# Why one of these puzzles is easy and the other is hard

Despite the old saying that we’re ruled by our emotions, it’s tempting to believe that we have at least some intuitive sense of logic.

The various forms of logic such as syllogisms and deductive and inductive reasoning1 seem so simple and fundamental that you might expect that the rules are hardwired into our brains.

After all, since we’re constantly told that our neurons are the equivalent of computer processors, shouldn’t our brains be able to handle a little bit of logic?

See how you do on these logical puzzles.

Each of the cards below has a letter on one side and a number on the reverse.

If I told you there was a rule stating that a card with a vowel on one side must have an even number on the reverse, which of these cards would you need to turn over to prove or disprove this rule?

Many people turn over A and 2 — but that’s not quite right. While turning over A will tell you whether “one side” of the rule is true (if vowel, then even number), turning over 2 won’t tell you any more.

It doesn’t matter whether 2 has a K or an A on its reverse — the rules doesn’t specify either being true. Along with A, the other card you need to turn over is 7. If 7 has an A on its reverse, then the rule is disproved no matter what the A has on its reverse.

You need to turn over A and 7.

Very few people solve this riddle on the first try. It shows that humans do not possess an innate set of abstract logic rules. Yet somehow we manage to get by without those rules.

Try this similar puzzle:

Say there’s a rule that you must be 21 or over to drink beer. Whose drinks and ages would you need to check to see if this bar is flouting the rules?

By simply swapping drinks and ages for cards A, K, 2, and 7, it’s obvious this time around that there’s no point checking what the 21 year old (think 2 card) is drinking — it wouldn’t make any difference to the rule if she were drinking cola or beer, whereas the 16 year old’s (think 7 card) drink is of much more interest.

## How it works

Why are logic problems so much easier when they’re expressed as real-life situations rather than in abstract terms?

One early hypothesis called memory cuing proposed that we solve logic problems by drawing on personal experience, without using any deductive reasoning. We’ve all experienced the problems of drinking ages enough times that we don’t even have to think about who should be drinking what, unlike playing with letter and number cards.

Despite the substantial evidence behind memory cuing,2,3 many scientists believe that in practice we use more than just experience — that there is in fact some thinking involved. Instead, researchers such as Cheng and Holyoak4 think that, while we might not be so good at pure logic, we’re excellent at the logic we need in real life — rules, permissions, and obligations.

This type of logic — deontic logic — is what helps us solve everyday logic problems, by developing what they call “pragmatic reasoning schemas.” Therefore, it shouldn’t be surprising that our ability with logic is domain- specific, that is, limited to analysing the complex web of permissions and obligations we encounter in life.

_This story comes from ‘Mind Hacks’ by Tom Stafford and Matt Webb.

It’s been suggested by Cosmides, aleading light of evolutionary psychology (the study of how evolution may have shaped the way we think), that the reason we seem to possess domain-specific logic is because it’s been selected for by evolution over countless generations.

Cosmides argues that the really important parts of Cheng and Holyoak’s pragmatic reasoning schemas are those about people.

In other words, we are all born with the mental logic required to understand the costs, benefits, and social contracts involved in dealing with other people. It’s a compelling argument, since the ability to make beneficial deals is a valuable survival trait.

However, Cosmides’ theory can’t be the whole story, since we have no problem in solving many logic problems that have nothing to do with costs, benefits, or indeed other people at all.

For example, the rule “If you’re going to clean up spilt blood, then you need to wear rubber gloves” is easily understood and applied even though it doesn’t concern other people.

Before resigning yourself to a life without logic, it’s worth remembering that along with the countless other skills that we aren’t born with, we can understand logic the hard way — by learning it.

Even if you don’t, you can still console yourself with the knowledge that you’re as good as any philosopher in the everyday logic that really matters.