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# Affirming the Conclusion Fallacy

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 well (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 premise is false (we will consider this next), then the if-then statement tells us nothing about the conclusion.

# Example: (Affirming the Conclusion Fallacy)

Example
If he is innocent, then when we hold him under water for sixty seconds he will 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?
1. To insure that the remaining wetlands survive, they must be protected by the government. This particular wetland is being neglected. Therefore, it will soon perish.
2. 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.
3. 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 reelected.
4. Every time Melinda has submitted her book for publication it has been rejected. So she should not bother with another rewrite.
5. When the government loses the power to tax one area of the economy, it just taxes another. The Supreme Court just overturned the sales tax, so we can expect an increase in the income tax.
Solution
To symbolize this argument, let the clause “he is innocent” be denoted by I, and let the clause “when we hold him under water for sixty seconds he will not drown” be denoted by ~D. Then the argument can be symbolized as

Notice that this argument is fallacious: the conclusion “he is innocent” is also a premise of the argument. Hence the argument is circular—it proves what was already assumed. The argument affirms the conclusion then invalidly uses it to deduce the premise. The answer will likewise be fallacious.

We start with answer-choice (A). The sentence

“To insure that the remaining wetlands survive, they must be protected by the government”

contains an embedded if-then statement:

“If the remaining wetlands are to survive, then they must be protected by the government.”

This can be symbolized as S—>P. Next, the sentence

“This particular wetland is being neglected

can be symbolized as ~P. Finally, the sentence

“It will soon perish

can be symbolized as ~S. Using these symbols to translate the argument gives the following diagram:

The diagram clearly shows that this argument does not have the same structure as the given argument. In fact, it is a valid argument by contraposition.

Turning to (B), we reword the statement

“when I eat nuts, I break out in hives”

as

“If I eat nuts, then I break out in hives.”

This in turn can be symbolized as N—>H.

Next, we interpret the clause

“there is a blemish on my hand

to mean “hives,” which we symbolize as H. Substituting these symbols into the argument yields the following diagram:

The diagram clearly shows that this argument has the same structure as the given argument. The answer, therefore, is (B).