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Formal schemas of induction as models

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Abstract

What is the relation or connection between formalizations of induction and the actual inductive inferences of scientists? Building from recent works in the philosophy of logic, this paper argues that these formalizations of induction are best viewed as models and not literal descriptions of inductive inferences in science. Three arguments are put forward to support this claim. First, I argue that inductive support is the kind of phenomenon that can be justifiably modeled. Second, I argue that these formalizations have the features that define models—that they have representors, artefacts, and idealizations. Third, I argue that these formalizations being models explains their plurality and revisability.

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Notes

  1. The terms ‘confirmation,’ ‘inductive support,’ ‘induction,’ and ‘inductive inference’ will be used almost interchangeably in this paper. They are of course different but related notions. ‘To confirm’ could be construed as synonymous to ‘to lend inductive support’. Moreover, the mental or psychological process of lending inductive support to a scientific theory is called induction or inductive inference. To be consistent, I will mostly employ the terms ‘inductive support,’ ‘induction,’ and ‘inductive inference’ instead of ‘confirmation’.

  2. For an in-depth discussion of these two senses of formality, see Dutilh-Novaes (2011).

  3. Given this, I will refer to these formalizations as formal schemas of induction beginning in Sect. 2.

  4. The summary is largely informed by Cook (2002).

  5. For a discussion of the desideratum of accuracy in the context of the sciences, see Chapter 6 of Weisberg (2013). For its discussion in the context of logic, see Baumgartner and Lampert (2008).

  6. This formulation of the desideratum of fruitfulness is informed by the discussion of Kitcher (2008) and Pinder (2022).

  7. Sharpening or precisification is a term of art used by philosophers to refer to the activity of making an inexact or imprecise concept (due to vagueness, indeterminacy, polysemy, etc.) more exact or precise. See Keefe (2014, p. 1378).

  8. To forestall misunderstanding, it should be noted that this claim is predicated on the traditional view of concepts which typically construe concepts as “beliefs about the concept’s referent” or as “representations of phenomena” (Brigandt & Rosario, 2020, pp. 102). This is why I take the polysemy, and hence the complexity, of the concept of inductive support as evidence or indication of the complexity of the phenomenon of inductive inference itself.

  9. I remain neutral on the issue of whether polysemous concepts require the stronger activities of improvement and replacement.

  10. To simplify the prose, I will drop the qualification ‘parameterized’ and continue to say that these intuitive notions are the target systems of these formal schemas. But when saying that, I should be construed as referring to their parameterized versions.

  11. The ceteris paribus clause here is meant to signal the fact that the admissibility of these formal schemas still depends on their satisfaction of the desiderata of adequacy discussed in Sect. 2. So, admissibility here should be understood as admissibility on account of the legitimacy of their target system.

  12. Bielik (2018) arrives at the same conclusion.

  13. I recognize that their admissibility still depends on how well they fair in the other desideratum of adequacy (e.g., accuracy, simplicity, and exactness). But if we accept, as many model-builders do, that fruitfulness is the primary desideratum of adequacy, then a plurality of models would still be expected.

  14. These arguments take inspiration from Russell’s reconstruction of purported arguments for the normativity of logic. See Russell (2020).

  15. This seems to be the upshot of the so called ‘accuracy’ argument provided by Joyce (1998) and Pettigrew (2016). This argument purports to show that agents who violate probabilism, and so logical omniscience, have less accurate attitudes compared to those who conform to probabilism.

  16. This argument closely follows Russell’s reconstruction of the argument from error for the normativity of logic. See Russell (2020).

  17. These various senses of the term ‘model’ are discussed by Thomson-Jones (2006, 2012).

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Acknowledgements

My gratitude goes to my teachers and colleagues Kelly Louise Rexzy P. Agra, Ben Carlo N. Atim, Romulo T. Bañares, Karen D. De Castro, Gerald Pio M. Franco, Zosimo E. Lee, Julius D. Mendoza, Olivia Mendoza-Santos, Narcisa Paredes-Canilao, and Franz Joseph C. Yoshiy II for very helpful comments on earlier versions of this paper. My thanks also goes to two anonymous referees whose comments and suggestions greatly improved this paper. I dedicate this first publication of mine to my family and my Balaysian and UP junior faculty friends. Their company, support, and unconditional love made this work possible.

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  1. Department of History and Philosophy, College of Social Sciences, University of the Philippines-Baguio, Baguio City, Philippines

    Vlademire Kevin D. Bumatay

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Bumatay, V.K.D. Formal schemas of induction as models. Synthese 200, 470 (2022). https://doi.org/10.1007/s11229-022-03921-6

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