The Conditional Syllogism
Answers to the Exercises


1.
If one chooses vice over virtue, one will suffer in life.
one is suffering in life.
Ergo, one has chosen vice over virtue.

Invalid.  Affirming the Consequent.

2.
If government is for the common good, it is not for the good of only the few.
Government is for the common good.
Ergo, government is not for the good of only the few.

Valid.  Affirming the Antecedent.

3.
If life exists on Mars, then Mars has an atmosphere.
Mars has an atmosphere.
Ergo, life exists on Mars.

Invalid.  Affirming the Consequent.

4.
If life involves quantity, it is physical.
Life does not involve quantity.
Ergo, life is not physical.

Invalid.  Denying the Antecedent.

5.
If atoms are ultimate particles, they are indivisible.
Atoms are not indivisible.
Ergo, they are not ultimate.

Valid.  Denying the Consequent.

6.
If the premises of this argument are true, then the conclusion of this argument is true (i.e., the argument is valid).
The conclusion of this argument is true.
Ergo, the premises of this argument are true.

Invalid.  Affirming the Consequent.

7.
If the premises of this argument are true, then the conclusion of this argument is true (i.e., the argument is valid).
The premises of this argument are not true.
Ergo, the conclusion of this argument is not true.

Invalid.  Denying the Antecedent.

8.
If you can type fast, you will be grateful later on.
You can type fast.
Ergo, you will be grateful later on.

Valid.  Affirming the Antecedent.

9.
If you breath in mold or mildew, you will get a cold.
You have a cold.
Ergo, you breathed in mold or mildew.

Invalid.  Affirming the Consequent.

10.
If you pray, God will draw close to you.
God did not draw close to you.
Ergo, you don’t pray.

Valid.  Denying the Consequent.

11.
If you eat right, you will be healthy.
I don’t eat right
Ergo, you are not healthy.

Invalid.  Denying the Antecedent.


12.
If you learn to think, life will be much easier for you.
Life is not much easier for me.
Ergo, you didn’t learn to think.

Valid.  Denying the Consequent.

13.
Eat lots of vegetables and fruit, and you reduce your risk of cancer.
I eat lots of veggies and fruit.
Ergo, I have reduced my risk of cancer.

Valid.  Affirming the Antecedent.

14.
If Henry has moral scruples against drinking, then Henry never drinks.
Henry never drinks.
Ergo, Henry has moral scruples against drinking.

Invalid.  Affirming the Consequent.

15.
If the defendant is willing to testify, then he is innocent.
The defenant is not willing to testify.
Ergo, the defendant is not innocent.

Invalid.  Denying the Antecedent.