Wason’s trials with logic

Suppose you are shown four cards, each with a number on one side and an alphabet on the other, kept on a table. The symbols on the card facing upwards are D, K, 3, 6. Then there is a rule that says if D is one side, the other side of the card is 3. Which two cards do you need to turn over to verify the rule?

Wason did this study in the 1960s with psychology and statistics students and found a large percentage of them suggesting the cards D and 3 as the leading choices to inspect. It is pointless to turn over 3 as there are no restrictions about what 3 can take on the other side; the rule is on D. The right answer is D and 6. Logical problems such as this are called formal logic as they are set up in certain forms of conditional statements (AND, OR, NOT, IF etc.).

According to Wason, these logics are of the form, if P then Q (P -> Q). P is called the antecedent, and Q is the consequent. The only violation of the rule (P -> Q) here is if P and not Q (P -> !Q). The other combinations, not P and Q (!P -> Q), and not P and not Q (!P -> !Q) are not violations.

To put some meaning to P and Q, consider this one: if it rains (P), I will take an umbrella (P) (P -> Q), the end of the statement. So what all can follow from this? If it doesn’t rain (!P), I may or may not take an umbrella and still, the rule is not broken (!P -> Q and !P -> !Q are possible). But, if it rains, I can not have a situation with no umbrella (P -> !Q is not possible) because I made that statement already. The truth table summarises all the arguments:

Interestingly, these logics are easier to follow in real life. Imagine a simple instruction to the cashier at the shop counter: allow alcohol only if the person is above 18. The employee knows whom to watch out for – the people who carry alcohol to check out and those who appear below 18. Not the man who is holding apple juice. It is ecologic logic or logic in the real world.

Reasoning about a rule: Wason

Rationality: Steven Pinker