# Logical

A necessary component of critical thinking is the ability to draw logical conclusions. Our students have to be able to draw logical conclusions given a set of rules and circumstances.

For example, take this rule: “If it’s raining, then it’s cloudy.” Which of the following conclusions are valid?

• It’s cloudy outside, therefore it must be raining.
• It’s not cloudy outside, therefore it must not be raining.
• It’s raining outside, therefore it must be cloudy.
• It’s not raining outside, therefore it must not be cloudy.

Look at it this way: for it to be raining, it must first be cloudy. It could be cloudy without raining, but it could not be raining without it being cloudy. If it’s not cloudy, it could not possibly be raining. It’s also just as true that if the conclusion is not true, then the condition is also not true. That is, if it has to be cloudy to be raining, and it’s not cloudy, then it can’t be raining.
Unfortunately, a lot of people have trouble with this, and explanations like the one I just provided make it even more confusing.

In 1966, Peter Wason devised the Wason Selection Test to test logical reasoning. The test works like this:

You are shown a set of four cards placed on a table each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which cards should you turn over in order to test the truth of the proposition that if a card shows an even number, then its opposite face shows a primary color?

Given a logical statement in the standard “if p, then q” format, the cards show p, not p, q, and not q. In order to check the validity of the proposition, it is necessary to test the p and not q cases.

The Philosophers Magazine has an online version of this test, which you can use to test your ability to draw logical conclusions. While the test statistics appear to be broken, the text states that 75-80% of test-takers get the answers wrong. Here’s how the site interprets these results:

There are a number of important implications of the fact that we tend to be bad at the Wason selection task One has to do with the notion of justified belief. If a belief is recognized to be based on defective reasoning, then to continue to believe it is not justified. But if we systematically, and unconsciously, reason badly, then the extent to which reason actually acts as a constraint on belief is a moot point.

Another implication has to do with what these tests tell us about the way that the human mind has evolved. According to Leda Cosmides & John Tooby, the results of the Wason selection task demonstrate that the human mind has not evolved reasoning procedures that are specialized for detecting logical violations of conditional rules. Moreover, they claim that this is the case even when these rules deal with familiar content drawn from everyday life. However, they argue that the human mind has evolved to detect violations of conditional rules, when these violations involve cheating on a social exchange. This is a situation where a person is entitled to some kind of reward only if they have fulfilled a particular requirement. Cheating involves taking the benefit, without fulfilling the condition for the benefit. It is Cosmides’s and Tooby’s finding that when the Wason selection task is constructed to reflect a cheating scenario, subjects perform considerably better than they do with the standard test. And moreover, they found additionally that this is not simply to do with the familiarity of cheating scenarios – subjects do better with an unfamiliar cheating scenario than they do with a familiar standard scenario.

Fascinating…