Abstract
Inspired by van Fraassen’s viewpoint, according to which logic is relevant to philosophy of science, in this chapter we aim to lead the way of applying logic to the study of abduction. Certainly van Fraassen seems to reject abduction, but many logicians have considered abduction as a prototype of scientific inference, and, at the last resort, this critical position is more about the so called inference to the best explanation than about abduction itself. We recover the original notion, due to Peirce, as an inferential process that permits to formulate explicative hypotheses. A couple of examples of abduction in scientific practices are given. Then we present the classical model of logical treatment of abduction (the AKM-model), its connection with the AGM-model of belief revision and its limits. In both cases the logical parameter is a classical logic, but a change of such parameter is methodologically justified: semantic tableaux are very illustrative, since some new rules could be necessary to obtain closed branches, that is to say, to obtain the corresponding keys to solve abductive problems. Then a dynamic perspective may be adopted, from which multimodal logics are suitable, so we study Bonano’s system with epistemic operators and another one with four modal operators.
This work has been carried out as part of the research project Alternative Interpretations of Non-Classical Logics, reference HUM5844 of the Ministry of Economy, Innovation and Science (Junta de Andalucía), and the project Consciousness, Logic and Computation, reference FFI2011-29609-C02-01 of the Ministry of Science and Innovation (Government of Spain).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
“La abducción es la inducción auténtica, es decir, el razonamiento científico empírico buscado (y no encontrado) por Francis Bacon,” in the original.
- 2.
Aliseda, Kakas or Kowalski, and Meheus or Magnani (Gabbay and Woods 2006).
- 3.
We follow the example given in a personal communication by A. Rivadulla, supplemented with data by Arsuaga (2001) and it has been presented in a methodological course (Master in Evolutive Biology, University of Sevilla). Moreover, the notion of preduction (Rivadulla 2007), used in the case of physics, has been slightly modified.
- 4.
“… el más antiguo indoeuropeo que podemos reconstruir (el IE I) consistía en una serie de raíces que adquirían funciones y valores semánticos y gramaticales mediante el orden de las palabras, el acento, elementos aglutinados, derivación, composición, etc. Solo en fecha posterior se crearon desinencias con valor gramatical (en el IE II); y en una posterior todavía, temas con valor gramatical. Esto sucedió cuando se creó el IE III y, dentro de él, cada uno de sus dos sectores, A y B,” in the original.
- 5.
A predicate defined in D is a subset of elements of D, a m-adic relation defined on D is a set of m-tuples of elements of D.
- 6.
A literal is an atomic sentence p, which is positive, or the negation of an atomic sentence ¬p, which is negative. p is complementary with ¬p, and vice versa.
- 7.
Given two sentences A and B, this principle (Pseudo-Scotus’s principle) says that A, ¬A |– B.
References
Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50, 510–530.
Aliseda, A. (2006). Abductive reasoning: Logical investigations into discovery and explanation (Synthese library, Vol. 330). Dordrecht: Springer.
Arsuaga, J. L. (2001). El enigma de la esfinge. Barcelona: Plaza y Janés, Círculo de Lectores.
Batens, D. (2007). A universal logic approach to adaptive logics. Logica Universalis, 1, 221–242.
Beuchot, M. (2002). Estudio sobre Peirce y la escolástica (Cuadernos de Anuario Filosófico, Serie Universitaria 150). Pamplona: Universidad de Navarra.
Bonano, G. (2005). A simple modal logic for believe revision. Synthese, 147(2), 193–228.
Carnielli, W. (2006). Surviving abduction. Logic Journal of IGPL, 14(2), 237–256.
Gabbay, D., & Woods, J. (2006). A practical logic of cognitive systems. Vol. 2: The reach of abduction: Insight and trial. Amsterdam: Elsevier.
Hempel, C. G., & Openheim, P. (1948). Toward a theory of the process of explanation. Philosophy in Science, 15(2), 135–175.
Hintikka, J. (1999). What is abduction? The fundamental problem of contemporary epistemology. In J. Hintikka (Ed.), Inquiry as inquiry: A logic of scientific discovery (pp. 91–113). Dordrecht: Kluwer Academic Publisher.
Lipton, P. (1996). Inference to the best explanation. London: Routledge.
Magnani, L. (2009). Abductive cognition: The epistemological and eco-cognitive dimensions of hypothetical reasoning (Vol. 3 of Cognitive system monographs). Dordrecht: Springer.
Martínez-Freire, P. (2010). Observaciones sobre el concepto de abducción. In H. van Ditmarsch, F. Salguero, & F. Soler (Eds.), Liber Amicorum Ángel Nepomuceno (pp. 77–84). Sevilla: Fénix Editora.
Nepomuceno-Fernández, A., Soler-Toscano, F., & Velázquez-Quesada, F. R. (2013). An epistemic and dynamic approach to abductive reasoning: Selecting the best explanation. Logic Journal of the IGPL. doi:10.1093/jigpal/jzt013.
Peirce, C. S. (1991). The essential Peirce. Selected philosophical writings (Vol. I). Bloomington: Indiana University Press.
Peirce, C. S. (1998). The essential Peirce. Selected philosophical writings (Vol. II). Bloomington: Indiana University Press.
Psillos, S. (1996). On van Fraassen’s critique of abductive reasoning. The Philosophical Quarterly, 46(182), 31–47.
Rivadulla, A. (2007). Abductive reasoning, theoretical preduction, and the physical way of dealing with nature. In O. Pombo & A. Gerner (Eds.), Abduction and the process of scientific discovery (pp. 199–210). Lisbon: Publidisa.
Rodríguez Adrados, F. (2008). Historia de las lenguas de Europa. Madrid: Editorial Gredos.
Soler, F., & Nepomuceno, A. (2006). Tarfa: Tableaux and resolution for finite abduction. In M. Fisher, W. van der Hoek, B. Konev, & A. Lisitsa (Eds.), Logic in artificial intelligence. 10th European conference, JELIA 2006 (pp. 511–514). Berlin: Springer.
Soler, F., Fernández, D., & Nepomuceno, A. (2012). A modal framework for modelling abductive reasoning. Logic Journal of IGPL, 20(2), 438–444.
Thagard, P., & Shelley, C. (1997). Abductive reasoning: Logic, visual thinking, and coherence. In M. L. Dalla Chiara et al. (Eds.), Logic and scientific methods (pp. 413–427). Dordrecht: Kluwer Academic Publisher.
van Ditmarsch, H., van der Hoeck, W., & Kooi, B. (2007). Dynamic epistemic logic. Dordrecht: Springer.
van Fraassen, B. (1980). The scientific image. Oxford: Clarendon.
van Fraassen, B. (1989). Laws and symmetry. Oxford: Clarendon.
van Fraassen, B. (2011a). Logic and the philosophy of science. Journal of the Indian Council of Philosophical Research, 27, 45–66.
van Fraassen, B. (2011b). Thomason’s paradox for belief, and two consequence relations. Journal of Philosophical Logic, 40, 15–32.
Woods, J. (2012). Cognitive economics and the logic of abduction. The Review of Symbolic Logic, 5(1), 148–161.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Nepomuceno, Á. (2014). Scientific Models of Abduction: The Role of Non Classical Logic. In: Gonzalez, W.J. (eds) Bas van Fraassen’s Approach to Representation and Models in Science. Synthese Library, vol 368. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7838-2_6
Download citation
DOI: https://doi.org/10.1007/978-94-007-7838-2_6
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-7837-5
Online ISBN: 978-94-007-7838-2
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)