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Denying the Premise Fallacy

This fallacy is not tested as often on the LSAT as the affirming-the-conclusion fallacy because it is usually easy to detect. 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.

 

Advance Concepts

Example: (A unless B)
Any person who scores poorly on the LSAT will not get into Law School unless he bribes the admissions officers or has a relative on the board of regents.

Based on the above statements, all of the following statements can be made EXCEPT.
  1. If a person who did poorly on the LSAT has neither the money to bribe the admissions officers nor a relative on the board of regents, then he will not get into law school.
  2. If a person did poorly on the LSAT, is in law school, and does not have a relative on the board of regents, then he must have bribed the admissions officers.
  3. If a person does not take the LSAT but has a relative on the board of regents, then he will get into law school.
  4. If a person is in law school and does not have relatives on the board of regents nor has ever committed bribery, then he must have done well on the LSAT.
  5. If a person did poorly on the LSAT, is in law school, and did not bribe anyone, then he must have a relative on the board of regents.
Solution
Let’s start by symbolizing the argument. Symbolize the phrase “will get into law school” as S.* Next, symbolize the phrase “he bribes an admission officer” as B. Finally, symbolize the phrase “has a relative on the board of regents” as R. Substituting the symbols into the argument, we get the following diagram:
~(B or R)<—>~S

which simplifies to
(B or R)<—>S

(Note: We’ll add the phrase “any person who scored poorly on the LSAT” to the diagram later.)
 
We now use this diagram to analyze each of the answer-choices. As for choice (A), from ~S we can conclude, by applying the contrapositive to the diagram, ~(B or R). From DeMorgan’s laws, we know that this is equivalent to ~B & ~R. This is the premise of (A). That is, (A) is a valid argument by contraposition. This eliminates (A).
 
Since choice (B) affirms S, we know from the diagram that B or R must be true. But choice (B) denies R. So from the meaning of “or,” we know that B must be true. This is the conclusion of choice (B). Hence, choice (B) is a valid deduction. This eliminates choice (B).
 
For simplicity we did not diagram the entire argument. But for choice (C), we need to complete the diagram. The premise of the argument is “any person who scores poorly on the LSAT.” This clause can be reworded as “If a person does poorly on the LSAT,” which can be symbolized as P. Affixing this to the original diagram gives
P—>[(B or R)<—>S].

Recall that if the premise of an if-then statement is true then the conclusion must be true as well. But if the premise is false, then we cannot determine whether the conclusion is true or false. Now (C) negates the premise, ~P. So its conclusion—that a person will get into law school, S—is a non sequitur.
 
Hence, (C) is the answer.
 




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