Evaluating Deductive Args

Here are the answers to the handout on evaluating deductive arguments that we did as group work in class. Perhaps I should have titled the handout "So Many Bad Args!"

1) All humpback whales are whales.
All whales are mammals.
All humpback whales are mammals.

P1- true
P2- true
structure- valid
overall - sound

2) (from Stephen Colbert)
Bush was either a great prez or the greatest prez.
Bush wasn’t the greatest prez.
Bush was a great prez.

P1- questionable ("great" is subjective)
P2- questionable ("great" is subjective)
structure- valid (it's either A or B; it's not A; so it's B)
overall- unsound (bad premises)

3) Some cats can speak German.
Sean has a cat.
Sean's cat can speak German.

P1- false
P2- true! (I have two; there they are! ------------>)
structure- invalid (the 1st premise only says some can speak German; Sean's cat could be one of the ones that doesn't)
overall- unsound (bad structure)

4) All knock-knock jokes are annoying.
Some knock-knock jokes are funny.
Some annoying things are funny.

P1- questionable ("annoying" is subjective)
P2- questionable ("funny" is subjective)
structure- valid (the premises establish that some knock-knock jokes are both annoying and funny; so some annoying things [those jokes] are funny)
overall - unsound (bad premises)

5) All whales are mammals.
All whales live in the ocean.
All mammals live in the ocean.

P1- true
P2- true (if interpreted to mean "Whales are the sorts of creatures whose natural habitat is the ocean.") or false (if interpreted to mean "Each and every living whale lives in the ocean," since some whales, like Shamu, live in SeaWorld or other zoos)
structure- invalid (we don't know much about the relationship between mammals and creatures that living in the ocean just from the fact that whales belong to each of those groups)
overall- unsound (bad structure)

6) Some dads have beards.
All bearded people are mean.
Some dads are mean.

P1- true
P2- questionable ("mean" is subjective)
structure- valid (if all the people with beards were mean, then the dads with beards would be mean, so some dads would be mean)
overall- unsound (bad 2nd premise)

7) This class is boring.
All boring things are taught by Sean
This class is taught by Sean.

P1-questionable ("boring" is subjective)
P2- false (nearly everyone would agree that there are some boring things not associated with your teacher Sean)
structure- valid
overall- unsound (bad premises)

8) All students in this room are mammals.
All humans are mammals.
All students in this room are humans.

P1- true
P2- true
structure- invalid (it's the same structure as argument #10 below; the premises only tell us that students and humans both belong to the mammals group; we don't know enough about the relationship between students and humans from this; for instance, what if a dog were a student in our class?)
overall- unsound (bad structure)

9) All hornets are wasps.
All wasps are insects.
All insects are scary.
All hornets are scary.

P1- true!
P2- true
P3- questionable ("scary" is subjective)
structure- valid (same structure as in argument #1, just with an extra premise)
overall- unsound (bad 3rd premise)

10) All women are mammals.
All men are mammals.
All men are women.

P1- true
P2- true
structure- invalid (just because men and women belong to the same group doesn't mean that men are women; same bad structure as in arg #8)
overall- unsound (bad structure)

11) If Sean sings, then students cringe.
Sean is singing right now.
Students are cringing right now.

P1- questionable (since you haven't heard me sing, you don't know whether it's true or false)
P2- false (I'm not singing now!)
structure- valid
overall- unsound (bad premises)

12) If Sean sings, then students cringe.
Sean isn't singing right now.
Students aren't cringing right now.

P1- questionable (again, you don't know)
P2- true
structure- invalid (from premise 1, we only know what happens when Sean is singing, not when he isn't singing; students could cringe for a different reason)
overall- unsound (bad 1st premise and structure)

13) If Sean sings, then students cringe.
Students aren't cringing right now.
Sean isn't singing right now.

P1- questionable (again, you don't know)
P2- true
structure- valid
overall- unsound (bad 1st premise)

14) If Sean sings, then students cringe.
Students are cringing right now.
Sean is singing right now.

P1- questionable (again, you don't know)
P2- false
structure- invalid (from premise 1, we only know that Sean singing is one way to guarantee that students cringe; just because they're cringing doesn't mean Sean's the one who caused it; again, students could cringe for a different reason)
overall- unsound (bad premises and structure)

Homework #1

The first official homework assignment is to evaluate each argument on the handout titled "Deductive Args" (the other side of this handout is titled "An Argument's Structure"). Determine whether each argument is valid or invalid (good or bad structure) and sound or unsound (overall good or bad).

The homework is due at the beginning of class on Friday, September 25th. It's worth 4% of your overall grade.