“... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”

Michael H. G. Hoffmann

doi:10.29333/ejmste/92553

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Michael H. G. Hoffmann ¹ ^*

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¹ Georgia Institute of Technology, USA^* Corresponding Author

Abstract

Peirce developed two different concepts—”abduction” and “diagrammatic reasoning”—that are interesting for theories of creativity in mathematics, the sciences, and in learning. He defined “abduction” as the “inference” from surprising, or unexplained, observations to an explanatory hypothesis. However, he does not provide much to explain how the process of creating new hypotheses might be possible. In this contribution, I start from a remark by Peirce claiming that diagrammatic reasoning might somehow be the foundation of abduction. Using an example from astronomy, I argue that at least one form of abduction is indeed based on diagrammatic reasoning: theoretic model abduction.

Keywords

abduction
consistency
creativity
diagrammatic reasoning
representational system
scientific discovery

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 14, Issue 9, September 2018, Article No: em1585

https://doi.org/10.29333/ejmste/92553

Publication date: 25 Jun 2018

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References

Bochenski, J. M. (1970 <1956>). Formale Logik (3. ed.). Freiburg i. Br.: Alber.
Boden, M. A. (2004 <1990>). The Creative Mind. Myths and Mechanisms (2nd ed.). London; New York: Routledge.
Burton, R. G. (2000). The Problem of Control in Abduction. Transactions of the Charles S. Peirce Society, 36(1), 149-156.
Campos, D. G. (2007). Peirce on the Role of Poietic Creation in Mathematical Reasoning. Transactions of the Charles S. Peirce Society, 43(3), 470-489.
Carnap, R. (1967). The logical structure of the world [and] pseudoproblems in philosophy; translated (Der logische Aufbau der Welt) (R. A. George, Trans. 2nd ed.). London: Routledge & K. Paul.
Cheng, P. C.-H., & Simon, H. A. (1995). Scientific Discovery and Creative Reasoning. In S. M. Smith, T. B. Ward & R. A. Finke (Eds.), The Creative Cognition Approach (pp. 205-228). Cambridge, Mass.: MIT Press.
Clark, A. (2007). Curing cognitive hiccups: A defense of the extended mind. Journal of Philosophy, 104(4), 163-192. https://doi.org/10.5840/jphil2007104426.
Clark, A., & Chalmers, D. (1998). The extended mind. Analysis, 58(1), 7-19. https://doi.org/10.1093/analys/58.1.7.
Euler, L. (1768). Lettres à une Princesse d’Allemagne. St. Petersburg: l’Academie Imperiale des Sciences.
Fann, K. T. (1970). Peirce’s Theory of Abduction. The Hague: Nijhoff. https://doi.org/10.1007/978-94-010-3163-9.
Gingerich, O. (1993). The eye of heaven: Ptolemy, Copernicus, Kepler. New York, NY: American Institute of Physics.
Glasgow, J., Narayanan, N. H., & Chandrasekaran, B. (Eds.). (1995). Diagrammatic Reasoning: Cognitive and Computational Perspectives. Menlo Park, CA: AAAI Press / The MIT Press.
Hoffmann, M. H. G. (1999). Problems with Peirce’s Concept of Abduction. Foundations of Science, 4(3), 271–305. https://doi.org/10.1023/A:1009675824079.
Hoffmann, M. H. G. (2005). Erkenntnisentwicklung. Ein semiotisch-pragmatischer Ansatz. Frankfurt am Main: Klostermann.
Hoffmann, M. H. G. (2007). Learning from people, things, and signs. Studies in Philosophy and Education, 26(3), 185-204. https://doi.org/10.1007/s11217-007-9027-5.
Hoffmann, M. H. G. (2009). Über die Bedingungen der Möglichkeit durch diagrammatisches Denken etwas zu lernen: Diagrammgebrauch in Logik und Arithmetik. Zeitschrift für Semiotik, 31(3-4), 241-274.
Hoffmann, M. H. G. (2011a). Cognitive conditions of diagrammatic reasoning. Semiotica, 186(1/4), 189-212. https://doi.org/10.1515/semi.2011.052.
Hoffmann, M. H. G. (2011b). “Theoric Transformations” and a New Classification of Abductive Inferences. Transactions of the Charles S Peirce Society, 46(4), 570-590.
Hoffmann, M. H. G., & Plöger, M. (2000). Mathematik als Prozess der Verallgemeinerung von Zeichen: Eine exemplarische Unterrichtseinheit zur Entdeckung der Inkommensurabilität. Zeitschrift für Semiotik, 22(1), 81–114.
Hutchins, E. (1995). Cognition in the wild. Cambridge, MA: MIT Press.
Kant, I. (CPR). Critique of pure reason (P. Guyer & A. W. Wood, Trans.). Cambridge 1998: Cambridge Univ. Pr. (quoted according to the first edition—A: 1781—or the second—B: 1787).
Kent, B. (1997). The Interconnectedness of Peirce’s Diagrammatic Thought. In N. Houser, D. D. Roberts & J. van Evra (Eds.), Studies in the Logic of Charles Sanders Peirce (pp. 445–459). Bloomington and Indianapolis: Indiana University Press.
Linton, C. M. (2004). From Eudoxus to Einstein: A history of mathematical astronomy. Cambridge, UK; New York: Cambridge University Press. https://doi.org/10.1017/CBO9780511541452.
Magnani, L. (2001). Abduction, Reason, and Science. Processes of Discovery and Explanation. New York: Kluwer Academic / Plenum Publishers. https://doi.org/10.1007/978-1-4419-8562-0.
Magnani, L. (2009). Abductive Cognition. The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning. Berlin: Springer. https://doi.org/10.1007/978-3-642-03631-6.
Magnani, L. (Ed.). (2010). Model-Based Reasoning in Science & Technology. Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-15223-8.
Magnani, L., & Nersessian, N. J. (Eds.). (2002). Model-Based Reasoning: Science, Technology, Values. New York: Kluwer Academic / Plenum Publisher. https://doi.org/10.1007/978-1-4615-0605-8.
Magnani, L., Nersessian, N. J., & Thagard, P. (Eds.). (1999). Model-based Reasoning in Scientific Discovery. New York: Plenum Publishers. https://doi.org/10.1007/978-1-4615-4813-3.
Nersessian, N. J. (2008). Creating scientific concepts. Cambridge, Mass.: MIT Press.
Neugebauer, O. (1975). A history of ancient mathematical astronomy. Berlin; New York: Springer-Verlag. https://doi.org/10.1007/978-3-642-61910-6.
Paavola, S. (2005). Peircean Abduction: Instinct or Inference? Semiotica, 153(1/4), 131-154. https://doi.org/10.1515/semi.2005.2005.153-1-4.131.
Paavola, S. (2007). Abductive logic of discovery with distributed means. In O. Pombo & A. Gerner (Eds.), Abduction and the Process of Scientific Discovery (pp. 47-62). Lisboa: CFCUL/Publidisa.
Paavola, S. (2011). Diagrams, iconicity, and abductive discovery. Semiotica, 186(1-4), 297-314. https://doi.org/10.1515/semi.2011.057.
Paavola, S., & Hakkarainen, K. (2005). Three Abductive Solutions to the Meno Paradox – with Instinct, Inference, and Distributed Cognition. Studies in Philosophy and Education, 24(3–4), 235–253. https://doi.org/10.1007/s11217-005-3846-z.
Paavola, S., Hakkarainen, K., & Sintonen, M. (2006). Abduction with dialogical and trialogical means. Logic Journal of the IGPL, 14(2), 137-150. https://doi.org/10.1093/jigpal/jzk010.
Peirce. (CP). Collected Papers of Charles Sanders Peirce (Volumes I-VI, ed. by Charles Hartshorne and Paul Weiss, 1931–1935, Volumes VII-VIII, ed. by Arthur W. Burks, 1958; quotations according to volume and paragraph). Cambridge, Mass.: Harvard UP.
Peirce. (EP). The Essential Peirce. Selected Philosophical Writings. Vol. 1 (1867–1893), Vol. 2 (1893–1913). Bloomington and Indianapolis 1992 +1998: Indiana University Press.
Peirce. (MS). The Charles S. Peirce Papers. Manuscript Collection in the Houghton Library, Harvard University. Available in the Peirce Microfilm edition. Pagination: CSP = Peirce / ISP = Institute for Studies in Pragmaticism.
Peirce. (NEM). The New Elements of Mathematics by Charles S. Peirce (Vol. I-IV). The Hague-Paris / Atlantic Highlands, N.J., 1976: Mouton / Humanities Press.
Peirce. (SEM). Charles S. Peirce, Semiotische Schriften (Vol. I-III). Frankfurt a.M. 1986-1994: Suhrkamp.
Peirce, C. S. (1906). Prolegomena to an Apology for Pragmaticism: The Monist 16: 492-546 (quoted from Peirce, CP, 4.530-572). https://doi.org/10.5840/monist190616436.
Peirce, C. S. (1909). (Fragments on Existential Graphs): MS 514; Transcription by Michael Balat, with commentary by John F. Sowa at: http://www.jfsowa.com/peirce/ms514.htm.
Quine, W. V. O. (1969). Epistemology Naturalized. In W. V. O. Quine (Ed.), Ontological relativity and other essays (pp. 69–90). New York Columbia Univ. Press.
Quine, W. V. O. (1971 <1951>). Two Dogmas of Empiricism from a Logical Point of View: 9 Logico-Philosophical Essays (2. ed., pp. 20–46). Cambridge, Mass.: Harvard Univ. Press.
Rescher, N. (1995). Peirce on Abduction, Plausibility, and the Efficiency of Scientific Inquiry. In N. Rescher (Ed.), Essays in the History of Philosophy (pp. 309–326). Aldershot Avebury.
Roberts, D. D. (1973). The Existential Graphs of Charles S. Peirce. The Hague Mouton.
Schurz, G. (2008). Patterns of abduction. Synthese, 164(2), 201-234. https://doi.org/10.1007/s11229-007-9223-4.
Semetsky, I. (2005). Learning by abduction: A geometrical interpretation. Semiotica, 157(1/4), 199–212. https://doi.org/10.1515/semi.2005.2005.157.1-4.199.
Shin, S.-J. (2002). The Iconic Logic of Peirce’s Graphs. Cambridge, MA: MIT Bradford Books.
Skagestad, P. (1999). Peirce’s inkstand as an external embodiment of mind. Transactions of the Charles S Peirce Society, 35(3), 551-561.
Stjernfelt, F. (2007). Diagrammatology: An Investigation on the Borderlines of Phenomenology, Ontology, and Semiotics. Dordrecht, NL: Springer. https://doi.org/10.1007/978-1-4020-5652-9.
Thagard, P. (2010). How Brains Make Mental Models. In L. Magnani (Ed.), Model-Based Reasoning in Science & Technology (pp. 447–461). Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-15223-8_25.
Venn, J. (1880a). On the Diagrammatic and Mechanical Representations of Propositions and Reasoning. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 9, 1-18.
Venn, J. (1880b). On the Forms of Logical Proposition. Mind, 5(19), 336-349. https://doi.org/10.1093/mind/os-V.19.336.

How to cite this article

APA

Hoffmann, M. H. G. (2018). “... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), em1585. https://doi.org/10.29333/ejmste/92553

Vancouver

Hoffmann MHG. “... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”. EURASIA J Math Sci Tech Ed. 2018;14(9):em1585. https://doi.org/10.29333/ejmste/92553

AMA

Hoffmann MHG. “... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”. EURASIA J Math Sci Tech Ed. 2018;14(9), em1585. https://doi.org/10.29333/ejmste/92553

Chicago

Hoffmann, Michael H. G.. "“... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 9 (2018): em1585. https://doi.org/10.29333/ejmste/92553

Harvard

Hoffmann, M. H. G. (2018). “... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), em1585. https://doi.org/10.29333/ejmste/92553

MLA

Hoffmann, Michael H. G. "“... and therefore in a Remote Sense Abduction Rests upon Diagrammatic Reasoning”". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 9, 2018, em1585. https://doi.org/10.29333/ejmste/92553