The most important aspect of the four comments on my target article lies in what we all seem to agree on. All of us see evidence that the notorious difficulty of Wason's simple problem grows out of a misinterpretation of the problem, not (as has usually been supposed) from an inability to make modus tollens inferences.
2. In all these accounts, correctly applying modus tollens can lead to what, given the intended meaning of the task, erroneously looks like a failure to correctly apply modus tollens. The accumulation of evidence pointing to this profoundly different interpretation of what is happening in the Wason puzzle is far more significant than the variation among us on just how the misinterpretation arises. Subjects -- including subjects of the very sort likely to be reading this discussion, not just naive or unintelligent subjects -- somehow misunderstand a task that seems transparent.
3. My own account was spelled out when I first discussed the matter a long time ago (Margolis 1987, pp. 141-56). On this view, subjects respond "as if" the four cards shown represented categories of cards not particular cards. A card showing "A" is mistakenly (and tacitly: subjects are not aware of what is guiding their intuition) responded to as if it represented the category of all cards with an A on either side. Wason's simple question turns out to generate a remarkably effective cognitive illusion because in a subtle way it goes against ordinary experience with questions of that form.
4. Is it credible that could happen? It takes stark evidence to support such an odd claim. But the two variants of the Wason task reported in my target article provide (it seems to me) very stark evidence indeed, especially when considered jointly.
5. Prudkov (2000) calls my account "correct but trivial", though supportive of Prudkov's view of human problem-solving. But Prudkov's "trivial" apparently means something like "seems like it ought to be trivial", since the explanation goes against the overwhelming majority of comments on Wason over several decades of intense discussion. Obviously, it is not trivial in the sense that anyone could see right away what accounts for the remarkable difficulty exhibited by this apparently simple task.
6. Laming (2000) points to an alternative interpretation of the nature of the misinterpretation that subjects seem to make. In both Laming's account and my own there is a secondary problem turning on the possibility that the "if" in Wason's "if/then" rule might be read as "if and only if". There is no serious disagreement on this aspect of the matter, and I set it aside. Where the two accounts seem to differ critically is on whether what is misinterpreted is the Wason rule itself (Laming) as against a misinterpretation of the task, given a correct reading of the rule (Margolis). Laming (6a) says I failed to express myself clearly. But actually Laming misreads what I think is said plainly enough, but is not what Laming expected.
7. Is it possible we have here a distinction without a difference? On Laming's account, subjects misunderstand the rule, thinking "if A is on one side of a card, then 3 is on the other side" means "if A is on the top, then 3 is on the bottom". On this account, subjects understand what they are asked to do (choose which of four particular cards should be inspected), but their answers reflect their misunderstanding of the rule they are asked to apply. On my account, the opposite holds. Subjects do not misunderstand the rule, but instead misunderstand the task. They respond as if the "A", "D", "3", and "7" they see are not each the top side of some particular card, but instead represent categories of cards which have "A", "D", "3" or "7" on either side. But perhaps both Laming's account and mine are ways to articulate a deeper process which does not distinguish between the two, as a bilingual person might have an intuition which he can articulate in either language but from a brain process that is not in any particular language.
8. Nevertheless, which interpretation works better would seem to be of some psychological interest. In particular, the "categories" account has an empirical basis (Margolis 1987, p. 152). So there is a principled reason for suspecting it is more likely to be right. And the evidence seems to support that. There is a great deal of overlap between the consequences of these two versions of misinterpretation. But for the experiments discussed in my target article (and particularly for both considered jointly), it seems to me the "categories" account provides a more straightforward account of why the usual Wason responses are sharply altered by some apparently trivial variation in the task.
9. Without experimental support, both Laming's version of misinterpretation and mine seem wholly improbable. Who would suppose, ex ante, that people would misunderstand such simple language? But it is also improbable that intelligent subjects are actually incapable of making modus tollens inferences that we can see these same people make without difficulty in everyday life -- and in other experimental paradigms, as Handley & Feeney (2000, para 3) point out. What makes the argument for misinterpretation strong, however surprising it may be, is that we can point to variants of the Wason problem (two in my target article, several others in the work Laming, Bucciarelli, and Handley & Feeney cite) which support that account. Across this now considerable array of experiments we see patterns of response that make sense in terms of some sort of misinterpretation account and not much sense or even no sense at all in terms of a more usual modus tollens account.
10. Handley & Feeney are generous to my account, and provide further evidence from their own experiments. But it appears that they are persuaded by only one side of that account. We both see responses consistent with an ability to draw modus tollens inferences. But on my account those inferences make no sense, since they are contingent on a misinterpretation of the task that makes no sense given the plain meaning of the instructions. And neither the misinterpretation nor the inference is explicit. Subjects just see turning certain cards as the right move. But what they see as the right move is in fact the wrong move, given what the problem clearly says. Contrary to Handley & Feeney, I would not want to describe all that as rational, though a misplaced sentence in my article may have given the contrary impression. See the correction in (16) below.
11. On an unrelated matter, Handley & Feeney indicate surprise that I did not consider a recent paper (Oaksford et al, 1997) which reports experiments directly based on Wason's RAST (reduced array selection task). But Wason's own version of RAST (and that of Oaksford et al) is much more complicated than the experiment discussed in my paragraphs 1-4, and the Oaksford et al mathematical analysis is also much more complicated. It would take a good deal of space to adequately describe all this, not to mention the space then required to explain why their argument seems to me unpersuasive. But a single point might be mentioned. Oaksford et al (p. 450) remark that "every theory of the selection task predicts that the p card should predominate." But in the Margolis/Griggs experiment (10) a trivial variation in wording yields a sharp predominance of not-p over p. So this easily replicated experiment seems to flatly contradict the Oaksford et al account of Wason. My view here is very much the same as Laming's. See his 1996 re-analysis of a related Oaksford et al paper.
12. Turning now to Bucciarelli (2000): she finds that the children in her study tend to respond with "categories", where the categorical responses she notices are compatible with but not the same as those ordinarily observed with adult subjects. Adults usually either got her problem right (a majority) or gave the common illusory response of "p & q". Small children, however, very rarely got the problem right but also rarely gave the "p & q" response. Instead they mainly responded with "p & not-p", or "q and not-q": both rare responses for adults.
13. But as described in my original discussion (Margolis 1987, p. 151), all of these (and "not-p & not-q" as well: which is what turns up in force in the Margolis/Griggs variant) are (pseudo)correct responses, given the "categories" misinterpretation and an "iff" interpretation of Wason's rule.[2] So the illusory responses from children are not so different from the usual illusory response of adults as might initially appear. But this suggest a curious possibility, and one sure to arouse skepticism. Reaching the "p & q" response requires only using modus ponens; but the other three responses require modus tollens for one of the cards [3]. Certainly small children cannot consciously draw modus tollens inferences.
14. Bucciarelli's results, on this interpretation, then raise the possibility that from sufficiently transparent interactions with the world (in which even 3-year olds have a good deal of experience) habits of mind that embody modus tollens might be entrenched very early. For, after all, the world is such that modus tollens always holds, even for a person much too young to have any conscious glimmer of what that means. So for a really transparent situation, might a monkey implicitly make modus tollens inferences? Outrageously, this argument suggests we might look for that. Yet suppose a monkey were presented with a pair of hard-to-open boxes, only one of which contains food. Would we be surprised if the monkey sniffed the nearer box, but only worked at getting into it if it smelled food. Would that be an application of (implicit) modus tollens: "if there were food, I could smell it; since it doesn't smell of food, I'll go to the other one."[4]
15. But I conclude as I began, by stressing that it seems to me the agreement among all these comments is more important than the disagreement. If the four commentators and I are collectively right, then the overwhelming majority of discussion over nearly three decades of study of the Wason problem has missed the main point.
16. CORRECTION: In my article, the intended final sentence of (6) appears at the beginning instead of the end of that paragraph. In this position, it seems to be saying that the misinterpretation of the Wason question (5) is not illusory (which I certainly did not intend) instead of saying that about the "if/iff" ambiguity, which I did intend. This has clearly misled several of the comments. I apologize.
[1]. In my target paper, the labels were A,D,3,7; and the rule was "if A, then 3". So the not-Q card was 7.
[2]. Wason's rule is identically worded in the two versions of the Margolis/Griggs experiment. The task is also identical. In one version, and coming as no surprise to anyone familiar with the problem, mostly "p & q" responses are elicited by the instruction: "Circle two cards to turn over to check whether the rule has been violated." But, very surprisingly, "p & q" as the dominant response switches to "not-p & not-q" when the instruction is turned around to read: "Figure out which two cards could violate the rule, and circle them." This appears (other than in terms of the "categories" account) a wholly bizarre kind of answer. In Bucciarelli's (2000) Table 1, for example, we see results of a version of Wason intended for young children. Upward of 200 results are reported. Small children respond quite differently from adults (in this children's version, in fact, most adults get the problem right). But not a single individual, child or adult, gives the not-p, not-q response that a majority give in the Margolis/Griggs experiment.
[3]. On the "iff" reading, each card consistent with the rule must be either "A/3" or "D/7" (p&q or not-p & not-q). So (using the categories misinterpretation of the task), checking the A & 3 cards will locate any violation -- any case of A/7 or D/3 -- but so would checking A & D, 7 & 3, or D & 3. But to realize that the "iff" interpretation of the rule ("if A then 3 & if 3 then A") implies "if D then 7" needs a modus tollens step.
[4]. The Greeks handed down the story of a dog trailing its master, which came to a three-way fork in the road. He sniffed one path (the wrong one), then another (also wrong), then raced down the remaining fork without troubling to sniff. I always supposed this story was apocryphal, and while I am not quite ready to believe even a two-fork version, it doesn't seem so obviously implausible as I supposed before thinking about Bucciarelli's result.
Bucciarelli, M (2000) Reasoning by categories in the wason selection task. PSYCOLOQUY 11(055) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/2000.volume.11/ psyc.00.11.055.reduced-wason-task.2.bucciarelli http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?11.055
Griggs, R. (1990) "Instructional effects on responses in Wason's selection task". British Journal of Psychology 81:197-204
Handley, S & Feeney, A. (2000) Deduction in the selection task. PSYCOLOQUY 11(108) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/2000.volume.11/ psyc.00.11.108.reduced-wason-task.4.handley http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?11.108
Laming, D. (2000) The reduced array selection task provides an implicit hint. PSYCOLOQUY 11(109) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/2000.volume.11/ psyc.00.11.109.reduced-wason-task.5.laming http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?11.109
Laming, D. (1996) On the analysis of irrational data selection. Psychological Review 103: 364-373
Margolis, H. (1987) Patterns, Thinking and Cognition. University of Chicago Press
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., 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
Prudkov P.N. (2000) Puzzles, riddles and Margolis's version of Wason's selection task. PSYCOLOQUY 11(107) ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/2000.volume.11/ psyc.00.11.107.reduced-wason-task.3.prudkov http://www.cogsci.soton.ac.uk/psyc-bin/newpsy?11.107