Denying the Antecedent

Translation: Spanish (Traducción en español)

Alias: Denial of the Antecedent

Type: Fallacy of Propositional Logic

Form Similar Validating Forms
Modus Ponens Modus Tollens
If p then q.
Not-p.
Therefore, not-q.
If p then q.
p.
Therefore, q.
If p then q.
Not-q.
Therefore, not-p.

Example:

…I want to list seventeen summary statements which, if true, provide abundant reason why the reader should reject evolution and accept special creation as his basic world-view. …

14. Belief in evolution is a necessary component of atheism, pantheism, and all other systems that reject the sovereign authority of an omnipotent personal God.

Source: Henry M. Morris, The Remarkable Birth of Planet Earth, (Creation-Life Publishers, 1972), pp. vi-vii.

Analysis

Counter-Example:

If it's raining, then the streets are wet.
It isn't raining.
Therefore, the streets aren't wet.

Exposition:

Together with Affirming the Consequent, this is a fallacy which involves either confusion about the direction of a conditional relation, or a confusing of a conditional with a biconditional proposition. Specifically, Denying the Antecedent occurs when a premiss of an argument denies the truth of the antecedent of a conditional premiss, then concludes by denying the truth of the conditional premiss' consequent (see the Form). This form of argument is non-validating because, from the fact that a sufficient condition for a proposition is false one cannot validly conclude the proposition's falsity, since there may another sufficient condition which is true. For instance, from the fact that it isn't raining, we cannot infer with certainty that the streets are not wet, since they may have been recently washed (see the Counter-Example).

Sibling Fallacy: Affirming the Consequent

Source:

A. R. Lacey, Dictionary of Philosophy (Third Revised Edition) (Barnes & Noble, 1996).


Analysis of the Example:

To say that q is a "necessary component" of p is to mean that if one has p one must also have q, that is: "if p then q". For example, "an engine is a necessary component of a functioning automobile" means that if one has a functioning car then one has an engine, rather than if one has an engine then one has a functioning car. So, Morris' argument is as follows:

If atheism/pantheism is true then evolution is true.
Atheism/pantheism is false.
Therefore, evolution is false.

Even if the first premiss were true—which it is not—it doesn't follow from a rejection of atheism or pantheism that one must reject evolution. There are many theistic religions which accept evolution as an historical fact.


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