Converse Error

Has nothing to do with shoes (despite what The Advertisement Server thinks).

Affirming the consequent:

This claim is most simply put as

If A, then B.
B.
Therefore, A.

It's a fallacy because at no point is it shown that A is the only possible cause of B; therefore, even if B is true, A can still be false. For example

If my car was Ferrari, it would be able to travel at over a hundred miles per hour.
I clocked my car at 121 miles per hour.
Therefore, my car is a Ferrari.
This is popular in conspiracy theories. Here the fallacy is fairly obvious; given the evidence, the car might be a Ferrari, but it might also be a Bugatti, Lamborghini, or any other model of performance car, since the ability to travel that fast is not unique to Ferraris. Hell, it might even be a Subaru Outback. Note that while this may appear to call all hypothesis / evidence experiments fallacious, they are based on additional evaluations of the likelihood of other theories, thus establishing that A is a likely cause of B.

Denying the antecedent:

The flip side of the above, where you say that because the initial conditions did not happen, the result is impossible.

If a person is wearing a hat, they have a head.
I am not wearing a hat.
Therefore I do not have a head.

Note that, by the contrapositive rule, these two fallacies are equivalent. For example, you could replace "If a person is wearing a hat, they have a head" by the logically identical statement "If a person has no head, they aren't wearing a hat" to turn the first example of denying the antecedent into an example of affirming the consequent.

Examples:

  • In American Dad!, Stan sinks his entire savings to build a rocket for Steve to win a contest.

    Stan: You gotta spend money to make money.
    Francine: But you didn't make any money!
    Stan: So logically, I didn't spend any money! *waves at the camera* Goodnight everybody!

  • In Yes, Prime Minister, Sir Humphrey Appleby explains the fallacy and how foolishly people can fall for it. He demonstrates the illogic of the fallacy by saying:

    All cats have four legs.
    My dog has four legs.
    Therefore my dog is a cat!

  • On the soundtrack album of Monty Python and the Holy Grail, a logician sorting out the movie's witch burning scene goes off on a tangent, stating that "given the premise 'all fish live underwater' and 'all mackerel are fish,' my wife concludes not that all mackerel live underwater but that if she buys kippers it will not rain, or that trout live in trees, or even that I do not love her anymore."
    • The witch-burning scene is itself an extended example of Converse Error, of course - with the punchline being that they somehow land on the correct answer anyway. Their reasoning runs:
    Ducks float.
    This woman shares a notable quality (weight) with a duck.
    Therefore, this woman must float.
    Wood floats.
    Therefore, this floating woman must be made of wood.
    Things made from wood burn.
    Witches burn.
    Therefore, this woman made of wood must be a witch!

Looks like this fallacy but is not:

  • Inference to the best explanation. The usual form of scientific reasoning, as well as a lot of Sherlock Holmes' "deductions" (though he's wrong to call them that, since this is a form of inductive reasoning).
    B.
    The best explanation for B would be A.
    Therefore, A (probably).
    • This differs from the Ferrari example above in that it posits a stronger connection between A and B than just A's truth entailing B's; B is actually giving some positive reason to prefer A over the other possibilities. Also, this form of argument isn't claiming deductive certainty, so the bar is a little lower for it being acceptable.
      • An example to compare with the Ferrari one above would be: I clocked my car at 121 mph, therefore it is likely to be a high-performance car (i.e. Ferrari, Bugatti, Lamborghini, etc...) rather than an average family car.
    • Scientific reasoning is frequently attacked by those who understand this fallacy, but not the scientific method, which has the following form:
    B.
    A is the best explanation for B, so I will claim "A is the most likely explanation."
    If A, then C.
    Therefore, if not C, not A (valid contrapositive).
    Is C true? Yes? I will increase my confidence that A is the correct explanation.
    If A, then D.
    Not D!
    I must provisionally reject A or modify it to account for D, then continue to seek new information and propose new possible explanations.\\

Alternative Title(s): Affirming The Consequent, Denying The Antecedent

http://tvtropes.org/pmwiki/pmwiki.php/Main/ConverseError