Each of the cards has a color on one side, and an alphanumeric symbol on the other.
Rule: If it is blue on one side, then it is a 5 on the other side.
Which cards-- the fewest necessary-- do you need to flip to check the rule?
The answer is the blue card and the G card. We'll come back to this.
Each of the colored sides describes whether or not a sweater is borrowed; the other side describes whether it was returned.
Here's the deal: If you borrow my sweater, you must return it.
Which cards-- the fewest necessary-- do you need to flip to check to see if someone broke the deal and has to face the wheel?
In formal logic, this is expressed:
(p then q) implies (not q then not p)
Go through it:
if p then q.
if p then q.
therefore not p.
Many people find formal logic difficult to understand because they read left to right and apply future to the right, past to the left. If/then statements, in language, become about what will happen:
If you shoot him, then he will have a bullet hole in his body (If p then q).
More generally, however, logic is operating in the other direction: what if there is not q?
He does NOT have a bullet hole in his body; therefore, you did NOT shoot him.
P then q also implies: without q existing first, p can never exist.
In any argument if p then q, the only two things you know for sure are: p, therefore q; and not q, therefore not p.
In the cards above, those are the only two cards you need to flip: p (the blue card); and not q (the G or the did not return my sweater). Flipping the 5, for example, is a waste of a flip, it tells you nothing: if it's blue on the other side, then it worked; if it is orange, did that really tell you anything?
"p then q" represents the form of a proposition, but it can be Englished any way you want:
If he plays baseball professionally, then he takes steroids.
If you work with HIV patients, then you must wear gloves.
If you borrow my sweater, you must return it.
Don't get tripped up by the words: "hey, it isn't true that baseball players take steroids." "I could borrow the sweater and not return it." This is about the form. If the premise is accepted that "if you are a baseball players you take steroids," can it be true that someone who doesn't take steroids is still a baseball player? No.
Which brings us to human beings: we suck at formal logic, but, we are excellent at logic as applied to human interactions. Did you do better with the sweater than the numbers?
We instinctively feel the rules of borrowing and returning; and the logic of what happens if "you DON'T return my sweater" (therefore you won't be allowed to borrow more sweaters.) This doesn't mean we don't violate those rules, or cheat; but we understand the rules.
But impersonal descriptions, abstractions (cards, ps and qs) are naturally very difficult for us. Unless you have committed to memory modus ponens and modus tollens and force yourself to rewrite the question in that form, you won't score better than 20% (which is why it is a good idea to do so.)
So if you take a bunch of people who are psychopaths, and compare them to those who are not psychopaths but of equal intelligence:
From The Economist's summarization of this study:
[The] test suggests that analysing social contracts and analysing risk are what evolutionary psychologists call cognitive modules--bundles of mental adaptations that act like bodily organs in that they are specialised to a particular job. This new result suggests that in psychopaths these modules have been switched off.
That would be one explanation; and if it was the only one, this would hardly be worth reporting in the first place. But there's another explanation.
Part 2 soon.