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Affirming the Consequent

(also known as: converse error, fallacy of the consequent, asserting the consequent, affirmation of the consequent)

New Terminology:

Consequent: the propositional component of a conditional proposition whose truth is conditional; or simply put, what comes after the “then” in an “if/then” statement.

Antecedent: the propositional component of a conditional proposition whose truth is the condition for the truth of the consequent; or simply put, what comes after the “if” in an “if/then” statement.

Description: An error in formal logic where if the consequent is said to be true, the antecedent is said to be true, as a result.

Logical Form:

If P then Q.

Q.

Therefore, P.

Example #1:

If taxes are lowered, I will have more money to spend.

I have more money to spend.

Therefore, taxes must have been lowered.

Explanation: I could have had more money to spend simply because I gave up crack-cocaine, prostitute solicitation, and baby-seal-clubbing expeditions.

Example #2:

If it’s brown, flush it down.

I flushed it down.

Therefore, it was brown.

Explanation: No!  I did not have to follow the, “if it’s yellow, let it mellow” rule -- in fact, if I did follow that rule I would probably still be single.  The stated rule is simply, “if it’s brown” (the antecedent), then (implied), “flush it down” (the consequent).  From this, we cannot imply that we can ONLY flush it down if it is brown.  That is a mistake -- a logical fallacy.

Exception: None.

Tip: If it’s yellow, flush it down too.

References:

Jevons, W. S. (1872). Elementary lessons in logic: deductive and inductive : with copious questions and examples, and a vocabulary of logical terms. Macmillan.



Registered User Comments

Jacob
Wednesday, November 14, 2018 - 05:04:48 PM
If I put all the tools away then there are no tools in the yard.
There are no tolls in the yard so they must have all been put away.

This is a logical problem I encounter at my part time job as an arborist. Several people worth with me and I can’t keep track of who puts what tool away, so we often infer that if there are no tools lying around the job site, then they must all have been put away, but if a guy walks by and steals a tool, then that tool is not in the truck just because we don’t see it in the yard.

Is this the fallacy of affirming the consequent?

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Bo Bennett, PhD
Thursday, November 15, 2018 - 08:37:49 PM
If I put all the tools away (P) then there are no tools in the yard (Q).
There are no tools in the yard (Q).
Therefore, they must have all been put away (?).

Not quite, because the concluding clause is not the same used in the premise... we have have is a non sequitur. If we changed this to "Therefore, I put all the tools away," then we would have this fallacy. Remember, this is a deductive fallacy so exact wording does matter.

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Molen
Monday, August 13, 2018 - 12:01:16 AM
Helly Sir,
I have a case in argumentation where some one did criminal things in the past but not being jailed until today. The actor was someone with a high range military position, investigated by a special team. The team revealed the actor proven committed to a crime.
Mr. A committed to a crime, he should have been in the jail. He is not in the jail, so he was not a criminal.
Is this a fallacy?
Thank you

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Bo Bennett, PhD
Monday, August 13, 2018 - 06:55:15 AM
What you actually have is this:

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

This is Denying the Antecedent, and is fallacious.

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Molen
Tuesday, August 14, 2018 - 12:20:21 AM
@Bo Bennett, PhD: Thank you for your response. I agree with "barking dog" example, it helps me to understand my case.
Thank you.

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erik coronado
Monday, September 24, 2018 - 06:41:17 PM
@Bo Bennett, PhD: I think it may have just been a typo but you have described modus tollens in:
If P then Q.
not Q.
Therefore, not P.

Denying the Antecedent is:
If P then Q
Not P.
Therefore, not Q.

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Bo Bennett, PhD
Tuesday, September 25, 2018 - 12:41:34 PM
@erik coronado: Thanks, Erik. Yes, oversight on my part.

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Kerri
Sunday, July 22, 2018 - 10:11:53 PM
Just wanted to say, I'm a student that has gone to SO many websites to achieve understanding with all of my classes, and your website is by far the most entertaining whilst still being super-informative. You have my gratitude.

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Krista Neckles
Monday, July 02, 2018 - 05:51:55 PM
Hello Sir,

There exists the pure hypothetical syllogism where one says:

If p then q
If q then r
Therefore if p then r

Supposedly this is valid. What is invalid is for instance:

If p then q
If r then q
Therefore if p then r.

What fallacy is this invalid form called?

Thanks!

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