WHAT IS LOGIC?
Logic is the study of the principles of reason – these are the principles we use to make good arguments. We also use them to explain and analyze different things. In this course, we will see how the principles of reason are used to do all these things, but for the most part, we will study these principles to learn how they are used to make good arguments. Once we learn that, we will practice making all sorts of arguments with them, until we are very, very good at it.
WHAT IS AN ARGUMENT?
We use the principles of reason to make good arguments. But what is an argument? In one sense, of course, an argument is two or more people disagreeing about something – about what is true or false, or right or wrong, or what they should do – maybe even shouting at each other. But logicians use the term in a more basic sense, where you make an argue by giving reasons for believing something. The argument is the reasons you’re giving and the belief they are reasons for. Stated more precisely, an argument is a group of statements where some of them are claimed to be good reasons for believing that another one of them is true. For example, in arguing over who will win the World Series in baseball, you might say, “The Yankees have the best hitters of any team in baseball. Plus, they have strong pitching. So they’re definitely going to win the World Series this year.” That is an argument – two statements claiming to be good reasons for believing that another statement is true.
STATEMENTS
But, you might ask, what exactly is a statement? Basically, a statement is a claim that something is true. Declarative sentences are sentences make statements. That is, they are sentences that are true or false. Some sentences are neither true for false, such as questions (“How was the traffic?”) and commands (“Turn around and go back!”). So questions and commands are not statements. But declarative sentences are either true or false so they are statements.
Introduction: What Is Logic?
Chapter One: Basic Logical Concepts
Chapter Two: Categorical Logic
Chapter Three: Sentence Logic
Chapter Four: Predicate Logic
Chapter Five: Second Order Logic
PREMISES AND CONCLUSIONS
Arguments are said to have premises and conclusions. The statements of an argument that are claimed to be good reasons for believing that another statement is true are the argument’s premises. And the statement they are claimed to be good reasons for believing is the argument’s conclusion.
In the argument about baseball, “The Yankees have the best hitters of any team in baseball” is a premise in the argument. “They [the Yankees] have strong pitching” is a another premise. And the last sentence, “They’re going to win the World Series this year,” is the conclusion.
So we have arguments, which are groups of statements where some of the statements (the premises) are claimed to be good reasons for accepting another statement – the conclusion.
COMPOUND STATEMENTS
A single statement can contain simpler several statements as components of it. A statement containing several simpler statements as components is called a “compound statement.” For example, we could have stated the above argument by saying: “The Yankees have the best hitters of any team in baseball and they have strong pitching, so they are definitely going to win the World Series this year.” The argument is now expressed by a single sentence that contains all three statements of the argument – the two premises and the conclusion.
PREMISE-CONCLUSION ORDER
The above argument has the premises at the beginning of the argument and the conclusion last. However, a conclusion can come anywhere in an argument – at the beginning, at the end, or even in the middle.For example, we can also express the baseball argument with the conclusion at the beginning by saying: “The Yankees are definitely going to win the World Series this year, because they have the best hitters of any team in baseball and they also have strong pitching.”
TYPES OF ARGUMENTS
There are two basic types of arguments: deductive arguments and inductive arguments. Deductive arguments claim to establish their conclusion with certainty – that is, they claim that because the premises are true, the conclusion must be true. For example, the following argument is deductive: “If all math courses are difficult, and calculus is a math course, than it must be the case that calculus is difficult.” If the premises of this argument are true, the conclusion must be true.
Inductive arguments do not claim that because their premises are true, their conclusion must be true. Instead, they make the weaker claim that because their premises are true, their conclusion is probably true. Here is an example of an inductive argument: “If most people with ADHD are troublemakers, and Tom has ADHD, then Tom is probably a trouble maker, too.” Arguments like this that establish their conclusions only with some probability are inductive arguments.
INDICATOR WORDS
Arguments often contain “indicator words,” like therefore or thus. These two words indicate that the statement that follows them is the conclusion. For example, in the argument “All mammals have lungs and all dogs are mammals. Therefore, all dogs have lungs,” the word therefore indicates that the statement “all dogs have lungs” is the argument’s conclusion. Other words, like because, indicate that the statement that follows them is a premise. And inductive arguments often use the word probably to indicate that what follows it is the conclusion of an inductive argument. Finally, deductive arguments might preface a conclusion with “therefore, it must be the case that.” For example, the above deductive argument might be expressed like this: “All mammals have lungs, and all dogs are mammals. Therefore, it must be the case that all dogs have lungs.”
Now here’s the catch. A person might make an inductive argument, that is, an argument where the conclusion is merely probable. For example, “Every book I have ever looked at in this library is in English. Therefore, probably all the books in it are in English.” Yet the person making the argument, in order to be emphatic, might express it by saying: “Every book I have ever looked at in this library is in English. Therefore, it must be the case that all the books in it are in English.” But even if they say the conclusion must be true, it is really at best probable, and the argument is inductive anyway.
We will look at these ideas more closely soon and look at other types of arguments, but first let’s summarize what we have seen so far and do some exercises to practice using those ideas.
1. Logic is the study of the principles of reason. We use the principles of reason to make good arguments
2. An argument is a set of statements some of which are claimed to be good reasons for believing that another of them is true.
3. A statement is a claim that something is true or false.
4. Declarative sentences are sentences that claim to be either true or false. They express statements.
5. The word “proposition” is sometimes used instead of “statement.” We will use the two words interchangeably.
6. A deductive argument is an argument that claims to have established its conclusion conclusively and without doubt.
7. An inductive argument is an argument that claims to have established that its conclusion is probably, not conclusively, true.
I. The following 5 passages each contain one argument. State the conclusion of each argument.
1. Cigarettes are an addictive drug and addictive drugs should all be banned. So cigarette smoking should be banned.
2. All sugar products should be banned, because sugar is an addictive drug, and addictive drugs should all be banned.
3.
4. I don’t need an eraser. Erasers are for people who make mistakes, and I never make mistakes.
5. All gamblers are losers, so in a poker game, no one ever wins.
II. Say whether the following arguments are inductive or deductive.
1. All poodles are dogs, and all dogs have fleas. Therefore, it must be the case that all poodles have fleas.
2. Since all dogs have fleas on them, and you were just petting a dog, you probably have fleas on you too.
3. Since all dogs have fleas on them, and you were just petting a dog, it must be the case that you have fleas on you too.
4.
5.
III. Say which of the following sentences are statements and which are not statements.
1. Cell phones are changing the world.
2. Turn your cell phones off in class!
3. You should always answer your cell phone if it rings in class.
4. Why would anyone want to have a smart phone?
5. Flip phones are very retro-chic.
In the next section, we will look at a few dozen basic properties of arguments and statements, and learn them all.
