Deductive Argument Forms
Either the game has been sold out, or it has been canceled. If it's been sold out, I won't be able to see it, and if it's been canceled, I won't be able to see it. So I won't be able to see the game. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
1. Dilemma (valid)
If stocks go up, bonds go down. If interest rates rise, bonds go down. Therefore, since stocks or interest rates will go up, bonds will go down. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
1. Dilemma (valid)
If tax credits are given for private education, then the government will be supporting religion; but if tax credits are not given for private education, then some parents will end up paying double tuition. Either tax credits will or will not be given for private education. Therefore, either the government will be supporting religion, or some parents will end up paying double tuition. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
1. Dilemma (valid)
If you enter the teaching profession, you will have no money for vacations; and if you do not enter the teaching profession, you will have no time for vacations. Since you must either enter or not enter the teaching profession, it follows that either you will have no money or no time for vacations. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
1. Dilemma (valid)
If she doesn't have a fever, then she doesn't have the flu. She doesn't have a fever. So she doesn't have the flu. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
1. Modus Ponens
Insurance companies contribute millions of dollars to political campaigns. But if that is so, then meaningful insurance reform is impossible. Therefore, meaningful insurance reform is impossible. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
1. Modus Ponens
Is the following argument an instance of Modus Ponens, Modus Tollens, or neither? If Miley Cyrus is a role model for today's youth, society is in decline. And, let's be honest, Miley Cyrus is a role model for today's youth. So, it's evident that society is in decline. 1. Modus Ponens 2. Modus Tollens 3. Neither
1. Modus Ponens
What is the form of the following argument? Film making is certainly an art form. That's because if film making involves the possibility for creativity, then it is an art form, and it does involve the possibility for creativity. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism
1. Modus Ponens
1. The Packers do not have the best record in the NFC North. 2. ____________________ 3. Thus, the Vikings have the best record in the NFC North. 1.Either the Vikings or the Packers have the best record in the NFC North. 2.If the Vikings don't have the best record in the NFC North, then the Packers do. 3.If the Packers have the best record in the NFC North, then the Vikings do. 4.If the Packers lost yesterday, they don't have the best record in the NFC North.
1.Either the Vikings or the Packers have the best record in the NFC North. 2.If the Vikings don't have the best record in the NFC North, then the Packers do.
If global warming continues over the next fifty years, glaciers and polar ice caps will continue to melt. If glaciers and polar ice caps continue to melt, sea levels will rise by several feet, pushing Florida's coast inland by one thousand feet. So if global warming continues, Florida's coast will move inland. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
2. Hypothetical Syllogism (valid)
If sea levels rise twenty feet worldwide, then coastal cities from New York to Sydney will be inundated. If the ice sheets on Antarctica slip into the sea, then sea levels will rise twenty feet worldwide. Therefore, if the ice sheets on Antarctica slip into the sea, then coastal cities from New York to Sydney will be inundated. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
2. Hypothetical Syllogism (valid)
If sea levels rise twenty feet worldwide, then coastal cities from New York to Sydney will be inundated. If the ice sheets on Antarctica slip into the sea, then sea levels will rise twenty feet worldwide. Therefore, if the ice sheets on Antarctica slip into the sea, then coastal cities from New York to Sydney will be inundated. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
2. Hypothetical Syllogism (valid)
If the sun is a variable star, then its energy will drop drastically at some point in the future. If the sun's energy drops drastically at some point in the future, then the earth will become a giant iceball. Therefore, if the sun is a variable star, then the earth will become a giant iceball. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
2. Hypothetical Syllogism (valid)
If philosophy class were fun, all students would major in philosophy. But obviously very, very few students actually major in philosophy. Therefore, philosophy class isn't fun. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
2. Modus Tollens
Is the following argument an instance of Modus Ponens, Modus Tollens, or neither? The phone can't be working. Look, if the phone's working, then Joe is on the phone catching up on all the scores. But Joe isn't on the phone. 1. Modus Ponens 2. Modus Tollens 3. Neither
2. Modus Tollens
1. If Joe fails the course, he will not have enough credits to graduate. 2. ____________________ 3. Thus, if Joe fails the course, he will need to take out additional loans. 1.Either Joe will fail the course or he will take out additional loans. 2.If Joe doesn't have enough credits to graduate, he will need to take out additional loans. 3.If Joe needs to take out additional loans, he will have enough credits to graduate. 4.Joe will fail the course.
2.If Joe doesn't have enough credits to graduate, he will need to take out additional loans.
1. Mary is eligible for the job only if she graduates from college. 2. ____________________ 3. Thus, Mary isn't eligible for the job. 1.Mary has graduated from college. 2.Mary has not graduated from college. 3.If Mary graduates from college, then she is eligible for the job.
2.Mary has not graduated from college.
If life is always better than death, then people do not commit suicide. But people do commit suicide. Therefore, life is not always better than death. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
2.Modus Tollens
Either the wealthiest people are the happiest, or it is not the case that money can buy everything. The wealthiest people are not the happiest. Therefore, money cannot buy everything. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid
3. Disjunctive Syllogism (valid)
Either you buy a lottery ticket for the school library fund, or you care nothing about the library. But surely you care about the library, so you'll buy a lottery ticket. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
3. Disjunctive Syllogism (valid)
If the sale of pornographic material continues, there will be an increase in sex-related crimes like rape and incest. If there is such an increase, then the moral fabric of society will gradually erode. And if the moral fabric of society gradually erodes, there will ultimately be a total collapse of civilization. Thus, if the sale of pornographic materials continues, there will ultimately be a total collapse of civilization. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
3. Hypothetical Syllogism
What is the form of the following argument? David Ortiz will be a hero in Boston if the Red Sox win the World Series. But provided that Koji Uehara continues playing the way he is now, the Red Sox will win the World Series. So provided that Koji Uehara continues playing the way he is now, it is David Ortiz who will become a hero in Boston. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism
3. Hypothetical Syllogism
What is the form of the following argument? Sir Walter Scott had it right: "O what a tangled web we weave when first we practice to deceive!"And of course, when we weave a tangled web, we ourselves can get trapped in the sticky tangle. So, we run the risk of getting caught in a sticky tangle if we start going down the deception road. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism
3. Hypothetical Syllogism
Is the following argument an instance of Modus Ponens, Modus Tollens, or neither? If Prohibition succeeded in the 1920s, then the war on drugs will succeed today. But Prohibition did not succeed in the 1920s. Therefore, the war on drugs will not succeed today. 1. Modus Ponens 2. Modus Tollens 3. Neither
3. Neither
If Prohibition succeeded in the 1920s, then the war on drugs will succeed in the 1990s. But Prohibition did not succeed in the 1920s. Therefore, the war on drugs will not succeed in the 1990s. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
4. Denying the Antecedent (invalid)
If TV viewing provides genuine relaxation, then TV enhances the quality of life. But TV viewing does not provide genuine relaxation. Therefore, TV does not enhance the quality of life. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
4. Denying the Antecedent (invalid)
Either industrial pollutants will be more stringently controlled, or acid rain will continue to fall. Industrial pollutants won't be more stringently controlled. So acid rain will continue to fall. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
4. Disjunctive Syllogism
Either the wealthiest people are the happiest, or it is not the case that money can buy everything. The wealthiest people are not the happiest. Therefore, money cannot buy everything. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
4. Disjunctive Syllogism
Max doesn't wear glasses. But we know he does wear some form of corrective lenses - either glasses or contacts. So Max must wear contacts. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
4. Disjunctive Syllogism
What is the form of the following argument? From The Lion, the Witch, and the Wardrobe, by C.S. Lewis: "Logic!" said the Professor half to himself. "Why don't they teach logic at these schools? There are only three possibilities. Either your sister is telling lies, or she is mad, or she is telling the truth. You know she doesn't tell lies and it is obvious that she is not mad. For the moment then and unless any further evidence turns up, we must assume that she is telling the truth." 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism
4. Disjunctive Syllogism
What is the form of the following argument? There's no doubt about it - Bob took the last donut from the philosophy lounge. Look, either Ted took the donut or Bob did, and there's no way that Ted took that donut. So, the donut-thief has got to be Bob. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism
4. Disjunctive Syllogism
If Mexico does not get its population growth under control, then its unemployment problem will never be solved. Mexico's unemployment problem will never be solved. Therefore, Mexico will not get its population growth under control. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
5. Affirming the Consequent (invalid)
If Michelangelo painted the ceiling of the Sistine Chapel, then he was familiar with stories from the Old Testament.Michelangelo was familiar with stories from the Old Testament. Therefore, Michelangelo painted the ceiling of the Sistine Chapel. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
5. Affirming the Consequent (invalid)
The Earth is spherical in shape. For the night sky looks different in the northern and southern parts of the earth, and this would be so if the Earth were spherical in shape. (Aristotle) 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
5. Affirming the Consequent (invalid)
If high school clinics dispense birth control devices, they are encouraging illicit sex; but if they don't dispense birth control, then they won't be able to stem the tide of teenage pregnancy. It seems that high schools either won't stem the tide of teenage pregnancy or will encourage more illicit sex among high school students. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
5. Dilemma
If taxes increase, needed governmental services will be extended, and if taxes decrease, the economy will improve. Since taxes must either increase or decrease, it follows that needed governmental services will be extended or the economy will improve. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
5. Dilemma
Melinda will either spend the night studying or not studying. If she spends the night studying, she will miss the party; but if Melinda does not spend the night studying, she will fail the test tomorrow. So Melinda is either going to fail her test or miss the party. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
5. Dilemma
Insurance companies contribute millions of dollars to political campaigns. But if that is so, then meaningful insurance reform is impossible. Therefore, meaningful insurance reform is impossible. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
6. Modus Ponens (valid)
Professional baseball players can command big salaries, and they can do so only if the public supports them strongly. So the public strongly supports professional baseball players. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
6. Modus Ponens (valid)
Sally will go to the dance if Charlie will. But Charlie will certainly go, so Sally will be there. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
6. Modus Ponens (valid)
Twenty percent of America's children have never seen a dentist. But if that is so, health care in America is not properly distributed. Therefore, health care in America is not properly distributed. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
6. Modus Ponens (valid)
After Butch drinks too much alcohol he always shouts obnoxiously and stammers. And there he is over there shouting and stammering right now. Butch must have had too much to drink. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
6. Other
Either tortured political prisoners in Turkey can openly complain of their mistreatment, or Turkey is not a democracy. Tortured political prisoners in Turkey can openly complain of their mistreatment. Thus, Turkey is a democracy. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
6. Other
Every whole number is either even or odd. Not every whole number is even. Therefore, every whole number is odd. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
6. Other
If Mexico does not get its population growth under control, then its unemployment problem will never be solved. Mexico's unemployment problem will never be solved. Therefore, Mexico will not get its population growth under control. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
6. Other
If coal burning continues, then heavy metals will be released into the atmosphere. If heavy metals are not released into the atmosphere, then nervous system damage will decrease. Therefore, if coal burning does not continue, then nervous system damage will decrease. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
6. Other
If it is possible to keep people alive indefinitely, then we face serious questions about the purpose and quality of such life. Therefore, since it is not possible to keep people alive indefinitely, we do not have to face those serious questions. 1. Modus Ponens 2. Modus Tollens 3. Hypothetical Syllogism 4. Disjunctive Syllogism 5. Dilemma 6. Other
6. Other
Future presidents will be allowed to serve a third term only if the Twenty-second Amendment is repealed. The Twenty-second Amendment will not be repealed. Therefore, future presidents will not be allowed to serve a third term. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
7. Modus Tollens (valid)
Without complications, life is uninteresting. But life is interesting, so there must be complications. 1. Dilemma (valid) 2. Hypothetical Syllogism (valid) 3. Disjunctive Syllogism (valid) 4. Denying the Antecedent (invalid) 5. Affirming the Consequent (invalid) 6. Modus Ponens (valid) 7. Modus Tollens (valid)
7. Modus Tollens (valid)
If P then Q Q Therefore, P
Affirming the Consequent (invalid)
If P then Q Not P Therefore, not Q
Denying the Antecedent
Either P or Q If P then R If Q then S Therefore, either R or S
Dilemma
Either P or Q Not P Therefore, Q
Disjunctive syllogism (valid)
If P then Q If Q then R Therefore, if P then R
Hypothetical syllogism
If P then Q P Therefore, Q
Modus Ponens (valid)
If P then Q Not Q Therefore, not P
Modus Tollens (valid)