Evaluating Deductive Arguments

Here are the answers to the handout on evaluating deductive arguments that we did as group work in class.

1) All bats are mammals.
All mamammals live on earth.
All bats live on earth.

P1- true
P2- true
support- valid
overall- sound

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

P1- questionable ("annoying" is subjective)
P2- true
support- 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)

3) All males in this class are humans.
All females in this class are humans.
All males in this class are females.

P1- true
P2- true
support- invalid (the premises only tell us that males and females both belong to the humans group; we don't know enough about the relationship between males and females from this)
overall- unsound (bad support)

4) No humans are amphibians.
All frogs are amphibians.
No frogs are humans.

P1- true
P2- true
support-  valid (the premises say that frogs belong to a group that humans can't belong to, so it follows that no frogs are humans)
overall- sound

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)
support- 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 support)

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

P1- true
P2- questionable ("mean" is subjective)
support- 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) Oprah Winfrey is a person.
Some people ate tacos yesterday.
Oprah Winfrey ate tacos yesterday.

P1- true
P2- true (you might not have directly seen anyone eat tacos, but you have a lot of indirect evidence... with all the Taco Bells, Don Pablos, etc., surely lots of people ate tacos yesterday)
support- invalid (the 2nd premise only says some ate tacos; Oprah could be one of the  people who didn't)
overall- unsound (bad support)

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

P1- true
P2- true
support- 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)
support- valid (same structure as in argument #1, just with an extra premise)
overall- unsound (bad 3rd premise)

10) 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
support- valid
overall- unsound (bad premises)

11) 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
support- 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)

12) All students in here are humans.
Most humans are shorter than 7 feet tall.
Most students in here are shorter than 7 feet tall. 

P1- true
P2- true!
support- invalid (the premises state a strong statistical generalization over a large population, and the conclusion claims that this generalization holds for a much smaller portion of that population; even though it's likely that most students in here are, in fact, shorter than 7 feet tall, it nevertheless could be true that the humans in here are a statistical anomaly)
overall- unsound (bad support)

13) (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)
support- valid (it's either A or B; it's not A; so it's B)
overall- unsound (bad premises)

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
support- 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)

15) 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
support- valid 
overall- unsound (bad 1st premise)

16) If there is no God, then life is meaningless.
Life isn't meaningless.
There is a God.

P1- questionable (that's not an obvious claim to prove or disprove)
P2- questionable (again, that's not an obvious claim to prove or disprove)
support- valid (the same structure as argument #15)
overall- unsound (bad premises)