The ability to understand and to incorporate the rules of basic logical inference in everyday activities.
Regarded as a universal human trait, the ability to think logically, following the rules of logical inference, has traditionally been defined as a higher cognitive skill. The field of cognitive child psychology was dominated for more than half a century by the Swiss philosopher and psychologist Jean Piaget, whose studies are considered fundamental. Piaget identified four stages of cognitive development. During the sensory-motor stage (ages 0-2), the child learns to experience the world physically and attains a rudimentary grasp of symbols. In the preoperational stage (ages 2-7), symbols are used, but thought is still "preoperational," which means that the child does not understand that a logical, or mathematical, operation can be reversed. The concrete operations stage (ages 6 or 7-11) ushers in logical thinking; children, for instance, understand principles such as cause and effect. The formal operations stage (12-adulthood), introduces abstract thinking (i.e., thought operations that do not need to relate to concrete concepts and phenomena).
Logical thinking, in Piaget's developmental scheme, is operational, which means that it does not appear before the concrete operations stage. While students of child cognition generally agree with Piaget's developmental milestones, subsequent research in the area has led researchers to question the idea that some logical thinking cannot appear in the preoperational stage. For example, Olivier Houdè and Camilo Charron tested a group of 72 children between the ages of five and eight, giving them various tasks related to classes of objects, and found that children who could not perform extensional logic tasks were nevertheless able to practice intensional logic. (Intension defines the properties of a class, while extension determines who or what can be a member of a particular class; if the intension of a class is "red objects," the extension will include any particular object that happens to be red.) However, Piaget knew that preoperational children could practice intensional logic, but, in his view, incomplete logical thought was, by definition, pre-logical. For example, children who understand the meaning (intensionality) of a "red objects" class may decide not to include certain red objects—for reasons that the experimenter would define as illogical (e.g.: "it's too little").
Houdè and Charron have identified an "operational proto-logic" in children whom Piaget would define as pre-logical. Instead of arbitrarily promoting purely intensional thinking to the rank of full-fledged (extensional and intensional) logical thought, Houdè and Charron decided to investigate the mental processes underlying seemingly illogical behavior. In a series of experiments involving children aged five to eight, a group straddling the pre-operational/operational boundary, the two researchers focused on the intensional logicians who failed the extensional logic (inclusion). Clearly, the act of not including some red object in the "red objects" class was, in a strictly Piagetian sense, illogical, or, more precisely, illogical behavior, but was that behavior determined by irrational thinking? To their surprise, they found, particularly in a modified form of the "partition" experiment (Piaget and Garcia, 1987), that, when shown the drawing of a circle (B) divided into two by a line (the two subclasses being A and A'), A' may be ignored as a subclass of B, not because of illogical thinking, but because A is more compelling from the point of view of perception. According to Pascual-Leone (Pascual-Leone, 1988), there is a misleading scheme underlying the perception of B, and a subclass is excluded. According to Houdè and Charron, the child understands the intensional logic, or meaning, of the "red objects" class, but stumbles at the extensional, or inclusion, level because of perceptual factors. Thus, the undeniable Piagetian shift, around the age of seven years, from non-inclusive to inclusive behavior does not indicate a quantum leap from pre-logical to logical thinking, but, rather, reflects the presence of an inhibiting mechanism, whereby the confusing effect of perception on cognition is neutralized. Thus, as Houdè and Charron have remarked, a non-inclusive six-year-old may have an inefficient inhibiting mechanism. These findings, although suggesting a continuum model of cognitive development, as opposed to the Piagetian idea of a quantum leap from pre-logical to logical thinking, does not, in fact question the foundations of Piaget's essentially developmental theory of cognition. Piaget himself, in his search for the origins of logical thinking, studied very young children, ever mindful of the relevance of other mental, and non-mental, factors and processes to the emergence of logical thought. Finally, Piaget's work was the foundation from which emerged the insight, corroborated by empirical observation, that the very young child is already a logician.
Philosophers specializing in the study of childhood have found that the logical repertoire of young children is not limited to intensional logic. Many utterances made by children, particularly statements involving the concepts of possibility and necessity, exhibit a grasp, albeit rudimentary, of modal logic, i.e., the branch of logic which formulates rules for propositions about possibility and necessity (Matthews, 1980). The fact that the discourse of young children fits easily into the formal context of modal logic, which is related to intensional logic, indicates that the children's logical aptitude may yield new surprises. Building on the rich legacy of Piaget's work, researchers have significantly expanded the field of cognitive development, gaining critical insights which will further elucidate the human paradigm. The crucial relevance of Piagetian and post-Piagetian studies for the inquiry concerning logical thinking in children lies in the fact that these studies have shed light on the important role played by non-logical, and non-mental, factors in the formation of logical thought.
Inhelder, Bärbel, and Jean Piaget. The Early Growth of Logic in the Child: Classification and Seriation. London: Routledge and Kegan Paul, 1964.
Matthews, Gareth B. Philosophy and the Young Child. Cambridge: Harvard University Press, 1980.
Pascal-Leone, J. "Organismic Processes for Neo-Piagetian Theories: A Dialectical Causal Account of Cognitive Development." In The Neo-Piagetian Theories of Cognitive Development: Toward an Integration. A. Demetriou, ed. Amsterdam: North-Holland, 1988.