish” is the part that makes an argument work. In fact, it is this third point that is the key to logic. Logic is not primarily concerned with the statements and propositions that make up an argument. (Are they true? False? Would most people accept them?) Instead logic is about the connections between these constituent parts of an argument. This connection is called inference, and it is what we will be trying to isolate and test throughout this book.

Propositions, statements, and sentences. The Monty Python skit uses different words for premises and conclusions: statements and propositions. But this is misleading. Both premises and conclusions are made from propositions. Further, statements are just one particular instance of a proposition expressed in a sentence. Let’s unpack this a little to get our definitions straight. What exactly is a proposition?

A proposition is an idea that is true or false.

Now a proposition is conveyed by a statement, but it is not exactly the same thing as a statement. For example, the statement

S1: “Abraham Lincoln is the president of the United States”

was true in 1864, but the same statement is false today. Statements, then, are bound by time, but propositions are not. When statement S1 was expressed in 1864, it was expressing the proposition “Abraham Lincoln is the president of the United States in 1864,” which is still true today. Similarly, the statement

S2: “This country has a president”

is true if you are in the United States, but false if you are visiting England. So statements are bound by place as well as time, but propositions are not. The proposition “The United States has a president” is true even if I h...