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affirming the consequent

Affirming the consequent (AC) is a formal fallacy, i.e., a logical fallacy that is recognizable by its form rather than its content. AC has the form:

If p then q.

q.

So, p.

p and q represent different statements. A statement with the form "if p then q" is called a conditional statement. p is called the antecedent and q is called the consequent of the conditional statement.

Arguments with the form AC are fallacious because they are invalid. Being invalid means that their conclusions do not follow from their premises, i.e., it is possible for their premises to be true and their conclusions false. A valid argument is one in which the conclusion follows from its premises, i.e., it is impossible for its premises to be true and its conclusion false.

Below are some examples of the fallacy of affirming the consequent:

If my astrologer is psychic, then she predicted the forest fires in Russia.


She predicted the forest fires in Russia.


So, my astrologer is psychic
.

***

If a god created the universe, we should observe order and design in Nature.


We do observe order and design in Nature.


So, a god created the universe.

***

If telepathy is present, we will get greater than chance results from our card-guessing experiment.

We got greater than chance results from our card-guessing experiment.

So, telepathy is present.

***

If he's lying, he will sweat.

He's sweating.

So, he's lying.

***

If the suspect is lying, then he will evoke a galvanic skin (from sweating).

The suspect evoked a galvanic skin response.

So, the suspect is lying.

In each of the above examples of the fallacy of affirming the consequent the premise of the argument may be true but the conclusion does not follow from the premises. The invalidity of these arguments has nothing to do with their content and is due entirely to their fallacious form. A statement p never follows from the statements if p then q and q. Even if the premises of an AC argument are true, the conclusion doesn't follow from them. Being fallacious, however, does not mean that the conclusion is false. For example, the following examples of AC have true conclusions:

If President Obama is a Christian, then he is not a Muslim.

He is not a Muslim.

So, President Obama is a Christian.

***

If President Obama was born in Hawaii, then he is an American citizen.

He is an American citizen.

So, President Obama was born in Hawaii.

Some might wonder: are not all conclusions from experimentation invalid on this ground from the point of view of formal logic? Don't scientists commit this fallacy when they reason that if my hypothesis is correct then we will observe x, y, and z when we do experiment E; we observed x, y, and z when we did experiment E; so our hypothesis is correct? Yes, they would, but that is not how competent scientists reason. They reason by the valid form of modus ponens:

If x, y, and z occur in experiment E as predicted by our hypothesis, then our hypothesis is confirmed. X, y, and z occurred in experiment E as predicted by our hypothesis. So, our hypothesis is confirmed

Competent scientists also reason by the valid form of modus tollens:

If our hypothesis is correct, then x, y, and z will occur in experiment E as predicted by our hypothesis. X, y, and z did not occur in experiment E as predicted by our hypothesis. So, our hypothesis is not confirmed.

Valid reasoning, however, is not enough to establish the truth of the conclusion. All premises must also be true in the above example. The key to solid, cogent reasoning about a scientific experiment is the justification of the first premise: is it really true that your hypothesis will be confirmed if what you predict occurs (or if your hypothesis is correct, then what you predict will occur)? Many researchers unjustifiably assume that if what they predict will occur does in fact occur, then they have confirmed their hypothesis. All of the examples above of affirming the consequent could be rewritten as valid arguments. For example, the following would be valid:

If we get greater than chance results from our card-guessing experiment, then telepathy occurred.

We got greater than chance results from our card-guessing experiment.

So, telepathy occurred.

See the psi assumption for more on this problem of assuming what should be proved (begging the question), though the problem is not restricted to psi researchers. Competent researchers must also consider x-factors (unknown and therefore uncontrolled for factors) that might also account for the results of their experiment.

See also denying the antecedent and topical index: critical thinking.

further reading

Browne, M. Neil & Stuart M. Keeley. Asking the Right Questions: A Guide to Critical Thinking (Prentice Hall, 2009).

Carroll, Robert Todd. Becoming a Critical Thinker - A Guide for the New Millennium (Boston: Pearson Custom Publishing, 2000).

Damer, T. Edward. Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments 4th edition (Wadsworth Pub Co, 2008).

Moore, Brooke Noel and Richard Parker. Critical Thinking (McGraw Hill, 2008).

Smith, Jonathan. 2009. Pseudoscience and Extraordinary Claims of the Paranormal: A Critical Thinker's Toolkit. Wiley-Blackwell.

Vaughn, Lewis. 2009. The Power of Critical Thinking: Effective Reasoning About Ordinary and Extraordinary Claims. Oxford University Press.

Last updated 26-Dec-2013

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