Deductive Reasoning Study Guide (page 2)
The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.
René Descartes, French philosopher, mathematician, scientist (1596–1650)
What is deductive reasoning? It's an argument based on two facts, or premises. If both are true, then it should follow that the conclusion of the argument must also be true. In this lesson, you'll learn how these arguments work and don't work. And you'll discover how to use deductive reasoning to construct your own strong arguments
You're exposed to deductive arguments, both good and bad, every day. In a magazine, you read an ad: "Brand X just can't get clothes clean. But with Cleany-Oh, your clothes are sparkly clean!" On TV, you hear a politician: "Higher taxes put people out of work. We need tax cuts. Tax cuts help to create jobs for people!" At a restaurant, you hear a parent say, "If you don't finish your supper, you won't get any dessert."
Understanding how these arguments work and do not work will help you construct strong arguments and make it easier to get your point across. And you'll know when someone else's argument is weak so you're not influenced by faulty reasoning. You'll also be aware if someone is presenting a strong argument that should influence you.
What Is Deduction?
Deduction is the process of drawing a specific conclusion from two things that are known, or general premises. All deductive reasoning includes these three parts:
- a major premise
- a minor premise
- a conclusion
For instance, we know that dogs have four legs, and we know that Fido is a dog. Therefore, since A and B are true, we can conclude with certainty that Fido has four legs. From this example, you may see that a deductive argument is sound when the premises are true, and the conclusion logically follows from the premises.
Qualities of a Deductive Argument
- Has two premises that provide a guarantee of the truth of the conclusion by providing support for it that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.
- Is described by the terms valid and invalid; when the premises are correct, and the conclusion that follows is correct, the argument is said to be valid. If either or both premises are incorrect, the argument is invalid.
- Is based on rules, laws, principles, or generalizations, as opposed to inductive arguments (see Lesson 14), whose major premises are based on observations or experiences.
The key to the credibility of a deductive conclusion lies in the premises. Since the conclusion must result from the premises, it is considered invalid if one or both of the premises is proven false. Therefore, the premises must be truthful facts, rules, principles, or generalizations. Just one word can change the premise from fact to fiction, such as the words "all" and "every."
Consider the following example:
- All dogs have brown fur.
- Spot is a dog.
- Spot has brown fur.
The truth is that some dogs have brown fur. The first premise is untrue, which makes the conclusion invalid.
A major premise is a statement of general truth dealing with categories rather than individual examples. It relates two terms:
- All women were once girls.
- Athletes are in good shape.
- Professors hold advanced degrees.
The subject of the major premise (women, athletes, professors) is called the antecedent; the verb phrase (were once girls, are in good shape, hold advanced degrees) is known as the consequent.
A minor premise is a statement that deals with a specific example of the major premise:
- My mother is a woman.
- Tiger Woods is an athlete.
- Dr. Shiu is a professor.
The minor premise either affirms the major premise, or denies it. When it affirms, part of the minor premise equates with the subject, or antecedent, of the major premise. When it denies, part of the minor premise does not equate with the consequent. For example:
- Children like top 40 music.
- Charles is a child.
In this case, the minor premise (Charles is a child) affirms the major premise by stating that it is something equal to the major premise (child).
- Children like top 40 music.
- Charles does not like top 40 music.
In this case, the minor premise denies the major premise by asserting that something is not the same as the consequent ("does not like" as opposed to "like").
Deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises. So if the argument is valid, the truth of the conclusion is contained within the truth of the premises. But, the conclusion must follow logically from and not go beyond or make assumptions about the premises.
Here is an example of a conclusion that follows the premises:
- Banks make money by charging interest.
- My bank charges me interest.
- My bank makes money.
Note that the conclusion has no additional information, and does not make assumptions or inferences about the premises. It is a valid conclusion.
Here is an example of a conclusion that goes beyond the truth of the premises:
- Ernest Hemingway wrote some great books.
- Ernest Hemingway wrote For Whom the Bell Tolls.
- For Whom the Bell Tolls is a great book.
Why is this conclusion invalid? Because the major premise states that some of Hemingway's books are great. The conclusion assumes that For Whom the Bell Tolls falls into that group, when there is no evidence in the premises that this is true.
Did you realize that you use deductive reasoning to prove math facts are accurate?
Two Forms of Deductive Argument
Deductive arguments are expressed in two common ways: syllogisms and conditionals.
Fact or Opinion?
As you learned in Lesson 8, you have to know the difference between a fact and an opinion. A fact is an objective statement that can be proven to be true, such as, "Saturn is one of the planets in our solar system." You can research to prove that Saturn is, indeed, a planet in our solar system. Is that statement always true? If the answer is yes, then it's a fact.
An opinion is a subjective statement based on personal beliefs. For example, "Saturn is the most beautiful planet in the solar system." This is a personal belief and open to debate. Other people might think Venus is the most beautiful planet, or Jupiter. The word beautiful is subjective, and tells you this is someone's opinion.
A syllogism is made up of two premises and a conclusion. The first premise describes a group, A, and a characteristic of that group, B: All vegetarians do not eat meat. The second premise places a person or thing, C, either within A or not within B: Gordon is a vegetarian. The conclusion states that C is B: Gordon does not eat meat.
A negative in a syllogism follows the same form. The word not in the second premise signals the negative. All vegetarians do not eat meat. Gordon is not a vegetarian. Gordon eats meat.
Here are a few examples of positive and negative syllogisms:
- Smart people do not believe in UFOs. (All A are not B)
- Lee does not believe in UFOs. (C is not B)
- Lee is smart. (C is A)
- The greatest jazz artists were all improvisers.
- Miles Davis was an improviser.
- Miles Davis was a great jazz artist.