Try this:
You are shown four cards. The cards each have a letter on one side and a number on the other side. Two of them have their letter up while the other two have their number up. The cards show A, G, 7 and 8. The question is: which card(s) must you flip in order to determine whether the following rule is true:
If there is an A on the one side, then there is a 7 on the other side.
EDIT: clarifying and concretizing the question. I think the above should be enough, but the below doesn’t really reveal anything new either, though it could help you make the correct assumptions. Maybe try once with the minimal explanation and another time with reading the clarification below.
Clarification:
To make such a card you can cut out a piece of paper (that is thick enough to show writing through it), and write a letter on it, then flip it and write a number on it. When presented to the person answering they are all four placed on a desk at the same time such that only the number or letter is showing.
Answer:
The answer is A and 8.
Apparently only 4-10% people get it right.
Lots of people want to check 7, however the rule doesn’t say that there must be an A if there is a 7. It only works the other way, there could be any other letter on the other side of the 7 and that would be consistent with the rule. And so flipping gains no information.
What you need to be doing is looking for ways to disprove the rule. One way to disprove it is by checking the 8 and if it has A on the other side then the rule is disproved.
By checking A you are checking a way to disprove the rule. However I don’t think that’s how people think about it. They probably think about it more as a way to gain supporting evidence. 44% chose A and 7, which I think is a choice that clearly shows looking for supporting evidence.
If there were a million cards with 7 should you flip any of them? No. But people might feel that by flipping more and more of them where the backside is an A then the probability of the rule being true increases.
I wouldn’t expect Bayesianism to believe that. I assume the theory is advanced enough to cover cases like this. At least in this type of simple form.
I heard about this from this video:
https://www.youtube.com/watch?v=XOiCFa5niuM
That’s where I got the percentages from, too.
This is the logic Popper uses to talk about why justificationism doesn’t work. They talk about Popper at 28:50.
People get answer correct when essentially the same puzzle is phrased using a social rule and a social situation. That’s interesting and I’ll be writing more about the psychology of this puzzle later.
How did I do? I got it correct. However the first time I was listening I was listening on it in the background. I didn’t pay that much attention so when I played it back I didn’t remember the answer. And I remember reasoning through each of the cards. It did take me some time, like 1-2 minutes. In the video they said that having taken logic classes correlates with getting the answer correct, which I have taken. I didn’t immediately think of checking 8 as a contrapositive but I did recognize it when I knew I had the correct answer. I think I ought to be able to get this faster and pretty much instinctively.