A Framework for Inductive Reasoning in Model-Based Science


  • Milagros Maribel Barroso Rojo Universidad Alberto Hurtado




induction, inductive reasoning, scientific inference, Norton's material theory of induction, models, Whewell’s induction


This paper argues that the linguistic approach to analyzing induction, according to which induction is a type of inference or argument composed of statements or propositions, is unsuitable to account for scientific reasoning. Consequently, a novel approach to induction in model-based science is suggested. First, in order to show their adherence to the linguistic treatment of induction, two strategies are reviewed: (i) Carnap and Reichenbach’s attempts to justify induction and (ii) Norton’s recent material theory of induction. Second, three reasons are provided to support the claim that the linguistic treatment of induction is insufficient in accounting for model-based reasoning in science. Finally, a framework focused on models—rather than statements or propositions—is suggested to address induction in science. William Whewell’s theory of induction is briefly outlined as an example of a non-propositional treatment of induction that is consistent with model-based scientific practice.


Achinstein, P. (2010). The War on Induction: Whewell Takes on Newton and Mill (Norton Takes on Everyone). Philosophy of Science, 77(5), 728-739. https://doi.org/10.1086/656540

Bailer-Jones, D. (1999). Tracing the Development of Models in the Philosophy of Science. In L. Magnani, N. J. Nersessian, & P. Thagard (Eds.), Model-Based Reasoning in Scientific Discovery (1st ed., pp. 23-40). Springer. https://doi.org/10.1007/978-1-4615-4813-3

Balzer, W., Moulines, C. U., & Sneed J. (1987). An Arquitectonic for Science: The Structuralist Program. Springer Dordrecht. https://doi.org/10.1007/978-94-009-3765-9

Barker, S. (1957). Induction and Hypothesis: A Study of the Logic of Confirmation. Cornell University Press. https://doi.org/10.7591/9781501741173

Barroso, M. (2023). Towards a Consilient Theory of Scientific Representation. Principia: an International jounal of epistemology, 27(2), 235-261.

Bogdan, R. (1976). Local induction. Stanford University.

Braithwaite, R. (1954). The nature of theoretical concepts and the role of models in an advanced science. Revue lnternationale de Philosophie, 8(1-2), 34-40.

Bueno, O., & French, S. (2018). Applying Mathematics. Immersion, Inference, Interpretation. Oxford University Press. https://doi.org/10.1093/oso/9780198815044.001.0001

Carnap, R. (1945). On Inductive Logic. Philosophy of Science, 12(2), 72-97. https://doi.org/10.1086/286851

Carnap, R. (1947). On the Application of Inductive Logic. Philosophy and Phenomenological Research, 8(1), 133-148. https://doi.org/10.2307/2102920

Carnap, R. (1950a). Empiricism, Semantics and Ontology. Revue Internationale de Philosophie, 4(11), 20-40. https://doi.org/10.1515/9781400838684-018

Carnap, R. (1950b). Logical Foundations of Probability. University of Chicago Press.

Carnap, R. (1956). The Methodological Character of Theoretical Terms. In H. Feigl & M. Scriven (Eds.), Minnesota Studies in the Philosophy of Science 1 (1st ed., pp. 38-76). University of Minnesota Press.

Carnap, R. (1959). Psychology in Physical Language. In J. A. J. Ayer (Ed.), Logical Positivism (1st ed., pp. 165-198). The Free Press.

Cartwright, N., Shomar, T., & Suárez, M. (1995). The tool box of science: Tools for the building of models with a superconductivity example. In W. E. Herfel, W. Krajewski, I. Niiniluoto & R. Wójcicki (Eds.), Theories and Models in Scientific Processes (pp. 137-49). Rodopi.

Da Costa, N. C. A., & French, S. (2003). Science and partial truth: a unitary approach to models and scientific reasoning. Oxford University Press.

Dardashti R., & Hartmann S. (2019). Assessing Scientific Theories The Bayesian Approach. In R. Dardashti, R. Dawid, & K. Thébault (Eds.), Why Trust a Theory? Epistemology of Fundamental Physics (1st ed., pp. 67-83). Cambridge University Press.

Dawid, R. (2016). Modelling Non-empirical Confirmation. In E. Ippoliti, F. Sterpetti, & T. Nickles (Eds.), Models and Inferences in Science. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 25. Springer Nature. https://doi.org/10.1007/978-3-319-28163-6_11

Dethier, C. (2018). William Whewell’s Semantic Account of Induction. HOPOS: The Journal of the International Society for the History of Philosophy of Science, 8(1), 141-56.

Downes, S. (2021). Models and Modeling in the Sciences. Routledge. https://doi.org/10.4324/9781315647456

Eberhardt, F., & Glymour, C. (2011). Hans Reichenbach’s Probability Logic. In D. M. Gabbay, S. Hartmann, & J. Woods (Eds.), Handbook of the History of Logic (1st ed., pp. 357-89). Elsevier. https://doi.org/10.1016/B978-0-444-52936-7.50010-0

Foster, M. (2011). The debate between Whewell and Mill on the nature of scientific induction. In D. M. Gabbay, S. Hartmann, & J. Woods (Eds.), Handbook of the History of Logic. (1st ed., pp.10-93). Elsevier. https://doi.org/10.1016/B978-0-444-52936-7.50003-3

Frigg, R., & Nguyen J. (2020). Scientific Representation. The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/win2021/entries/scientific-representation/

Giere, R. N. (1988). Explaining science: a cognitive approach. University of Chicago Press. https://doi.org/10.7208/9780226292038

Hacking, I. (1975). The emergence of probability. A philosophical study of early ideas about probability, induction, and statistical inference. Cambridge University Press.

Hempel, C. (1970). On the ‘Standard Conception’ of Scientific Theories. In M. Radner et al. (Eds.), Minnesota Studies in the Philosophy of Science IV (pp.142-163). University of Minnesota Press.

Hempel, C. (1965). Scientific Explanation. Essays in the Philosophy of Science. The Free Press.

Hesse, M. (1953). Models in physics. British Journal for the Philosophy of Science, 4(15), 198-214.

Hutten, E. H. (1954). The role of models in physics. British Journal for the Philosophy of Science, 4(16), 284-301.

Jeffrey, R. (1975). Carnap’s Empiricism. In G. Maxwell & R. Anderson Jr. (Eds.) Induction, Probability and Confirmation. Minnesota Studies in the Philosophy of Science 6 (1st ed., pp. 37-49). University of Minnesota Press.

Kelly, T. (2010). Hume, Norton, and Induction without Rules. Philosophy of Science, 77(5), 754-764. https://doi.org/10.1086/656548

Kemeny, J. (1951). Review of Logical Foundations of Probability, by R. Carnap. The Journal of Symbolic Logic, 16(3), 205-207.

Kemeny, J. (1953). A Logical Measure Function. Journal of Symbolic Logic, 18(4), 289-308.

Koperski, J. (1998). Models, Confirmation, and Chaos. Philosophy of Science, 65(2), 624-648. https://doi.org/10.1086/392663

Lenz, J. (1958). Problems for the Practicalist’s Justification of Induction. Philosophical Studies, 9(1-2), 4-8.

Levi, I. (1973). Gambling with Truth. Knopf.

McCaskey, J. (2020). Reviving Material Theories of Induction. Studies in History and Philosophy of Science Part A, 83, 1-7. https://doi.org/10.1016/j.shpsa.2019.12.006

McKinsey, J., Sugar, A., & Suppes, P. (1953). Axiomatic Foundations of Classical Particle Mechanics. Indiana University Mathematics Journal, 2(2), 253-72.

Mill, J. S. (1843). A Sistem of Logic: Ratiocinative and Inductive. John W. Parker Ed.

Morgan, M., Morrison M. (1999). Models as Mediators: Perspectives on Natural and Social Science (Ideas in Context). Cambridge University Press. https://doi.org/10.1017/CBO9780511660108

Moulines, C.U. (2002). Introduction: Structuralism as a Program for Modelling Theoretical Science. Synthese, 130(1), 1-11. https://doi.org/10.1023/A:1013892808077

Norton, J. (2003). A Material Theory of Induction. Philosophy of Science, 70(4), 647-670. https://doi.org/10.1086/378858

Norton, J. (2005). A little survey of induction. In P. Achinstein (Ed.), Scientific Evidence: Philosophical Theories and Applications (1st ed., pp. 9-34). Johns Hopkins University Press.

Norton, J. (2014). A Material Dissolution of the Problem of Induction. Synthese, 191(4), 671-690. https://doi.org/10.1007/s11229-013-0356-3

Norton, J. (2021). The Material Theory of Induction. University of Calgary Press. https://doi.org/10.2307/j.ctv25wxcb5

Raisis, V. (1999). Expansion and Justification of Models: The Exemplary Case of Galileo Galilei. In L. Magnani, N. J. Nersessian, P. Thagard (Eds.), Model-Based Reasoning in Scientific Discovery (1st ed., pp.149-164). Springer. https://doi.org/10.1007/978-1-4615-4813-3_10

Redhead, M. (1980). Models in Physics. The British Journal for the Philosophy of Science, 31(2), 145-163.

Reichenbach, H. (1933). Carnap’s Logical Structure of the World [1933c]. In M. Reichenbach & R. S. Cohen (Com.), Hans Reichenbach Selected Writings 1909-1953, (pp. 405.408). Springer Dordrecht. https://doi.org/10.1007/978-94-009-9761-5_42

Reichenbach, H. (1949). The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability. University of California Press.

Reichenbach, H. (1957). Experience and prediction: an analysis of the foundations and the structure of knowledge. University of Notre Dame Press.

Reichenbach, H. (1968). The Rise of Scientific Philosophy. University of California Press.

Russell, B. (2009). Human knowledge: its scope and limits. Routledge. https://doi.org/10.4324/9780203875353

Salmon, W. (1967). Carnap’s Inductive Logic. The Journal of Philosophy, 64(21), 725-739.

Salmon, W. (1974). The pragmatic justification of induction. In R. Swinburne (Ed.), The Justification of Induction (1st ed., pp.85-97). Oxford University Press.

Snyder, L. (1997). The Mill-Whewell Debate: Much Ado about Induction. Perspectives on Science, 5(2), 159-98. https://doi.org/10.1162/posc_a_00523

Sober, E. (1988). Reconstructing the Past: Parsimony, Evolution, and Inference. MIT Press.

Suárez, M., & Cartwright, N. (2008). Theories: Tools versus Models. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 39(1), 62-81. https://doi.org/10.1016/j.shpsb.2007.05.004

Suppes, P. (1960). A Comparison of The Meaning and Uses of Models In Mathematics and The Empirical Sciences. Synthese, 12, 287-301. https://doi.org/10.1007/BF00485107

Sprenger, J. (2011). Hempel and the Paradoxes of Confirmation. In D. M. Gabbay, S. Hartmann, & J. Woods (Eds.), Handbook of the History of Logic 10, (1st ed., pp.235-63) Elsevier. https://doi.org/10.1016/B978-0-444-52936-7.50007-0

Tarski, A. (2006). The Concept of Truth in Formalized Languages. In J. Corcoran (Ed.), Logic, Semantics, Metamathematics. Papers from 1923 to 1938 by Alfred Tarski, (1st ed, pp. 152-278). Hackett Publishing Company.

Van Fraassen, B. (1989). Laws and Symmetry. Oxford University Press. https://doi.org/10.1093/0198248601.001.0001

Whately, R. (1827). Elements of Logic. J. Mawman.

Whewell, W. (1840). The Philosophy of the Inductive Science, Founded Upon Their History, vol. 1. John W. Parker West Strand.

Whewell, W. (1847). The Philosophy of the Inductive Science, Founded Upon Their History, vol. 2. John W. Parker West Strand.

Whewell, W. (1858). Novum Organon Renovatum. Being The Second Part of the Philosophy of the Inductive Science. John W. Parker and Son, West Strand.Williams, D. (1948). Induction and the Future. Mind, LVII(226), 226-229. https://doi.org/10.1093/mind/LVII.226.226

Winther, R. (2021). The Structure of Scientific Theories. The Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/archives/win2016/entries/structure-scientific-theories/

Worrall, J. (2010). For Universal Rules, Against Induction. Philosophy of Science, 77(5), 740-753. https://doi.org/10.1086/656823

Wright, G. (1965). The Logical Problem of Induction. Oxford Basil Blakcwell.




How to Cite

Barroso Rojo, M. M. (2023). A Framework for Inductive Reasoning in Model-Based Science. Revista De Humanidades De Valparaíso, (23), 259–285. https://doi.org/10.22370/rhv2023iss23pp259-285




Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.