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Denying the Antecedent

(also known as: inverse error, inverse fallacy)

Description: It is a fallacy in formal logic where in a standard if/then premise, the antecedent (what comes after the “if”) is made not true, then it is concluded that the consequent (what comes after the “then”) is not true.

Logical Form:

If P, then Q.

Not P.

Therefore, not Q.

Example #1:

If it barks, it is a dog.

It doesn’t bark.

Therefore, it’s not a dog.

Explanation: It is not that clear that a fallacy is being committed, but because this is a formal argument following a strict form, even if the conclusion seems to be true, the argument is still invalid.  This is why fallacies can be very tricky and deceptive.  Since it doesn’t bark, we cannot conclude with certainty that it isn’t a dog -- it could be a dog who just can’t bark.

The arguer has committed a formal fallacy, and the argument is invalid because the truth of the premises does not guarantee the truth of the conclusion.

Example #2:

If I have cable, then I have seen a naked lady.

I don’t have cable.

Therefore, I have never seen a naked lady.

Explanation: The fallacy is more obvious here than in the first example. Denying the antecedent (saying that I don’t have cable) does not mean we must deny the consequent (that I have seen a naked lady).

The arguer has committed a formal fallacy, and the argument is invalid because the truth of the premises does not guarantee the truth of the conclusion.

Exception: None.

Tip: If you ever get confused with formal logic, replace the words with letters, like we do in the logical form, then replace the letters with different phrases and see if it makes sense or not.

References:

Kiersky, J. H., & Caste, N. J. (1995). Thinking Critically: Techniques for Logical Reasoning. West Publishing Company.



Registered User Comments

Krista Neckles
Monday, May 14, 2018 - 07:58:59 PM
Hello Sir,

I read the examples you provided. I suppose that if the antecedent and consequent were switched around there would no longer be a fallacy?

I apologize in advance if it seems that my question is foolish. I really want to use formal logic more often.

Thank you Sir.

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Bo Bennett, PhD
Wednesday, May 16, 2018 - 08:17:42 AM
You mean:

If P, then Q.
Not Q.
Therefore, not P.

Using same example:

If I have cable, then I have seen a naked lady.
I have never seen a naked lady.
Therefore, I don't have cable.

This is valid. So not a fallacy.

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Krista Neckles
Wednesday, May 16, 2018 - 07:53:38 PM
@Bo Bennett, PhD: Thank you Sir. The reason I was asking was because I am going to participate in a debate and my argument will go as follows:

It would be appropriate to develop different diagnostic criteria for females if it is proven that females with autism present differently than males with autism.

It is not adequately proven that females with autism present differently then males.

Therefore it would not be appropriate to develop seperate diagnostic criteria for females with autism.

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Bo Bennett, PhD
Thursday, May 17, 2018 - 06:41:06 AM
@Krista Neckles: So let's rephrase this and plug in variables...

If it is proven that females with autism present differently than males with autism (P), then it would be appropriate to develop different diagnostic criteria for females (Q).

It is not adequately proven that females with autism present differently then males (NOT P).

Therefore, it would not be appropriate to develop separate diagnostic criteria for females with autism (NOT Q).


So you would be Denying the Antecedent and committing the fallacy. I think you were trying to reverse the order of the antecedent and consequent, but that doesn't change the fact that they are still the antecedent and consequent. Thinking about your statement logically, it is possible that it would be appropriate to develop different diagnostic criteria for females for other reasons. To see this more clearly, let's create a similar example:

If meeting person x for the first time (P), then it would be appropriate to shake hands with him (Q).

It is not the first time you are meeting person x (NOT P).

Therefore, it would not be appropriate to shake hands with person x (NOT Q).


See the problem? This is more obvious because we know it is appropriate to shake hands with people for other reasons, like when saying goodbye, congratulations, etc.

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Krista Neckles
Thursday, May 17, 2018 - 01:04:07 PM
@Bo Bennett, PhD: Hello Sir,

Thank you so much for your help! I suppose I need to update my knowledge on modus ponens and modus tollens.

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