Conditional Reasoning

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

If...then...

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.

Conditional traps

A couple of definitions: In the statement 'If A then B', A is the antecedent and B is the consequent.

You can affirm or deny either the antecedent or consequent, which may lead to error.

Denying the consequent

Denying the consequent means going backwards, saying 'If B is false, then A must also be false.' Thus if you say 'If it is raining, I will get wet', then the trap is to assume that if I am not getting wet then it is not raining.

Denying the antecedent

Denying the antecedent is making assumptions about what will happen if A is false. Thus if you say 'If it is raining, I will get wet' and is not raining, I might assume that I will not get wet. But then I could fall in the lake.

Affirming the consequent

This is making assumptions about A if B is shown to be true. Thus if I make the statement 'If it is raining, I will get wet', then if I am getting wet it does not mean that it is raining.

The card trap

A classic trap was used by Wason and Johnson-Laird (1972) to show how

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.

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

Syllogistic Reasoning