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Denying the Premise Fallacy

The fallacy of denying the premise occurs when an if-then statement is presented, its premise denied, and then its conclusion wrongly negated.

Example: (Denying the Premise Fallacy)

Example

The senator will be reelected only if he opposes the new tax bill. But he was defeated. So he must have supported the new tax bill.

The sentence “The senator will be reelected only if he opposes the new tax bill” 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:

 

 

[Note: Two negatives make a positive, so the conclusion ~(~T) was reduced to T.] This diagram clearly shows that the argument is committing the fallacy of denying the premise. An if-then statement is made; its premise is negated; then its conclusion is negated.

 





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