Children’s understanding of the idea of logical necessity: The effect of counter-suggestions

Orlando Lourenço


This study examined the child’s understanding of the idea of logical necessity in 40 preoperational and 40 operational children in the context of a number conservation task and a liquids conservation task. The first task followed the typical Piagetian clinical method. The second task also used this method, but it employed counter-suggestions that Piaget, in a surprising way, rarely, if ever, used in his experiments. Children’s performance on the number conservation task allowed us, in a pre-experimental phase, to classify those children, aged between 5 and 7 years, as preoperational (40) or operational (40). Results show that: (1) from the number conservation task to the liquids conversation task, there was a significant change in preoperational and operational children’s epistemic status and its corresponding idea of logical necessity; (2) children refused a non-justified counter-suggestion coming from a putative knowledgeable adult less than a justified contra-suggestion coming from a hypothetical child; (3) operational children often invoked the identity argument on both tasks and the reversibility argument was practically absent; (4) children invoked the compensation argument on the liquids conservation task more than on the number conservation task.


Piaget, Children, Counter-suggestions, Logical necessity, Operational arguments.


Achenbach, T. (1978). Research in developmental psychology: Concepts, strategies, methods. New York: The Free Press.

Acredolo, C. (1981). Acquisition of conservation: A clarification of Piagetian terminology, some recent findings, and an alternative formulation. Human Development, 24, 120-137.

American Psychological Association [APA]. (2010). Publication manual of the American Psychological Association (6th ed.). Washington, DC: American Psychological Association.

Appelbaum, M., & McCall, R. (1983). Design analysis in developmental psychology. In P. H. Mussen (Ed.), Handbook of child psychology (Vol. I, pp. 415-476). New York: Wiley.

Asch, S. (1955). Opinions and social pressure. Scientific American, 193, 35-35.

Beilin, H. (1992). Piaget’s enduring contribution to developmental psychology. Developmental Psychology, 28, 191-204.

Bibok, M., Müller, U., & Carpendale, J. (2009). Childhood. In U. Müller, J. Carpendale, & L. Smith (Eds.), The Cambridge companion to Piaget (pp. 229-254). Cambridge: Cambridge University Press.

Bickhard, M. (2009). Interactivism: A manifesto. New Ideas in Psychology, 27, 85-95.

Bond, T., & Tryphon, A. (2009). Piaget and method. In U. Müller, J. Carpendale, & L. Smith (Eds.), The Cambridge companion to Piaget (pp. 171-199). Cambridge: Cambridge University Press.

Braine, M. (1959). The ontogeny of certain logical operations: Piaget’s formulations examined by nonverbal methods. Psychological Monographs: General and Applied, 73, 1-41.

Brainerd, C. (1978). Piaget’s theory of intelligence. Englewood Cliffs, NJ: Prentice-Hall.

Bringuier, J. (1980). Conversations with Jean Piaget. Chicago: University of Chicago Press. (Original work published 1978)

Bruner, J. S. (1966). On the conservation of liquids. In J. S. Bruner, R. R. Olver, & P. M. Greenfield (Eds.), Studies in cognitive Growth (pp. 183-207). New York: Wiley.

Bryant, P., & Trabasso, T. (1971). Transitivity inferences and memory in young children. Nature, 232, 456-458.

Caroff, X. (2002). What conservation anticipation reveals about cognitive change. Child Development, 17, 1015-1031.

Carpendale, J., & Lewis, C. (2004). Constructing an understanding of mind: The development of children’s social understanding within social interaction. Behavioral and Brain Sciences, 27, 79-96.

Case, R. (1985). Intellectual development: Birth to adulthood. Orlando, FL: Academic Press.

Chapman, M. (1988). Constructive evolution: Origins and development of Piaget’s thinking. Cambridge: Cambridge University Press.

Chapman, M. (1992). Equilibration and the dialectics of organization. In H. Beilin & P. Pufall (Eds.), Piaget’s theory: Prospects and possibilities (pp. 39-59). Hillsdale, NJ: Erbaum.

Cohen, D. (1983). Piaget: Critique and assessment. London & Camberra: Croom Helm.

Commons, M., Richards, F., & Armon, C. (Eds.). (1984). Beyond formal operations. New York: Praeger.

Demetriou, A., Makris, N., Kazi, S., & Spanoudis, G. (2018). Mapping the dimensions of general intelligence: An integrated differential-develpmental theory. Human Development, 61, 4-42.

Eslinger, P., & Robinson-Long, M. (2010). Crucial developmental role of prefrontal cortical systems in social cognition and moral maturation: Evidence from early prefrontal lesions and fMRI. In P. Zelazo, M. Chandler, & E. Crone (Eds.), Developmental social cognitive neuroscience (pp. 251-267). New York & London: Psychology Press.

Feldman, D., & Benjamin, A. (2004). Piaget’s stages: The unfinished symphony of cognitive development. New Ideas in Psychology, 22, 175-185.

Flavell, J. (1963). The developmental psychology of Jean Piaget. Princeton, NJ: Van Nostrand.

Flavell, J. (1982). Structures, stages and sequences in cognitive development. In W. Collins (Ed.), The concept of development (pp. 1-28). Hillsdale, NJ: Erlbaum.

Flavell, J. (1992). Cognitive development: Past, present and future. Developmental Psychology, 28, 998-1005.

Gazzaniga, M. (2005). The ethical brain: The science of our moral dilemmas. New York: Harper Perennial.

Gelman, R., & Baillargeon, R. (1983). A review of some Piagetian concepts. In P. H. Mussen (Ed.), Handbook of child development (Vol. 4, pp. 167-230). New York: Wiley.

Gopnik, A. (1996). The post-Piaget era. Psychological Science, 7, 221-338.

Heritage, J., & Raymond, G. (2005). The terms of agreement: Indexing epistemic authority and subordination in talk-in-interaction. Social Psychology Quarterly, 68, 15-38.

Horgan, J. (1999). The undiscovered mind. NewYork: Free Press.

Inhelder, B., & Céllerier, G. (1992). Le cheminement des découvertes de l’enfant [The child’s process of discoveries]. Lausanne: Delachaux et Niestlé.

Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from adolescence to adulthood. New York: Basic Books. (Original work published 1955)

Inhelder, B., Sinclair, H., & Bovet, M. (1974). Learning and the development of cognition. London: Routledge & Kegan Paul. (Original work published 1974)

Lourenço, O. (2012). Piaget and Vygotsky: Many resemblances and a crucial difference. New Ideas in Psychology, 30, 281-295.

Lourenço, O. (2014). Piaget, Jean. In D. C. Phillips (Ed.), Encyclopedia of educational theory and philosophy (Vol. 2, pp. 623-628). Los Angeles: Sage.

Lourenço, O. (2016). Developmental stages, Piagetian stages in particular: A critical review. New Ideas in Psychology, 40, 123-137.

Lourenço, O., & Machado, A. (1996). In defense of Piaget’s theory: A reply to 10 common criticisms. Psychological Review, 103, 143-164.

McGarrigle, J., Grieve, R., & Hughes, M. (1978). Interpreting inclusion: A contribution to the study of the child’s cognitive and linguistic development. Journal of Experimental Child Psychology, 25, 528-550.

Meyerson, E. (1960). Identity and reality. New York: Dover Publications, Inc. (Original work published 1908)

Miller, A. (1986). Certainty and necessity in the understanding of Piagetian concepts. Developmental Psychology, 22, 3-18.

Miller, A., Brownell, C., & Zukier, H. (1977). Cognitive certainty in children: Effects of concept, developmental level and method of assessment. Developmental Psychology, 13, 236-245.

Miller, A., Custer, L., & Nassau, G. (2000). Children’s understanding of the necessity of logically necessary truths. Cognitive Development, 15, 383-403.

Miller, A., & Lipps, L. (1973). Extinction of conservation and transitivity of weight. Journal of Experimental Child Psychology, 16, 388-402.

Müller, U., Carpendale, J., & Smith, L. (Eds.). (2009). The Cambridge companion to Piaget. Cambridge: Cambridge University Press.

Overton, W. (Ed.). (1990). Reasoning, necessity, and logic: Developmental perspectives. Hillsdale, NJ: Erlbaum.

Perner, J. (1991). Understanding the representational mind. Cambridge, MA: MIT Press.

Perret-Clermont, A. (1979). La construction de l’intelligence dans l’interaction sociale [The construction of intelligence in social interactions]. Berne: Peter Lange.

Piaget, J. (1918). Recherche [Research]. Lausanne: La Concorde.

Piaget, J. (1929). The child’s conception of the world. London: Kegan Paul Trench Trubner. (Original work published 1926)

Piaget, J. (1932). The moral judgment of the child. London: Kegan Paul Trench Trubner. (Original work published 1932)

Piaget, J. (1950a). Introduction à l´épistémologie génétique. Vol. 1: La pensée mathématique [Introduction to genetic epistemology, Vol. 1: Mathematical thinking]. Paris: Presses Universitaires de France.

Piaget, J. (1950b). Introduction à l´épistémologie génétique. Vol. 2: La pensée physique [Introduction to genetic epistemology, Vol. 2: Physical thinking]. Paris: Presses Universitaires de France.

Piaget, J. (1950c). Introduction à l´épistémologie génétique. Vol. 3: La pensée biologique, la pensée psychologique, et la pensée sociologique [Introduction to genetic epistemology, Vol. 3: Biological thinking, psychological thinking, and sociological thinking]. Paris: Presses Universitaires de France.

Piaget, J. (1966). Psychology of intelligence. Totowa, NJ: Littlefield, Adams & Co. (Original work published 1947)

Piaget, J. (1967). Logique et connaissance scientifique [Logic and scientific knowledge]. Dijon: Gallimard.

Piaget, J. (1978). Recherches sur la généralisation [Experiments on generalization]. Paris: Presses Universitaires de France.

Piaget, J. (1983). Piaget’s theory. In P. Mussen (Ed.), Handbook of child psychology (Vol. 1, pp. 103-128). New York: Wiley.

Piaget, J. (1985). The equilibration of cognitive structures. Chicago: Chicago University Press. (Original work published 1975)

Piaget, J. (1986). Essay on necessity. Human Development, 29, 301-314.

Piaget, J. (1987a). Possibility and necessity: The role of possibility in cognitive development (Vol. 1). Minneapolis: University of Minnesota Press. (Original work published 1981)

Piaget, J. (1987b). Possibility and necessity: The role of necessity in cognitive development. Minneapolis: University of Minnesota Press. (Original work published 1983)

Piaget, J. (2001). Studies in reflecting abstraction. Hove: Taylor & Francis. (Original work published in 1977)

Piaget, J. (2004). Reason. New Ideas in Psychology, 24, 1-29.

Piaget, J., & Inhelder, B. (1969a). The psychology of the child. New York: Basic Books. (Original work published 1966)

Piaget, J., & Inhelder, B. (1969b). Intellectual operations and their development. In P. Fraisse & J. Piaget (Eds.), Experimental psychology: Its scope and method (Vol. 7, pp. 147-203). London: Routledge and Kegan Paul. (Original work published 1963)

Piaget, J., & Inhelder, B. (1974). The child’s construction of quantities. London: Routledge & Kegan Paul. (Original work published 1941)

Piaget, J., & Szeminska, A. (1980). La genèse du nombre chez l’enfant (6ème éd.). [The child’s conception of number]. Neuchâtel: Delachaux et Niestlé. (Original work published 1941)

Ricco, R. (1990). Necessity and the logic of entailment. In W. Overton (Ed.), Reasoning, necessity, and logic: Developmental perspectives (pp. 45-65). Hillsdale, NJ: Erlbaum.

Saltzstein, H., Dias, M., & Millery, M. (2004). Moral suggestibility: The complex interaction of development, culture and contextual factors. Applied Cognitive Psychology, 18, 1079-1096.

Siegal, M. (1991). Knowing children. Hillsdale, NJ: Erlbaum.

Smedslund, J. (1961). The acquisition of conservation of substance and weight in children. I: Introduction. Scandinavian Journal of Psychology, 2, 11-20.

Smith, L. (1993). Necessary knowledge: Piagetian perspectives on constructivism. Hillsdale, NJ: Erbaum.

Smith, L. (Ed.). (1996). Critical readings on Piaget. London: Routledge.

Smith, L. (1997). Necessary knowledge and its assessment in intellectual development. In L. Smith, J. Dockrell, & P. Tomlinson (Eds.), Piaget, Vygotsky and beyond (pp. 224-241). London: Routledge.

Smith, L. (2009). Piaget’s developmental epistemology. In U. Müller, J. Carpendale, & L. Smith (Eds.), The British companion to Piaget (pp. 64-93). Cambridge: Cambridge University Press.

Turiel, E. (1983). The development of social knowledge: Morality and convention. Cambridge: Cambridge University Press.

Zelazo, P., Chandler, M., & Crone, E. (Eds.). (2010). Developmental social cognitive neuroscience. New York & London: Psychology Press.



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