Responses

There are three main responses to the fact that people are dreadful at solving the quartet presented in the last section:

The Mental Logic Response

According to this response, which is promoted (e.g.) by Lance Rips [Rips, 1994] and David O'Brien [O'Brien, 1995], humans do naturally acquire the ability to deduce abstractly, but they are restricted to a deductive scheme having considerably less power than standard first-order logic -- and this scheme is not adequate to crack problems like those seen in the quartet displayed in the previous section.

The Pragmatic Reasoning Schemas Response

This response -- the chief advocates for which are Cheng and Holyoack (e.g., [Cheng and Holyoak, 1985], [Holyoak and Cheng, 1995]) -- springs from the fact that when conditionals like the one seen in the selection task are changed into ``deontic" conditionals, performance improves substantially. For example, Griggs and Cox [Griggs and Cox, 1982] showed that deontic conditionals like

• If a person is drinking beer then the person must be over 18.

tended to elicit correct selections. Here is an example of a schema that the previous conditional might be an instantiation of:

• If the precondition is not satisfied, then the action must not be taken.

The Mental Models Response

The response has been championed for quite a while now by Johnson-Laird (e.g., [Johnson-Laird, 1995], [Johnson-Laird, 1997]). Logicians will identify the response with semantic tableaux, but Johnson-Laird prefers a somewhat idiosyncratic specification, and he has recently produced a computer program that instantiates this specification. According to this program, a disjunction is represented by two models, one in which obtains, and one in which obtains; the two models are written (one to a line) as

If the reasoner now learns that is false, she strikes out the first model and is left with the second -- in which is true. (This then becomes a mental models version of unit resolution.)

Now as a matter of fact we see fatal problems infecting each of these responses (as well as the others we don't explicitly consider), but our objective here is just to air the responses in order to place our own in the full context of the psychology of reasoning and Piaget's . We turn now to our own response.