Materials needed

• Props and costumes (not necessary but fun) for enacting any of the skits
• Construction paper and markers to make signs
• Copies of the handout (see Supplemental Materials section below)

Description:

An argument is a deductive argument when we can arrive at the conclusion solely on the basis of information contained in the premises (the reasons, evidence, or support given for each conclusion).

Introduction

In philosophy, an “argument” does not mean the kind of fight you get into with your brother or sister, classmate, or parents (e.g., getting upset and calling the other person names).

In a philosophical context, an “argument” is a sequence of statements used to support, provide evidence for, prove, or back up a conclusion. In order to convince another person (or persons) of a particular position, we create arguments to establish and provide support for our position.

• A statement is a sentence or a claim that asserts something is either true or false.
• A conclusion is a statement that is supported or backed up by other statements.
• The statements that provide reasons, evidence, or support for the conclusion are called premises.

For example, Rebecca might argue for a later bedtime by offering strong support for why her parents should let her stay up an extra half-hour (see example below).

Rebecca: Due to the fact that I had to wake up at 6:00 am in order to be ready in time for car pool, my bedtime has always been 8:30 pm. Given that Mrs. Green is now in charge of morning carpool, she comes at 6:30 am and I have an extra half hour to sleep in. Now, I can go to bed a half-hour later and still get the same amount of sleep. Therefore, I should be allowed to stay up until 9:00 pm.  

Premises and conclusions are often easy to spot because they follow words that act as indicators, or guide-posts, giving the reader notice that a premise or a conclusion is about to appear in the body of the text. (Conclusion indicators and premise indicators are addressed in the accompanying handout.)

First, identify the conclusion:

Therefore, (conclusion indicator) I should be allowed to stay up until 9:00 pm.

Second, what are the premises that work to support the conclusion?

P1. Due to the fact that (premise indicator) I had to wake up at 6:00 am, my bedtime has always been 8:30 pm.

P2: Given that (premise indicator) Mrs. Green is now in charge of carpool, I have an extra half-hour to get ready in the morning.

P3. I can go to bed a half-hour later and get the same amount of sleep as before.

Activity 1

1. Give students the handout (see Supplemental Materials). Have students complete numbers 1-5 and review the answers as a class. Have students do number 6 and then share their examples with the class. Explain that P1, P2, etc. is shorthand for Premise 1, Premise 2. When they are proficient in being able to identify parts of an argument and also provide their own examples, move on to kinds of deductive arguments.
2. We will learn four types of arguments. These four argument forms are all deductive arguments, which means that we can arrive at the conclusion solely from the information provided in the premises.

Type 1: Modus ponens

Arguments in the following form are called modus ponens. The “P” and the “Q” can stand for any statement you choose, just be sure to keep your “Ps and “Qs” consistent throughout a given argument.

P1. If P is true, then Q is true.

P2. P is true.

____________________

Therefore, Q is true.

When we substitute “P” for “it rains” and “Q” for “we get to watch a movie” the argument would look like this:

P1. If it rains then we get to watch a movie.

P2. It is raining.

__________________

Therefore we get to watch a movie.

Type 2: Modus tollens

Another argument form, modus tollens, is of the following form:

P1. If P is true, then Q is true.

P2. Q is not true.

_____________________

Therefore, P is not true.

When we substitute our “Ps” and “Qs” a modus tollens argument might look like this:

P1. If I do all of my chores, then I get a new puppy.

P2. I didn’t get a new puppy.

___________________________

Therefore, I didn’t do all of my chores.

Type 3: Hypothetical syllogism

Hypothetical Syllogism is of the following form:

P1. If P is true, then Q is true.

P2. If Q is true, then R is true.

________________________

Therefore, if P is true, then R is true.

This argument form can be expressed using common language. Consider the following example:

P1. If I finish my homework, then I can log onto Facebook.

P2. If I can log onto Facebook, then I can instant message Avi.

____________________________

Therefore, if I finish my homework, I can instant message Avi.

Type 4. Disjunctive syllogism

Disjunctive syllogism can take two (very similar) forms. These are:

P1. Either P is true or Q is true.

P2. P is not true

_______________

Therefore, Q is true.

Similarly, disjunctive syllogism could also take the form where Premise 2 states that Q is not true. For example:

P1. Either P is true or Q is true.

P2. Q is not true.

________________

Therefore, P is true.

When we substitute our “Ps” and “Qs” it would look like this:

P1. Either Esther is a drama queen or Michael has a mean sense of humor.

P2. Esther is not a drama queen.

_____________________

Therefore, Michael has a mean sense of humor.

OR, using the same example, disjunctive syllogism could also look like this:

P1. Either Esther is a drama queen or Michael has a mean sense of humor.

P2. Michael does not have a mean sense of humor.

_________________________

Therefore, Esther is a drama queen.

3. Ask students to make their own examples of each of the four argument forms on the handout. Have students share their examples with the class, or come up to the board and write their examples on the board. Let the class determine whether the examples are done correctly, and if not, determine what would be needed to fix the example. Once students are proficient in understanding how these four forms work, have them do the following activity.

Activity 2:

1. Each student will make four signs using construction paper and markers. The name of an argument form should be on the front, and structure of the form should be on back.
2. Next, for the capstone activity students will create skits that enact each of these forms.

• First, form small groups depending upon class size. Write the names of the forms on small pieces of paper and put these in a hat or bucket. Each group will draw two forms from the hat and keep it secret.
• Groups should go to private corners of the room or perhaps work in the hall to ensure that other groups do not know which argument form they drew. Each group will develop two skits (using props and costumes if provided) that illustrate the argument forms they drew. Encourage students to make these funny, as it can be easier to remember things that make you laugh.

An example of a skit could be the following:

Suppose a group wants to enact hypothetical syllogism in front of the class.

One student might pretend to be a dog trainer, another student the dog in training, and the third student the dog owner. The dog owner says to the trainer: “All my dog wants to do is play dead all day. I brought him here for training because my neighbor tells me that if Bailey (the dog) plays dead all day he will only eat fruit rollups. The trainer attempts to get the dog to roll over, shake, and do a few other tricks, but all the dog does is play dead. The trainer responds to the owner: “Well, if Bailey will only eat fruit roll ups, then all the other dogs will want to be his best friend.” At this point, the dog sits right up and says to both the owner and the trainer: “In this case, if I play dead all day then all the other dogs will want to be my best friend! Sounds like a plan!”

P1. If P is true, then Q is true.

P2. If Q is true, then R is true.

________________________

Therefore, if P is true, then R is true.

3. Finally, each group will perform their first skit and the audience will hold up their sign at the end of each skit, showing which one they think it is. It is important that students don’t call out answers but hold up signs. After all the groups have presented their first skit, each group will present their second in the same manner.

Supplemental Materials

A couple of additional resources are as follows:

Weston, Anthony. A Rulebook for Arguments (4th ed.). Indianapolis: Hackett Publishing, 2009.

Hurley, Patrick. A Concise Introduction to Logic. Belmont, California: Wadsworth Publishing, 2011.

Handout: A Little Logic

Conclusion Indicators:

Therefore, thus, so, hence, in conclusion, consequently

Premise Indicators:

Because, since, assuming that, given that, the fact that, due to the fact

Note: Not all premises or conclusions will be introduced by these indicators. There are additional indicators that are not included here, and often times one must determine the conclusion and premises from contextual cues.

Exercise 1

Circle the conclusion and underline each of the premises in the following arguments:

1. It is true that 2 x 3 = 6, and it is also true that 6 x 1 + 6. Thus, we can conclude with certainty that (2 x 3) = (6 x 1).
2. All dogs love to chew on shoes. Bailey is a dog. Therefore, Bailey loves chewing on shoes.
3. Mario’s parents let him watch movies that are rated PG-13. I will be 13 in less than two years, and I am very mature for my age. Given these facts, I should also be allowed to watch movies that are rated PG-13.
4. Today we have a grammar quiz that I haven’t studied for. I need an A on the quiz or my parents won’t let me get on Facebook for a week. So, today I need to spend lunchtime studying instead of sitting with my friends.
5. Everyone either loves Mrs. Harper or they think she is a boring teacher. I don’t love her. Consequently, I think that she is a boring teacher.

Come up with your own argument and label the premises/conclusion!

Exercise 2

Come up with your own examples! Be as creative as you like. Just make sure you follow the exact form provided in substituting your “Ps” and “Qs.”

Modus ponens:                                       Your example of modus ponens:

P1. If P is true, then Q is true.

P2. P is true.

____________________

Therefore, Q is true.

Modus tollens:                               Your example of modus tollens:

P1. If P is true, then Q is true.

P2. Q is not true.

_____________________

Therefore, P is not true.

Hypothetical Syllogism                   Your example of hypothetical syllogism:

P1. If P is true, then Q is true.

P2. If Q is true ,then R is true.

________________________

Therefore, if P is true, then R is true.

Come up with two examples of Disjunctive Syllogism:

P1. Either P is true or Q is true.                   Your example:

P2. P is not true.

_______________

Therefore, Q is true.

P1. Either P is true or Q is true.                    Your example:

P2. Q is not true.

________________

Therefore, P is true.

This lesson plan, created by Ayesha Bhavsar, is part of a series of lesson plans in Philosophy in Education: Questioning and Dialogue in Schools, by Jana Mohr Lone and Michael D. Burroughs (Rowman & Littlefield, 2016).