Custom Search

Sunday, January 23, 2011

LOGICAL AND CONDITIONAL REASONING

LOGICAL AND CONDITIONAL REASONING
Logical reasoning
A special form of problem solving is logical reasoning. In these kinds of task, people are required to draw conclusions that necessarily follow from a given, but not to draw conclusions about what might possibly follow. For example, in this syllogistic reasoning task, two premises enable conclusions to be drawn:
If all men have blood, and John is a man, then, necessarily, John has blood.
But syllogisms are not always this easy, and some can lead to false conclusions. For example:
If some As are Bs, and some Bs are Cs, what can be said about the relation of As to Cs?
A common error is to say: Some As are Cs. But while this may be case, it is not necessarily true. Those Bs that are Cs might be the ones that are not As. Johnson-Laird (1983) suggested that when people get this wrong, it is not because they are not ‘logical’; it is because they have an inadequate representation of the problem – what he calls a mental model. Johnson-Laird was able to show that forming such models is harder with some premises than others, and that the harder it is (i.e. the more complex the mental models), the more likely it is that we will make an error.

Conditional reasoning
Another much studied type of logical reasoning is conditional reasoning, which deals with ‘if–then’ statements. For instance: If a green light comes on, then the ball has rolled left. Suppose the ball has rolled left. What can we conclude? A common error is to conclude that the green light must have come on (Rips & Marcus, 1977), but this is not a necessary conclusion. The ball could have rolled left for any number of other reasons.

[Phillip Johnson-Laird (1936– ) has been a major contributor to the nature of reasoning and also to the psychology of language, becoming particularly well known through his book Mental Models (1983). Much of this work was conducted in conjunction with Peter Wason, especially regarding his work on deduction (as evaluated, for example, using the Wason selection task). Johnson-Laird proposed and developed the theory of mental models, which seeks to explain how understanding works through mental representations of the situations depicted by a text or problem description. According to Johnson-Laird, humans are not always rational, but they are not intrinsically irrational either.]


This error is called ‘confirming the antecedent’. Does the fact that the error occurs mean that people are not logical? This is the wrong way of thinking about the issue. Like the logical error, what it means is that some people have the wrong representation of the problem, and this leads to false conclusions. For instance, the abstract form of the problem, ‘If A then B. B, so . . . ?’, suggests that there is only A and B to consider, in which case it is reasonable to suppose that if B, then A. But, in general, there can always be some other cause for B – it simply is not stated. So it is easy to confirm the antecedent. For instance, if you commit murder, you go to jail. But if you go to jail . . . this does not mean you committed murder!

Detecting cheats
A very important way of testing if–then statements is known as the Wason Selection – or four-card problem (Wason, 1966). In this task, the participant is given a rule, and four cards are laid out that have information written on both sides. For example: Rule: If a card has a vowel on one side, then it has an even number on the other side. Card 1: A Card 2: D Card 3: 4 Card 4: 7 The task is to verify (i.e. test) whether the rule holds by turning over the two cards that will enable this to be determined. Which cards would you turn over to verify the rule? Try it before you continue reading. The most frequent response is to check A and 4. Turning A will provide information that is consistent with the rule if there is an even number on the other side of the card, and will falsify the rule if there is an uneven number, so that is fine. But turning 4 will achieve nothing, because the rule does not say, ‘If a card has an even number on one side, it will have a vowel on the other.’ Turning this card is very much lik confirming the antecedent. In fact, the crucial second card to turn is the card with the 7, because if this has a vowel on it, then the rule is false.


This problem is hard to think about. But real-life versions can be much easier. For instance:
If a student is drinking beer, then they are over 18.
Card 1: Over 18
Card 2: Drinking beer
Card 3: Drinking Coke
Card 4: Under 18
How would you test the rule? Most people would now think the crucial card to turn was card 4, ‘Under 18’, because if that had ‘Drinking beer’ on the other side, there is a clear violation of the rule. This is because testing for under-age drinking is an example of detecting cheating, which is something we appear to be good at (Cosmides, 1989; Gigerenzer & Hug, 1992). The argument is that we have social rules to live by, and that we are naturally attuned to be able to test whether these rules are being broken. Clearly the representation of the problem is crucial to how reasoning takes place. When a concrete form of the problem is used, we can bring in specific procedures that we have access to for detecting cheats, which is something that is socially important. With an abstract version of the task, this is not possible.

No comments: