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Fallacies: Affirming the Consequent

In this video, Matthew C. Harris explains the fallacy of affirming the consequent, the formal fallacy that arises from inferring the converse of an argument. He also explains why you sometimes cannot conclude that you should bathe in a tub of peanut butter.

Speaker: Matthew C. Harris, Duke University.
Created by Gaurav Vazirani.

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  • male robot hal style avatar for user David Cian
    So what the video is saying is that: "If P, then Q" does not imply that "If Q, then P", right?
    (9 votes)
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  • leaf green style avatar for user rhouts
    Is it always the case that an argument is invalid when it's an instance of the logical form of the fallacy of affirming the consequent?
    (13 votes)
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    • leaf green style avatar for user Nancy
      That isn't what he asked, though. His question sounds more like the same thing the above questioner asked. Can a valid argument be in a form resembling the "affirmation of the consequent", or does it only appear that way because, for instance, we know that what's-his-name is going to complain tomorrow?
      (3 votes)
  • spunky sam blue style avatar for user dvdsknz
    Do you think this concept is basically, an offshoot of Correlation does not necessarily equal causation fallacy?
    (3 votes)
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    • leaf green style avatar for user Agent Smith
      If you confuse sufficient and necessary conditions, you get the fallacy of affirming the consequent. Also called converse error.
      If I punch you then you will feel pain. "Punching you" is sufficient for "you to feel pain". The antecedent is sufficient for the consequent.
      However "you feel pain" is not sufficient to say that "i punched you". Someone could have made you watch all the episodes of star wars back to back or i could have hit you with a baseball bat.
      Therefore the consequent is not sufficient for the antecedent. If you think so, you have committed the fallacy.
      Confusing correlation with causation is a fallacy of causal arguments. You are right in seeing a connection because
      If there is causation then there has to be correlation ( this is true)
      And to think that If there is correlation then there is causation (the crux of the fallacy) is indeed the fallacy of affirming the consequent.
      (4 votes)
  • leaf green style avatar for user David León
    P1: If the door is open, then it is not closed.
    P2: The door is not closed.
    C1: Then, the door is open

    Did I make the fallacy of affirming the consequent?
    (3 votes)
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    • leaf green style avatar for user Agent Smith
      1. Yes, this is an instance of affirming the consequent fallacy. The argument is invalid.
      2. P1 and P2 are true and so is C1
      The combination of the two, which are conflicting, causes the problem. If you look at 1, we have committed a fallacy but 2, makes us "feel" as if the argument is sound.
      What this shows, to me at least, is that validity is a truth guarantor, provided the premises are true. If an argument form does not guarantee the truth of the conclusion, it is invalid - as is the case here. The other important thing to note is the truth of premises and conclusion has nothing to do with validity, save the case where we have a valid argument with true premises, in which case, the conclusion must be true.
      Coming to the argument itself, P1 is incomplete. It should read as "The door is closed IF AND ONLY IF the door is not closed". This correction will render the argument sound.
      Another way to look at it is to understand open = not closed.
      So, the door is open = not the door is closed
      So P1 actually is if the door is open, then it is not not open. in other words, what you are saying is:
      P1: If the door is open, then the door is open
      P2: The door is open
      Therefore C1: The door is open
      Presented this way, there is no fallacy. It has the valid form modus ponens
      (2 votes)
  • duskpin ultimate style avatar for user tuannb1997
    Am I right to express the general concept of the fallacy of affirming the consequent in another way like this: The fallacy of affirming the consequent is made when someone, relying on the truth about C - consequence - and Q - Outcome in the event of P,
    Cause - which has been confirmed, deduces that P is the Conclusion ?
    (3 votes)
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  • hopper cool style avatar for user Deadpool
    If time-travel is possible, then I will build a working time-machine. (If P, then Q)
    I built a working time-machine. (Q)
    Therefore, time-travel is possible. (Therefore, P)

    According to the video, this argument is fallacious. But looking at it, it seems logical. If I have built a working time-machine, then time travel HAS to be possible. Is this argument wrong?
    (2 votes)
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    • purple pi teal style avatar for user Maria
      I think it's still fallacious because there could be other reasons for you to build a time machine. (You accidentally build one, you could make one just to see if it works, you could make one to rescue your great-grandpa...)
      As long as you can think of another reason for Q, it's fallacious.

      If you were to say "If and only if time travel is possible, I will build a time machine," it would fix it, because you would be stating that P is the ONLY reason for Q.
      (1 vote)
  • aqualine ultimate style avatar for user Leo Karakolov
    This one was quite confusing to me. I've followed along well enough up until I reached this point - and even upon rewatching the video once, I still don't understand it.

    One of my questions is, why wouldn't this be called Affirming the Antecedent rather than Affirming the Consequent? Doesn't that make more sense...? It's what's after the IF that is fallacious or wrong here, and to my limited understanding you use the Conclusion to make yourself believe (falsely) that the Antecedent (IF X) is true. I don't know. Am I going about this the right way?
    (1 vote)
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    • leaf green style avatar for user David Greene
      In the conditional statement "If P, then Q", P is the antecedent and Q is the consequent. As described in the video, affirming the consequent is as follows:

      P1: If P, then Q.
      P2: Q.
      C: Therefore, P.

      (Note: The order of the premises is irrelevant and has no effect on the conclusion in most forms of logic, including classical logic. In the above example, P1 is a conditional statement and P2 is a declarative statement.)

      The declarative statement (P2) affirms (states as true) the consequent (Q) of the conditional statement (P1) in order to infer its antecedent (P) as the conclusion (C). This is fallacious (and, thus, an invalid argument form) because P is not stated to be the only sufficient condition for Q, so other conditions may be able to account for Q even if P is false. Understanding what affirming the consequent means, we can now construct an argument which affirms the antecedent, which is as follows:

      P1: If P, then Q.
      P2: P.
      C: Therefore, Q.

      This is simply modus ponendo ponens ("the mode that affirms by affirming" in Latin), also known as modus ponens, which is a valid argument form. "Affirming the antecedent" is simply another term for modus ponens, since the argument form is when the antecedent (P) is affirmed in the declarative statement (P2). It is one of the most basic forms of argument and is occasionally mentioned in the videos throughout this course. For example, it is briefly explained at in the "Fallacies: Formal and Informal Fallacies" earlier in this course. You can watch it here: https://www.khanacademy.org/partner-content/wi-phi/critical-thinking/v/formal-informal-fallacy

      Here are some examples to help clarify these two argument forms. This is an instance of affirming the consequent:

      P1: If it it is raining today, then I am staying inside all day.
      P2: I am staying inside all day.
      C: Therefore, it is raining today.

      This is fallacious because it raining today may not be the only condition which causes me to stay inside my home for the entire day. I might stay inside simply because I do not want to go outside today, even though it is not raining. In other words, C is not the logical consequence of P1 and P2 because P2 affirms the consequent of P1, which is fallacious; therefore the argument—and argument form—is invalid.

      Now, here is an example of affirming the antecedent (modus ponens):

      P1: If it is raining today, then I am staying inside all day.
      P2: It is raining today.
      C: Therefore, I am staying inside all day.

      This is not fallacious because the fact that it is raining today is a sufficient condition for my staying inside all day as per the conditional statement in P1. Because that sufficient condition has been met in P2, C logically follows. In other words, C is the logical consequence of P1 and P2 because P2 affirms the antecedent of P1, which is not fallacious; therefore the argument—and argument form—is valid.

      I think the nature of the confusion you were having was multiplex, though I may be mistaken of just what that nature was. Here's my best guess:

      1. You thought antecedents and consequents could themselves be fallacious. Statements can only be true or false; more specifically, statements possess degrees of truth or falsity relative to their certainty. Only arguments can be fallacious, since a fallacy is an error in an argument's form (formal fallacy) or argument's content (informal fallacy). Antecedents and consequents are components of a conditional statement which themselves follow the same logic as statements: they can be true or false, but they cannot be fallacious because they are not arguments.

      2. You misunderstood what "affirming the consequent" means, believing that "affirming" means "identifying as fallacious". Affirmation in logic (and in general) simply means to state as true. Thus, "affirming the consequent" means "stating as true the consequent". Think of terms like "affirming the consequent" as a sentence: "(The declarative statement [P2] is) affirming the consequent (of the conditional statement [P1])."

      Assuming that my previous two assumptions are correct, you concluded that "affirming the antecedent" is a more appropriate term for the fallacy because the antecedent was that which was identified as fallacious. Thus, "affirming the antecedent" to you meant "identifying as fallacious the antecedent", which is what you did according to the rationale described in 1 and 2. That rationale was predicated on a fundamental misunderstanding certain key concepts in logic, however, which is what caused you to misunderstand the fallacy as a whole, thus leading to your confusion.

      If I'm wrong, then I have no idea what caused the confusion you had about this topic. I took my best shot. Hopefully, I have clarified this issue for you. If I have not, feel free to comment and I will try to explain further. And if I'm mistaken anywhere above, please do correct me.
      (1 vote)
  • old spice man green style avatar for user zak Tiyeho
    some one to help me answer thi syllogism
    If life exists on Mars,then Mars has an atmosphere.
    Mars has an atmosphere.
    Ergo,life exists on mars.
    (1 vote)
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  • blobby green style avatar for user Dan Last
    At the end of the video you say: "To affirm the consequent is to infer the truth of the antecedent of a CONDITIONAL statment from the truth of the CONDITIONAL and its consequent."

    So thats quite confusing, you use conditional twice. Your basically just saying it twice... that your inferring the truth of a conditional statement from the truth of the conditional. It's just repeating itself. Why do you make it loop like that.
    (1 vote)
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    • mr pants teal style avatar for user monkey77
      He mentions the conditional for the first time to clarify that he is talking about the antecedent which is part of it and then a second time to say how the truth is inferred(via the truth of the conditional and its consequent). He was not repeating himself.
      (1 vote)
  • blobby green style avatar for user Mark Rosenkoetter
    Would it be fair to say this would be the same as confusing the sufficient and necessary conditions of an argument?

    P1: A>B
    P2: B
    C: A
    (1 vote)
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    • duskpin ultimate style avatar for user Leonie  Hauri
      Yes. When using the form 'If P, then Q' P is sufficient for Q, but that does not mean that P is necessary for Q. If P is necessary for Q, then committing this fallacy is actually not a problem because your conclusion will still be true. For example:

      P1: If I have a child, then I am a parent.
      P2: I am a parent.
      C: Therefore, I have a child.

      In that case having a child is necessary for being a parent, so the conclusion comes out true. However, in the examples in the video, P was only sufficient for Q in which case this fallacy has occurred.
      (1 vote)

Video transcript

(intro music) Hello, I'm Matthew Harris, and I'm a philosophy grad[br]student at Duke University. And today, I'll be discussing[br]the formal fallacy of affirming the consequent, and why you sometimes cannot conclude that you should bathe[br]in a tub of peanut butter. Affirming the consequent occurs when someone tries to infer the truth of the antecedent of a[br]conditional statement from the truth of the[br]conditional and its consequent. But let's see what this means in more detail. There are two kinds of logical fallacies: formal and informal. Both kinds are defective[br]argumentative patterns. First, we have informal fallacies, which lack support for the conclusion because of a flaw in its content. We also have formal fallacies, which all have in common[br]with affirming the consequent that they have defects in[br]the forms of the argument and that they are invalid. Just to be clear, let's go[br]over a few more definitions. We make conditional[br]statements all the time. They're generally easy to spot because they usually are of the form "if P, then Q." Here, "P" is the antecedent. An easy way to spot antecedents is to remember that they typically come after the word "if,"[br]whether or not they're at the beginning, middle[br]or end of sentences. If you need help remembering that, just remember that the antecedent comes before the other logically, and that it sounds a lot like "ancestor." The consequent of the conditional is the part that typically follows after the word "then." It should be easy to remember because it sounds like "consequence" and basically is just that. So let's take the following[br]conditionals for examples. Suppose someone tells you the following true conditionals and statement: "If the neighbors ate Susan's parrot, "then Susan is angry," and "Susan is angry." Just because it is true[br]that if the neighbors had eaten the parrot, then[br]she would have been angry, and it is also true that she is angry, does not mean that she's angry because they ate her parrot. Perhaps she's mad because her parrot isn't very interesting. Or maybe she's angry that it doesn't know how to use the toy car that she spent all afternoon building for it. Nevertheless, it does not[br]follow from the conjunction of the true conditional[br]and the true consequent that the antecedent is true. Let's look at a few more examples: "If Tom has a good reason to complain, "then Tom will complain tomorrow." Now, maybe you know Tom well, so you know that this is true. Maybe you even know that it's true that he will complain tomorrow. But it would not follow that Tom has a good reason to complain. Maybe he just doesn't know any better way to get attention. Now, let's take a look[br]at one more example. Consider this conditional[br]and the assertion: "If you are allergic to peanut butter, "then it would be a bad idea "to bathe in a tub of peanut butter," and "it is a bad idea to bathe "in a tub of peanut butter; "therefore, you are[br]allergic to peanut butter." Just because it is true that it would be a bad idea to bathe in[br]a tub of peanut butter if you are allergic, and it is also true that it is a bad idea to bathe in a tub of[br]peanut butter in general, does not mean that you are[br]allergic to peanut butter. If you were to conclude this, then you would be committing the fallacy of affirming the consequent. So that's the formal fallacy of affirming the consequent, and a few examples that you[br]could use in the future. Subtitles by the Amara.org community