deductive arguments

Module 10: Evaluating Arguments - Deductive Argument Patterns – Spring 2026

Fayetteville State University

Critical Thinking Online

Instructor: Dr. Jon Young

In this module, you will learn:

Distinguish the technical meaning of “valid” and “sound” from everyday use where both may be used to refer to a good argument.

Define conditional statement, antecedent, and consequent.

Explain that in a true conditional statement the antecedent is a sufficient condition for the consequent and the consequent is a necessary condition of the antecedent.

Identify specific examples as necessary and/or sufficient conditions.

Explain why recognizing argument pattern (form, structure) facilitates argeument evaluation.

Apply two valid forms of the conditional syllogism: Modus Ponens (Affirming the Antecedent) and Modus Tollens (Denying the Consequent)

Apply two invalid forms of the conditional syllogism: Affirming the Consequent and Denying the Antecedent.

Apply two additional argument patterns: Hypothetical Syllogism and the Disjunctive Syllogism.

In this module, you will

Read this PowerPoint Introduction to the Module. The unusual length of this Module Introduction (89 slides!) reflects the complexity of the lesson. (Please read this introduction carefully.)

Read Section 3.4 of the textbook. This one of the shortest reading assignments of the semester, but one of the most complex!)

Earn at least 6 of 10 points on the Quiz.

Submit the writing assignment.

Contribute to the Discussion.

Recall: Deductive vs. Inductive Arguments

Premises support conclusions in one of two ways: they are intended to provide probable support of the conclusion (inductive arguments) OR they are intended to provide absolute support for the conclusion (deductive arguments).

In a strong inductive argument, if the premises are true then the conclusion is probably true.

In a valid deductive argument, if the premises are true the conclusion must be (is certainly) true.

The focus of this lesson is on deductive arguments and, more specifically, argument patterns thare always valid or invalid.

Note: Much to memorize in this lesson

I strongly encourage you to make flash cards of these terms and argument patterns. You can use index cards or make PowerPoint slides or use a flash card program if you can find a free one.

Flash cards, though admittedly low-tech, are nonetheless the based aid to memorizing that I have found.

Argument Patterns (Forms)

An argument pattern or form refers to the structure of an argument, the relationship of premises to conclusion. When examining the pattern, form, or structure of the argument, you are not concerned about the the specific content of each premise or conclusion.

Argument patterns can be represented as formulas using variables. We will use p and q to represent the statements that form the content of an argument. See example below. (Sometimes in the PPT, I will use A and B instead of p and q.)

If Quentin is is a ballet dancer, then he must be in good physical condition can be represented as If p, then q. (p= Quentin is a ballet dancer; q = he must be in good physical condition.

Use variables to state the pattern of each.

I may have either chicken or a vegetarian meal. I don’t like chicken. Therefore, I will choose the vegetarian meal.

If Jamelle graduated with Honors, then he must have earned a cumulative GPA of 3.2 or higher. Jamelle graduated with Honors. Therefore, he must have earned a cumulative GPA of 3.2 or higher.

If the dam bursts, then the farmlands will be flooded. If the farmlands are flooded, the crops will be devastated. Therfore, if the dam bursts, the crops will be devastated.

If you want to earn an A in this class, you must devote approximately nine hours a week to completing the reading and assignments. You are spending @ three hours a week. Therefore, you must not want an A in this class.

p =I may have either chicken or q = a vegetarian meal. I don’t like chicken. Therefore I will choose the vegetarian meal. Either p or q. Not p. Therefore q.

p = Jamelle graduated with Honors; q = he must hearned a cumulative GPA of 3.2 or higher. If p, then q. p. Therefore q.

If p = the dam bursts, then q = the farmlands will be flooded. If the farmlands are flooded, r = the crops will be devastated. Therefore, if the dam bursts, the crops will be devastated. If p, then q. If q, then r. Therefore if p, then r.

If p = you want to earn an A in this class, then q = you must devote approximately nine hours a week to completing the reading and assignments. You are spending @ three hours a week. Therefore, you must not want an A in this class. If p. then q. Not q. Therefore not p.

Why focus on argument patterns?

By identifying the pattern or form of an argument we can evaluate more clearly whether the premises are intended to provide conclusive or probable support for the conclusion.

We can also then identify some arguments patterns that are always valid and some that are always invalid. Identifying such patterns is much easier than trying to figure out if an argument is valid or invalid by looking at the specific content of the arguments.

This lesson focuses on deductive argument patterns; subsequent lessons will look at inductive argument patterns.

Why focus on argument patterns?

Remember our guiding definition of critical thinking: the systematic evaluation and formulation of beliefs, or statements, by rational standards.

One of the most valuable, long-term consequences of studying critical thinking is developing the ability to look not just at the content of arguments, but their structure (pattern, form). Once you can identify these patterns you are much better able to evaluate them.

Conditional Statements

Three valid argument patterns and two invalid forms that we will study are based on conditional statements.

A conditional statement uses “if” and “then” to connect two events such that one follows the other. Example: If it rains on Saturday, then the game will be cancelled.

Conditionals may be stated in several ways: “If it rains on Saturday, the game will be canceled.” Or, “The game will be canceled, if it rains on Saturday.”

Conditional statements have the form: “If p, then q”* (Or q, if p.)

p is the antecedent (comes first)*, q is the consequent* (comes second) (Don’t be puzzled if you see me use a and b in the place of p and q.)

*You must memorize – make flash cards

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Let’s make sure you understand

A conditional statement has this form: ____________________

Another way of stating the conditional is __________________

In the conditional the phrase that follows “If” is the ______________ and the phrase that follows “then” is the ___________________.

Write a conditional statement.

Let’s make sure you understand

A conditional statement has this form: If p, then q.

Another way of stating the conditional is q, if p.

In the conditional the phrase that follows “If” is the antecedent and the phrase that follows “then” is the consequent.

Write a conditional statement. If you were paying attention to the previous slide, then you had no trouble getting these items correct.

If a conditional statement is true, then… (This info not in textbook.)

The antecedent (p) is a sufficient condition for the consequent (q), which means that if you have p you must have q. p guarantees q.*

The consequent (q) is the necessary condition for the antecedent (p), which means that if you will not have p without q.*

Consider: If the temperature outside is below 32 degrees F, then the water on the sidewalk is frozen.

If this is a true conditional (which it is), the temperature below 32 guarantees (sufficient condition) the water on the sidewalk is frozen; if you don’t have frozen water on the sidewalk then you cannot have a temperature below 32 degrees F (necessary condition).

*You must memorize – make flash cards.

Necessary, sufficient conditions? Both? Neither

Earning 360 or more points in this class; earning a final grade of A in this class.

Presence of oxygen; human-like life.

Having a driver’s license; legally driving a motor vehicle.

Getting a Covid vaccine; not becoming infected with Covid.

Joseph flirting with women other than his girlfriend; Joseph’s girlfriend getting angry.

Sexual intercourse between man and woman; woman getting pregnant.

Earning 360 or more points in this class; earning a final grade of A in this class.

You can develop two true conditional statements: 1. If you earn 360 or more points in the class, you will earn a final grade of A. 2. If you earn an A in this class, then you must have earned 360 or more points. You can make two true conditional statements because either condition is necessary AND sufficient condition for the other.

Presence of oxygen; human-like life.

A true conditional statement: If a planet has human-like life, then the planet must have oxygen. Oxygen is a necessary condition for human-like life, but it is NOT a sufficient condition. Presence of oxygen does NOT guarantee human-like life.

Having a valid driver’s license; legally driving a motor vehicle.

True conditional statement: If you are driving a motor vehicle legally, then you must have a valid driver’s license. Having a valid driver’s license is a necessary, but not a sufficient condition, for legally driving a motor vehicle. (I may get a driver’s licence, but never drive a car.)

Being enrolled in this class; earning credit toward your degree for this class.

True conditional statement: If you earn credit for this course then you must be enrolled in it. Being enrolled is a necessary condition for earning credit, but being enrolled is not a sufficient condition for earning credit. (You could be enrolled and fail the course and thus earn no credit.)

Joseph’s girlfriend getting angry; Joseph flirting with women other than his girlfriend.

True conditional statement: If Joseph flirts with women who are not his girlfriend, then his girlfriend will get angry. The first condition is a sufficient condition for the second (at least in most relationships), but is not a necessary condition since his girlfriend may get angry for many other reasons.

Sexual intercourse between man and woman; woman getting pregnant.

True conditional: If the woman is pregnant, then she must have had sexual intercourse with a man. (With the exception of Mary.) The second condition is a necessary condition for the former, though not a sufficient condition since sexual intercourse does not guarantee pregnancy.

Did you get it? Which of these conditional are true? False.

If the planet has oxygen, then it is sure to have human-like life.

If you own a car like the Batmobile, then you must not be poor.

If you earn a high salary, then you must have a college degree.

If you are a human being, then you can produce intelligible speech.

If you are at least 18 years of age, then you own an automatic rifle.

If you are alive, then you are breathing.

If Bernardo loves spaghetti, then he must be Italian.

If you are breaking the law, then you are driving at speeds that exceed the speed limit.

Did you get it? Which of these conditional is true? False.

If the planet has oxygen, then it is sure to have human-like life. False. Oxygen is not a sufficient condition for human-like life; it does not guarantee it. If you reverse the antecedent and consequent, you have a true conditional statement: If the planet has human like life, then it must have oxygen. Note here the consequent is a necessary condition for the antecedent.

If you own a car like the Batmobile, then you must not be poor. True. The antecedent is a sufficient condition for the consequent. If you have a car like the Batmobile, then you must not be poor.

If you earn a high salary, then you must have a college degree. False. The antecedent does not guarantee the consequent; neither is the consequent necessary for the antecedent. Earning a college degree increases your chances of earning a high salary (that’s why you’re here, isn’t it?), but (unfortunately) does not guarantee it..

If you are a human being, then you can produce intelligible speech. False. The antecedent is not a sufficient condition (does not guarantee) the consequent. A person in a coma cannot produce intelligible speech. Neither is the consequent a necessary condition for the antecedent since some non-human species are able to produce intelligible speech (monkeys, dolphins.)

Did you get it? Which of these conditional is true? False.

If you are at least 18 years of age, then you own an automatic rifle. False, the antecedent does not guarantee the consequent. If you reverse the antecedent and consequent you have a true conditional. If you own an automatic rifle, then you must be at least 18 years of age. Here, the consequent is a necessary condition for the antecedent.

If you are alive, then you are breathing. The antecedent is a necessary and sufficient condition for the consequent, just as the consequent is a necessary and sufficient condition for the antecedent.

If Bernardo loves spaghetti, then he must be Italian. False. The antecedent is not a sufficient condition (does not guarantee) the consequent nor is the consequent a necessary condition for the antecedent.

If you are driving at speeds that exceed the speed limit, then you are breaking the law. True. The antecedent is a sufficient condition (guarantees) the consequent.

Do you get it?

A conditional claim has this form:

The phrase that follows “If” is the _______________

The phrase that follows “then” is the ______________

In a true conditional statement: p is a ________________ condition for q, meaning that p guarantees q.

If a true conditional statement: q is a ______________ condition, meaning that without q you cannot have A.

Consider: If (p) you earn at least 92% of the total points in this class, then (q) you will make an A for the course.

__ guarantees __; if you don’t have ___, you cannot have ___.

Do you get it?

A conditional claim has this form: If p, then q.

The phrase that follows “If” is the antecedent.

The phrase that follows “then” is the consequent.

In a true conditional statement: p is a sufficient condition for q, meaning that p guarantees q.

If a true conditional statement: p is a necessary condition, meaning that without q you cannot have p.

Consider: If (p) you earn at least 92% of the total points in this class, then (q) you will make an A for the course.

p guarantees q; if you don’t have q, you cannot have p.

The relationship of antecedent to consequent gives us three valid argument forms; here’s one:

Modus Ponens (Affirming the Antecedent

If A, then B. (Premise 1)

A. (Premise 2)

Therefore B. (Conclusion.)

(You must memorize this form; make flashcard)

Note if A guarantees B. then if we affirm A, then we must be able to affirm B. That’s why any argument in this form is always valid. If your premises are true, then your conclusion must be true.

This form is called Modus Ponens or Affirming the Antecedent. (note the second name is based on what you do in the second premise: when you say A as the second premise, you are affirming the antecedent.)

Any argument in this pattern is valid.

Which of the following is NOT in the form of Modus Ponens (Affirming the Antecedent)?

If Jamal flirts with a lot of girls at the party, then Tasha (Jamal’s girlfriend) will be angry with him. Unfortunately, Jamal couldn’t help himself and flirted with lots of girls at the party. Therefore Tasha was very angry.

If Young’s uncle is a monkey, then he is sure to like eating bananas and swinging from tree to tree. I saw Young’s uncle eating bananas and swinging from tree to tree the other day. Therefore, Young’s uncle is a monkey.

Benjamin will go to the doctor if his temperature is above 99 degrees. His temperature is 101. Therefore Benjamin will go to the doctor.

Which of the following is NOT in the form of Modus Ponens (Affirming the Antecedent)?

If (A) Jamal flirts with a lot of girls at the party, then (B) Tasha (Jamal’s girlfriend) will be angry with him. Unfortunately, Jamal couldn’t help himself and flirted with lots of girls at the party. Therefore Tasha was very angry. Form: If A, then B. A. Therefore B. (Affirms the antecedent)

If (A) Young’s uncle is a monkey, then (B) he is sure to like eating bananas and swinging from tree to tree. I saw Young’s uncle eating bananas and swinging from tree to tree the other day. Therefore, Young’s uncle must be a monkey. If A, then B. B. Therefore A. (affirms the consequent, not the antecedent.)

(B) Benjamin will go to the doctor if (A) his temperature is above 99 degrees. His temperature is 101. Therefore Benjamin will go to the doctor. Remember B, if A is equivalent to If A, then B. A. Therefore B. (Affirms the antecedent.)

Step by step with specific example:

If the flight is cancelled, then Beale will need to drive 700 miles to see her parents. Unfortunately the flight has been cancelled. Therefore Beale must drive 700 miles to see her parents.

Step 1: Identify antecedent and consequent. Remember antecedent comes after “If” and consequent comes after “then.” So:

A = flight is cancelled

B = Beale will need to drive 700 miles to see her parents.

Step 2: (crucial!) Look at second premise and ask: Does it affirm or deny A or does it affirm or deny B. In this example the second premise states, “the flight has been cancelled.” So it affirms A.

Step 3: (crucial!): Look at the conclusion and ask: Does it affirm or deny A, affirm or deny B. In this case, it affirms B.

The form is If A, then B. A. Therefore B. Modus Ponens or Affirming the Antecedent. ANY ARGUMENT IN THIS FORM IS VALID SO IF YOU SUPPLY TRUE PREMISES, YOUR CONCLUSION MUST BE TRUE. YOU HAVE A SOUND ARGUMENT WHICH CANNOT BE REASONABLY REJECTED.

Consider the following:

If Carlos is afraid of spiders, then he will not want to go on the camping trip. I heard that he has a phobia about spiders. Therefore, he is sure to miss the camping trip.

If the hospital increases capacity by at least 50%, then it will be able to meet the demands of pandemic. The hospital has not increased capacity by 50%. Therefore, the hospital will not meet the demands of the pandemic.

If Monique has a semester GPA of 4.0, then she must have made all As. She did not make an A in all of her classes. Therefore Monique does not have a semester GPA of 4.0.

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee.

All are Affirming the Antecedent

Only 2 and 4 are Affirming the Antecedent

1 only is Affirming the Antecedent

A (antecedent) B (consequent) What form?

If Carlos is afraid of spiders, then he will not want to go on the camping trip. I heard that he has a phobia about spiders. (Affirms A) Therefore, he is sure to miss the camping trip. Modus Ponens (Affirming the Antecedent) - Valid

If the hospital increases capacity by at least 50%, then it will be able to meet the demands of pandemic. The hospital has not increased capacity by 50%. (Denies A) Therefore, the hospital will not meet the demands of the pandemic. Denying the antecedent – invalid. The first statement does not rule out possibility that hospital may take other steps to meet the demands of the pandemic (i.e., curtailing admissions to those doing elective surgery) (We will study this form later in this lesson.)

If Monique has semester GPA of 4.0, then she must have made all A. She did not make an A in all of her classes. (Denies B) Thefore Monique does not have a semester GPA of 4.0. Modus Tollens (Denying the consequent) – valid (we will study this form later in this lesson)

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. (Affirms B) I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee. Affirming the consequent – invalid - Studying hours and hours is a necessary condition for winning, but not a sufficient condition (does not guarantee A.) (We will study this form later in this lesson.)

Let’s review: Which of the following is FALSE?

Any argument in the form “If A, then B. A. Therefore B,” is valid, which means that if the premises are true, the conclusion must be true.

If you have true premises and put them in this form, then you have a sound argument, whose conclusion cannot reasonably be rejected.

Any argument in the form “If A, then B. A. Therefore B,” is valid, which means that if the premises are true, the conclusion may be true.

This argument form is valid because in a true conditional statement, the antecedent is the sufficient condition for the consequent. So, if you have A, you must have B.

The name of this form is Modus Ponens (Affirming the Antecedent)

Let’s review: Which of the following is FALSE?

Any argument in the form “If A, then B. A. Therefore B,” is valid, which means that if the premises are true, the conclusion must be true. TRUE

If you have true premises and put them in this form, then you have a sound argument, whose conclusion cannot reasonably be rejected. TRUE

Any argument in the form “If A, then B. A. Therefore B,” is valid, which means that if the premises are true, the conclusion may be true. FALSE – This is a valid form – if the premises are true the conclusion must be true.

This argument form is valid because in a true conditional statement, the antecedent is the sufficient condition for the consequent. So, if you have A, you must have B. TRUE

The name of this form is Modus Ponens (Affirming the Antecedent) TRUE

Which of the following is in the form of Modus Ponens?

If you drive a hybrid vehicle, then you save a lot of money on gasoline. You drive a hybrid. Therefore you save a lot of money on gasoline.

If the Broncos win their next game, they will play in the championship game. The Bronco won the game. Therefore, they will plan in the championship game.

If the temperature is over 100 degrees, then all the flowers will wilt. The flowers did not wilt. Therefore the temperature did not exceed 100 degrees.

If Marsha is cheerleader, then she is able to yell loudly and dance vigorously. Marsha yells loudly and dances vigorously. Therefore, she is a cheerleader.

If you have a GPA of 3.2 or higher, then you will graduate with honors. Your GPA is 3.5. Therefore, you will graduate with honors.

Which of the following is in the form of Modus Ponens?

If you drive a hybrid vehicle, then you save a lot of money on gasoline. You drive a hybrid. Therefore you save a lot of money on gasoline. Modus Ponens

If the Broncos win their next game, they will play in the championship game. The Bronco won the game. Therefore, they will plan in the championship game. Modus Ponens

If the temperature is over 100 degrees, then all the flowers will wilt. The flowers did not wilt. Therefore the temperature did not exceed 100 degrees. If A, then B. Not B. Therefore not A. Modus Tollens (We will study this form later in this lesson.)

If Marsha is cheerleader, then she is able to yell loudly and dance vigorously. Marsha yells loudly and dances vigorously. Therefore, she is a cheerleader. If A, then B. B. Therefore. (Affirming the Consequent. We will study this form later in this lesson.)

If you have a GPA of 3.2 or higher, then you will graduate with honors. Your GPA is 3.5. Therefore, you will graduate with honors. Modus Ponens

Affirming the Antecedent (Modus Ponens)

If Jim is a good student, then he goes to class on time.

Jim is a good student.

Therefore, he goes to class on time.

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First step: Identify A and B:

If (A) Jim is a good student, then (B) he goes to class on time.

Jim is a good student.

Therefore, he goes to class on time.

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2. Does the second premise affirm or deny A, or does it affirm or deny B?

If (A) Jim is a good student, then (B) he goes to class on time.

Jim is a good student.

(affirms A, the antecedent)

Therefore, (B) he goes to class on time.

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3. Does the conclusion affirm or deny A, or does it affirm or deny B?

If (A) Jim is a good student, then (B) he goes to class on time.

Jim is a good student.

Therefore, he goes to class on time. (affirms B, the consequent)

The form is: If A, then B. A, Therefore B. Modus Ponens - Affirming the antecedent – Any argument in this form is valid.

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Invalid form: Affirming the Consequent

The relationship of antecedent to consequent in a conditional statement also yields an invalid form, known as Affirming the Consequent. It looks very much like the valid form of Modus Ponens (Affirming the Antecedent), but it is NOT the same.

As the name suggests, the second premise of the arguments affirms the consequent.) Note this form is always invalid.

The title of the form should enable you to guess what it is. Can you guess it:

Premise 1: If A, then B.

Premise 2 (what goes here? A or B?): ____

Premise 3 (what goes here? A or B?): ____

Invalid form: Affirming the Consequent

The relationship of antecedent to consequent in a conditional statement also yields an invalid form, known as Affirming the Consequent. (As the name suggests, the second premise affirms the consequent.) Note this form is always invalid.

The title of the form should enable you to guess what it is. Can you guess it:

Premise 1: If A, then B.

Premise 2 (what goes here? A or B?): B

Premise 3 (what goes here? A or B?): A

If B is the consequent, then to affirm the consequent is to state B in the second premise.

Modus Ponens (always valid) vs. Affirming the Consequent (always invalid)

Modus Ponens – Affirming the Antecedent – Premise 1: If A, then B. Premise 2: A. Conclusion: Therefore B. (Note: premise 2 affirms the antecedent.) This form is always valid, which means that if you put true premises in this form, you will have a sound argument. It is unreasonable to reject the conclusion of a sound argument.

Affirming the Consequent – Premise 1: If A, then B. Premise 2: B. Conclusion: Therefore A. (The second premise affirms B, hence, the name Affirming the Consequent.) This form is always invalid. Note that B is a necessary condition for A, but not sufficient; B does not guarantee A.

Affirming the Consequent (always invalid)

This simple example helps me remember this form.

If it rained last night (A), then the sidewalks are wet (B). The sidewalks are wet. (affirms B, the consequent). Therefore, it must have rained last night. (A)

Why is this argument invalid? Why do the premises NOT guarantee the truth of the conclusion?

What if the water sprinklers were turned on last night? Then the premises would be true, but the conclusion false.

No argument in the form of Affirming the Consequent will guarantee the truth of the conclusion. So, you cannot construct a sound argument using this form.

Example of Affirming the Consequent

Remember this example from a few previous slides?

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee.

Let’s go step by step: Step 1:

A (antecedent) = ____________________

B (consequent) = _____________________

Example of Affirming the Consequent

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee.

Let’s go step by step: Step 1:

A (antecedent) = Zoey won the Spelling Bee (Remember: follow “If”)

B (consequent) = she must have studied hours and hours studying the official word list. (Remember: follows “then”)

Example of Affirming the Consequent

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee.

Let’s go step by step: Step 2:

Does the second premise affirm A or deny A or affirm B or deny B.

________________

Example of Affirming the Consequent

Remember this example from a few previous slides?

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee.

Let’s go step by step: Step 2:

Does the second premise affirm A or deny A or affirm B or deny B.

Affirms B. (I know for a fact that she spent hours and hours studying the official word list.)

Example of Affirming the Consequent

If Zoey won the Spelling Bee, then she must have studied hours and hours on the official word list. I know for a fact that she spent hours and hours studying the official word list. Therefore, she must have won the Spelling Bee.

Let’s go step by step: Step 3: Why is it invalid? Can the premises be true and the conclusion false? Yes. Just because Zoey studied hours and hours does not guarantee that she won the Spelling Bee. I would assume that many contestants studied the official list for hours and hours. But, not all will win.

Stated differently, studying hours and hours is a necessary condition for winning the Spelling Bee; if you don’t study for hours and hours you can’t win. But studying hours and hours is NOT a sufficient condition because it does not guarantee winning.

What is true of this example is true of all arguments in this form.

Consider this example of Affirming the Consequent

If human-like beings exist on another planet, then that planet must have oxygen. Scientist have discovered traces of oxygen on Planet X, which is 100 million light years away. So human-like beings exist on Planet X.

What are A and B?

A = ________________________________

B = ________________________________

What is the form of the argument?

_________________________________

Is that argument valid or invalid? Why

Consider the example of Affirming the Consequent

If human-like beings exist on another planet, then that planet must have oxygen. Scientist have discovered traces of oxygen on Planet X, which is 100 million light years away. So human-like being exist on Planet X.

What are A and B?

A = human-like beings exist on another planet

B = that planet must have oxygen

What is the form of the argument?

If A, then B. B. Therefore A.

Is that argument valid or invalid? Why?

Once you recognize the form of affirming the consequent, you know the argument is invalid, which means the premises could be true and the conclusion false. Think about it: If it is true that scientists have detected oxygen on Planet X, then human-like beings may exist on Planet X, but the existence of oxygen alone does not guarantee it.

Stated differently, the consequent is a necessary condition for the antecedent, but not a sufficient condition. (Without the consequent, it is impossible to have the antecedent, but it does not guarantee the antecedent.)

Let’s review:

What is the conditional statement: ____________________

The phrase that follows “If,” is the ___________________

The phrase that follows “then,” is the __________________

In a true conditional, the antecedent is a _____________ condition for the consequent, which means A guarantees B.

In a true conditional, the consequent is a _____________ condition for the antecedent, which means that if without the consequent, you can’t have the antecedent.

What is the valid argument form, Modus Ponens (Affirming the Antecedent) ?

What is the invalid argument form, Affirming the Consequent?

Let’s review:

What is the conditional statement: If A, then B.

The phrase that follows “If,” is the antecedent.

The phrase that follows “then,” is the consequent.

In a true conditional, the antecedent is a sufficient condition for the consequent, which means A guarantees B.

In a true conditional, the consequent is a necessary condition for the antecedent, which means that if without the consequent, you can’t have the antecedent.

What is the valid argument form, Modus Ponens (Affirming the Antecedent) ? If A, then B. A. Therefore B.

What is the invalid argument form, Affirming the Consequent?

If A, then B. B. Therefore A.

Which of the following is NOT in the form of Affirming the Consequent?

If there was a bomb threat at the airport (A), then all flights will be cancelled (B). All flights have been cancelled (B). Therefore, there must have been a bomb threat at the airport (A). Affirming the Consequent – Invalid - Flights could have been cancelled for another reason.

If James is an All American football player (A), then he must be in excellent physical condition (B). James is in excellent physical condition (B). Therefore James is an All-American football player (A). Affirming the Consequent Being in excellent physical condition does NOT guarantee that one is an All-American football player.

If Reynaldo has lived his entire life in Brazil (A), the he has never eaten Kentucky Fried Chicken (Be). Reynaldo says he has never eaten Kentucky Fried Chicken (B). Therefore, he must lived his entire life in Brazil (A). Affirming the Consequent - Invalid What if Reynaldo is a vegetarian? Then he would not have eaten KFC.

If Marlon remembers seeing the original Jurassic Park when it first came out in 1993 (A), then he must be at least 30 years old (B). Marlon vividly remembers seeing the original Jurassic Park when it first came out (A). Therefore he must be at least 30 years old. Affirming the Antecedent. This argument is valid. If the premises are true the conclusion must be true.

If the wind was blowing at more than 25 miles per hour (A), then the hot air balloon race had to be cancelled (B). The balloon race was cancelled (B). Therefore, the winds were blowing at more than 25 miles per hour (A). Affirming the Consequent – The balloon race could be cancelled for reasons other than high winds. Invalid - The truth of these premises do not guarantee the truth of the conclusion.

Two new forms: one valid, one invalid

Remember in a true conditional statement, If A (antecedent), then B (consequent), the antecedent is a sufficient condition for the consequent and the consequent is a necessary condition for the antecedent.

The fact that the antecedent is a sufficient condition for (guarantees) the consequent gives us the valid form Modus Ponens (Affirming the Antecedent): If A, then B. A. Therefore B. Any argument in this form is valid.

If the consequent is a necessary condition for the antecedent, if we deny the consequent (i.e., claim it is not true), then we must deny the antecedent (i.e., the antecedent cannot be true).

The form is: If A, then B. Not B. Therefore, not A.

It’s name: Modus Tollens (Denying the Consequent) (Make flash card)

Any argument in either of these two forms (Modus Ponens, Modus Tollens) is VALID, which means that if the premises are true, then the conclusion must be true. If you put true premises in either form, then you have a sound argument, whose conclusion cannot be reasonably rejected.

Did you get it?

What is the form of Modus Tollens (Denying the Consequent):

If A, then B.

__________ What goes here? Type in Chat.

Not A.

Give an example:

Did you get it?

What is the form of Modus Tollens (Denying the Consequent):

If A, then B.

Not B

Not A.

Give an example:

If you were paying attention to the previous slide, then you would have easily provided an example. You did not easily provide an example. Therefore, you were not paying attention to the previous slide.

Analyze example – step by step

If Octavia earned an A in biology, she must have completed all the lab assignments. Unfortunately, Octavia did not complete all the lab assignments. Therefore she did not earn an A in biology.

Step 1: Identify A (antecedent) and B (consequent)

A = Octavia earned an A in biology.

B = She must have completed all the lab assignments.

Step 2: Identify the pattern.

First premise: If A, then B.

Second premise: Affirm or Deny A? Affirm or Deny B? See “not” in second premise – so it denies B, Not B.

Third premise: Affirm or Deny A? Affirm or Deny B? See “not” in third premise? Denies A

The form is: If A, then B. Not B. Therefore Not A.

If the consequent is necessary condition for antecedent, then if B is denied, A must also be denied. Any argument in this form is valid.

Which of the following is NOT Modus Tollens (Denying the Consequent)

If it rained last night, then the sidewalks are wet. The sidewalks are not wet. Therefore it did not rain last night.

If you reading this slide, then you must be in Young’s Critical Thinking class. You are not in Young’s Critical Thinking class. Therefore you are not reading this slide.

If you are my friend, then you would not have lied to me. But, you lied to me. Therefore, you are not my friend.

If Abilene attracts a million tourists per year, then the city has many fine hotels. The city does not attract a million tourists per year. Therefore the city does not have many fine hotels.

If English is Emily’s native tongue, then she must have grown up in a country whose first language is English. But Emily did not grow up in a country whose first language is English. Therefore, English is not Emily’s native tongue.

Which of the following is NOT Modus Tollens (Denying the Consequent)

If (A) it rained last night, then (B) the sidewalks are wet. The sidewalks are not wet (Not B). Therefore it did not rain last night (Not A).Modus Tollens

If (A) you reading this slide, then (B) you must be in Young’s Critical Thinking class. You are not in Young’s Critical Thinking class (not B). Therefore you are not reading this slide (not A). Modus Tollens

If (A) you are my friend, then (B) you would not have lied to me. But, you lied to me (not B)*. Therefore, you are not my friend (Not A). Modus Tollens

*Note: B already includes “not” so denying B means removing “not” from the statement.

If (A) Abilene attracts a million tourists per year, then (B) the city has many fine hotels. The city does not attract a million tourists per year (Not A). Therefore the city does not have many fine hotels (Not B). This example denies the antecedent so it is NOT Modus Tollens.

If (A) English is Emily’s native tongue, then (B) she must have grown up in a country whose first language is English. But Emily did not grow up in a country whose first language is English (not B). Therefore, English is not Emily’s native tongue (Not A). Modus Tollens

Invalid form: Denying the Antecedent

Any arguments in the form of Modus Tollens, Denying the Consequent, If A, then B. Not B. Therefore not A, is always valid. If you provide true premises in this form, they you have a sound argument, and a sound argument is one whose conclusion cannot reasonably be rejected.

Arguments in the form of Denying the Antecedent will always be invalid. You should be able to guess this form.

If A, then B. _____________. Not B. What goes in the blank?

Invalid form: Denying the Antecedent

Any arguments in the form of Modus Tollens, Denying the Consequent, If A, then B. Not B. Therefore not A, is always valid. If you provide true premises in this form, they you have a sound argument, and a sound argument is one whose conclusion cannot reasonably be rejected.

Arguments in the form of Denying the Antecedent will always be invalid. You should be able to guess this form.

If A, then B. Not A. Not B. (To say “not A” is to deny the antecedent.)

Invalid form: Denying the Antecedent

Why is this form always INvalid? The antecedent is a sufficient condition for the consequent, NOT a necessary condition.

The example from a few slides ago show how this works.

If (A) Abilene attracts a million tourists per year, then (B) the city has many fine hotels. The city does not attract a million tourists per year (Not A). Therefore the city does not have many fine hotels (Not B). Denying the Antecedent

Attracting a million tourists per year guarantees that Abilene has many fine hotels. A is sufficient for B. But having a million tourists is NOT a necessary condition for having many fine hotels since Abilene may still have many find hotels for reasons other than having a million tourists a year.

What is true of this example is true of any argument in this form.

Which of the following is NOT Denying the Antecedent?

If Wilmington is hit by three bad hurricanes every year, then the city has a very well-developed emergency management system. But Wilmington is not hit by three bad hurricanes every year. Therefore, Wilmington does not have a well-developed emergency management system.

If Sherrod eats broccoli and runs a mile every day, then he is very healthy. But Sherrod does not eat broccoli and he doesn’t run a mile every day. Therefore, he is not very healthy.

If Marcia drives a Hybrid, then she saves money on gasoline. Marcia does not drive a Hybrid. Therefore, Marcie does not save money on gasoline.

If Bernard loaned Samuel $100 so Samuel could repair his car, then Bernard is a very good friend to Samuel. But Bernard was not able to loan Samuel $100. Therefore, Bernard is not a very good friend to Samuel.

If Tamika has COVID 19, then she has a fever, shortness of breath, and respiratory problems. But, she does not have a fever, shortness of breath, and respiratory problems. Therefore, she does not have COVID 19.

Which of the following is NOT Denying the Antecedent?

If (A) Wilmington is hit by three bad hurricanes every year, then (B) the city has a very well-developed emergency management system. But Wilmington is not hit by three bad hurricanes every year (Not A). Therefore, Wilmington does not have a well-developed emergency management system (not B).

If (A) Sherrod eats broccoli and runs a mile every day, then (B) he is very healthy. But Sherrod does not eat broccoli and he doesn’t run a mile every day (not A). Therefore, he is not very healthy (not B).

If (A) Marcia drives a Hybrid, then (B) she saves money on gasoline. Marcia does not drive a Hybrid (not A). Therefore, Marcie does not save money on gasoline (Not B).

If (A) Bernard loaned Samuel $100 so Samuel could repair his car, then (B) Bernard is a very good friend to Samuel. But Bernard was not able to loan Samuel $100 (not A). Therefore, Bernard is not a very good friend to Samuel (not B).

If (A) Tamika has COVID 19, then (B) she has a fever, shortness of breath, and respiratory problems. But, she does not have a fever, shortness of breath, and respiratory problems (not B). Therefore, she does not have COVID 19 (not A). If A, then B. Not B. Therefore Not A. – Modus Tollens – Denying the Consequent Note: This argument is valid in form, but the first premise is false since we know that some people have the virus but do not have the symptoms.

Two valid argument forms

Two INvalid argument forms

Conditional Syllogism: Two valid forms

Affirming the Antecedent (Modus Ponens)

If __, then __.

__

Therefore ____

Denying the Consequent

(Modus Tollens)

If __, then __.

__

Therefore ____