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Arguments, Premises, and Conclusions
HOW LOGICAL ARE YOU?
After a momentary absence, you return to your table in the library only to find your smartphone is missing. It was there just minutes earlier. You suspect the student sitting next to you took it. After all, she has a guilty look. Also, there is a bulge in her backpack about the size of your phone, and one of the pouches has a loose strap. Then you hear a “ring” come from the backpack—and it’s the same ringtone that you use on your phone. Which of these pieces of evidence best supports your suspicion?
Logic may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study of logic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.
An argument, in its simplest form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose of logic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad.
As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one’s parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A statement is a sentence that is either true or false—in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:
- Chocolate truffles are loaded with calories.
- Melatonin helps relieve jet lag.
- Political candidates always tell the complete truth.
- No wives ever cheat on their husbands.
- Tiger Woods plays golf and Maria Sharapova plays tennis.
The first two statements are true, the second two false. The last one expresses two statements, both of which are true. Truth and falsity are called the two possible truth values of a statement. Thus, the truth value of the first two statements is true, the truth value of the second two is false, and the truth value of the last statement, as well as that of its components, is true.
Unlike statements, many sentences cannot be said to be either true or false. Questions, proposals, suggestions, commands, and exclamations usually cannot, and so are not usually classified as statements. The following sentences are not statements:
- Where is Khartoum? (question)
- Let’s go to a movie tonight. (proposal)
- I suggest you get contact lenses. (suggestion)
- Turn off the TV right now. (command)
- Fantastic! (exclamation)
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