Valid or Invalid Syllogisms
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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. Please help me determine if the arguments below are valid or invalid and what form they take and check the first one i did please. Thank you.
1. 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.
Valid Modus Ponens (Affirming the Antecedent)
2. 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.
3. 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.
4. 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.
5. "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."
6 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.
7 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.
8 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!
9 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.
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Solution Summary
This solution provides examples to understanding syllogisms by using simple equations that can be used to check whether or not answers provided for hypothetical syllogismn problems provided are correct according to the rules that govern conditional arguments in Philosophy. Provided as well are 9 arguments whose validities are determined using the equations on hypothetical syllogisms.
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Dear Student,
As per your request, I decided to help you with the hypothetical syllogisms you posted using the definition of what a valid & invalid argument is in your current course, as qouted:
"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. Please help me determine if the arguments below are valid or invalid and what form they take and check the first one i did please. Thank you "
Simple Equations to guide you, adopted from the definition you required/presented which we will use to check the answers we have determined:
V (valid) = +P( positive/affirmed antecedent) & -Q (negative/denied consequent)
I (invalid) = -P (negative/denied antecedent) & +Q (positive/affirmed consequent)
Also, lets use the equations for valid hypothetical arguments:
p (antecedent) ---> r ...
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