978-0534601744 Chapter 5

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Chapter 5: Logical Structure of Arguments

ACTIVITY #5.1: INTRODUCTION TO LOGICAL STRUCTURE.

(Do prior to reading chapter 5)

(To help students start to understand the basic logical structure of arguments.)

Students seem to like this lesson because of the use of candy and because it provides them something concrete to understand the basic

concepts of logic. It helps to stress that they’re not expected to know everything about logic based on this activity, but it’s is just

meant to introduce them to the concepts they’ll read about in chapter 5. It helps if you can have fun doing it, and are ready to ad lib

and act a little like a magician.

• Bring containers of M&Ms to class. It would probably be good to have each labeled with a number as

below:

Container #1: all red

• Have a student come to you and get out the container #1. Say, “I have a container of M&M’s. All of the

It is red

• We’ve just done an example of one kind of logical structure called a categorical syllogism. They take the

form:

All A’s are B’s

C is an A

Therefore, C is a B

• You have to be careful that you don’t try to reverse the process. For example:

All the M&M’s in the container are red.

The M&M in my hand is red

• Take Container, #2 and show it to the student assistant. “I have another container of M&M’s. All of the

yellow M&M’s are in that container, plus some other colors.” Also show the assistant the other containers

to confirm there are no yellow M&M’s in them. Have the student turn her or his back, and take out a

• “What can you conclude about the color of my M&M if you know I have an M&M from that same

container?”

• “Why?”

• “This same container doesn’t have any red M&M’s in it.” Have the assistant confirm the statement, then

turn her/his back. Take out a red M&M from the first container. “What can you conclude if you know I

• Have the assistant turn her/his back again. Take out an M&M from Container #2 (without any red

• “This is a variation of the categorical syllogism. Instead of identifying a characteristic that all the items do

have, we identify a characteristic all the items do not have.”

• Take container #3. “I have a container with both green and orange M&M’s in it.” Have the assistant

confirm the statement. “ I can take either a green one or an orange one.” Have assistant turn her/his back,

• “That’s another type of logical structure called a disjunctive syllogism.

• Get out container #4 with only brown M&M’s. “Now I have a container that only has brown M&Ms in

it.” Have assistant confirm the statement. “So you know that if I take a piece of candy from that container,

it will be brown.” Take an M&M out of the container.

• Take an M&M from another container, but not a brown one. “What do you know if I have a piece of

• “What can you conclude about the color of the M&M if you know I have a piece of candy that was not in

• What can you conclude about which container my piece of candy came from if you know I have a brown

• That’s an example of a third type of logical structure, called a conditional syllogism. It’s also called a

hypothetical syllogism.

If I take a piece of candy from this container, it will be brown.

The piece of candy I have is not brown.

Therefore, it did not come from this container.

If I take a piece of candy from this container, it will be brown.

You don’t know anything about the color of candy that are not from that container; the minor

premise denies the antecedent.

If I take a piece of candy from this container, it will be brown.

The piece of candy I have is brown.

You don’t know if all the brown candies are from a particular container; the minor premise affirms

the consequent.

ACTIVITY #5.2: CONSTRUCTING SYLLOGISMS. (To help students develop the ability to create basic arguments

using formal logical structure.)

STEP 1: Divide students into groups of three.

STEP 4: Reconvene and discuss any problems the students had or any insights they gained. Clarify the

differences between the types of syllogisms, and the standards of validity for each. During this time,

(Note: you might want to have the students keep the syllogisms they create as the basis of arguments for future exercises.)

ACTIVITY #5.2a: INTERPRETING ARGUMENTS. (To help students understand that the parts of a

syllogism may be presented in any order, and that interpreting the order is important to determining validity.)

PREPARATION: Have the students keep the syllogisms they wrote for Activity 5.2.

STEP 1: Have the students form the same groups that they did for Activity 5.2 and get out the syllogisms

they wrote.

STEP 2: Have each group choose one of their valid syllogisms from Activity 5.2. Then, each group is to

STEP 3: Assign each group a number, 1 through 6. (If there are more than six groups, repeat numbers.)

STEP 4: Pick a group, and have one member of that group write the syllogism that corresponds to the

STEP 5: Ask a student in the class to identify the major premise, minor premise, and the conclusion of the

STEP 6: Repeat steps 4 and 5 with the rest of the groups.

ACTIVITY #5.3: TRANSFORMING ARGUMENTS TO SYLLOGISMS. (To help students start developing

the ability to analyze arguments using formal logic.)

PREPARATION: Go to http://www.gre.org/argutop.html and select arguments that correspond to the analysis

STEP 1: Give all the students one of the arguments below or a short argument that you construct yourself

(either as handouts or projected on a screen).

STEP 7: Repeat steps 2-6 until you’re out of time.

#1: The following appear in a memo from the chief executive of a video game company…

CONCLUSION: Purchase of rights to “Squirrel Power” will undoubtedly be a wise

investment.

PREMISES: (1) The author’s last three books have been best sellers, and the movie based on

the author’s first book was highly profitable. (2) It will save time in development, thereby

reducing our costs.

#2: The following appeared in a newsletter offering advice to investors…

CONCLUSION: Old Dairy stockholders should sell their shares and other investors should

not purchase stock in the company.

#3: The following appeared in a letter from the manager of a rock band named Double Rice…

CONCLUSION: The band should hire Ad Lib to duplicate the Megalopolis ad campaign on

a nationwide scale.

#4: “A recent sales study indicated that consumption of seafood dishes in Bay City restaurants has

increased by 30 percent”

CONCLUSION: A new Bay City restaurant specializing in seafood will be quite popular and

profitable.

#5: The following appeared in a memo from the chairperson of the school board in the town of Saluda…

CONCLUSION: The Saluda school board should hire Mr. Schade to plan and direct the

general music education programs for the entire Saluda school system.

#6: The following appeared in a memorandum from the president of Excello Food Markets…

CONCLUSION: We should stock a full line of organic food products in all our markets.