Writing Tutor: Deductive Reasoning Think More ... Write More

Dr. Otto

In Analyze a Problem, I identified two gaps – information gap and logical gap – that separate a problem from its solution. Now I want to show you the relationship between these two gaps.

Analyze a Problem

Look at this example where I try to answer the question/problem – Is Peter mortal?

All men are mortal. (Premise 1 - factual statement - true)Peter is a man. (Premise 2 - factual statement - true)Therefore, Peter is mortal. (Conclusion – factual statement - true)) As you can see, I came up with two factual statements:

All men are mortal. Peter is a man.

Sound premises

All men are mortal. Peter is a man.

Before I say anything with these two statements, I have to determine whether they are true or sound.

The first statement is sound because all men are liable or subject to death – history confirms this statement.

The second statement is sound because I know Peter is a man ... I have known him for many years.

So, I can safely say that these two premises are sound.

Valid

All men are mortal. Peter is a man. Therefore, Peter is mortal.

But is the conclusion valid? Yes, because it flows logically from the two premises.  

 

Conclusion

The Conclusion is a factual statement:

Therefore, Peter is mortal. The conclusion has to be sound (true) because it flows from sound factual statements. It is impossible for the conclusion to be false if the premises are true.

It is valid because it flows logically from the two premises.

In short, here we have a conclusion that is both sound and valid. These are the two conditions that a deductive argument must meet.

Factual statements

We can make a second observation.

Notice that the premises and conclusion are all factual statements. In other words, when the premises are factual statements, the conclusion must also be a factual statement.

Sometimes writers fail to meet one or the other condition. Look at this example:

•Everyone who eats steak is a Canadian. (Premise 1 – false statement)•John eats steak. (Premise 2 – true statement)

•Therefore, John is a Canadian. (valid but not sound/true)

Valid

•Everyone who eats steak is a Canadian. (Premise 1 – false statement)•John eats steak. (Premise 2 – true statement)

•Therefore, John is a Canadian. (valid but not sound/true)

Is this a valid and sound argument? Lets apply the two conditions.

First, is the argument valid? Yes because the conclusion flows logically from the two premises.

If the first premise is true then John, who is a steak eater, must be a Canadian.

Sound

•Everyone who eats steak is a Canadian. (Premise 1 – false statement)•John eats steak. (Premise 2 – true statement)

•Therefore, John is a Canadian. (valid but not sound/true)

Second, are the premises sound? No, because there are people who eat steak but are not Canadians! In other words, the first premise is false.

Hence, the argument is valid, but not sound.

Sound/Valid

Can an argument be sound but not valid? Look at this example:

•There are 32 books on the top-shelf of the bookcase •There are 12 on the lowest shelf of the bookcase.

•Therefore, there are 44 books in the bookcase.

True/Valid•There are 32 books on the top-shelf of the bookcase •There are 12 on the lowest shelf of the bookcase.

•Therefore, there are 44 books in the bookcase.

First, are the premises true? Let’s assume that we can count the books on the top and bottom shelves and that we can confirm that there are 32 books on the top shelf and 12 books on the bottom shelf for a total of 44 books on the two shelves. In other words, the two shelves have a total of 44 books, which makes the two premises true.

Second, is the argument valid? The premises say nothing about the number of books on the other selves in the bookcase ... there may be some or none. Hence, the conclusion does not flow logically from the premises. In other words, the argument is invalid.

How is deductive reasoning applied in a text? What does it look like: • when the premises are sound and the conclusion is valid?•when the premises are sound and the conclusion is invalid?•when a premise is false and the conclusion is valid?

Let’s address these questions in the following text.

Mount Everest is known as the tallest mountain in the world. However, according to some geographers, Mauna Kea is the tallest mountain. Mount Everest is located on the Asian Continent in the Himalaya mountain range. Its elevation is 29,028 ft. above sea level. Mauna Kea, a dormant volcano is located on the main island of Hawaii. Its height of 33,465 ft. is greater than the height of Mount Everest. However, the base of Mauna Kea is on the floor of the Pacific Ocean which is18,000 feet below sea level. In other words, only 13,796 feet of the mountain stands above sea level. If the bases of both mountains were at sea level, Mauna Kea would be 4400 feet taller. Hence, Mount Everest stands taller but Mauna Kea is higher. However, since Mauna Kea stands on the floor of the Pacific Ocean, Mount Everest stands taller. Look at the following diagram.

Mount Everest and Mauna Kea

Let’s look at the following deductive arguments in the paragraph: • the premises are sound and the conclusion is valid

Premise 1 – Mount Everest is 29,028 feet above sea level (true)Premise 2 – Mauna Kea is 33,465 feet high but only 13,796 feet above sea

level (true)Therefore Mount Everest is the tallest mountain (valid)

Explanation: Based on the information in the paragraph, both premises are true

The conclusion has to be sound (true) because it flows from sound factual statements. It is impossible for the conclusion to be false if the premises are true.

It is valid because it flows logically from the two premises.

In short, here we have a conclusion that is both sound and valid.

Paragraph analysis (cont.): • The premises are sound and the conclusion is invalid

Premise 1 – Mount Everest elevation level is 29,028 feet above sea level (true)

Premise 2 – Mauna Kea is 33,465 feet high (true)Therefore Mauna Kea is the tallest mountain (invalid)

Problem: Although the two premises are true, premise #2 does not indicate the elevation level of Mauna Kea above sea level. Therefore, it cannot be determined from the two true premises whether Mauna Kea is taller than Mount Everest. Hence, the conclusion is invalid.

Paragraph analysis (cont.): • A premise is false and the conclusion is valid

Premise 1 – Mount Everest is 29,028 feet tall (true)Premise 2 – Mauna Kea is 33,465 feet tall (false)Therefore Mauna Kea is the tallest mountain (valid)

Problem: Premise two is false because Mauna Kea sits on the floor of the Pacific Ocean which is18,000 feet below sea level. Only 13,796 feet of the mountain stands above sea level. Therefore, Mount Everest, which is 29,028 feet above sea level is the tallest mountain.

The paragraph points out that some geographers claim that Mauna Kea is the tallest mountain by maintaining that Mauna Kea is 33,465 feet tall.

Summary

Back to the information gap and logical gap that separate a problem from its solution.

Deductive reasoning applies two specific criteria to solve problems that involve an information gap and a logical gap. They are:

• Are the premises sound/true?• Is the argument valid?

In summary, to solve problems that involve an information gap and a logical gap:

* The information (premises) must be sound/true.

* The logical relationship between the premises must be valid.

Try this …

1. At www.sponsoravillage.ca, go to Writing and to Deductive Reasoning. Read the ESSAY and complete the template.

2. Write an essay using correct deductive reasoning. After you are pleased with your essay, edit it for grammar to create a reader’s draft.

If you have any questions about the writing process, send them to Ask Dr. Otto at www.sponsoravillage.ca.Enjoy your writing experience.