[etangent]

It seems to me that the selection task is tricky because it concerns interpretation of language. "Every card that has a D on one side has a 3 on the other" makes a claim: that there is a directional dependency "D => 3" but it makes no claim that "3 => D". However the absence of the latter claim is not stated explicitly, it is supposed to be inferred from the original statement. The English language seems to lack a way to encode unambiguously the "A => B" relationship. So it should not be surprising that students used to looking out for language pitfalls when checking proofs also happen to be the students who do better on this task.

[two_handfuls]

> The English language seems to lack a way to encode unambiguously the "A => B"

It doesn’t: “If A then B” encodes it unambiguously.

It’s just that as you said, many people don’t think hard about the difference between this and similar-but-different concepts like “B only if A”.

It’s not the language itself, it’s the way people use the language and think about what it says (or in this case, don’t).

[BoiledCabbage]

> It doesn’t: “If A then B” encodes it unambiguously.

No, actually it doesn't

> Some authors have argued that participants do not read "if... then..." as the material conditional, since the natural language conditional is not the material conditional.

> It’s just that as you said, many people don’t think hard about the difference between this and similar-but-different concepts like “B only if A”.

While a nice simplistic answer it's likely not what's going on here. There is more here than "People just aren't good at thinking".

If your statement were true, then you'd be forced to say that the following statement is also obviously true:

"If the Nazis won World War II, then everybody would be happy"

The fact that you can rightfully say that sentence is false, means that your comment above about implication and "if" statements is wrong.[1] Language is more complex then you're giving it credit.

[1] - https://en.m.wikipedia.org/wiki/Paradoxes_of_material_implic...

[hardlianotion]

For what it's worth, I think that the problem lies in the solution feeling "obvious" and people being a little lazy - I don't think the problem lies with inability.

I also think that if A then B is unambiguous, the counter that languages are different doesn't really fit with what I think I observe in the wild. For the full house, I also fail to see how that means I must accept that your example statement is obviously true.