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A psychological theory of reasoning as logical evidence: a Piagetian perspective

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Abstract

Many contemporary logicians acknowledge a plurality of logical theories and accept that theory choice is in part motivated by logical evidence. However, just as there is no agreement on logical theories, there is also no consensus on what constitutes logical evidence. In this paper, I outline Jean Piaget’s psychological theory of reasoning and show how he used it to diagnose and solve one of the paradoxes of material implication. I assess Piaget’s use of psychology as a source of evidence for logical theory in light of reservations raised by psychologism, and I highlight some ramifications for exceptionalism and anti-exceptionalism about logic by considering his use of psychology as logical evidence in the framework of genetic epistemology, Piaget’s research programme. I conclude that Piaget’s psychological theory of reasoning not only plausibly serves as a source of evidence for logical theory but also makes a strong case for anti-exceptionalism about logic.

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Notes

  1. Following Hjortland (2019, Sec. 2; see also 2017, Secs. 3 & 4), I will use ‘logical theory’ to denote an account of logical properties such as validity, consistency, formality, truth preservation, provability, etc.

    However, I will continue to use ‘logic’ in the singular rather than the plural to refer to logical theories in a generic way despite logical pluralism.

  2. Since the logical operators are simply alternative expressions for disjunctions of conjunctions, the 16 logical operators are the operands of the grouping (cf. Seltman and Seltman 1985).

  3. Piaget was not well acquainted with contemporary developments in mathematical logic (Grize 2013, p. 149).

  4. Shapiro (2000, pp. 108–9) draws attention to changes in the meaning of ‘analyticity’ introduced by Frege and I use the term here in this sense.

  5. The examples come from (Restall 2006, p. 65).

  6. Like p → q and p ⊃ q, p ↔ q denotes the formal truth of the logical operator p≡q.

  7. In ‘Paradoxes of Material Implication—a Piagetian Perspective’, I also conclude that CL and Piaget’s logical theory would constitute rival logical theories.

  8. Referring to natural language intuitions as a source of logical evidence, Priest (2016, p. 44) requires them to be robust; i.e., purged of performance errors. However, there is no independent criteria for their robustness; the people making the mistakes simply recognised them when the error is pointed out.

  9. Piaget (Piaget and Grize 1972, pp. 15:7–8) comes to the same conclusion about logic but by considering logic itself.

  10. According to Priest (2016, pp. 40–1), logic is a social science; theory and subject matter in logic may not therefore enjoy the same independence as in the natural sciences.

References

  • Apostel, L. (1982). The future of piagetian logic. Revue Internationale De Philosophie, 36, 567–611.

    Google Scholar 

  • Barnes, B. (1977). Interests and the growth of knowledge. Routledge.

  • Bond, T. G. (1978). Propositional logic as a model for adolescent intelligence—Additional considerations. Interchange, 9, 93–98. https://doi.org/10.1007/BF01816518

    Article  Google Scholar 

  • 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). Cambridge: Routledge.

    Google Scholar 

  • Collins, H. (1983). An empirical relativist programme in the sociology of scientific knowledge. In K. Knorr-Cetina & M. Mulkay (Eds.), Science observed: Perspectives on the social study of science (pp. 115–140). Sage Publications Inc.

  • Flavell, J. H., & Wohlwill, J. F. (1969). Formal and functional aspects of cognitive development. In D. Elkind & J. H. Flavell (Eds.), Studies in cognitive development: Essays in Honor of Jean Piaget (pp. 67–120). Oxford University Press.

  • Frege, G. (1993). Der Gedanke: Eine Logische Untersuchung. In Logische Untersuchungen, 4., durchges. und bibliographisch erg. Aufl., 1219:30–53. Kleine Vandenhoeck-Reihe. Goettingen: Vandenhoeck und Ruprecht.

  • Frege, G. (1998). Grundgesetze der Arithmetik begriffsschrifftlich abgeleitet. 2. Nachdr. d. Ausg. Jena 1893–1903. Vol. 32. Olms-Paperbacks. Hildesheim: Olms.

  • Gabbay-Dov, M., & Woods, J. (2005). The practical turn in logic. In D. M. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (2nd ed., Vol. 13, pp. 15–122). Dordrecht: Springer. https://doi.org/10.1007/1-4020-3521-7_1

    Chapter  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Haack, S. (1978). Philosophy of logics. Cambridge University Press.

  • Haase, M. (2009). The laws of thought and the power of thinking. Canadian Journal of Philosophy, 35, 249–297. https://doi.org/10.1080/00455091.2009.10717650

    Article  Google Scholar 

  • Halmos, P. R., & Steven, G. (1998). Logic as algebra (Vol. 21). Washington D.C: The Mathematical Association of America.

    Book  Google Scholar 

  • Hanna, R. (2006). Rationality and logic. Cambridge: MIT Press.

    Book  Google Scholar 

  • Hjortland, O. T. (2017). Anti-exceptionalism about logic. Philosophical Studies, 174, 631–658. https://doi.org/10.1007/s11098-016-0701-8

    Article  Google Scholar 

  • Hjortland, O. T. (2019). What counts as evidence for a logical theory? The Australasian Journal of Logic, 16, 250–282. https://doi.org/10.26686/ajl.v16i7.5912

    Article  Google Scholar 

  • Inhelder, B., & Jean, P. (1969). The psychology of the child. Translated by Helen Weaver. New York: Basic Books.

  • Jaakko, H., & Gabriel, S. (2007). What is Logic? In D. Jacquette (Ed.), Philosophy of Logic (pp. 13–40). Harvard: Harvard University Press.

    Google Scholar 

  • Jacquette, D. (1997). The dialectics of psychologism. Philosophy & Rhetoric, 30, V–VIII.

    Google Scholar 

  • Jacquette, D. (2001). Psychologism revisited in logic, metaphysics, and epistemology. Metaphilosophy, 32, 261–278. https://doi.org/10.1111/1467-9973.00187

    Article  Google Scholar 

  • Jacquette, D. (2003a). Introduction: Psychologism the philosophical shibboleth. In Philosophy, psychology, and psychologism. Philosophical Studies Series. (pp 1–19) Springer: Dordrecht. https://doi.org/10.1007/0-306-48134-0_1.

  • Jacquette, D. (2003b). Philosophy, psychology, and psychologism: Critical and historical readings on the psychological turn in philosophy. Vol. 91. Philosophical Studies Series. New York: Kluwer Academic Publishers.

  • Jacquette, D. (2007). Introduction: philosophy of logic today. In D. Jacquette (ed.) Philosophy of logic today. Handbook of the Philosophy of Science. (pp. 1–12) Netherlands: North Holland.

  • Johnson-Laird, P. N. (2006). How we reason. Oxford University Press.

  • 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.

    Google Scholar 

  • Kitchener, R. F. (1996). Jean Piaget: the Unknown Sociologist? In L. Smith (Ed.), Critical Readings on Piaget (pp. 28–50). New York: Routledge.

    Chapter  Google Scholar 

  • Kitchener, R. F. (2004). Piaget’s social epistemology. In J. I. M. Carpendale & U. Mueller (Eds.), Social interaction and the development of knowledge (pp. 45–66). Mahwah, NJ: Lawrence Erlbaum Associates Publishers.

    Google Scholar 

  • Kitchener, R. F. (2009). On the concept(s) of the social in Piaget. In U. Müller, J. I. M. Carpendale, & L. Smith (Eds.), The Cambridge companion to Piaget (pp. 110–131). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Kuhn, T. (1960). The structure of scientific revolutions. Chicago: University of Chicago Press.

    Google Scholar 

  • Kusch, M. (2006). Psychologism. Continuum Encyclopedia of British Philosophy.

  • Kusch, M. (2015a). Psychologism. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford: Metaphysics Research Lab.

    Google Scholar 

  • Kusch, M. (2015b). Psychologism, history of. In J. D. Wright (Ed.), International encyclopedia of the social and behavioral sciences. Oxford: Elsevier. https://doi.org/10.1016/B978-0-08-097086-8.03139-1

    Chapter  Google Scholar 

  • Lammenranta, M. (2018). Epistemic circularity. Internet Encyclopedia of Philosophy. Retrieved December 16, from https://iep.utm.edu/ep-circ/.

  • Lloyd, G. E. R. (2007). Cognitive variations: reflections on the unity and diversity of the human mind. oxford Scholarship Online.

  • Lloyd, G. E. R. (2010). History and human nature: cross-cultural universals and cultural relativities. Interdisciplinary Science Reviews, 35, 201–214. https://doi.org/10.1179/030801810X12723585301318

    Article  Google Scholar 

  • Lockhart, T. (2016). Frege on anti-psychologism and the role of logic in thinking. Theoria: A Swedish Journal of Philosophy, 82, 302–328. https://doi.org/10.1111/theo.12101

    Article  Google Scholar 

  • Martin, B. (2020). Identifying logical evidence. Synthese. Springer. https://doi.org/10.1007/s11229-020-02618-y.

  • Martin, B., & Hjortland, O. T. (2021). Evidence in logic. In M. Lasonen-Aarnio., C. Littlejohn (eds.) The routledge handbook of the philosophy of evidence, Preprint. Routledge Handbooks in Philosophy. Retrieved June 10, 2020, from https://www.academia.edu/42231700/Evidence_in_logic.

  • Mohanty, J. N. (1997). The Concept of “Psychologism” in Frege and Husserl. Philosophy & Rhetoric, 30, 271–290.

    Google Scholar 

  • Overton, W., & Newman, J. (1982). Cognitive development: A competence-activation/utilization approach. In T. M. Field, A. Huston, H. C. Quay, L. Troll, & G. E. Finley (Eds.), Review of human development (pp. 217–240). Wiley.

  • Pelletier, F. J., Elio, R., & Hanson, P. (2008). Is logic all in our heads? From naturalism to psychologism. Studia Logica, 88, 3. https://doi.org/10.1007/s11225-008-9098-5

    Article  Google Scholar 

  • Piaget, J. (1950a). Introduction à l’épistémologie génétique. (I) La pensée mathématique. Electronic version from Fondation Jean Piaget pour recherches psychologiques et épistémologiques. Pagination according to 1st edition 1950. Vol. 1. 3 vols. Paris: Presses Universitaires de France.

  • Piaget, J. (1950b). Introduction à l’épistémologie génétique. (III) La pensée biologique. La pensée psychologique. La pensée sociologique. Electronic version from Fondation Jean Piaget pour recherches psychologiques et épistémologiques. Pagination according to 1st edition 1950. Vol. 3. 3 vols. Paris: Presses Universitaires de France.

  • Piaget, J. (1952). The origins of intelligence in children. Translated by Margaret Cook. New York: International Universities Press Inc.

  • Piaget, J. (1957). Logic and psychology. Translated by W. Mays and F. Whitehead. New York: Basic Books Inc.

  • Piaget, J. (1970). Structuralism. Translated by Chaninah Maschler. New York: Basic Books Inc.

  • Piaget, J. (1971a). Genetic epistemology. Translated by Eleanor Duckworth. Woodbridge Lectures 8. New York: W. W. Norton and Company Inc.

  • Piaget, J. (1971b). Biology and knowledge: An essay on the relations between organic regulations and cognitive processes. Translated by Beatrix Walsh. London: University of Chicago Press.

  • Piaget, J. (1977a). Logic and psychology. In H. E. Gruber & J. J. Vonèche (Eds.), The essential Piaget (pp. 445–477). New York: Basic Books, Inc.

    Google Scholar 

  • Piaget, J. (1977b). The stages of intellectual development in childhood and adolescence. In The essential Piaget, ed. Howard E. Guber and J. Jacques Vonèche, tran. H. E. Gruber, 814–819. New York: Basic Books, Inc.

  • Piaget, J. (1977c). Phenocopy in biology and the psychological development of knowledge. In H. E. Gruber & J. J. Vonèche (Eds.), The essential Piaget (pp. 803–813). New York: Basic Books.

    Google Scholar 

  • Piaget, J. (2001). The psychology of intelligence. Translated by Malcolm Piercy and D. E. Berlyne. Routledge Classics. New York: Routledge.

  • Piaget, J., & Beth, E. W. (1966). Mathematical epistemology and psychology. Translated by W. Mays. Softcover reprint of hardcover 1st edition. Vol. 12. Synthese Library. Dordrecht, Holland: Springer Netherlands.

  • Piaget, J., & Grize, J.-B. (1972). Essai de logique opératoire. 2e éd. du Traité de logique, essai de logistique opératoire (1949). Vol. 15. Collection Sciences Du Comportement. Paris: Dunod.

  • Priest, G. (2016). Logical disputes and the a priori. Princípios: Revista de Filosofia 23. Universidade Federal do Rio Grande do Norte: 29–57.

  • Quine, W. V. O. (1966). The ways of paradox. In W. V. O. Quine & W. V. Quine (Eds.), The ways of paradox and other essays (pp. 3–20). New York: Random House.

    Google Scholar 

  • Read, S. (1995). Thinking about logic: An introduction to the philosophy of logic. Oxford University Press.

  • Restall, G. (2006). Logic. An introduction. e-book. Fundamentals of Philosophy. New York: Routledge.

  • Restall, G., & Beall, J. C. (2000). Logical pluralism. Australasian Journal of Philosophy, 78, 475–493. https://doi.org/10.1080/00048400012349751

    Article  Google Scholar 

  • Restall, G., & Beall, J. C. (2001). Defending logical pluralism. In Proceedings of the 1999 conference of the society of exact philosophy. (pp. 1–22). Stanmore: Hermes Science Publishers.

  • Russell, G. (2019). Logical pluralism. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Stanford: Metaphysics Research Lab.

    Google Scholar 

  • Rutherford, D. E. (1966). Introduction to Lattice Theory. Reprint. University Mathematical Monographs. London: Oliver and Boyd Ltd.

  • Seltman, M., & Seltman, P. (1985). Piaget’s logic: A critique of genetic epistemology. George Allen & Unwin.

  • Shapin, S. (1982). The history of science and its sociological reconstruction. History of Science, 20, 157–211. https://doi.org/10.1177/007327538202000301

    Article  Google Scholar 

  • Shapin, S. (2008). The scientific revolution. Chicago: University of Chicago Press.

    Google Scholar 

  • Shapiro, S. (2000). Thinking about mathematics: The philosophy of mathematics. Oxford University Press.

  • Smith, L. (1987). A constructivist interpretation of formal operations. Human Development, 30, 341–354. https://doi.org/10.1159/000273192

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Sober, E. (1978). Psychologism*. Journal for the Theory of Social Behaviour, 8, 165–191. https://doi.org/10.1111/j.1468-5914.1978.tb00398.x

    Article  Google Scholar 

  • Stenning, K., & van Lambalgen, M. (2008). Human reasoning and cognitive science. London: MIT Press.

    Book  Google Scholar 

  • Urbanski, M. (2011). Logic and cognition: Two faces of psychologism. Logic and Logical Philosophy, 20, 175–185. https://doi.org/10.12775/LLP.2011.009

    Article  Google Scholar 

  • van Benthem, J. (2008). Logic and reasoning: Do the facts matter? Studia Logica, 88, 67–84. https://doi.org/10.1007/s11225-008-9101-1

    Article  Google Scholar 

  • Wigner, E. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics, 13, 291–306.

    Article  Google Scholar 

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    M. A. Winstanley

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This article belongs to the topical collection "Anti-Exceptionalism about Logic", edited by Ben Martin, Maria Paola Sforza Fogliani, and Filippo Ferrari.

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Winstanley, M.A. A psychological theory of reasoning as logical evidence: a Piagetian perspective. Synthese 199, 10077–10108 (2021). https://doi.org/10.1007/s11229-021-03237-x

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