Abstract
What I call theoretical abduction (sentential and model-based) certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanations occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action and of external representations in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. I will present some aspects of this kind of reasoning derived from the “cognitive” history of the discovery of the non-Euclidean geometries. Geometrical diagrams are considered external representations which play both a mirror role (to externalize rough mental models), and an unveiling role (as gateways to imaginary entities). I describe them as epistemic mediators able to perform various abductive tasks (discovery of new properties or new propositions/hypotheses, provision of suitable sequences of models as able to convincingly verifying theorems, etc.).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Boi, L., 1991,Le probléme mathématique de l’espace. Une quéite de l’intelligible, Springer, Berlin.
Boutilier, C. and Becher, V., 1995, Abduction as belief revision, Artificial intelligence, 77:43–94.
Call, J., 2000, Representing space and objects in monkeys and apes,Cognitive Science 24(3):397–422.
Giere, R., 2002, Models as parts of distributed cognitive systems, in this volume, pp. 227–241.
Glasgow, J.I. and Papadias, D., 1992, Computational imagery, Cognitive Science 16:355–394.
Hoffmann, M., 1999, Problems with Peirce’s concept of abduction,Foundations of Science 4(3): 271–305.
Hoffmann, M., forthcoming, How to get it. Diagrammatic reasoning as a tool of knowledge development and its pragmatic dimension, in: Special Issue Abductive Reasoning in Science, Foundations of Science, L. Magnani and N.J. Nersessian, eds.
Hutchins, E., 1995, Cognition in the Wild, MIT Press, Cambridge, MA.
Kant, L, 1929, Critique of Pure Reason (1781–1787), translation by N. Kemp Smith, Mac-Millan, New York, reprint 1998.
Lobachevsky, N.J., 18291830, 18351838, Zwei geometrische Abhandlungen, aus dem Russischen bersetzt, mit Anmerkungen und mit einer Biographie des Verfassers von Friedrich Engel, B.G. Teubner, Leipzig. Originally published as O nachalakh geometrii, Kasanki Vestnik, Feb.-March, 1829: 178187; April, 1829: 228241; Nov.-Dec., 1829: 227243; March-April, 1830: 251283; July-Aug., 1830: 571636, and Novye nachala geometrii, Uchonia sapiski Kasanskava Universiteta 3, 1835: 348; 2, 1836: 398; 3, 1836: 350; 1, 1837: 397; 1, 1838: 3124; 3, 1838: 365.
Lobachevsky, N.J., 1891, Geometrical Researches on the Theory of Paralleles [1840], translated by G.B. Halsted, University of Texas, Austin.
Lobachevsky, N.J., 1897, The introduction to Lobachevsky’s New Elements of Geometry [1835], translation from the Russian, with a preface by G.B. Halsted, Transactions of Texas Academy 2:117. Originally published in: N.J. Lobachevsky, Novye nachala geometrii, Uchonia sapiski Kasanskava Universiteta 3, 1835: 3–48.
Lobachevsky, N.J., 1929, Pangeometry or a Summary of Geometry Founded upon a General and Rigorous Theory of Parallels, in: A Source Book in Mathematics, D.E. Smith, ed., McGraw Hill, New York, pp. 360–374.
Magnani, L., 1992, Abductive reasoning: philosophical and educational perspectives in medicine, in: Advanced Models of Cognition for Medical Training and Practice, D. A. Evans and V.L. Patel, eds., Springer, Berlin, pp. 21–41.
Magnani, L., 1999a, Creative abduction and hypothesis withdrawal in science, in: Methodo logical Aspects of Discovery and Creativity, J. Meheus and T. Nickles, eds., Kluwer, Dordrecht, forthcoming.
Magnani, L., 1999b, Model-based creative abduction, in: L. Magnani, N.J. Nersessian, and P. Thagard, eds., pp. 219–238.
Magnani, L., 2000, Action-based abduction in science, in: Workshop Scientific Reasoning in Artificial Intelligence and Philosophy of Science, ECAI 2000 Workshop Notes, A. Aliseda and D. Pearce, eds., Berlin, pp. 46–51.
Magnani, L., 2001a, Abduction, Reason, and Science. Processes of Discovery and Explanation, Kluwer Academic/Plenum Publishers, New York.
Magnani, L., 2001b, Philosophy and Geometry. Theoretical and Historical Issues, Kluwer Academic, Dordrecht.
Magnani, L., N.J. Nersessian, and Thagard, P., eds., 1999, Model-Based Reasoning in Scientific Discovery, Kluwer Academic/Plenum Publishers, New York.
Magnani, L. and Dossena, R., 2002, Perceiving the infinite and the infinitesimal world: unveiling and optical diagrams and the construction of mathematical concepts, submitted to CogSei2002.
Nersessian, N.J., 1995a, Opening the black box: cognitive science and history of science. Technical Report GIT-COGSCI 94/23, July. Cognitive Science Report Series, Georgia Institute of Technology, Atlanta, GA. Partially published in: Osiris 10:194–211.
Nersessian, N.J., 1995b, Should physicists preach what they practice? Constructive modeling in doing and learning physics, Science and Education 4:203–226.
Nersessian, N.J., 1998, Kuhn and the cognitive revolution, Configurations 6:87–120.
Nersessian, N.J., 1999, Model-based reasoning in conceptual change, in: L. Magnani, N.J. Nersessian, and P. Thagard, eds., pp. 522.
Newell, A., 1990, Unified Theories of Cognition, Harvard University Press, Cambridge, MA.
Norman, D.A., 1993, Things that Make Us Smart. Defending Human Attributes in the Age of the Machine, Addison-Wesley, Reading, MA.
Peirce, C.S., 19311958(CP), Collected Papers, 8 vols., C. Hartshorne and P Weiss (vols. I-VI), eds., and A.W. Burks (vols. VII-VIII), ed.. Harvard University Press, Cambridge, MA.
Piaget, J., 1974, Adaptation and Intelligence, University of Chicago Press, Chicago, IL.
Ramoni, M., Stefanelli, M., Magnani, L., and Barosi, G., 1992, An epistemological framework for medical knowledge-based systems,IEEE Transactions on Systems, Man, and Cybernetics 22(6):1361–1375.
Rosenfeld, B.A., 1988, A History of Non-Euclidean Geometry. Evolution of the Concept of a Geometric Space (1976), Springer, Berlin.
Tall, D., forthcoming, Conceptual and formal infinities, Educational Studies in Mathematics.
Thagard, P., 1992, Conceptual Revolutions, Princeton University Press, Princeton, NJ.
Torretti, R., 1978, Philosophy of Geometry from Riemann to Poincaré, Reidel, Dordrecht.
Trafton, J.G., Trickett, S.B., and Mintz, F.E., forthcoming,, Connecting internal and external representations: spatial transformations of scientific visualizations, in: Special Iissue Model_Based Reasoning: Visual, Analogical, Simulative, Foundations of Science, L. Magnani and N.J. Nersessian, eds.
Zhang, J., 1997, The nature of external representations in problem solving, Cognitive Science 21(2):179–217.
Zhang, J. and Norman, D.A., 1994, Representations in distributed cognitive tasks, Cognitive Science 18:87–122.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Magnani, L. (2002). Epistemic Mediators and Model-Based Discovery in Science. In: Magnani, L., Nersessian, N.J. (eds) Model-Based Reasoning. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-0605-8_18
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0605-8_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-5154-2
Online ISBN: 978-1-4615-0605-8
eBook Packages: Springer Book Archive