Given this statement， we know that if Danielle is accepted to graduate schoo
l， then she must have done well on the GRE. Note： Students often wrongly int
erpret this statement to mean：
“If Danielle does well on the GRE， then she will be accepted to graduate sch
ool.“
There is no such guarantee. The only guarantee is that if she does not do we
ll on the GRE， then she will not be accepted to graduate school.
“A only if B” is logically equivalent to “if A， then B.”
Affirming the Conclusion Fallacy
A——>B
B
Therefore， A
Remember that an if-then statement， A——>B， tells us only two things： （1） If
A is true， then B is true as well. （2） If B is false， then A is false as wel
l （contrapositive）。 If， however， we know the conclusion is true， the if-then
statement tells us nothing about the premise. And if we know that the premi
se is false （we will consider this next）， then the if-then statement tells u
s nothing about the conclusion.
Example： （Affirming the Conclusion Fallacy）
If he is innocent， then when we hold him under water for sixty seconds he wi
ll not drown. Since he did not die when we dunked him in the water， he must
be innocent.
The logical structure of the argument above is most similar to which one of
the following？
（A） To insure that the remaining wetlands survive， they must be protected by
the government. This particular wetland is being neglected. Therefore， it w
ill soon perish.
（B） There were nuts in that pie I just ate. There had to be， because when I
eat nuts I break out in hives， and I just noticed a blemish on my hand.
（C） The president will be reelected unless a third candidate enters the race
…… A third candidate has entered the race， so the president will not be reele
cted.
（D） Every time Melinda has submitted her book for publication it has been re
jected. So she should not bother with another rewrite.
（E） When the government loses the power to tax one area of the economy， it j
ust taxes another. The Supreme Court just overturned the sales tax， so we ca
n expect an increase in the income tax.
