hypothetical syllogisms can have two valid and two invalid structures. The two valid structures are affirming the antecedent or modus ponens and denying the consequent or modus tollens. The two invalid structures or fallacies are denying the antecedent and affirming the consequent. We are to determine if the following arguments are valid or invalid and what form they take.
1)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 who got an A.
my answer- invalid and modus ponens
2) "I'm still eating too much ice cream" lamented George. "My waist measurement is the same as it was 6 months ago. I know if I didn't eat so much ice cream, I would reduce my waist size."
my answer- valid and modus tollens
3) If I could understand hypothetical syllogisms, I would get a passing grade. Hurray! I got a passing grade, so I must have understood hypothetical syllogisms.
my answer- invalid and modus ponens
Can you please check my answers.
Your answers are mostly correct, but there is a small error in your second answer.
1) 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 who got an A.
Your answer: Invalid and modus ponens.
Actually, this argument is valid, and the correct form is affirming the consequent. Modus ponens is when you affirm the antecedent. Here's how you can determine the form:
1) If a person knows the material, that person will get an A.
2) Madeline got an A.
3) Therefore, Madeline must have known the material for the test.
The form of this argument is:
If P, then Q.
Q.
Therefore, P.
2) "I'm still eating too much ice cream" lamented George. "My waist measurement is the same as it was 6 months ago. I know if I didn't eat so much ice cream, I would reduce my waist size."
Your answer: Valid and modus tollens.
Actually, this argument is invalid. The form you mentioned, modus tollens, is correct, but the argument itself does not follow that form. Here's how you can determine the form:
1) If I didn't eat so much ice cream, I would reduce my waist size.
2) My waist measurement is the same as it was 6 months ago.
3) Therefore, I'm still eating too much ice cream.
The form of this argument is:
If P, then Q.
Not Q.
Therefore, not P.
3) If I could understand hypothetical syllogisms, I would get a passing grade. Hurray! I got a passing grade, so I must have understood hypothetical syllogisms.
Your answer: Invalid and modus ponens.
Actually, this argument is valid, and the correct form is affirming the consequent. Here's how you can determine the form:
1) If I could understand hypothetical syllogisms, I would get a passing grade.
2) I got a passing grade.
3) Therefore, I must have understood hypothetical syllogisms.
The form of this argument is:
If P, then Q.
Q.
Therefore, P.
Overall, your understanding of the valid and invalid structures is correct, but there were minor errors in identifying the specific forms in two of the arguments. Always remember to carefully analyze the structure of the argument and ensure it aligns with the correct form.
Your answers are correct!
1) The argument is invalid because it commits the fallacy known as affirming the consequent. The valid form would be "if a person gets an A, then that person must have known the material." However, the argument states "if a person knows the material, then that person will get an A," which is the reverse of the valid form.
2) The argument is valid and follows the modus tollens structure. It states "if I didn't eat so much ice cream, then I would reduce my waist size." Since George's waist size is unchanged, it can be concluded that he is still eating too much ice cream.
3) The argument is invalid because it commits the fallacy of affirming the consequent. The valid form would be "if I understood hypothetical syllogisms, then I would get a passing grade." However, the argument states "I got a passing grade, so I must have understood hypothetical syllogisms," which is the reverse of the valid form.