This paper examines two questions concerning deductive reasoning ability. One concerns the existence of such an ability and in particular the bearing of errors in reasoning upon that issue; the second concerns the fundamental educational consequence of the first question.
In educational circles and the informal logic movement there has recently been much debate about the possible nonexistence of abilities such as deductive reasoning ability, provoked by McPeck's book Critical Thinking and Education (1981). As McPeck has noted (1985, p. 50), similar views, stressing the context bound nature of disciplined reflection, were an important element in Hirst's notorious philosophy of the educational curriculum (1974). An immediate and attractive riposte is to point to the aseptically formal nature of logic, and to note that modus tollens, for instance, works equally well in history, theology, or mathematics. To follow such arguments, to use such arguments in critical reflection, can then be said to show the existence of a general deductive reasoning ability.
Much of this debate remains at a commonsensical level. Perhaps people could use modus tollens indifferently in any area, but do they? And when we find that they don't, what are we then to say? Norris (1985b) has raised many of these issues in the course of a review of McPeck's book. He wants us to consider the question of the existence of deductive reasoning ability as a scientific question about human beings and their properties, and he wants us, reasonably enough, to conduct the debate within a self-consciously realistic psychological framework, as set out in an earlier paper (Norris, 1985a).
If we look at deductive reasoning ability as something like a grasp of syntactic rules of inference or a knowledge of entailments between propositions (the two alternatives discussed by Harman, 1984), its existence would then depend on its theoretical power. We seek the best explanatory theory of human behaviour, and we have to see what that theory contains that is closest to such an ability. Such a theory might attribute to human beings a grasp of Fregean logic plus a set of interfering systems - the interferences taking care of the manifold sources of error in fairly simple reasoning tasks set to ordinary human beings (the known importance of content (Ennis, 1981); the greater difficulty of symbolic formulations, especially with sentential variables (Brandon, 1985b); the strong tendency to ignore the actual problem set, especially among unschooled subjects (Scribner, 1979); etc.). But Norris' point is that it is equally likely that our best theory will avoid anything recognizable as a system of classical, first order logic, as indeed Johnson-Laird (1983) has recently urged. What competencies we really have must wait upon the theory.
While Norris may well be right in characterizing our ignorance of psychological processes, his formulations remain somewhat awkward since they are indulgent to a kind of language (talk of ability, competence, etc.) that does not require future psychology for its correct application. Elsewhere (1986) he tries, for instance, to distinguish generic from specific claims about ability, but it is not difficult for McPeck (1986) to undermine his remarks as an attempt at conceptual analysis. I would suggest that Norris were better off eschewing abilities of all sorts just as modern science eschews talk of the dormitive virtues undoubtedly possessed by various drugs (cf. Brandon, 1985a). At the common sense level there is no more difficulty in attributing a highly specific ability than a broad and general one.
But this may be a counsel of impractical perfection; this sort of talk is pervasive in educational and psychological research, though without much awareness of its peculiarities. I shall look briefly at two problematic aspects: what counts as grasping a rule, and how rules are to be identified.
An adequate grasp of a concept requires not only applying it to paradigm cases but also refusing to apply it to paradigm non-cases. An adequate grasp of a rule would also seem to require both recognition of when it is to be followed and recognition of when it does not apply. But often research ignores this second requirement. Thus, to use an example from the empirical work on deductive competence by Ennis and Paulus (1965), one constructs a set of questions embodying what we know to be valid examples of modus ponens or contraposition and uses performance on these items as a measure of mastery or lack of mastery of these principles. One can then report that 62% of 11th grade students in the schools tested have mastered modus ponens while only 12% have mastered (i.e. can recognize in this test the invalidity of) denying the antecedent.
But what is it to master modus ponens? Should it include a recognition that denying the antecedent is not an instance of modus ponens? What the percentages report is action in accordance with a rule, but that may be a far cry from obedience to a rule. In a replication of some of this work in Jamaica (Nolan and Brandon, 1984), it was found that while 36% of 205 comprehensive secondary school students (grades 7 to 11) showed mastery of modus ponens on its own, only 1.5% (3 individuals) have mastered this principle and have grasped the invalidity of denying the antecedent. What exactly have the other 34% mastered?
This question raises the second issue, of identifying the rules in use. Error can arise in different ways. A rule can in general be misapplied either by applying the correct rule to the wrong case, or by applying an incorrect rule to right or wrong cases. With simple logical rules it may be difficult to envisage mistakes of the first sort, but again Norris' warning is pertinent. We could construct a device that was, as it were, dyslexic with respect to conditionals (so that it could not distinguish between if p then q and if q then p) and had modus ponens as a rule of inference, and a different device that clearly differentiated the two conditionals but embodied a deviant rule of inference: given either component of a conditional, infer the other. The output of such devices could be distinguished if they both also had modus tollens as another rule of inference.
Talk of abilities, competencies, etc. usually has a normative aura. As Gellner (1974) once remarked, knowing how to do X is often a matter of knowing how to do X well. This makes it difficult to allow for the fact that the processes people actually use may be very different from the rules sanctioned in our explicit theories of such activities. Of course, it is not impossible to consider this contingency, witness work on "dirty heuristics" (Kahneman, Slovic and Tversky, 1982; Cherniak, 1984) or Johnson-Laird's speculations already referred to; but typically in educational (and psychological - Johnson-Laird claims that no one had previously discovered the "figural effect" in research on syllogisms because they had only used standard text-book problems) research one offers respondents problems that exemplify normatively grounded rules in the hope of extracting from their responses some idea of the actual rules in use. (It is worth noting in passing that this feature renders otiose a lot of the fuss about "validity" and "reliability" in such research since the questions are paradigmatic instances of some rule or other; if subjects' responses fail to correlate nicely that may only show how "deviant" the subjects are, not that the questions are not tapping their intended target. It must be admitted, however, that in my terms most users of such tests are mistakenly thinking that what they are doing is revealing existing processes close to those sanctioned by the rules. As Petrie has said, "we must turn current testing assumptions upside down" (1986, p. 13).)
The Jamaican work on deductive reasoning can again show the effects of this blinkering of one's vision by the correct rules. In fact the first investigation already mentioned involved marking answers right or wrong in terms of standard logical schemata before they were entered into the computer, so it is no longer possible even to explore alternative rules directly. In another investigation, testing only six principles of deductive logic, it is possible to compare the results when data are interpreted from the standpoint of ordinary logic with what happens when it is assumed that respondents employ deviant rules of inference. (It must be noted that in neither investigation was the use of exploratory factor analysis an element in the planning of the research, and in the case in hand it is only doubtfully warranted.) Taking the standard interpretation first, an oblique rotation using SPSS defaults of a factor analysis of the six principles yielded two factors, one loading (above 0.2) on the four valid principles, the other loading on the two invalid principles (correlation between the factors was 0.15). When deviant rules were used to score raw answers (specifically the rule that if p then q and q imply p and its analogue for quantified statements) then a slightly different picture emerged. This can be seen in Table 1. It is not a dramatic change but it may indicate what could happen. The first factor now loads on one of the deviant rules while the second factor which loads heavily on the deviant principles also includes a small loading on the principles involving the rule of detachment. The correlation between the factors is now 0.26.
Table 1: Factor Pattern Coefficients (N = 228)
| NORMAL | SCORING | DEVIANT | SCORING | |
| FACTOR 1 | FACTOR 2 | FACTOR 1 | FACTOR 2 | |
| MODPON | 0.700 | -0.100 | 0.598 | 0.218 |
| MODTOL | 0.596 | 0.059 | 0.685 | -0.145 |
| HYPSYL | 0.540 | -0.000 | 0.462 | 0.218 |
| DENCON | 0.644 | 0.046 | 0.691 | -0.075 |
| AFFCON | -0.101 | 0.751 | 0.218 | 0.518 |
| QAFCON | 0.111 | 0.607 | -0.118 | 0.732 |
Of course, both these analyses operate on the assumption that we are looking for something like a mental logic of the syntactic sort rejected by Johnson-Laird. The point is simply that the normal neglect of non-standard rule systems (syntactic or not) can easily blinker the analysis and interpretation of typical cognitive research in education.
To close, I wish to turn to what is perhaps the most important educational issue in the debate alluded to earlier. Does it matter to educators whether there is a deductive reasoning ability of whatever kind?
Educational debates about the existence of generalized reasoning skills seem to presuppose that if it were discovered, or established by argument, that unaccommodated man lacks such things that would be the end of the argument. But the fact that most of us cannot solve 4536 times 962.41 in our heads is no reason whatsover against giving schoolchildren the ability to solve it with pencil and paper (or a pocket calculator). So, one might think, the fact that many people cannot recognize logically fallacious arguments need not stand in the way of giving, them techniques so to do. It is in general no objection to new technology that it does things differently, especially if it does them more efficiently.
Of course, knowing how untutored people do things can be of tremendous help in planning how to aid them, and it could make a significant difference if we viewed their performance as a result of interferences with an underlying correct grasp of the logical situation instead of as reflecting an inadequate understanding thereof. But, however we should best theorize untutored practice, there is always the possibility that what would be best would be to replace existing abilities with the self-conscious application of logic's "target forms", to use Kielkopf's (1984) expression.
As Johnson-Laird notes, logic is not as easy as elementary arithmetic in that it does not yield such straightforward algorithms. But still it can be taught; it does give people convenient tricks to allow them to cope with the complexities of ordinary expression; and its existence is a standing refutation of any extreme view that there is nothing general to be said about thinking and criticism. As McPeck argues, it may be that some of us are inclined to overemphasize the benefits to be gained from the study of logic and play down the epistemology he prefers, but that is really a matter to be settled by experience. My point is that we should not be discouraged from attempting it on the grounds that people do not actually think like that (cf. Resnick, 1985). Education, here as elsewhere, may be mainly an uprooting of a person from what he would otherwise do, rather than confirming him in it.
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