Deductive Argument Questions and Examples

1. If you study hard, you’ll get an A.

The above is not an argument. What is it? What is the antecedent? What is the consequent? Under what combinations of true and falsity of the antecedent and consequent is this statement true? When the antecedent is false, why is the entire statement considered true?

2. Does whether an argument is logically valid depend on the truth of the premises? Why or why not?

3. In a deductively valid argument, if the premises are true, is the conclusion is logically guaranteed to be true? Why or why not?

Deductive Argument Examples: Diagram these out with p's and q's, then look at your list of deductive arguments and fallacies and say which argument it best fits the example. The say whether it is logically valid or invalid. The first is done for you.

4. If you study hard, you’ll get an A.
You studied hard.
Therefore, you’ll get an A.

p = you study hard
q = you'll get an A

If p then q
p
Therefore q.
Modus ponens

5. If you study hard, you’ll get an A.
You didn’t study hard.
Therefore, you won’t get an A.

6. If you study hard, you’ll get an A.
You got a A.
Therefore, you studied hard.

7. If you study hard, you’ll get an A.
You didn’t get an A
Therefore, you didn’t study hard.

8. It was either the chicken or the potato salad that made me sick.
It wasn’t the potato salad (because Bob had some, and he was fine).
So, it must have been the chicken.

9. If it’s going to rain tomorrow, I’d better get the lawn mowed today.
It is going to rain tomorrow.
So, I better get the lawn mowed today.

10. If you want a realistic choice of your candidate winning, you either gotta vote Democrat or Republican. If you vote Democrat, you get socialism, racial demagoguery, and nanny state nonsense. If you vote Republican, you get religious moralism and endless wars. So, in America, you’re stuck either picking a socialist, race-hustling schoolmarm or a Bible-thumping warmonger.

11. If Sanders and Warren don’t drop out of the Democratic primary, they will split the progressive vote, and Biden will win the nomination.
Neither Sanders nor Warren will drop out.
Therefore, Biden will win.

12. If Bernie Sanders’ health doesn’t hold up, he’s not going to win the Democratic primary.
Sanders made a full recovery from his heart attack; his health is holding up.
Therefore he’s going to win the primary.

13. If those mushrooms were poisonous, I’d be showing symptoms by now.
I’m not showing any symptoms.
Therefore, those mushrooms weren’t poisonous.

14. If Socrates is a man, then Socrates is moral.
Socrates is a man.
Therefore, Socrates is mortal.

15. Either Hillary knew her home brew email server was illegal or she didn’t.
If she knew it was illegal, she is corrupt and guilty of a crime.
If she didn’t know it was illegal, she is incompetent and unfit for office.
So either Hillary is corrupt and guilty of a crime or incompetent and unfit for office.

16. Either God wants to prevent evil, but can’t, or he can prevent evil, but doesn’t want to.
If he wants to prevent evil, but can’t, he’s not omnipotent.
If he can prevent evil, but doesn’t want to, he’s not good.
Therefore God is either not omnipotent or not good.

17. If the problem is a dead battery, then the engine won’t turn over.
The engine won’t turn over.
Therefore, the problem is a dead battery.

18. It’s either the battery or the alternator.
I tested the battery and it’s fine, so that's not it.
It must be the alternator.

19. If you ban guns, then law abiding citizens will turn their guns in but criminals will keep theirs.
If law-abiding citizens are disarmed and criminals aren’t, then crime will increase.
Therefore, if you ban guns, crime will increase.

20. If the Bible is the Word of God, then God commanded genocide (e.g. Joshua, 1 Sam 15).
The Bible is the word of God.
Therefore, God commanded genocide.

21. If the Bible is the Word of God, then God commanded genocide.
God would never command genocide!
Therefore, the Bible isn’t the word of God.

22. What do you think “one man’s modus ponens is another man’s modus tollens” mean?

23. Death is not an evil. For either death is an endless sleep or a transition to a better life. If it’s an endless sleep it’s not an evil (because you have to be conscious to experience something bad). If it’s a transition to a better life it’s not an evil. Who wouldn’t enjoy meeting the heroes of old and finally getting to talk to the gods? So, either way, death is not an evil.