Evaluating Deductive Arguments

Here are the answers to the handout on evaluating 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) Some dads have beards.
Some bearded people are mean.
Some dads are mean.

P1- true
P2- questionable ("mean" is subjective) or true ("Some" makes it easy to find one or two)
support- valid (the premises say the bearded dads will be mean)
overall- unsound (bad support)

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 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 (the premises only tell us one type of mammal has wings, not necessarily all mammals)
overall- unsound (bad support)

6) All Facebook posts are annoying.
Some Facebook posts are false.
Some annoying things are false.

P1- questionable ("annoying" is subjective)
P2- true
support- valid (the premises establish that some Facebook posts are both annoying and false; so some annoying things [those posts] are false)
overall - unsound (untrue first 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 support)

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 (untrue 3rd premise)

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

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 (untrue premises)

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 falseP2- false

-valid

overall- unsound (untrue 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
support- valid (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 (untrue 1st premise and bad support)

13) 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 (untrue premises and bad support)

14) 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 (the premises say Sean singing guarantees that students cringe; since we know students aren't cringing, we know Sean can't be singing)
overall- unsound (untrue 1st premise)

15) 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; while it could be true that the humans in here are a statistical anomaly, given the strength of the generalization, it's likely that most students in here are, in fact, shorter than 7 feet tall)
overall- unsound (not perfect, since the support isn't perfect, but pretty good)

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)
P2- questionable (again, that's not an obvious claim)
support- valid (the same structure as argument #13)
overall- unsound (untrue premises)