We contrast Margolis's account of Wason's Selection Task with recent decision-theoretic accounts and discuss evidence bearing on his claims concerning the roles of interpretation and deductive inference in the task.
2. Margolis argues that the patterns of performance on the task are not reflective of an inability appropriately to apply Modus Tollens (MT) reasoning when deriving the consequences of turning the 7 card. He views them as resulting instead from pragmatic factors that cue people to read the rule in a certain way. On this account people's selections can be viewed as logical in the context of their own interpretation of the task.
3. In the reasoning literature there has long been an anomaly between people's performance on the conditional arguments tasks, where relatively high rates of MT reasoning are shown, and performance on the selection task, where there is an apparent failure to make the same inference. Margolis' account may provide an explanation of this anomaly in a simple, but elegant way: People do not make MT on the standard selection task because there is no need to. The selection of the A card alone exhausts all the possible cases of A and hence no more inferential work is needed. In the RAST task this category is not available and hence people will then apply MT in deriving the consequences of turning over the category of not-q cards.
4. The arguments task also demonstrates high rates of the fallacious inferences, Affirmation of the Consequent and Denial of the Antecedent. This pattern of performance suggests that given limited context people often interpret conditional rules as their obverse, a fact that also sits well with Margolis' proposal that this interpretational factor is an important determinant of selections on the task.
5. Like Margolis, other authors have argued extensively that the choice patterns on the selection task should be viewed as rational. In contrast to Margolis, however, these alternative views argue that logic is not the appropriate normative criterion on which to judge performance (e.g. Kirby, 1994; Oaksford & Chater, 1994). These alternative approaches see the task as one of decision making in which the probabilities associated with the instances mentioned in the rule cue the selection of certain cards.
6. Oaksford and Chater present a Bayesian analysis of the selection task based on principles of information gain and uncertainty reduction. In their approach cards are selected on the basis of their informativeness. The informativeness of each card is a function of the probability of the items mentioned in the rule. Under an assumption of rarity, i.e. that P(p) and P(q) are low, the A and 3 cards are most informative, the 7 card is less informative and the D card provides no information whatsoever. The approach captures the intuitive judgement that it is more sensible to look for ravens or black things when testing the rule "All ravens are black" in the classic Ravens Paradox. Surprisingly, Margolis does not consider this approach in discussing the reduced array task, despite Oaksford & Chater's recent paper which discusses this task in detail (Oaksford, Chater, Grainger & Larkin, 1997).
7. Whilst Margolis and Oaksford & Chater agree that participants who select the A and 3 cards on the selection task are behaving rationally, they would clearly disagree about the basis on which such selections may be characterised as rational. Margolis would point to logical criteria, whilst Oaksford & Chater would emphasise information gain. In emphasising the role of logic and arguing that people's selections are driven by a consideration of the logical consequences of turning the cards, Margolis stresses the role of explicit processing in the task.
8. We have recently run a series of studies that were designed to demonstrate that people's choices on the task are, at least to some extent, driven by the explicit consideration of what might be on the reverse side of the cards. In a series of three experiments, Feeney and Handley (in press) presented participants with standard abstract rules of the following kind:
If there is an A on one side of the card then there is a 3 on the other side
together with a second rule containing an alternative antecedent:
If there is an L on one side of the card then there is a 3 on the other side.
Participants were asked to test the truth or falsity of the first rule. The presence of the second rule significantly suppressed the rates of q card selection relative to a single rule control. This finding was interpreted as indicating that people's selections were being influenced by the inferences that they made about the obverse side of the q card. In the example above, the second rule may have cued participants to realise that there could be either an A or a letter other than A on the other side of the 3 card, either way providing no information regarding the truth or falsity of the rule. This effect can be seen as analogous to the finding that a second rule with an alternative antecedent suppresses the Affirmation of the Consequent fallacy on the conditional arguments task (see, for example, Rumain, Connell & Braine, 1983; Byrne, 1989).
9. The similarity between the suppression shown on the selection task and on the arguments task lends support to an account of this phenomenon based on explicit deductive processes. Indeed, further support for this view was demonstrated in Feeney and Handley, Experiment 3, where suppression of not-p card selections was also shown, a finding analogous to the suppression of the Denial of the Antecedent fallacy on the arguments task (Byrne, 1989).
10. Our findings sit well with Margolis's account of the RAST. They may be interpreted as demonstrating that the presence of a second rule disambiguates the status of the rule to be tested, ensuring that it is understood to be a conditional rather than a biconditional. Secondly, our results strongly support Margolis' suggestion that explicit deductive inferences play a role in the task.
Byrne, R.M.J. (1989). Suppressing valid inferences with conditionals. Cognition, 31, 61-83.
Feeney, A. & Handley, S.J. (in press). The suppression of q card selections: Evidence for deductive inference on Wason's selection task. Quarterly Journal of Experimental Psychology.
Kirby, K.N. (1994). Probabilities and utilities of fictional outcomes in Wason's four-card selection task. Cognition, 51, 1-28.
Margolis, H. (2000) Wason's Selection Task With Reduced Array. PSYCOLOQUY 11(005) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/2000.volume.11/ psyc.00.11.005.reduced-wason-task.1.margolis http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?11.005
Oaksford, M & Chater, N. (1994). A rational analysis of the selection task as optimal data selection. Psychological Review, 101, 608-631.
Oaksford, M., Chater, N., Grainger, B. & Larkin, J. (1997). Optimal data selection in the reduced array selection task (RAST). Journal of Experimental Psychology: Learning, Memory & Cognition, 23, 441-458.
Rumain, B., Connell, J. & Braine, M.D.S. (1983). Conversational comprehension processes are responsible for reasoning fallacies in children as well as adults: if is not the biconditional. Developmental Psychology, 19, 471-481.