There are 4 cards. They are randomly chosen from a deck of cards in which every card has a letter on one side and a number on the other. Please indicate which of the cards you would have to turn over in order to find out whether the card obeys this rule: "If a card has a vowel on one side, then it has an even number on the other side." Turn over only those cards that are necessary to establish that the rule is being followed.
Card 1 shows N
Card 2 shows 4
Card 3 shows A
Card 4 shows 3
Your choices are:
1. Card 3 only
2. Cards 1, 2, 3, and 4
3. Cards 3 and 4
4. Cards 1, 3, and 4
5. Cards 1 and 3
From Mindware, p. 209, hardcover.
Less than 20% of Oxford University students can solve ... the card problem.
The answer is choice 3.
From Mindware, p. 216, hardcover.
I wasn't going to use the puzzle in this post but the statistic was so astounding that I felt compelled. If less than 20% of college students can reason deductively the answer, what does that say about non-college educated people? Is this the source of our problem of the uneducated voting against their best interest?
The next section of Mindware by Richard Nisbett talks about reasoning or logic. There's a few puzzle problems that you can test yourself against to see the strength of your reasoning ability. Some section of it gets a little obtuse for me but just power through it because it is worth reading, if only for some eye opening statistics.
The author talks about basically 2 kinds of reasoning systems: the Western hyper rational reasoning with its deductive and inductive reasoning and the Eastern's holistic dialectical reasoning. Depending on what methodology you use, you can end up with different answers.
Deductive reasoning is top down, of which the card problem is an example. You start from some basic rules and from those premises you build your conclusion. Inductive reasoning is bottoms up and forms the basis of the scientific method where you perform tests and then draw your conclusions.
The big takeaway though is that some of the deductive reasoning may feel to be valid (which is different from being true) just because it feels like it is right. A valid conclusion is when the conclusion logically follows from the premises. If the conclusion is illogical, then it is invalid, even if the premises are true, or at least plausible. In addition, the conclusion could be valid but untrue because some of the premises are untrue. There are a lot of traps here.
I wonder if those traps are the source of our problem because we are working off of premises and conclusions that feels like they are true when they may not be. Chapter 13 is well worth reading to see some of the examples of pitfalls.
How can we better learn how to work through these logic problems? One suggestion offered by the author is to draw Venn diagrams as an aid. And I find them very helpful in working through the complicated puzzles. I would also offer doing lots of logic puzzles.
Dialectical reasoning sounds a lot like holding two opposing ideas in one thought. One person argues for one set of ideas and the other argues for the contradictory set of ideas. And then the third stage is to reconcile the two opposing ideas or do some kind of synthesis to solve the conflict. The thing about dialectical thinking is that it leads to a more holistic view and involves empathy, the concept of the yin and yang or contradiction, and the idea of change. Out of this concept of dialectical reasoning, there is a belief that people can change and that people are full of contradictions. Also, there is a belief that trends will level off or reverse itself. Nothing stays the same.
There is an interesting section on the Chinese belief on intelligence and academic achievement. The Chinese have the belief that study will help improve your academics whereas the Americans hold on to the idea of talent. So while Chinese American students may have comparable IQ to American students, they score better on the SAT tests by a third of standard deviation. Also, Chinese Americans are 62% more likely to work in professional, managerial or technical fields. (Mindware, p. 234)
Okay, time to wrap this up.
Which to use? Dialectical or Deductive?
Deductive is best for scientific inquiry - most of the time - but dialectical reasoning is better for the affairs of human, such as human conflicts. As Americans, how do we develop dialectical skills? I'm not sure and the author really doesn't offer any suggestions. The only thing I could come up with is to keep an open mind, apply empathy and consider the situation the person may be in, realize people's performance can vary and change, and realize that your assumptions may be wrong.