¡¡¡¡Given this statement£¬ we know that if Danielle is accepted to graduate schoo
¡¡¡¡l£¬ then she must have done well on the GRE. Note£º Students often wrongly int
¡¡¡¡erpret this statement to mean£º
¡¡¡¡¡°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¡ª¡ª>B
¡¡¡¡B
¡¡¡¡Therefore£¬ A
¡¡¡¡Remember that an if-then statement£¬ A¡ª¡ª>B£¬ tells us only two things£º £¨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£º £¨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.
