The psychology of reasoning is a branch of cognitive psychology that studies that way
in which humans use logic to come to conclusions based on available information.
But not all reasoning is valid, and people may use invalid reasoning to come to illogical conclusions.
So just how logical are we as humans? And for that matter - how logical are you?
A logic test developed by Peter Wason in 1963 revolutionised the field of reasoning.
This classic selection task features cards with letters on one side and numbers on the other
side. Subjects are then presented with 4 cards and a rule: If a card has a vowel on one side,
it must have an even number on the other side.
And the task is this: which card (or cards) must be turned over in order to determine
whether or not the rule has been followed.
So basically, you must turn over cards which can guarantee whether this rule is true or false
I'll give you a few seconds if you want to pause the video and think about it, before
revealing the answer...
OK... the correct answer is...the cards which must be turned over are:
A and 7
These are the two cards which must be turned over to assess whether or not the rule has been followed.
Various studies has shown extremely poor results for tasks like this, in which only 4% of participants
get the correct answer. The most common wrong answer being A and 2.
This can possibly be explained by confirmation bias. The rule mentions both a vowel and an
even number, so it may seem logical to choose the vowel and even number cards. While this
may seem logical, as I will demonstrate, it's actually fundamentally illogical.
I'll now go through each card and explain why you do or do NOT need to turn over each card over.
The key to this task is you need to understand that you must try to falsify the rule, not confirm it
So the first card, A, this is the most obvious, and virtually all participants correctly conclude
that this card must be turned over. Because of course, if there's an odd number on the
opposite side, the rule has been broken.
Now the next card, the K card, this is basically an irrelevant card, which cannot give us any information.
If we turn it over and it's an odd number, that's fine. If we turn it over
and it's even number... that's also fine. So if neither outcome breaks the rule, there’s
no need to turn the card over.
The 2 card is where things get tricky... and where most participants slip-up. If we read
the rule again, "If a card has vowel on one side, it must have an even number on the other
side". Now, it's important to realise is that this rule only goes one way. Therefore we cannot
conclude that if there's an even number on one side, there must be a vowel on the other side.
This is not the case.
If we turn the 2 card over, and there's a consonant on the other side... that's fine.
This does NOT break the rule. And obviously, if we turn it over and there's a vowel, this
also doesn’t break the rule. So again, if neither outcome can break the rule, then we
cannot obtain any relevant information from this card, and therefore there is no need
to turn it over.
Finally, the 7 card. This card must be turned over. Why? To make sure that there is NOT
a vowel on the other side. If there is, this breaks the rule because the card has a vowel
on one side and an odd number on the other side.
So looking at both potential outcome of all 4 cards, we can see that there are only two
ways in which the rule can be broken, and therefore these two, and only these two, cards
that must be turned over to determine whether or not the rule has been followed.
This rule is basically just an "If, then" statement. Or it can be written as “P therefore
Q” in which P is the antecedent, and Q is the consequent. Each of the 4 cards represent
the 4 possible premises: P, not P, Q, not Q.
So ‘P’ would be a vowel. ‘Not P’ would be a consonant. ‘Q’ would be an even number.
And ‘Not Q’ would be an odd number.
Now when presented with each of these premises, we can make inferences. These can be divided
into two types of reasoning - inductive reasoning, and deductive reasoning. Inductive reasoning
is invalid, while deductive reasoning is valid.
The first and most obvious is when presented with P (in this example, the A card), since
the rule is P therefore Q, given P, we can obviously deduce that Q must follow. This
is known as affirming the antecedent, or modus ponens, which is a valid, deductive form of reasoning
Next when presented with ‘not P’, in this example, the card K, we could infer ‘not Q’.
This is known as denying the antecedent, which uses inductive reasoning and is therefore invalid.
Just because you're presented with 'not P' does NOT necessarily mean that ‘not Q’ must follow.
When presented with Q, people often infer P. But like I said, the rule only goes one
way. So just because the rule is "P therefore Q", does not mean we can turn it around and
say "Q therefore P". This is known as affirming the consequent, which is another invalid form of reasoning
Now, finally, when presented with ‘not Q’, we can infer ‘not P’. This is often missed
by participants of tasks like this, despite being a valid, logical form of reasoning - known
as denying the consequent, or modus tollens. This is valid because if we have ‘not Q’,
the only logical conclusion would be ‘not P’.
If we apply this to a real-world example, we could say something like “All tigers
have stripes” as our premise. Then we could make inferences using both deductive and inductive reasoning
for example:
“If it’s a tiger, it has stripes”
“If it’s not a tiger, it doesn't have stripes”
"If it has stripes, its a tiger"
"If it doesn't have stripes, it's not a tiger"
Looking at the results of the card selection task, one might quickly jump to the conclusion
that humans are not very good and reasoning, and are therefore illogical. But one important
thing to note is that content is crucial to a task like this, and that participants perform
significantly better when presented with cards that have real-life applicable examples.
This can be seen in a different form of the card selection task. This time, each card
represents a person. On one side of the card is the drink in which that person is drinking,
and on the other side is their age.
Participants are presented with 4 cards, and the following rule: "If a person is drinking alcohol,
they must be 18 years or older".
The task is once again to turn over cards in order to determine whether or not the rule
(or in this case, the law) is being followed.
In this case, 72% of people correctly predict that the cards 'Beer' and '16' must be turned over
The 'Beer' card has to be turned over, to make sure the person drinking that is old
enough. The ‘Water’ card is irrelevant, since it doesn't matter what age the person is.
The ‘25’ card is also irrelevant since it doesn't matter whether they're drinking
alcohol or not, since they're over 18. And the ‘16’ card must be turned over, to
make sure that person is not drinking alcohol.
It's much easier for us to reason in tasks like this because we can actually apply it
to real-life scenarios.
In terms of actual variables, this test is actually quantitatively identical to the first.
The statement "If a person is drinking alcohol, they must be 18 years or older", is just another
"If P, then Q" statement, where drinking alcohol is P and being 18 year or older is Q.
The 4 cards also represent the same 4 premises as before - P, not P, Q, not Q.
This also helps highlight why certain inferences are illogical. The most common wrong answer
in the first task was the A and 2 cards. But as stated earlier, turning over the 2 card
is illogical. The 2 card, is representing the premise Q. In this real-world example,
representing the Q premise is the 'age 25' card.
So it becomes more obvious why this is illogical. Just because a person is over 18, does not
necessarily mean they are drinking alcohol. So no matter what they're drinking, they're
not breaking the law, and therefore there is no need to turn over that card.
So the rule P therefore Q cannot be simply turned around to Q therefore P. "If a person
is drinking alcohol, they must be at least 18 years or older" cannot be turned around
to "If a person is 18 years or older, they must be drinking alcohol". This is inductive
reason and is therefore invalid.
It’s worth pointing out though, it’s possible to be wrong by using deductive reasoning,
and vice versa, it’s possible to arrive at a correct conclusion using inductive reasoning.
Deductive reasoning is only as correct as its premise. So given an incorrect premise
like “all birds can fly”, we could use modus tollens to logically deduce that
"if it can’t fly, it’s not a bird”. This is obviously false because a penguin is a
species of bird that can’t fly.
And if we return to our tiger example, if we see a tiger, and say “It has stripes,
therefore it’s a tiger”. This is an invalid form of reasoning, yet we have arrived at
a correct conclusion.
In fact, inductive reasoning is actually incredibly useful, and we use it on a daily basis with
incredible accuracy. Some of the most obvious statements and assumptions we make, are actually
using inductive reasoning.
Things as obvious as “the sun will rise tomorrow” or “if I drop this coin, it
will fall to the ground”. These statements, though obvious, are actually using inductive reasoning
How do we really know the sun will rise tomorrow? Because it’s risen every day of our lives
so far? But nothing that has happened in the past can guarantee what will happen in the
future, we can only make predictions, and increase the certainty of our predictions,
but we can never guarantee outcomes.
In fact, everything we know about the universe, we know through inductive reasoning. How do
you think we get these premises in the first place? How do we know that all tigers have
stripes? Through inductive reasoning. But there’s no way to know for sure that all
tigers have stripes. Maybe there’s an undiscovered species of tiger in a jungle somewhere with
no stripes. It’s just that every tiger anyone has ever seen has had stripes, so we can say
with a high degree of confidence that all tigers have stripes. But it’s impossible
to know for sure.
In fact, according to the strictest rules of logic, it’s impossible to know ANYTHING
for sure. Through scientific research, we can only increase the likelihood that something
is true, but can never actually confirm it.
A famous philosophical quote states that “Nothing can be known, not even this”
But just because something can’t be known with 100% certainty, when all the scientific
evidence points to something, any rational person would accept it as fact.
So when it comes to reasoning, it’s not just about logic, but also about common sense,
and rationality too.
Thanks for watching.