Affirming the Consequent
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[edit] Definition
Affirming the consequent is a formal logical fallacy where a participant invalidly reverses an implication. The most general structure of this argument runs something like the following:
- A implies B (equivalently, if A, then B)
- B
- Therefore, A.
This is a fallacy because the initial premise states that A is sufficient for B to be true, but not necessary.
[edit] Example
Example 1:
- Antagonist: All birds have wings. I saw an animal with wings. Therefore it must have been a bird.
This argument overlooks the fact that there are other animals that have wings but which are not birds, such as bats and insects.
Example 2:
- Antagonist: If it rained, the pavement would be wet. Since the pavement is wet, it must have rained.
This argument overlooks the fact that the wetness could have been caused by something else, such as someone washing graffiti off the pavement.
Example 3:
- Antagonist: "All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident." (Arthur Schopenhauer). My ideas are being ridiculed and violently opposed. Therefore they are true, and will eventually be accepted as being self-evident.
This argument overlooks the fact that many incorrect and dangerous ideas have also been ridiculed and opposed.
In all the examples, there are other possible explanations for the observed facts.
[edit] Exceptions to the Rule
As with many fallacies, the argument of affirming the consequent should be evaluated on a case-by-case basis. Almost all arguments from effects to causes can be viewed, formally, as examples of this fallacy, but such arguments are often considered to be "rational" arguments. For example the following argument is technically an example of affirming the consequent but would be accepted by most people.
Example:
- Protagonist: If the defendant committed the crime, his fingerprints will be on the murder weapon. Since his fingerprints are on the weapon, he is obviously guilty.
The key to analyzing an argument of this form is to consider the alternate hypotheses that could also produce the observed behavior. If it isn't raining, then how did the pavement get wet? If the defendant didn't commit the crime, how did his fingerprints get on the gun? If the alternate hypotheses are considered to be sufficiently implausible, then the original argument should be accepted.
Alternatively (but equivalently), one can consider whether or not the statement "if A then B" is being presented as a shorthand for "A if and only if B," where A is being considered to be both necessary and sufficient. If a normal observer would consider the statement "if B then A" to be a reasonable and true statement, then inference from effects to causes is still rational.
