The Nature of Propositional Deduction—a Piagetian Perspective
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Keywords

operations of thought
grouping
structure
propositional reasoning
propositional deduction
Boolean algebra
lattice
logic

Abstract

DOI: https://doi.org/10.26333/sts.xxxv2.03

Logic was once thought to describe the laws of thought; however, a plurality of logics has now replaced classical logic, obscuring rather than clarifying the nature of deduction with an embarrassment of riches. In cognitive science, on the other hand, logic is not thought to be a psychological theory of human reasoning. Research on human reasoning has focussed on deduction, although human reasoning is thought to be much richer, and two competing theories dominate contemporary discourse in cognitive science—the syntactic, formal-rule, and the semantic, mental-model theory. Jean Piaget also proposed a psychological theory of reasoning, and, in contrast to the dominant theories, he advocated an operatory theory. Deduction is an integral part of Piaget’s theory, and, in this paper, I briefly outline Piaget’s operatory theory of propositional reasoning before explicating the nature of deduction embodied in it. I conclude that the nature of propositional deduction according to Piaget lies in the interpropositional grouping, a natural structure at the heart of propositional reasoning constituted by a closed system of operations of thought regulated by laws of transformation. I then argue that the nature of propositional deduction lies specifically in the lattice constituted by the inclusion/order relations between the propositions of the interpropositional grouping. Piaget did not conceive of the interpropositional grouping as a logic; nevertheless, I wind up arguing that a logic conceived as Piaget intimated would complement the plurality of logics with a natural logic.

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References

Apostel, L. (1982). The Future of Piagetian Logic. Revue Internationale de Philosophie, 36, 567–611.

Bond, T. G. (1978). Propositional Logic as a Model for Adolescent Intelligence—Additional Considerations. Interchange, 9, 93–98. doi:10.1007/BF01816518

Bond, T. G. (2005). Piaget and Measurement II: Empirical Validation of the Piagetian Model. In L. Smith (Ed.), Critical Readings on Piaget (pp. 178–208). Abingdon: Routledge.

Byrne, R. M. J., Johnson-Laird, P. N. (2009). ‘If’ and the Problems of Conditional Reasoning. Trends in Cognitive Sciences, 13(7), 282–287. doi:10.1016/j.tics.2009.04.003

George, R. (1997). Psychologism in Logic: Bacon to Bolzano. Philosophy & Rhetoric, 30(3), 213–242.

Grize, J.-B. (2013). Operatory Logic. In B. Inhelder, D. de Caprona, A. Cornu-Wells (Eds.), Piaget Today (pp. 149–164). Abingdon: Taylor and Francis.

Halmos, P. R. (2016). Algebraic Logic. Mineola, NY: Dover Publications Inc.

Halmos, P. R., Givant, S. (1998). Logic as Algebra (Vol. 21). Retrieved from: http://archive.org/details/logicasalgebra0000halm

Harman, G. (1984). Logic and Reasoning. In H. Leblanc, E. Mendelson, A. Orenstein (Eds.), Foundations: Logic, Language, and Mathematics (pp. 107–127). Dordrecht: Springer Netherlands. doi:10.1007/978-94-017-1592-8_7

Harman, G. (1986). Change in View: Principles of Reasoning. Cambridge, MA: The MIT Press.

Hintikka, J., Sandu, G. (2007). What is Logic? In D. Jacquette (Ed.), Philosophy of Logic (pp. 13–40). Netherlands: North Holland.

Inhelder, B., Piaget, J. (1958). The Growth of Logical Thinking from Childhood to Adolescence. London: Routledge, Chapman and Hall.

Jacquette, D. (2007). Introduction: Philosophy of Logic Today. In D. Jacquette (Ed.), Philosophy of Logic Today (pp. 1–12). Netherlands: North Holland.

Johnson-Laird, P. N. (1999). Deductive Reasoning. Annual Review of Psychology, 50(1), 109–135.

Johnson-Laird, P. N. (2006). How we Reason. Oxford: Oxford University Press.

Johnson-Laird, P. N., Byrne, R. M. J., Schaeken, W. (1992). Propositional Reasoning by Model. Psychological Review, 99(3), 418–439.

Kesselring, T. (2009). The Mind’s Staircase Revised. In U. Mueller, J. I. M. Carpendale, L. Smith (Eds.), The Cambridge Companion to Piaget (pp. 372–399). New York: Cambridge University Press.

Piaget, J. (1952). The Origins of Intelligence in Children. New York: International Universities Press Inc.

Piaget, J. (1957). Logic and Psychology. New York: Basic Books Inc.

Piaget, J. (1970). Structuralism. New York: Basic Books Inc.

Piaget, J. (1971a). Genetic Epistemology. New York: W. W. Norton & Company Inc.

Piaget, J. (1971b). Biology and Knowledge: An Essay on the Relations Between Organic Regulations and Cognitive Processes. Chicago; London: University of Chicago Press.

Piaget, J. (1977). The Stages of Intellectual Development in Childhood and Adolescence. In H. E. Guber, J. J. Vonèche (Eds.), The Essential Piaget (pp. 814–819). New York: Basic Books, Inc.

Piaget, J. (2001). The Psychology of Intelligence. London; New York: Routledge.

Piaget, J., Beth, E. W. (1966). Mathematical Epistemology and Psychology (vol. 12). Dordrecht, Holland: Springer Netherlands. doi:10.1007/978-94-017-2193-6

Piaget, J., Grize, J.-B. (1972). Essai de logique opératoire [Essay on Operational Logic] (vol. 15). Paris: Dunod.

Posy, C. J. (1997). Between Leibniz and Mill: Kant’s Logic and the Rhetoric of Psychologism. Philosophy & Rhetoric, 30(3), 243–270.

Restall, G., Beall, J. C. (2000). Logical Pluralism. Australasian Journal of Philosophy, 78(4), 475–493. doi:10.1080/00048400012349751

Restall, G., Beall, J. C. (2001). Defending Logical Pluralism. In J. C. Beall, G. Restall (Eds.), Proceedings of the 1999 Conference of the Society of Exact Philosophy (pp. 1–22). Stanmore: Hermes Science Publishers.

Rips, L. J. (2008). Logical Approaches to Human Deductive Reasoning. In J. E. Adler, L. J. Rips (Eds.), Reasoning. Studies of Human Inference and Its Foundations (pp. 187–205). Cambridge: Cambridge University Press.

Russell, G. (2019). Logical Pluralism. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2019). Retrieved from: https://plato.stanford.edu/archives/sum2019/entries/logical-pluralism/

Rutherford, D. E. (1966). Introduction to Lattice Theory. Edinburgh, London: Oliver and Boyd Ltd.

Seltman, M., Seltman, P. (1985). Piaget’s Logic: A Critique of Genetic Epistemology. London: George Allen & Unwin.

Shapiro, S. (2014). Varieties of Logic. Oxford: OUP.

Smith, L. (1987). A Constructivist Interpretation of Formal Operations. Human Development, 30(6), 341–354. doi:10.1159/000273192

Smith, L., Mueller, U., Carpendale, J. I. M. (2009). Introduction. Overview. In L. Smith, U. Mueller, J. I. M. Carpendale (Eds.), The Cambridge Companion to Piaget (pp. 1–44). New York: Cambridge University Press.

Stenning, K., van Lambalgen, M. (2008). Human Reasoning and Cognitive Science. Cambridge, MA, London: The MIT Press.

Stenning, K., van Lambalgen, M. (2011). Reasoning, Logic, and Psychology. Wiley Interdisciplinary Reviews: Cognitive Science, 2(5), 555–567. doi:10.1002/wcs.134

van Benthem, J. (2007). Logic in Philosophy. In D. Jacquette (Ed.), Philosophy of Logic (pp. 65–99). Amsterdam: North-Holland. doi:10.1016/B978-044451541-4/50006-3

van Benthem, J. (2008). Logic and Reasoning: Do the Facts Matter? Studia Logica, 88(1), 67–84. doi:10.1007/s11225-008-9101-1

Winstanley, M. A. (2021). A Psychological Theory of Reasoning as Logical Evidence: A Piagetian Perspective. Synthese. doi:10.1007/s11229-021-03237-x