Safalra's Website Philosophy Logical Fallacies Denying The Antecedent

# Denying The Antecedent

Denying The Antecedent (also called Denial Of The Antecedent) refers to the fallacy of using an argument of the form:

1. If A then B
2. not A
3. Therefore not B

An argument of this form is most convincing when the statement 'if B then A' seems plausible.

## Equivalence to Affirming The Consequent

Denying The Antecedent is equivalent to the fallacy of Affirming The Consequent, as the above argument can be rewritten:

1. If not B then not A
2. not A
3. Therefore not B

## Example

This fallacy is commonly employed by lawyers to claim that the absence of some particular evidence proves their client's innocence. If a person, P, has disappeared, and evidence suggests that the defendant has murdered P, but P's body is not found, a lawyer may argue that without a body thier client cannot be charged with murder. More formally:

1. If P's body is found then my client could have murdered P
2. P's body has not been found
3. Therefore my client could not have murdered P

## A note on Bayes' Theorem and absence of evidence

The phrase 'absence of evidence is not evidence of absence' is an informal expression of the idea that Denying The Antecedent is a fallacy, but the truth is more complex.

Bayes' Theorem can be seen as a probabilistic variation on Denying The Antecedent in which the argument is valid. It tells us that the probability of not B given not A is equal to the probability of not A and not B divided by the probability of not A. If A implies B, then the probability of not A and not B equals the probability of not B. Therefore, as long as A was not certain to be false, the discovery of the falsity of A increases our assessment of the probability of the falsity of B.