# 1.1: Logic As the Science of Argument

Adam is happy, or so I tell you. If you don't believe me, I try to convince you with an argument: Adam just got an 'A' on his logic exam. Anyone who gets an 'A' on an exam is happy. So Adam is happy. A logician would represent such an argument in this way:

(1) Premises a) Adam just got an 'A' on his logic exam.

b) Anyone who gets an 'A' on an exam is happy.

We ordinarily think of an argument as an attempt to convince someone of a conclusion by offering what a logician calls premises, that is, reasons for believing the conclusion. But in order to study arguments very generally, we will characterize them by saying:

An Argument is a collection of declarative sentences one of which is called the conclusion and the rest of which are called the premises.

An argument may have just one premise, or it may have many.

By declarative sentences, I mean those, such as 'Adam is happy.' or 'Grass is green.', which we use to make statements. Declarative sentences contrast with questions, commands, and exclamations, such as 'Is Adam happy?', 'Cheer up, Adam!' and 'Boy, is Adam happy!' Throughout this text I will deal only with declarative sentences; though if you continue your study of logic you will encounter such interesting topics as the logic of questions and the logic of commands.

For an argument to have any interest, not just any premises and conclusion will do. In any argument worth its name, we must have some connection or relation between the premises and conclusion, which you can think of intuitively in this way:

Ordinarily, the premises of an argument are supposed to support, or give us reasons, for believing the conclusion.

A good way of thinking about logic, when you are beginning to learn, is to say that logic is the study of this reason-giving connection. I like to say, more generally, that logic is the science of arguments. Logic sets out the important properties of arguments, especially the ways in which arguments can be good or bad. Along the way, logicians also study many things that are not themselves arguments or properties of arguments. These are things which we need to understand in order to understand arguments clearly or things which the study of arguments suggests as related interesting questions.

In order to see our subject matter more clearly, we need to distinguish between inductive and deductive arguments. Argument (1) is an example of a deductive argument. Compare (1) with the following:

(2) a) Adam has smiled a lot today.

b) Adam has not frowned at all today.

c) Adam has said many nice things to people today, and no unfriendly things.

The difference between arguments (1) and (2) is this: In (I), without fail, if the premises are true, the conclusion will also be true. I mean this in the following sense: It is not possible for the premises to be true and the conclusion false. Of course, the premises may well be false. (I, for one, would suspect premise (b) of argument (I).) But in any possible situation in which the premises are true, the conclusion will also be true.

In argument (2) the premises relate to the conclusion in a different way. If you believe the second argument's premises, you should take yourself to have at least some fairly good reasons for believing that the conclusion is true also. But, of course, the premises of (2) could be true and the conclusion nonetheless false. For example, the premises do not rule out the possibility that Adam is merely pretending to be happy.

Logicians mark this distinction with the following terminology:

• Valid Deductive Argument: An argument in which, without fail, if the premises are true, the conclusion will also be true.
• Good Inductive Argument: An argument in which the premises provide good reasons for believing the conclusion. In an inductive argument, the premises make the conclusion likely, but the conclusion might be false even if the premises are true.

What do we mean by calling an argument 'deductive' or 'inductive', without the qualifiers 'valid' or 'good'? Don't let anyone tell you that these terms have rigorous definitions. Rather,

We tend to call an argument 'Deductive' when we claim, or suggest, or just hope that it is deductively valid. And we tend to call an argument 'Inductive' when we want to acknowledge that it is not deductively valid but want its premises to aspire to making the conclusion likely.

In everyday life we don't use deductively valid arguments too often. Outside of certain technical studies, we intend most of our arguments as inductively good. In simple cases you understand inductive arguments clearly enough. But they can be a bear to evaluate. Even in the simple case of argument (2), if someone suggests that Adam is just faking happiness, your confidence in the argument may waver. How do you decide whether or not he is faking? The problem can become very difficult. In fact, there exists a great deal of practical wisdom about how to evaluate inductive arguments, but no one has been able to formulate an exact theory which tells us exactly when an inductive argument is really good.

In this respect, logicians understand deduction much better. Even in an introductory formal logic course, you can learn the rules which establish the deductive validity of a very wide and interesting class of arguments. And you can understand very precisely what this validity consists in and why the rules establish validity. To my mind, these facts provide the best reason for studying deductive logic: It is an interesting theory of a subject matter about which you can, in a few months, learn a great deal. Thus you will have the experience of finding out what it is like to understand a subject matter by learning a technical theory about that subject matter.

Studying formal logic also has other, more practical, attractions. Much of what you learn in this book will have direct application in mathematics, computer science, and philosophy. More generally, studying deductive logic can be an aid in clear thinking. The point is that, in order to make the nature of deductive validity very precise, we must leaq a way of making certain aspects of the content of sentences very precise. For this reason, learning deductive logic can pay big dividends in improving your clarity generally in arguing, speaking, writing, and thinking.

Exercise $$\PageIndex{1}$$

Explain in your own words what an argument is. Give an example of your own of an inductive argument and of a deductive argument. Explain why your example of an inductive argument is an inductive argument and why your example of a deductive argument is a deductive argument.

## Contributors

• Paul Teller (UC Davis). The Primer was published in 1989 by Prentice Hall, since acquired by Pearson Education. Pearson Education has allowed the Primer to go out of print and returned the copyright to Professor Teller who is happy to make it available without charge for instructional and educational use.