Accused of a fallacy? Suspect a fallacy? Ask Dr. Bo and the community!

Quickly register to comment, ask and respond to questions, and get FREE access to our passive online course on cognitive biases!

# 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.

Jacob
Friday, May 17, 2019 - 12:28:18 PM
I have a friend who told me this.

"I am depressed, and I heard that high intelligence causes depression, therefore I must be highly intelligent."

Even before I knew about fallacies I suspected there was many things wrong with this statement. First, it is perhaps not a fact that high intelligence causes depression. Let's say for the sake of argument that high IQ does cause depression.

High IQ causes depression
I am depressed
Therefore I have a high IQ

Is this affirming the consequent?

working...

Bo Bennett, PhD
Friday, May 17, 2019 - 04:54:06 PM
Yes, good example.

working...

Jim Stascavage
Saturday, December 29, 2018 - 10:01:02 AM
With regard to the Affirming the Consequent fallacy, doesn't an 'if and only if' logical expression affirm the antecedent if the consequent is true?

2 replies

working...

Bo Bennett, PhD
Saturday, December 29, 2018 - 11:48:19 AM
You mean "If and only if P, then Q. Q. Therefore, P"? Good observation. Yes, this avoids the fallacy as far as I can tell.

working...

Jim Stascavage
Saturday, December 29, 2018 - 11:51:56 AM
@Bo Bennett, PhD: I only brought it up because you used the XOR exception in Affirming a disjunct. Maybe not the same, but close enough to me.

working...

Jacob
Friday, November 23, 2018 - 12:26:39 PM
Now that I understand this fallacy better I see it more and more. This is one I heard while talking to a friend. We were talking about men’s shelters and women’s shelters as a refuge for domestic abuse. This is after I watched the film “The Red Pill”. The film said that there were 5000 shelters for women and only one for men. I talked about this with a friend. I argued what the movie argued, that there needs to be more men’s shelters. She argued that there didn’t need to be more. She reasoned that there being 5000 women’s shelters was proof that that was how many women’s shelters were needed and there being 1 men’s shelter was proof that that was how many men’s shelters were needed.

This is obviously is bad logic. I dont know when they started making women’s shelters, but there was a time when there were none, and many were needed even though none existed. The same is true for men’s shelters.

Is this an example of affirming the consequent?

If women’s shelters are needed then women’s shelters will be built.
Women’s shelters were built, therefore they were needed.

I think this is an example of a formal deductive fallacy but inductive reasoning like this is normal, common, and useful. Here is a classic inductive argument. Where there is smoke there is fire. Isn’t this the fallacy of affirming the consequent? Fire causes smoke not the other way around.

If there is fire, then there is smoke
There is smoke, therefore there is fire

Fire causing smoke does not mean that smoke causes fire, but the two are so reliably seen together that this is a reliable induction. There are all kinds of scenarios where 99.999 percent of the time B is caused by A and only A. Therefore if B then A.

working...

McCarthy
Thursday, December 27, 2018 - 07:32:51 AM
Wth the men's shelters it sounds like circular reasoning, that's all the shelters we have because that's all we need and we know that's all we need because that's all we have.

working...

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?

working...

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.

working...

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

4 replies

working...

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.

working...

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.

working...

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.

working...

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

working...

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.

0 replies

working...

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!

0 replies

working...

### Become a Logical Fallacy Master. Choose Your Poison.

Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions; perfect for educators, debaters, or anyone who wants to improve his or her reasoning skills.

Get the book, Logically Fallacious by Bo Bennett, PhD by selecting one of the following options:

### Not Much of a Reader? No Problem!

Enroll in the Mastering Logical Fallacies Online Course. Over 10 hours of video and interactive learning. Go beyond the book!

Enroll in the Fallacy-A-Day Passive Course. Sit back and learn fallacies the easy way—in just a few minutes per day, via e-mail delivery.

Have a podcast or know someone who does? Putting on a conference? Dr. Bennett is available for interviews and public speaking events. Contact him directly here.

Website Software Copyright 2019, Archieboy Holdings, LLC.