Testing syllogisms and conditional arguments for validity
To be a valid syllogism, the conclusion must be proven by the reasons. Carefully study the following syllogisms and decide if they are valid or invalid:
1. All zebras are striped animals.
No zebras are polar bears.
Therefore, no polar bears are striped animals.
2. All clowns are funny individuals.
Some sad people are clowns.
Therefore, some sad people are funny individuals.
3. Some sticky substances are yucky things.
All taffy is a sticky substance.
Therefore, some taffy is a yucky thing.
4. All items made of gold are expensive items.
Some rings are items made of gold.
Therefore, some rings are expensive items.
5. All flies are winged creatures.
All butterflies are winged creatures.
Therefore, all butterflies are flies.
The following are examples of syllogistic arguments that are missing the conclusions. Study the two reasons very carefully and complete the syllogism with the conclusion that logically follows. Make sure to include key words such as “some”, “all”, etc.
6. All fragile things are breakable things.
Some glasses are fragile things.
7. All mammals are warm-blooded animals.
All whales are mammals.
8. All books are things with pages.
Some books are mysteries.
9. All flowers are pretty objects.
All pansies are flowers.
10. No animals are plants.
All sheep are animals.
Reprinted with permission of the authors Elizabeth T. Tice, PhD and Jay Gallagher, PhD.
Hypothetical syllogisms (conditional arguments) can have two valid and two invalid structures. The two valid structures are affirming the antecedent (modus ponens) and denying the consequent (modus tollens). The two invalid structures, or fallacies, are denying the antecedent and affirming the consequent. Determine if the arguments below are valid or invalid and what form they take. The first one has been done for you.
(NOTE: The term “modus pollens” has been used in some texts as a version of “modus ponens.” For the purposes of this exercise, “modus ponens” will be used.)
For the items below, select one of the following 4 possible answers:
1: VALID – Modus Ponens (Affirming the Antecedent)
2: VALID – Modus Tollens (Denying the Consequent)
3: INVALID – Denying the Antecedent
4: INVALID – Affirming the Consequent
SAMPLE: Chris and Nick would be very happy if the Browns beat the Steelers. The Browns did beat the Steelers, so Chris and Nick are very happy, indeed.
This can be re-written into the following format:
If A (Antecedent), then B (Consequent).
Affirm A (Antecedent), therefore B (Consequent).
A= The Browns beat the Steelers, B= Chris and Nick would be very happy.
Affirm A = The Browns did beat the Steelers, so Chris and Nick are very happy, indeed.
Modus Ponens (Affirming the Antecedent)
11. Madeline must have known the material for the test, because if a person knows the material, that person will get an A, and Madeline was one of the students that got an A.
12. Anastasia believes that if she treats people honestly and with an open mind, she will have diverse friendships. She is honest and open-minded and has friends all over the world.
13. Roberto thought that if he worked very hard, his boss would give him a raise or a promotion. He made sure she noticed him, but she did not give him a raise or promotion. He thought he must not have worked hard enough.
14. “I’m still eating too much ice cream,” lamented George. “My waist measurement is the same as it was six months ago. I know if I didn’t eat so much ice cream, I would reduce my waist size.”
15. The best way to make sure we pay fewer taxes is to elect conservatives. We must not have elected enough conservatives, because we are paying more taxes.
16. If my neighbor were a decent human being, he wouldn’t let his yard trash fall onto my property. But he’s not a decent human being, so we get to clean his trash as well as ours.
17. We’ll have fun and learn a lot in this course, if we have great facilitator. We do have a great facilitator; therefore we are learning a lot and having fun doing it!
18. If I could understand the concept of hypothetical syllogisms, I would get a passing grade. Hurray! I got a passing grade, so I must have understood the concept of hypothetical syllogisms.