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Conditional Reasoning


Disciplines Argument > Types of reasoning > Conditional Reasoning

If...then... | The card trap | So what?



Conditional reasoning is based on an 'if A then B' construct that posits B to be true if A is true.

Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false. In effect you also need a statement of the form 'If not A then ...'.

A classic form of conditional reasoning is in using syllogisms, where a general major premise is combined with a more specific minor premise to form a conclusion. Syllogisms are easy to get wrong and there are many fallacies.

The card trap

A classic trap was used by Wason and Johnson-Laird (1972) to show how poor we really are at reasoning.

Four cards are laid out as below:










The conditional statement is now given: 'If a card has one vowel on one side, then it has an even number on the other side.'

The question is to decide which are the minimum cards that need to be turned over to prove that the conditional statement is true.

More than half of people questioned said E and 4.

To affirm the antecedent, E is correct. E is a vowel and thus should have an even number on the other side. If there was an odd number on the other side, the statement would be false, so E must be turned over to check for this.

But choosing 4 is affirming the consequent. Even though 4 is even, it can have a vowel or consonant on the other side and the statement is not falsified.

Only 4% said E and 7. The 7 could deny the consequent and hence must be checked. If there was a vowel on the other side, the statement would be false.

And what of K? There is nothing to say that a card cannot have letters on both sides. If there is a vowel on the other side, then the statement is also wrong.

A common variant of this shows cards with 3, 8 (faces), and Red and Brown (backs), and asked 'Which card (or cards) should you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?' The answer is 8 and Brown. Only a card which has an even number on one the face and which is not red on the back invalidates the rule 'If even, then other side red'.

So what?

Be careful about if-then statements, both in your own use and in those that others use. It does, of course also mean that you can make statements that are logically false and few people will challenge you.

See also

Syllogisms, Fallacies


Wason, P. C. (1966). Reasoning. In Foss, B. M.. New Horizons in Psychology. Harmondsworth: Penguin.

Wason, P. and Johnson-Laird, P. (1972). Psychology of Reasoning: Structure and Content. Harvard University Press, Cambridge, MA


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