mavant comments on An overview of the mental model theory - LessWrong

11 Post author: ScottL 17 August 2015 01:18PM

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Comment author: mavant 23 August 2015 06:51:41PM *  0 points [-]

The Ace is in both statements and both statements cannot be true as per the requirement.

No.

deal :: IO CardHand

deal = do

x <- randomBoolean

if x

then generateHandsContainingEitherOrBothOf (King, Ace)

else generateHandsContainingEitherOrBothOf (Queen, Ace)

Asking a trick question and then insisting on a particular reading does not constitute evidence of a logical fallacy being committed by the answerer.

Comment author: ScottL 23 August 2015 11:09:38PM *  0 points [-]

It's not a trick question. It's pretty much the same as the example used in the literature and then I have a few other examples that are straight from the literature. The literature on mental models is mainly on deductive reasoning. That is why the question is in the format it is.I have rephrased it to try to make it more clear that it is not about which algorithm is correct.

Note that the robot is a black box. That is, you don't know anything about how it works, for example the algorithm it uses. You do, however, have two statements about the what the possibilities of what the dealt hand could be. These two statements are from two different designers of the robot. The problem is that you know that one of the designers lied to you and the other designer told the truth. This means that you know that only one of the following statements about the dealt hand is true.

Can you please let me know if you think this helps. Also, did you have the same problem with the second problem.

The thing is that the problem requires a particular reading because a different reading makes it a totally different problem. Under your reading the question really is:

The dealt hand will contain cards from only one of the following sets of cards:

  • K, A, K and A
  • Q, A, Q and A

Obviously, that's a totally different problem. If you have any suggestions on how to improve the question, let me know.

Comment author: mavant 24 August 2015 01:22:24AM 2 points [-]

The fact that it's the same phrasing used in the literature is really concerning, because it means the interpretation the literature gives is wrong: Many subjects may in fact be generating a mental model (based on deductive reasoning, no less!) which is entirely compatible with the problem-as-stated and yet which produces a different answer than the one the researchers expected.

One could certainly write '(Ace is present OR King is present) XOR (Queen is present OR Ace is present)' which trivially reduces to '(King is present OR Queen is present) AND (Ace is not present)', but that gives the game away a bit - as perhaps it should! The fact that phrasing the knowledge formally rather than in ad-hoc English makes the correct answer so much more obvious is a strong indicator that this is a deficiency in the original researchers' grasp of idiomatic English, not in their research subjects' grasp of logic.

It's difficult for me to look at the problem with fresh eyes, so I can't be entirely certain whether the added 'black box' note helps. It doesn't look helpful.

What would be really useful would be a physical situation in which the propositional-logic reading of the statements is the only correct interpretation. There is luckily a common silly-logic-puzzle trope which evokes this:

The dealer-robot has two heads, one of which always lies and one of which always tells the truth. You don't know which is which. After dealing the hand, but before showing it to you, the robot dealer takes a peek.

One of the robot's heads has told you that the dealt hand contains either a king or an ace (or both).

The robot's other head has told you that the dealt hand contains either a queen or an ace (or both).

Comment author: Jiro 24 August 2015 01:21:42AM 2 points [-]

It's not a trick question. It's pretty much the same as the example used in the literature

Those two statements are not mutually exclusive.

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