The key concept in deductive logic is the concept of validity. One good way to learn to understand the concept of validity better is to discover what makes arguments invalid.
Prepare: To prepare to respond to this prompt read carefully the required portions of Chapters 3 and 4, paying special attention to the sections from Chapter 3 about validity and using the counterexample method. Take a look as well at the required resources from this week, especially those that discuss the concept of validity.
Reflect: Choose an argument from the following list of arguments (try to make sure not to choose the same argument as someone else). Consider the way in which the reasoning is actually invalid (perhaps subtly). Think about why that argument is invalid in the sense that it would be possible for all of the premises to be true and the conclusion false.
Choose from the following list of argument options.
1. If the maid was guilty then she would have had to been at the scene during the crime. However, she was seen a mile away only minutes before the crime, and she has no car. She must be innocent.
2. Everyone has to eat food with adequate calories. A bag of Doritos is food with adequate calories, so everyone should eat a bag of Doritos.
3. All winos drink alcohol. All alcoholics drink too much. Therefore all winos are alcoholics.
4. He won’t go to the wedding since he doesn’t like mushy stuff and weddings are mushy.
5. I can’t go to the movies with you – I have a test tomorrow and I have to study.
6. Capital punishment is wrong because it kills a human being.
7. To go to the movie you have to have a ticket. To buy a ticket you must pay money. Thus, to go the movie you must pay money.
8. All dogs have fur. All mammals have fur. So all dogs are mammals.
9. If he makes a lot of money then he dresses nice and has a fancy car. He does dress nice and have a fancy car. So he must make a lot of money.
10. He will cry during the movie if he is a big softie. He cried during the movie. Therefore he is a big softie.
11. If I wear that cologne then women will love me. I bought that cologne, so women are going to love me.
12. No snakes are mammals. No mammals are birds. Therefore no snakes are birds.
13. Every dog with brown fur hates cats. Some dogs have red fur. Therefore some dogs love cats.
14. To fix your care you will need money. However, to have money you have to have money. It appears that you need to get a job.
15. Only adults can legally drink. John is too young to legally drink. Therefore, John is not an adult.
16. Mike loves pickles. Pickles come from cucumbers. Therefore Mike loves cucumbers.
17. If you don’t do your chores then you can’t have any dessert. You really like dessert, so you will certainly do your chores.
18. You can have soup or salad. You are having the salad, so you won’t be having any soup.
19. You will get an A if you study hard and always come to class. You came to class every time and studied. You are bound to get an A.
20. He broke the record for rushing yards in a game on that last play. No one else has broken the record since then. Therefore he still holds the record.
21. He won the election. The election was for governor. So he will be the next governor.
22. The sun has risen every morning for millions of years. The sun rises because the earth turns every 24 hours. Therefore the sun will rise again tomorrow morning.
23. If he loved you he would have shown up on time with flowers. He must not love you.
24. Abortion kills a human being, therefore abortion is wrong.
25. Julie is allergic to gluten. So she won’t be having any bread.
26. Only women can have babies, so women are more important to the survival of the species.
27. You shouldn’t use drugs because they are addictive and can ruin people’s lives.
28. You shouldn’t go out with that guy. He rides a motorcycle and goes to bars.
29. In order to buy a car you will need money. But, to have money you need to get a job. But to go to a job you will need to be able to get to work. So, you will not be able to buy a car.
30. Capital punishment kills a human being. It is wrong to kill a human being except in self-defense. So capital punishment is wrong.
31. If you talk to Mike about politics then he will yell at you. If he yells at you then you will be hurt and it will damage your friendship. Therefore you shouldn’t talk to Mike about politics.
32. Either the maid or the butler did it. For the butler to have done it he would have had to have been at the mansion yesterday. The butler was away all day yesterday. So the maid did it.
33. It is always wrong to kill a human being unless it is in self-defense. Abortion kills a human being. So abortion is wrong unless the mother’s life is in danger due to the pregnancy.
34. You shouldn’t tell someone to do something unless you would be willing to do it yourself. You’ve never gone to war. So you shouldn’t vote for others to go to war.
35. Government intervention is justified if it is necessary to protect the welfare of the people and does not violate anyone’s constitutional rights. Therefore, government intervention is justified in this specific case because it is necessary to protect the welfare of the people.
Write: Put the argument into standard form, clearly identifying the premises and conclusion. Once you have done so then demonstrate that the argument is invalid in one of two ways: Either explain a scenario in which the premises could be true and the conclusion false, or find another argument with the same form that has true premises and a false conclusion. Once you have done so, make sure to explain how your argument refutes the validity of the original argument. Mention if you think that there is anything that could be done to make the original argument valid.
Guided Response: Read the reflections of your classmates and analyze the counter example that they have presented. Provide another example that demonstrates that the same argument is invalid. In particular, if you believe that the argument is invalid, explain a way in which it would be possible for the premises to be true and the conclusion false or give another argument of the same form in which the premises are true and the conclusion is false.
By the way, why can valid arguments have false conclusions? And, why are premises/reasons never valid or invalid?