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 symbolssintosthe argument yields the following diagram:
N――H
H
Therefore, N
The diagram clearly shows that this argument has the same structure as the g
iven argument. The answer, therefore, is 。
Denying the Premise Fallacy
A――B
~A
Therefore, ~B
The fallacy of denying the premise occurs when an if-then statement is prese
nted, its premise denied, and then its conclusion wrongly negated.
Example:
The senator will be reelected only if he opposes the new tax bill. But he wa
s defeated. So he must have supported the new tax bill.
The sentence The senator will be reelected only if he opposes the new tax b
ill contains an embedded if-then statement: If the senator is reelected, then he opposes the new tax bill. This in turn can be symbolized as R――~T. The sentence But the senator was defeated can be reworded as He was not reelected, which in turn can be symbolized as ~R. Finally, the sentence He must have supported the new tax bill can be symbolized as T. Using these symbols the argument can be diagrammed as follows: