# How Logical Are You? (Psychology of Reasoning)

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.

I can never know something for sure but yet its rational to accept it as fact?! Rather if i know that i can never know something for sure it is rational to accept it can incorrect, thus i should humble myself.

Does it count of I used a pencil and paper to arrive at the correct answer?

Your voice is annoying

Ii

Basically, you're looking for A not B.

I’m only seeing people go on about how they “got it” but won’t even bother to explain how they came to their conclusion.

I am the 4%!

A and 7 I got it correct . I don't think it was very difficult. You have to remember that cards

withouta vowel might also have an even number on the other side.this is easy for someone who has studied logic

0:30 I didn't catch the part where they have stuff on the other side, so I got really confused there

and I also thought that 'side' meant left and right, not front and back.

oh my you reminds my college life it's so difficult to think about logic

So the way the question is worded made me think that even numbers where exclusive to vowels, which isn’t the case.

Cartoon logic makes no sense.

hahaha i got the first question wrong i really am so stupid

For the people whining about the question, that "double sides were not mentioned!" – Yeah, if you want intelligence above average, you should've been able to figure it out on your own.

Took me a while until i understood why i was wrong, im dumb. Good video though.

if it's not AK47, it's not logic lol

Go to hell 😂

The test seems poor to me. There is nothing here to imply the rule works

one wayonly. "If a card has a vowel on one side(which side exactly? The one we see? The hidden one?)it must have an even number on the other side".I only have one question to any one who can answer it …I'm bad at math…but I'm excellent at physics chemistry and all the other science subjects…I don't know why but when it comes to math and calculus application in physics I can do it easily no matter how difficult the problem is …but when it comes to MATH itself I mean pure math…I struggle with it… oh pleaaaase someone help me 😢

Ambiguity caused by a poorly expressed question doesn't translate to capacity of reasoning. This is bullshit

God damnit i failed

How is it fine if the K card has an even number? It would break the rule.

You speak ao fast I was not able to understand the questions and also their answers

Ak47

Not

Ak27

Triggerd

That rule about the 2 card makes no sense. How does one know which side of the card is the original side, you didn't explain the concept properly

6:02 Jesus fucking Christ only 72% of people? Wow…

9:05 one of the criteria that tigers fall into are 'it must have stripes', so there is no way an animal without stripes is a tiger.

Why am i thinking about KSP when i hear the background music?

new gun: the AK 27, thanks for making a new gun suggestion

I chose A and 7.

Assume the rule is true and the rule is not reversible, then a "1-a" card can exist, however if I filp it, it will become a "a-1" card, which is impossible as a card that has a vowel on one side must have an even number on the other side. That's why I think the if-statement has to be reversible otherwise contradiction will occur.

8:15 is just not right, it is completely illogical.

Y’all mfs belong on r/iamverysmart

10% other clearly on Americans

All of my friends think which must be flipped

Friend 1: A27

Friend 2: A27

Friend 3: A

Friend 4: A2

Friend 5: A

Friend 6: A27

Friend 7: A2

Me: A7

I realised what the question was about only after the solution was made clear to me (i.e the question is very poorly constructed…)

I didn't even understand the first question lol

I didn't understand why I got Wason wrong until I saw this. Now it makes sense. I still think the wording of Wason is confusing though as I thought you were looking for a fault in the card printing machine..

To all the people who got it wrong and blame the question and people who got it right and are going full r/iamverysmart about it, I understood the question and still got it wrong. Nobody's perfect _o_/

The results of the initial problem aren't very promising, but the results of the second one are. When things matter enough to provoke cognition, thought occurs. The trick is to reveal how important some things really are (and when they are), not to rote program human beings to care about everything all the time (which is exhausting and inefficient). Mind, an uneducated (or lesser-educated) mind will fail even during important situations, so it's still necessary to teach and learn and engage with one another in the pursuit of a more perfect understanding.

Apathy reigns while meaning rests. Share your thoughts and feelings more freely with those around you, and the world will be better for it.

What about things that can be known a priori? Can’t those be known with 100% certainty?

It would've been helpful to know these aren't real cards that only have 2 sides

Your accent sucks

Turn over all of them. It’s a 50% chance that it has an even number on the other side. This will further prove that if a card has a vowel it will also have an even number.

Or so I think ._.

I got A 2 7

If the cards are same then if all the even number are on the other side of all the cards having vowel than why not the opposite is true?

So Peter Wason must have been a used car sales man. That is the only logical conclusion substantiated by the language of his question. "If a car has great gas efficiency, it must be from our lot." he would say. So when a poor idiot would buy a car from him just to find out a donkey gets better gas mileage than the car, Mr. Wason would reply: "I never implied that the statement is applicable in reverse as well!"

I didnt understand shit. I guessed K and 7 and first by the way xD

I don't understand it. Can anyone explain to me?

Im very dumb

I say the 1 way rule is bull. It didn't say the SHOWN side. It said if it has a vowel on one side, then the other is even. That means if the other side, hidden side (which is one side) is a constanant, and the shown side (which is also the other side when compared to the hidden side(which is one side)) is an even number, the rule is incorrect, meaning you need to check all cards to make sure the rule is true, as the cards are not linked in any way, shape, or form and the rule doesn't allow you to not check a card (even if it is not a number or character, because you don't know what's on the other side, unless ofc, both sides are shown). In my brain, cards are 2d, 2 sides. If one side is a vowel, then other side is an even number. I picture a vowel being on one side, and an even being on the other. The rule says this, meaning you can flip the card and say that the even is on the shown side, then a vowel must be on the hidden side. Since it didn't say which side is "one side", this is all true. Meaning the answer is all cards. Plus I don't see why converse and inverse don't work, while contrapositive does.

Can someone please explain me i seriously didnt get it i am very bad in logic i am trying to improve my logic but i didnt understand from where those 2 numbers came from and what we have to follow

I underthought the first one and overthought the second one xd

It would have been more logical if he had used beer and water card example at first

You should recommend some books in the subject.

that's an amazing explanation!

I guess the 7% percent people got it right now

My logic was. To change 2 into 4

The only way one discovers true logic and knowledge is to finally discover what Socrates expressed so very far in the past: The only thing I know for certain is that I don't know Shite…paraphrasing of course…

What does logic even mean ?

I cant believe I got the first one

I got the first one correct but I didnt think about all that other stuff he was talking about to get my answer

actually you only need to turn over the K card lol

But "any reasonable person would believe it" is a bandwagon fallacy/appeal to authority, not logic!

putangina ganon ba ko kabobo ala ako maintindihan

Why not turn all the cards over?

I'm in the 10% of other…

laughingthis… this hurt my head and I thought about this for a good hour

https://youtu.be/1OE4CcxkQf0

Is the host eating gum while broadcasting?

Damn. At first my answer was just A but when he revealed the answer (being A and 7) I immediately realized my mistake.

lol, i choosed to turn no cards.

I think it's better for to jump from a bridge XD

I think this is not that difficult. Just don't rush into the answer

As far as falsification being the only true evidence Karl Popper once said " there arw two types of theories, theories that have been disproven and theories yet to be disproven". Understanding logic tests and how people rarely use logic make one afraid to go in front of a jury, or even most judges.

Bad teacher

I take issue with the idea that the vowel : even number relationship is only one way. The nature of cards is such that each individual card has only two outcome sets, represented by two sides. Now, these cards being “cards” indicate that they will have no more than or less than two sides (to suggest that the rule doesn’t state that cards have to be two sided is just unnecessarily annoyingly literal). Therefore, given these 2 potential outcome sets, we are left with 4 qualifiers – vowel, consonant, even, odd. By indicating that for a rule to be true a card with a vowel on one side must have an even number on the other side is effectively saying that the vowel qualifier directly yields the even qualifier, which, because there are only 2 outcome sets per card, indicates that this rule is then reciprocal, meaning if you flip over the “2” and get a B, you have disproven a rule. That might be our if scope of this because it’s technically a proof by induction… but still

I got the ak27 correct and the beer and 16 thing wrong lol

Isn't there a more interesting test?

Letters and numbers are boring af

By the way, the premise that ''deductive reasoning is always correct'' always annoyed me in Sherlock Holmes. Because deductive reasoning CAN lead to incorrect results.

Thanks for clarifying this point in the video.

Instinctively on the first I knew turning over A & 2 would be wrong but I didn't know why so I had to keep watching to know why it was wrong 😅

Surely you must turn over the K as well. What's to say there's not a vowel on the other side? Or are we only testing from the perspective of this side of the cards…?

How long did 5.1k-people pause video?

Holy moly I got a lightbulb flipped

no Logical at all

lol i didn't even understand what the question meant

If you have good logical thinking. You don't want to do bad things to society.

your voice is annoying

You can know you have conscious experiences. You can make that into a premise onto which you can deductively conclude you conscious has substance in some form, which means your conscious experience and the medium it functions in have the property of existence.

Even if everything is deterministic and we lack all free will, you can still use this reasoning to have SOME true knowledge.

In mother russia the only logic you need is making the 2 a 4

oh myyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Most people: “Dang I got that card question wrong”

Me, suffering through majoring in computer science: “wtf is this? we aren’t in 2nd grade”

I like how the ones who claim that they didn't understand the first question didn't go back over it till they understood it (which is a lie, they totally understood it, they just have an over-inflated opinion of themselves, think they possess above average intelligence and are just emotional that they are just average, will ignore it and go on pretending that they are very logical and wont realise their mistake until it's too late to do anything about it). To be honest, don't feel bad, most people think they are above average, it's a pretty average attitude. Don't get me started on the high number of people claiming to have gotten it right, either explicitly or implicitly. Do not, I repeat, do not trust humans to self report honestly.

Think how dumb those people are who are complaining about not understanding the first question. Then remember that half of the world is dumber than that. 🙂

I cant believe only 72% of people got the beer one correct. People are so damn stupid. Dear god.

At the end you show a graphic that depicts evolution, while doing so you say when all the science points to something any rational person would accept it as fact (I may be paraphrasing), is this at all related to religion?

Sad to see the 5k dislikes. Be careful about the use of 'common sense' and 'rationality' though.

This was so good! I got caught by the A2 trap and now all I wanna do is learn how to think logically

From tricky question you made a conclusion