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Abductive inference within a pragmatic framework

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Abstract

This paper presents an enrichment of the Gabbay–Woods schema of Peirce’s 1903 logical form of abduction with illocutionary acts, drawing from logic for pragmatics and its resources to model justified assertions. It analyses the enriched schema and puts it into the perspective of Peirce’s logic and philosophy.

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Notes

  1. We can safely ignore the IBE-accounts, as they are not what Peirce means by abduction (Campos 2011; Mcauliffe 2015).

  2. Applications of \(\mathsf {LP}\) to philosophical questions are provided in Carrara et al. (2017a, b), Carrara and Chiffi (2014), Carrara et al. (2014). See Bellucci and Pietarinen (2017) on Peirce on the logic of assertions.

  3. The contrary does not hold: “The absence of assertibility is not assertibility of absence”.

  4. A variety of standards of evidence is used, for instance, in legal argumentation, namely: scintilla of evidence, preponderance of evidence, clear and convincing evidence, beyond reasonable doubt. See Gordon and Walton (2009). Scintilla of evidence means any form of weak and indirect evidence.

  5. Further extensions of \(\mathsf {LP}\) are given in Bellin (2014), Bellin et al. (2014, 2015).

  6. Considerations of different weights of evidence to refute or cause doubt on different kinds of hypotheses are not taken into account.

  7. That is, by this comparative we mean the justifiability iff we are more justified in doubting k rather than in believing it, after a duly consideration of total evidence. A closely related notion would be to think of the justifiability of the former as less compelling than the justifiability of the latter.

  8. We assume that \(\kappa _1\) and \(\kappa _2\) are independent, uncorrelated formulæ. Otherwise adjoining them might yield misleading predictions.

  9. The idea here is that the agent keeps an open mind, as evidence may easily get reinterpreted.

  10. For instance, we may want to be able to reason about plausibility of hypotheses. Unlike probability, plausibility measures are not required to be additive, among other things.

  11. When unnecessary, the indication of the justification function will be omitted.

  12. Similar modal translations have been recently analyzed by Shramko (2005, 2016).

  13. See Ma and Pietarinen (2015, 2017) for a logical elaboration of Peirce’s later, interrogative schemas of abduction, and Pietarinen and Bellucci (2014) on retroduction.

  14. The G–W schema is intended to replace what may be called the standard schema for abduction, since the previous standard (or obsolete) schemas were not able to handle the requisite features of Peirce’s abductive reasoning, such as subjunctive conditions. On the details of this line of criticism, see Woods (2012, 2013, pp. 366–377), Pietarinen (2014).

  15. “C(H) is read ‘it is justified (or reasonable to) conjecture that H’ ” (Gabbay and Woods 2005, p. 47).

  16. Here we can notice the germs of illocutionary force that are present in the original formulation of the G–W schema. But they have not been made explicit, let alone incorporated into the logical schema.

  17. There are some variations and renditions of the standard schematism. For example, for an interpretation of the G–W schema in dialogical logic see Barés Gómez and Fontaine (2017).

  18. The word “fact” occurs in the G–W schema and it is intended to indicate (in a general sense) those conditions that hypotheses should meet in reality.

  19. Since in Step 8 the conditional is in a subjunctive mood it may strike one as an epistemic variant of doxastic adherence conditions, such as “If p were true, the subject would believe that p”, as used by Nozick (1981) in his tracking theory of knowledge, for example. In Nozick’s analysis of knowledge, there is also the sensitivity condition, which states that “If p weren’t true, the subject wouldn’t believe that p. But as soon as we consider an epistemic variant of the sensitivity condition in the abductive schema, as something like \((8^{\S })\)\(\lnot H\rightsquigarrow \lnot (R(K(H), T))\), we notice that the clause \((8^{\S })\) now states that if H were untrue, then the epistemic goal would be attained when K is revised upon the addition of H. In \((8^{\S })\), when we say that “if H were untrue”, it is not clear whether it is the act of hypothesizing or the content of the hypothesis that is to be rejected. The formalism used in the schema does not clearly distinguish the propositional content from the illocutionary force of the hypothesis. At any rate, neither reading yields any principle relevant for abductive inference. Thus, unlike what happens in Nozick’s tracking theory of knowledge it is not fruitful to have anything like (an epistemic version of) the sensitivity condition in the G–W schema. Nozick’s tracking theory is intended to suggest a certain analysis of knowledge, while abduction is an ignorance-preserving or mitigation procedure related to presumptive forms of reasoning. It is thus reasonable and natural to think that the two have very different epistemic and formal properties.

  20. Peirce tells that synechism is a “synthesis of tychism and of pragmatism” (Pietarinen 2015). This is worth a good notice. Pragmatism, in turn, concerns the significance of “what can become actual” (MS 280; Pietarinen 2008).

  21. Peirce wrote to F. A. Woods (6 November 1913): “I think logicians should have two principle aims: First, to bring out the amount and kind of security (approach to certainty) of each kind of reasoning, and second, to bring out the possible and esperable uberty, or value in productiveness, of each kind”.

  22. There are other important and related considerations which we cannot take up in the present context, such as the fundamental question of the justification of abduction. Although this matter is related to the discussion of scientific values, the justification concerns the leading principles of abduction—that nature is explainable—and although value-laden we need not go further in that topic in the present context.

  23. See Searle and Vanderveeken (2005) on formalizing speech acts and illocutionary forces, and (Bellucci 2018) for a detailed exposition of how various speech acts arise from Peirce’s later classification of signs.

  24. From a pragmatic perspective, a justified conjecture expresses the possibility that a propositional content may be asserted (see e.g. Bellin 2014). This may be too weak, since the conclusion of the abductive schema is not only that something may be the case, nor that we would have gained some confidence to assert that possibility, but that there really is further content in the conclusion to justify why it would be worth engaging in further investigation of that promise. In Peirce’s terms, such hypotheses are “investigands” (Ma and Pietarinen 2017; Peirce 1905). They are connected to Peirce’s theory of the economy of research.

  25. There is an important update process going on here. For an elaboration of this and the adjacent steps, see Ma and Pietarinen (2017), which sets the abductive process within the framework of dynamic epistemic logic for sub-beliefs, using a modification of neighborhood semantics.

  26. For a brilliant discussion on abduction in relation and contradistinction to theories of knowledge, see Woods (2017).

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Acknowledgements

The authors thank the anonymous reviewers of the present journal for their invaluable comments and suggestions. An early version of the paper was presented at the workshop Explanatory Practices: Interaction, Dialogues, and Cognitive Processes, University of Lisbon. We thank Tommaso Bertolotti, Matthieu Fontaine, Cristina Barés Gómez, Angel Nepomuceno, Gonçalo Santos and all the other speakers in the workshop.

Funding

The work of the Daniele Chiffi is supported by the Portuguese Foundation for Science and Technology, project (PTDC/MHC-FIL/0521/2014; PI: E. Rast). The work of the Ahti-Veikko Pietarinen is supported by the Estonian Research Council (PUT 1305, Abduction in the Age of Fundamental Uncertainty; PI: A.-V. Pietarinen).

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Authors and Affiliations

  1. Faculdade de Ciências Sociais e Humana, IFILNOVA Institute of Philosophy, Universidade Nova de Lisboa, Av. de Berna, 26-C, 1069-061, Lisbon, Portugal

    Daniele Chiffi

  2. Ragnar Nurkse Department of Innovation and Governance, Tallinn University of Technology, Akadeemia tee 3, 12618, Tallinn, Estonia

    Daniele Chiffi & Ahti-Veikko Pietarinen

  3. School of Humanities and Social Sciences, Nazarbayev University, Block 8, Room 8.201 - Kabanbay Batyr Ave., 53, Astana, Republic of Kazakhstan, 010000

    Ahti-Veikko Pietarinen

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  1. Daniele Chiffi
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Correspondence to Daniele Chiffi.

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Chiffi, D., Pietarinen, AV. Abductive inference within a pragmatic framework. Synthese 197, 2507–2523 (2020). https://doi.org/10.1007/s11229-018-1824-6

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