Denying the Antecedent
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[edit] Definition
Denying the antecedent 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)
- not-A
- Therefore, not-B.
This is a fallacy because the initial premise states that A is sufficient for B to be true, but not necessarily necessary. For example, all birds have wings (if something is a bird, then it has wings), but there are things that aren't birds that still have wings, such as insects and bats.
[edit] Example
Example 1:
- Antagonist: Jim always plays chess at lunch on Wednesday. Since today is Thursday, he must not be playing chess.
Example 2:
- Antagonist: If it rained, the pavement would be wet. Since it hasn't rained in a week, the pavement must be dry.
In either case, there are other possible reasons that could cause the consequent to be true. Nothing keeps Jim from playing chess on other days, and someone might have wanted to wash graffiti off the pavement.
[edit] Exceptions to the Rule
As with many fallacies, the argument of denying the antecedent should be evaluated on a case-by-case basis. Especially in informal speech, people have a tendency to use statements like "if A then B" to mean "if A then B, and if not-A then not-B." When such a meaning is implied by the context, then the argument may still be rational.
Example:
- Antagonist: You're the best speaker in the group; we know that if you do the presentation, it will go well.
- Protagonist: Well, I'm on a business trip that week, so I can't do the presentation. I guess it won't go well unless we reschedule the trip.
The key to analyzing an argument of this form is to consider the alternate hypotheses that could also produce the behavior. If it isn't raining, then how did the pavement get wet? Are there any other speakers who could give the presentation? If the alterate 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.
