part 2

5

Unit III

Lesson 2: Formal Reasoning

Introduction

Perhaps the most key concept when thinking about argumentation is the role of logic and reasoning. So often, arguments are compared to structures, like houses, where it is imperative that you establish a foundation, a frame, walls, and a roof. In comparing an argument to building a house, you can understand that each element supports the other elements. If one wall is missing, then the house is significantly weakened and is not a sound structure. Likewise, if each element in the house is strong and well done, then the house will stand for a long time. The same is true of an argument that is made with a strong introduction and thesis statement, literature review, body section, and conclusion. In this lesson, we will be discussing how strong arguments are made through the basic building blocks of argumentation—reasoning and conclusions.

Deductive and Inductive Reasoning

The basics of reasoning are deductive and inductive reasoning, which are referred to as the two types of formal reasoning; the use of reason is to derive conclusions, inferences, and judgments. Deductive and inductive reasoning are often confused with one another, so let’s discuss the differences:

· Deductive reasoning: This type of reasoning assumes that if all premises are true, then the conclusion of the logical thought process must also be true. This reasoning is often referred to as a “top-down” model because it takes into account generally understood truths in order to come to conclusions about specific instances.

· Inductive reasoning: If these specific examples are true, then we can generalize about a large group of things. This type of reasoning is often thought of as a “bottom-up” model because specific examples lead to a general truth.

We use both types of reasoning in our daily lives. Let’s look at some examples:

· Deductive reasoning: Moves from the general to the specific.

· Generalization: Joey is allergic to citrus fruit.

· Specific example: Clementine is a citrus fruit.

· Conclusion: Joey is allergic to clementines.

· Inductive reasoning: Moves from the specific to the general.

· Specific: Joey is allergic to oranges, grapefruit, limes, and lemons.

· Generalization (Conclusion): Joey is allergic to citrus fruit.

Avoiding Mistakes in Deductive Reasoning

In both of the scenarios above, the conclusions seem sound because both are logical and reasonable. Let’s discuss the common issues of both forms of reasoning:

Deductive reasoning: The most common issue with deductive reasoning is that if even one of the premises is incorrect, then the conclusion is likely incorrect. The most common form of deductive reasoning is the syllogism, a nearly mathematical means of determining knowledge, the earliest uses of which come from Aristotle. Let’s look at the most widely referenced example:

· Premise 1: All men are mortal.

· Premise 2: Socrates is a man.

· Conclusion: Therefore, Socrates is mortal.

In the example above, you can replace each of the aspects of the premise with a letter to better see the formula.

· Premise 1: A is B.

· Premise 2: C is A.

· Conclusion: Therefore, C is B.

Another way to understand the syllogism is to think about the “be” verbs, like is and are, as equal symbols (=). As we know from mathematics, when you have two numbers and there is an equal sign between them, then they hold the same value.

· Premise 1: A = B.

· Premise 2: C = A.

· Conclusion: Therefore, C = B.

Look at the syllogism this way: You can see that if A and B are equal and A and C are equal, then it only logically follows that B and C will also be equal. So, how can this formula lead to illogical conclusions? Let’s look at an example:

· Premise 1: All women love to paint their nails.

· Premise 2: Stephanie is a woman.

· Conclusion: Therefore, Stephanie loves to paint her nails.

The conclusion above is perfectly reasonable; however, the first premise is inaccurate: Not all women love to paint their nails. The assumptions of the first premise cause the conclusion to be unsound because while Stephanie might love to paint her nails, she could also dislike painting her nails. Herein lies the problem. If you are researching, you have to make sure that each premise, each generalization is sound. There are some ways that you can protect yourself from errors like this:

· Premise 1: Many women love to paint their nails.

· Premise 2: Stephanie is a woman.

· Conclusion: Therefore, Stephanie might love to paint her nails.

The main thing to take away from this discussion is that you want to be sure that your reasoning is sound as you begin to understand your topic. One way to do that is to avoid premises that are unfairly general. Not only do unfair generalizations lead to inaccurate conclusions, but they can cause the reader to mistrust you as you lay out your argument.

Avoiding Mistakes in Inductive Reasoning

Inductive reasoning results in a probable conclusion, not a certainty. The reason for this difference between deductive and inductive reasoning is that inductive reasoning draws out the best conclusion possible given the premises.

· Generalization: Most students use the online library to find their research.

· Conclusion: Most students at this university will use the online library to find their research.

As we discussed earlier, the problem is that the conclusion may be logical, but still false.

· Generalization 1: 90% of people in our office recycle their paper coffee cups.

· Generalization 2: 85% of people in the office next door recycle their paper coffee cups.

· Conclusion A: It is likely that most people in offices recycle their paper coffee cups.

· Conclusion B: It is likely that the newly hired person in the office will also recycle his or her paper coffee cup.

There is nothing wrong with conclusion A because the wording allows for alternatives: “It is likely that….” However, Conclusion B is faulty because the 90% statistic has no real bearing on the recycling habits of one individual. These are two specific instances: (1) the people in the offices and (2) the newly hired person in one office. There is no induction. In order for inductive reasoning to work, a specific instance must be related to a larger generalization.

Let’s look at one more conclusion with the same generalizations:

· Conclusion C: It is likely that the people in the office building across the street recycle their paper coffee cups.

Again, Conclusion C is “likely,” but not certain, because inductive reasoning only establishes a high level of probability.

Let’s look at two new generalzations:

· Generalization 1: People respond well to positive reinforcement.

· Generalization 2: 53% of people in our office recycle their paper coffee cups.

· Conclusion: If we positively reinforce the behavior of recycling in our office, then we can reward those who already recycle and increase the percentage who recycle paper coffee cups.

The above is an example of using two distinctive, unrelated generalizations in order to come to a generalization about a group of people. There is no problem with this logic, but the conclusion may be inaccurate because certain elements have not been taken into account, such as an office culture that is so saturated with positive reinforcement that employees no longer respond or are overwhelmed with competitions and activities. However, these concerns point to outside of the purview of the premises, and the conclusion of inductive reasoning can only come to a conclusion based on what is present.

Using Reasoning to Come to Conclusions

Both deductive and inductive reasoning can be confusing and difficult if you are using them for the first time. The key here is that you understand that there are different ways to come to conclusions about different situations. Further, you need to understand how people reason and come to conclusions so that you can become a better reader and thinker. When you begin to think about all of the conclusions we come to each day, you can see that reasoning is part of nearly every decision we make.

· Deductive reasoning: Coffee Chain A always has good coffee. If I am out of town and see a Coffee Chain A, then I know I can get a good cup of coffee.

· Inductive reasoning: Drinking soda before bed keeps me awake most of the night. If I drink this soda, I will be awake all night.

Do not be intimidated by formal reasoning, as it can be a helpful tool to help you come to conclusions about the world around you. Be wary of arguments based on false premises or faulty reasoning between premises. Further, it will guide the conclusions that you come to as you begin to write about your chosen research topic.

Check for Understanding

1. Is the following an example of deductive or inductive reasoning?: “All of the students like to go to the Pizza Palace. Mary is a student, so Mary probably likes to go to the Pizza Palace too.”

2. Is the following an example of deductive or inductive reasoning?: “Most of the books are on sale today. If you pick up a book, it is probably on sale.”

3. Is the following an example of deductive or inductive reasoning?: “All cell phones have resale value. This iPhone is a cell phone, so it probably has some resale value.”

4. Is the following an example of deductive or inductive reasoning?: “Most of the people who go to space want to return some day. If you ask Guion S. Bluford, the first African-American astronaut, if he wanted to return to space, he would probably say ‘yes.’”

Review

1. Deductive reasoning assumes that if all premises are true, then the conclusion of the logical thought process must also be true.

2. Inductive reasoning assumes that if these specific examples are true, then we can generalize about a large group of things.

3. The syllogism is an example of deductive reasoning and is a kind of mathematical proof for knowledge.

4. Inductive reasoning results in probable, not certain, conclusions, based upon the premises that are present.

Answer Key

1. Deductive

2. Inductive

3. Deductive

4. Inductive