Evaluating Deductive Arguments

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

1) All kangaroos are marsupials.
All marsupials are mammals.
All kangaroos 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 people are funny.
Sean is a person.
Sean is funny.

P1- true (we might disagree over who specifically is funny, but nearly all of us would agree that someone is funny)
P2- true (each "Sean" in this handout refers to your teacher, Sean Landis)
structure- invalid (the 1st premise only says some are funny; Sean could be one of the unfunny people)
overall- unsound (bad structure)

4) All email forwards are annoying.
Some email forwards are false.
Some annoying things are false.

P1- questionable ("annoying" is subjective)
P2- true
structure- valid (the premises establish that some email forwards are both annoying and false; so some annoying things [those forwards] are false)
overall - unsound (bad first premise)

5) All bats are mammals.
All bats have wings.
All mammals have wings.

P1- true
P2- true (if interpreted to mean "All bats are the sorts of creatures who have wings.") or false (if interpreted to mean "Each and every living bat has wings," since some bats are born without wings)
structure- invalid (we don't know anything about the relationship between mammals and winged creatures just from the fact that bats belong to each group)
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 Sean)
structure- valid
overall- unsound (bad premises)

8) All students in here are mammals.
All humans are mammals.
All students in here are humans.

P1- true
P2- true
structure- invalid (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 students in here are humans.
All humans are shorter than 10 feet tall.
All students in here are shorter than 10 feet tall.

P1- true
P2- true!
structure- valid (same structure as arg #1)
overall- sound

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
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- valid (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)