Part B: Identify the
Forms
A
B
*1. If the solution turns blue litmus paper red, then the solution contains
acid. The solution turns blue litmus paper red. So, the solution contains acid.
A
B
1.
If A, then B.
2. A.
So, 3. B.
modus ponens
A
B
2. If the solution turns blue litmus paper red, then the solution
contains acid. The solution does not contain acid. So, the solution does not turn blue litmus paper red.
not B
not A
1.
If A, then B.
2. Not B.
So, 3. Not A.
modus tollens
A
B
not A
3. Lewis is a famous author only if he knows how to write.
But Lewis is not a famous author. Hence, Lewis does not know how to write.
not B
1.
If A, then B.
2. Not A.
So, 3. Not B.
none
A
B
B
*4. If Susan is a famous author, then she knows how to write. Moreover,
Susan knows how to write. So, she is a famous author.
A
1.
If A, then B.
2. B.
So, 3. A.
none
A
B
A
B
5. Souls transmigrate. But it is wrong to eat animals if souls
transmigrate. Hence, it is wrong to eat animals.
1. A.
2. If A, then B.
So, 3. B.
modus ponens
A
B
6. Either Jones is an innocent bystander, or Jones fired a shot
at the mayor. Jones is
not an innocent bystander. Therefore, Jones fired a shot at the mayor.
not A
B
1.
Either A or B.
2. Not A.
So, 3. B.
disjunctive syllogism
A
B
B
*7. Rilke is a dreamer if he is a poet. Therefore, Rilke is a poet.
1. If B, then A.
So, 2. B.
none
A
B A
C
8. Either you marry young, or you wait. If you
marry young, you incur a high risk of
B
D
divorce. If you wait, the field of available
partners grows ever smaller. So, either you
C
D
incur a high risk of divorce, or the field
of available partners grows ever smaller.
1. Either A or B.
2. If A, then C.
3. If B, then D.
So, 4. Either
C or D. constructive dilemma
not A
B
A
9. It is not wrong to kill spiders. But if spiders have eternal
souls, then it is wrong to kill them. Thus, it is false that spiders have eternal souls.
not B
1.
Not A.
2.
If B, then A.
So, 3. Not B.
modus tollens
A
B
*10. If you study hard,
you refine your communication skills. If you refine your
B
C
A
communication skills, then your job opportunities
increase. Hence, if you study hard,
C
your job opportunities increase.
1. If A, then B.
2. If B, then C.
So, 3. If
A, then C. hypothetical syllogism
A
B
not A
11. If Mubarak is from Egypt, then he is from Africa. Therefore, if
Mubarak is not from Egypt, then he is not from Africa.
not B
1.
If A, then B.
So, 2. If not A, then not
B. none
A A
B
B
12. Ben is a rat. Ben is a rat only if Ben is a mammal. So, Ben is a mammal.
1. A.
2. If A, then B.
So, 3. B.
modus ponens
A
B
not B
*13. Sam is wealthy if he has over a billion dollars. But Sam does not have over
a billion dollars. Therefore, Sam is not wealthy.
not A
1.
If B, then A.
2. Not B.
So, 3. Not A.
none
A
B
A
14. There is life on Mars given that there is life on Earth. Hence, there
is life on Mars.
1. If B, then A.
So, 2. A.
none
A
not B
15. It is true that corrupt institutions are hard to reform. It is false
that individuals are totally depraved. Therefore, if corrupt institutions are hard to reform, then individuals are totally
depraved. A B
1. A.
2.
Not B.
So, 3. If A, then B. none
Part
C: More Forms to Identify
A
B
A
B
*1. The sky is blue. The sky is cobalt blue only if it is blue. Hence, the
sky is cobalt blue.
1. A.
2. If B, then A.
So, 3. B.
none
not A
B
2. Abortion in the case of ectopic pregnancy is not wrong. But
if it is always wrong to kill an innocent human being, then abortion in the case of ectopic pregnancy is wrong. So, it is
not always wrong to kill an innocent human.
A
not B
1.
Not A.
2.
If B, then A.
So, 3. Not B.
modus tollens
A
B
A
3. Kidnapping is wrong if society disapproves of it. Kidnapping
is wrong. So, society disapproves of kidnapping.
B
1.
If B, then A.
2. A.
So, 3. B.
none
A
B
B
*4. Eating meat is unhealthy if meat contains a lot of cholesterol. Meat
does contain a lot of cholesterol. Therefore, eating meat is unhealthy.
A
1.
If B, then A.
2. B.
So, 3. A.
modus ponens
A
B
5. Either the "eye for an eye" principle is interpreted
literally, or it is interpreted
A
C
figuratively. If it is interpreted literally,
then the state should torture torturers, maim
B
maimers, and rape rapists. If the "eye
for an eye" principle is interpreted figuratively,
D
then it does not necessarily demand death
for murderers. So, either the state should
C
D
torture torturers, maim maimers, and rape
rapists, or the "eye for an eye" principle does not necessarily demand death for murderers.
1. Either A or B.
2. If A, then C.
3. If B, then D.
So, 4. Either
C or D. constructive dilemma
A
6. Affirmative action is preferential treatment of disadvantaged
groups, and preferential
treatment of disadvantaged
groups is reverse discrimination. If affirmative action is
A
preferential treatment of disadvantaged groups
and preferential treatment of
disadvantaged groups
is reverse discrimination, then affirmative action is wrong. Hence,
affirmative action is wrong.
B
B
1.
A.
2.
If A, then B.
So, 3. B.
modus ponens
A
B
B
*7. If the
zygote lacks a brain, then the zygote lacks a soul. If the zygote lacks a soul, then
C
killing the zygote is permissible. So, if
the zygote lacks a brain, then killing the zygote is permissible. A
C
1.
If A, then B.
2. If B, then C.
So, 3. If
A, then C. hypothetical syllogism
A
B
not B
8. If Mary is a psychiatrist, then she is a physician. Mary
is not a physician. Therefore, Mary is a psychiatrist.
A
1.
If A, then B.
2. Not B.
So, 3. A.
none
A
B
not A
9. If you want to ruin your life, you should take hard drugs.
But you don't want to ruin your life. So, you should not take hard drugs.
not B
1.
If A, then B.
2. Not A.
So, 3. Not B.
none
A
B
*10. Lying causes social discord. Hence, lying is wrong.
1. A.
So, 2. B.
none
not A
A
11. It is not true that acts are right because God approves them. But either
acts are right because God approves them, or God approves of acts because they are right. Therefore, God approves of acts
because they are right.
B
B
1.
Not A.
2.
Either A or B.
So, 3. B.
disjunctive syllogism
A
B
not A
B
12. If Dracula is a vampire, then he is dangerous. But Dracula is not a
vampire. Hence, he is dangerous.
1. If A, then B.
2. Not A.
So, 3. B.
none
A
B
*13. Either the animals used in research are a lot like humans, or they are not a lot
like
A
C
humans. If the animals are a lot like humans,
then experimenting on them is morally
B
D
questionable. If the animals are not a lot
like humans, then experimenting on them is
C
D
pointless. So, either experimenting on animals
is morally questionable, or it is pointless.
1. Either A or B.
2. If A, then C.
3. If B, then D.
So, 4. Either
C or D. constructive dilemma
A
A
14. The state cannot uphold the value of life by taking it. And if the state
cannot uphold the value of life by taking it, then the death penalty should be abolished. Therefore, the death penalty should
be abolished. B
B
1.
A.
2.
If A, then B.
So, 3. B.
modus ponens
A
B
15. If my society approves of genetic engineering, then genetic engineering
is right. But my society does not approve of genetic engineering. Hence, genetic engineering is not right.
not A
not B
1.
If A, then B.
2. Not A.
So, 3. Not B.
none
Part D: Still More Forms to Identify
A
B
not B
*1. Overeating is foolish only if it causes disease. Overeating does
not cause disease. So, overeating is not foolish.
not A
1.
If A, then B.
2. Not B.
So, 3. Not A.
modus tollens
A
2. Either films depicting graphic violence have caused the increase
in violent crime or bad
B
A
parenting has caused it (or both). Movies
depicting graphic violence have caused the
increase
in violent crime. Therefore, bad parenting has not caused the rise in violent crime.
not B
1. Either A or B (or both).
2. A.
So, 3. Not B.
none
A
A
3. Corporations contribute huge sums of money to political campaigns.
If that is so, then
B
corporations exert undue influence on elections. So, corporations exert undue influence on elections.
B
1.
A.
2.
If A, then B.
So, 3. B.
modus ponens
A
B
*4. You will win the chess tournament if you are very good at chess. Unfortunately,
you are not very good at chess. Hence, you will not win the chess tournament.
not B
not A
1.
If B, then A.
2. Not B.
So, 3. Not A.
none
A
B
not A
5. Either virtue is good for its own sake, or it is good
as a means to an end. It is not the case that virtue is good for its own sake. So, virtue is good as a means to an end.
B
1.
Either A or B.
2. Not A.
So, 3. B.
disjunctive syllogism
A
B
6. You should be an optimist if pessimists are less likely to
succeed than optimists. And it is a fact that pessimists are less likely to succeed than optimists. Therefore, you should
be an optimist. B A
1. If B, then A.
2. B.
So, 3. A.
modus ponens
A
B
*7. If God can arbitrarily decide what is morally right, then God can make
cruelty right. And
C
D
if God cannot arbitrarily decide what is morally
right, then morality is not entirely in
A
God's
control. But either God can arbitrarily decide what is morally right, or God cannot
C
arbitrarily decide what is morally right.
Therefore, either God can make cruelty right, or morality is not entirely in God's control.
B
D
1.
Either A or C.
2. If A, then B.
3. If C, then D.
So, 4. Either
B or D. constructive dilemma
A
8. The
dinosaurs vanished due to a sudden, extreme drop in temperature. The earth must
B
have suffered some sort of cataclysm millions
of years ago, assuming that the dinosaurs
A
vanished due to a sudden, extreme drop in
temperature. So, the earth must have suffered
some
sort of cataclysm millions of years ago.
B
1.
A.
2.
If A, then B.
So, 3. B.
modus ponens
A
B
B
A
9. Assuming that you treat like cases alike, you are fair. Hence,
you are fair only if you treat like cases alike.
1. If A, then B.
So, 2. If
B, then A. none
A
*10. The death penalty is inequitably applied to the poor and minorities. And
given that the
A
B
death penalty is inequitably applied to the
poor and to minorities, it is unjust. Therefore, the death penalty is unjust.
B
1.
A.
2.
If A, then B.
So, 3. B.
modus ponens
A
B
C
11. Philosophy is important if ideas are important. And assuming that ideas
change lives, ideas are important. Hence, if philosophy is important, then ideas change lives.
B
A
C
1.
If B, then A.
2. If C, then B.
So, 3. If
A, then C. none
A
B
C
12. If you join the military, you give up a lot of freedom. If you go to
college, you incur
D
A
C
enormous debts. However, you either join the military, or you go to college. Therefore, you either
give up a lot of freedom, or you incur enormous debts.
B
D
1.
If A, then B.
2. If C, then D.
3. Either A or C.
So, 4.
Either B or D. constructive dilemma
A
B
*13. Mercy killing is morally permissible only if it promotes a greater amount of happiness
for everyone affected than the alternatives do. And mercy killing does promote a greater amount of happiness for everyone
affected than the alternatives do. Therefore, mercy killing is morally permissible. B
A
1.
If A, then B.
2. B.
So, 3. A.
none
A B
A
C
14. You must either love
or hate. If you love, then you suffer when your loved ones suffer. If
B
D
C
you hate, then you suffer when your enemies
flourish. Hence, either you suffer when your loved ones suffer, or you suffer when your
enemies flourish.
D
1.
Either A or B.
2. If A, then C.
3. If B, then D.
So, 4. Either
C or D. constructive dilemma
A
B
B
15. A severe depression will occur given that the economy collapses.
The economy collapses if inflation soars. So, inflation soars only if a severe depression will occur.
C
C
A
1.
If B, then A.
2. If C, then B.
So, 3. If
C, then A. hypothetical syllogism
