The Wason Selection Task, Part V

Margolis's claim is that his explanation does away with the longstanding idea that people are bad at modus tollens reasoning on the WST.

I’ll do my best to show you how he gets there. I'll set off what I understand as the two parts of his argument in blockquotes (the second part of his argument shown below actually is a quote, though I've partitioned it).

The First Part of the Argument

(1) Subjects perform very poorly on the 4-card version of the Wason Selection Task, but a "clear majority" finds the correct answer to the reduced-array selection task. These results are produced by a combination of two factors: (a) subjects are misunderstanding the cards as categories in both tasks and (b) some subjects interpret the "if" in the task as a simple "if" [the most common interpretation] and others interpret it as "if and only if."

(2) The misunderstandings in the 4-card version yield mostly "incorrect,” though “logical,” answers, whereas the same misunderstandings produce "correct and logical” answers in the 2-card version.

(3) For the 4-card version, there are in fact several logical responses, given that subjects misunderstand the cards as categories. For the "if" reading, either P or not-Q would be logical. For the "if and only if" reading, there are four logical responses: P and Q, P and not-P, Q and not-Q, not-P and not-Q.

(4) The correct answer, P and not-Q, is not a logical answer, given the misreading.

With the first part of his argument, Margolis shows us that there is an explanation that both fits the results and does not require us to postulate a general inability to handle modus tollens. In fact, the correct answer in the reduced-array selection task, which a "clear majority" of subjects choose, does seem to require modus tollens reasoning.

However, the most common responses to the 4-card task (either P alone [the “if” reading”] or P and Q [the “if and only if” reading]) involve modus ponens reasoning, not modus tollens. So what remains to be shown is that people can handle modus tollens in the 4-card task. (Margolis might likely disagree that this second part is necessary.)

The Second Part of the Argument

[1] The [not-P, not-Q] response [ed.: a response involving modus tollens] is in fact another correct response to the illusory reading of the cards as categories.

[2] That [this response] is almost never seen shows the effect of the salience of [the P and Q cards] in the rule.

[3] But the wording of the [instruction] has a recency advantage over the wording in the rule. This turns out to be so strong that the predominant response is reversed by reversing the order in which the two clauses in the [instruction] are presented. . . . The exceptionally heavy [P and Q] responses are elicited by making the task read: "Circle two cards to turn over to check whether the rule has been violated." But [P and Q] as the dominant response switches to [not-P and not-Q] when the instruction is turned around to read: "Figure out which two cards could violate the rule, and circle them."

I have a few problems with Margolis's conclusions. First, even if the categories explanation were the only one possible to explain subjects' performance on the 4-card task, it is not required to explain subjects' improved performance on the RAST. Indeed, Margolis himself says that it seems as though subjects are still interpreting the cards as categories in the 2-card version. This, of course, is not proof that they are. Other explanations should be considered.

For example, it should be noted that there are a total of 15 possible responses to the 4-card task. Subjects may choose a single card (4 possibilities), a pair of cards (6 possibilities), three cards (4 possibilities), or all the cards (1 possibility). In the reduced-array selection task, there are only 3 possible responses: each individual card or both cards. If subjects were guessing perfectly randomly from all available possibilities, the correct answer in the 4-card task would theoretically show up about 6.7% of the time. In the RAST, that jumps to about 33.3% of the time—nearly a 400% increase in correct answers. Even when we discount the three- and four-card possibilities in the 4-card version (without similarly dismissing the possibility of selecting both cards in the 2-card version), the theoretical number of correct answers in the 2-card version is more than triple that in the 4-card version.

Of course this doesn't fully explain the "clear majority" of correct responses to the 2-card version, but it should cast some doubt on the idea that a category misreading explains all of the improvement.

Second, the reduced-array selection task ostensibly tests subjects using only the “difficult” cards—the one they choose incorrectly most often (Q) and the one they incorrectly almost never choose (not-Q). Yet, the former is not often chosen by itself in the 4-card version. The Q response is most often paired with the P response. Thus, it may be that there is only one “difficult” card in the RAST—the not-Q card. The fact that subjects choose this card in the RAST may be explained by using Margolis’s own words:

Other than for rhetorical purposes, we do not ask questions with obvious answers.

These objections, however, are not the most important disagreement I have with Margolis. For that, I'll require another post.

Wason Task: Part I | Part II | Part III | Part IV | Part V | Part VI