THE FACILITATING EFFECT OF THE HIERARCHICAL ORGANISATION OF CONCEPTS TO THE SYLLOGISTIC REASONING

Abstract

1. Introduction The traditional tasks of logical reasoning can be both strikingly easy and extremely difficult for adults as well as children. From the four possible conditional reasoning problems, modus ponens (if p then q, p, therefore q) seldom invokes errors starting from six-year old children (Staudenmayer, Bourne 1977, Wildman, Fletcher 1977). However, even adults are reluctant to draw a perfectly valid conclusion from modus tollens (if p then q, not q, therefore not p), or are prone to make invalid conclusions with the conditional problems of the form denial of the antecedent (if p then q, not p, therefore not q) and affirmation of the consequent (q, therefore p). The amount of correct answers to the latter three tasks gradually increases with age, although adults' performance is far from perfect (see Overton 1990 for a review). Another group of tasks of traditional logic, categorical-syllogisms, appear to be more difficult. Similarly to the conditional problems, some of the possible 64 categorical syllogisms are solved correctly by preschoolers (e.g. All A are B, All B are C, therefore all C are A) (Dias, Harris 1988, Hawkins et al. 1984), however many other syllogisms are frequently solved incorrectly. The developmental data provided for the easier subset of 28 syllogisms regarding 9-year-old children and adults indicates that children solve correctly approximately one-third and adults one-half of the syllogisms (Bara et al. 1995). Thus, both in case of conditional syllogisms and categorical syllogisms, some development seems to occur. Several ideas about the origins of the development of logical reasoning have been suggested. According to the theory of mental models, children's deficiencies in syllogistic reasoning stem from their yet limited working memory abilities and skills in searching for counterexamples (in finding several alternative mental models for a particular syllogism) (Bara et al. 1995). Thus, according to this view, the growth of logical reasoning has nothing inherently logical about it (these are not the inferential rules that matter), instead the development is rooted in the increase of working memory abilities and knowledge base to interpret particular premises (Johnson-Laird et al. 1986). The theory of mental logic developed by Braine (1978, 1990) takes a different route. It divides logical skills into primary and secondary skills. Primary skills consist of inferential rules that are either innate or develop very early and are available to all of us. An example of one primary inferential rule is the above mentioned modus ponens; it is automatic and universally obvious to all people. Secondary skills, although based on the primary skills, are considered to be the result of education and have more academic nature. The correct answers to modus tollens would require some secondary skills; here it is necessary to construct a longer chain of reasoning where the primary rule of modus ponens and the reductio ad absurdum rule are applied. Therefore, fallacies with modus tollens are frequent and they gradually diminish with the cognitive development of a child. These longer reasoning chains impose greater demands on memory and often the use of written language is necessary. Another characteristic feature of secondary skills is the requirement to accept the strategy of minimal commitment--focus is not on what the speaker means, however imprecisely and elliptically it might have been expressed (as is the case with everyday reasoning), but on what the sentence is committed to (Braine 1978). Additionally, in non-academic everyday reasoning situations people use all the information available, whereas in case of more advanced logical tasks they should compartmentalise information, i.e. use only the information contained in the premises. Hence, Braine's theory, in contrast to the theory of mental models, proposes that specific skills that are introduced in school may be the constituent factors for the development logical reasoning. …