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Active Inference and Abduction


The background target of the research going into the present article is to forge an intellectual alliance between, on the one hand, active inference and the free-energy principle (FEP), and on the other, Charles S. Peirce’s theory of semiotics and pragmatism. In the present paper, the focus is on the allegiance between the nomenclatures of active and abductive inferences as the proper place to begin reaching at that wider target. The paper outlines the key conceptual elements involved in a naturalistic rendering of Peirce’s late semiotic and logical notion of abductive reasoning. The target is a cognitive-biological model of abduction which preserves the functional integrity of an organism and fulfils the existential imperative for living beings’ evidence of existence. Such a model is an adaptation of Peirce’s late logical schema of abduction proposed in his largely unpublished works during the early 20th century. The proposed model is argued to be a feasible sketch also of recent breakthroughs in computational (sensu Bayesian) cognitive science.

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  1. Let us discharge a potential circularity worry from the get-go, namely that Peirce’s theory of inquiry is validated by scientific facts, and that this would come around to a scientific assertion of the Free Energy Principle and the relationship of FEP to abduction and to the other types of reasoning of induction and deduction, while a criticism of the Free Energy Principle is that its veracity or validity cannot be tested scientifically: “if principles must be falsifiable to be scientific and FEP is unfalsifiable, then FEP is not a scientific principle” (Colombo, 2018: 22). We thank the reviewer for raising this point; our response is, in brief, threefold. First, FEP is formulated as a mathematical principle applied to neurobiology, among other fields of current and prospected future applications. Mathematical propositions do not draw their validity from the requirement of being experimentally testable yet do not cease to be part of science. Second, any uncriticed application of Popper’s falsifiability criterion to scientific propositions both over- and undergenerates and hence would miss the intended target. Accordingly, we would prefer to frame the critical issue of the FEP’s validity in terms of Peirce’s fallibilism with Isaac Levi’s corrigibilism (Levi, 1991), and not falsifiability. Third, Peirce’s three stages of the logic of science (abduction-deduction-induction) is validated, and in a non-trivial way, both by these modes of reasoning themselves as well as by their interconnectedness, as described in detail in Pietarinen and Bellucci (2014). For example, if the proposed justification of abduction holds, and if its naturalised form indeed is active inference as we currently propose, then the leading principle of the latter has ipso facto been validated.

  2. Agents that perform inference are active inquirers situated and evolved in the world throughout the evolutionary history of the universe. Thus speaking of ‘scientists’ and ‘organisms’ interchangeably, such as by the common term of an ‘agent’, is not sloppy language or a category mistake; differences in meaning between the two extremities are differences of emphasis and ways of seeing. We thank the reviewer for raising this worry. One can conceive a ‘scientist’ in its widest terms as any organism that has the highest degree of exposure to doubt, random variables and objective chance, yielding the highest degree of sophistication in the hierarchies of its active inferences, and with supreme analytic powers that constitute its generative self-model.

  3. The reference R is to Peirce (1967) by the Robin manuscript number. The reference NEM is to Peirce (1976) by volume and page number.

  4. Indeed all thought is embodied in signs, according to Peirce: “That which is communicated from the Object through the Sign to the Interpretant is a Form; that is to say, it is nothing like as existent, but is a power, is the fact that something would happen under certain conditions. This Form is really embodied in the object, meaning that the conditional relation which constitutes the form is true of the Form as it is in the Object. In the Sign it is embodied only in a representative sense, meaning that whether by virtue of some real modification of the Sign, or otherwise, the Sign becomes endowed with the power of communicating it to an Interpretant” (R 793, c.1906). A thought is also an enactment, given that “a thought is a cognition and therefore a sign” (R 499(s), 1906; LF 3), and that “a Thought, being of the nature of a Representation, cannot be ‘present’ to consciousness. A thought is something that has to be enacted, and until it is enacted, its meaning has not been given, even to itself” (R 478, 1903; LF 2/2).

  5. Relatedly, Peirce defined thought as a variety (generality) of signs, which obtains in the universe whether embodied in the mind (or its generalisation or quasi-minds): “A thought is not per se in any mind or quasi-mind. I mean this in the same sense as I might say that Right or Truth would remain what they are though they were not embodied, and though nothing were right or true. But a thought, to gain any active mode of being must be embodied in a sign. A thought is a special variety of sign” (Peirce to Victoria Welby, March 9, 1906, R L(etter) 484; LF 3). The term “quasi-mind” is of particular importance as it emphasises the continuous, synechistic nature of the organism and its sub-units “welding” into the environment by the exchange of information, along the lines of the properties of Friston blankets: “This quasi-mind is itself a sign, a determinable sign” (ibid.), possessing the three necessary characteristics: the “special qualities of susceptibility, or possibility of determination … be subject to reactions, each of which is an actual event, happening once and never again … [and have] in the third place, dispositions and habits” (R 283(s), 1906; LF 3).

  6. Some notable exceptions include Bellucci (2018); Hookway (2003); Kruijff (2005); Niño (2007); Bellucci and Pietarinen (2020); Pietarinen (2020).

  7. The reference LF is to Peirce (2019–2021) by volume number.

  8. Reference CP is to Peirce (1931–1958) by volume and paragraph number.

  9. Some other proposals to naturalise Peirce’s sign triad as a property of adaptive open systems have been Kilstrup (2015); Herrmann-Pillath and Salthe (2010), Pietarinen (2004).

  10. We thank the reviewer’s pressing the point of the discrepancy between Bayesian and frequentist interpretations. Let us also appeal to the fact that Peirce’s logical approach to fundamental assumptions of science, including his tychism, echoes the spirit of Jaynes (1995/2003: xii), who wrote: “[N]either the Bayesian nor the frequentist approach is universally applicable, so in the present more general work we take a broader view of things. Our theme is simply: Probability Theory as Extended Logic. The ‘new’ perception amounts to the recognition that the mathematical rules of probability theory are not merely rules for calculating frequencies of ‘random variables’; they are also the unique consistent rules for conducting inference (i.e. plausible reasoning) of any kind”. Yes, this sounds quite right, especially when including “abductive reasoning” as the reasoning class of such plausible reasoning, we might add.

  11. Cf. R 318 (1907) on what Peirce around 1906 began eloquently as downregulation of cognition to descriptions in terms of “quasi-minds” (LF 3). One may feel these akin to proto-cognitions and proto-biosemiotics in modern terms, as in Sharov and Vehkavaara (2015).

  12. Synechism, we emphasise, is to be rightly interpreted in terms of (non-epistemic) scientific values, instead of as an ontological doctrine (Chiffi & Pietarinen, 2017). As a scientific value, it stands on equal methodological footing with the economy of research, tychism, and pragmaticism: If you cannot find integers in Schrödinger’s equation, put them on hold. Relatedly, the notion of the quasi-mind or proto-cognition refers to a collective, rather than a singular instance or a unit of biosemiotic information processing.

  13. An alternative avenue not pursued in the present paper due to lack of space is to interpret the abductive conclusion along the lines of practical syllogism, and the related modes of the conclusion in terms of the STIT-logic that analyses ways in which agents can orient themselves among the futures by eliminating certain possibilities (STIT refers to the logic of action involving the modality of ‘see-to-it-that’; see Belnap et al., 2001).

  14. Here the distinction between proto- and eusemiosis (Sharov & Vehkavaara, 2015) may provide to be a useful distinction, bearing in mind that those terms (objectless sign manipulation in terms of quali-sin-legisigns vs. the full non-degenerate sign-object-interpretant triads) refer to the two ends in what may be a continuum of endlessly scalable cognitions.

  15. A clarification of the term ‘ambiguity’ is to not restrict its meaning to lexical ambiguity in the standard linguistic sense. It also refers to semantic, pragmatic and action-oriented sources of ambiguities, which are to be identified and resolved through repeated uses of one’s conceptual resources across novel, interactive and communicational contexts. In contrast to risk, then, ambiguity concerns uncertainty, vagueness and unknown events.

  16. The reference EP is to Peirce (1998) by volume and page number.

  17. It is fashionable in science policy circles to talk (and to measure) about the “impact” of one’s scientific projects; what Peirce is telling is that the real impact of science is the impact of hypotheses upon other, new and emerging hypotheses, which in turn yields better and more refined science and greater reduction of uncertainty. What matters is the webbing of slightly different research questions and the diversity of meanings, often subtle, of the questions asked. Investing on the same sort of research to be pursued in laboratories across the world would not only be uneconomical but positively harmful, as that would increase competition and bias (such as the Winner’s curse) and surge the false discovery rates. “What a world of futile controversy and of confused experimentation might have been saved”, Peirce adds to his discussion of the quality of caution, “if this principle had guided investigations…!” (EP 2:109).

  18. The reference RLT is to Peirce (1992).

  19. As argued in (Pietarinen & Issayeva, 2019), Peirce’s theory of signs may be viewed as a general theory of cognition which is neither internalist nor externalist concerning the meanings of mental representations. These conclusions resonate quite well with the modern synthesis in contemporary cognitive sciences that has reckoned issues such as embodiment of thoughts, enactment, as well as the fancied and unreal nature of the self and agency formation as some of the central concerns.

  20. Here Dewey’s student George Herbert Mead’s elaboration of the collective as the primary unit is particularly noteworthy. Phenomena such as symbiosis and reciprocal and gradidient multi-scale intergration (Sims, 2020) appears as biological evidence for (take, for instance, polychate formations) these early pragmatistic and sociological arguments for ‘group cognition’.


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One of the authors (Pietarinen) acknowledges that the article is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University) and the Tallinn University of Technology grant SSGF21021. We both thank Karl Friston for his comments on an early version and we thank the reviewers of Biosemiotics for their helpful comments and suggestions.

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Pietarinen, AV., Beni, M.D. Active Inference and Abduction. Biosemiotics 14, 499–517 (2021).

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  • Abduction
  • Active inference
  • Free-energy principle
  • Friston blanket
  • Triadic relations
  • Peirce