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Active Inference and Abduction
Active Inference and Abduction
Majid D. Beni,
Tallinn University of Technology, Tallinn, Estonia
Middle East Technical University AQ2 , Ankara, Turkey
Received: 12 June 2020 / Accepted: 28 April 2021
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unpublished works during the early 20th century.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.
This paper outlines the key conceptual elements involved in a naturalistic rendering
of Charles S. Peirce’s late semiotic and logical notion of abductive reasoning. The
target is a naturalistic, biological model of abduction, which preserves the
functional integrity of an organism and fulfils the evolutionary imperative for living
being’s evidence of existence. Such a model is also a cognitively and
computationally feasible adaptation of Peirce’s late logical schema of abduction, as
he came to propose it in his largely unpublished works during the early 20th
The sketch of the model is feasible not only within the context of Peirce’s work, but
also against the backgrounds of recent breakthroughs in computational
neuroscience, as will be argued in the present paper. This larger goal, which can
only be achieved in a very sketchy fashion in the present paper, is to forge an
intellectual alliance between active inference under the free-energy principle (FEP)
on the one hand, and Peirce’s theory of semiotics and pragmati(ci)sm on the other.
Here the focus is on the allegiance between the nomenclatures of active and of
abductive inferences, which seems to us the proper place to begin reaching out for
such wider objectives of the present mission.
There are two parts in the proposed theoretical integration of the two nomenclatures
to be accomplished, one new and one old, concerning the fundamental status of the
models of active and of scientific inference and inquiry. On the one hand, there is
the modern variational Free Energy Principle (FEP) and its guidance of the process
of reasoning which in the current literature is termed active inference (Friston,
2010). On the other hand, one also needs to gather a historically accurate and
precise interpretation of the guiding principles of abductive inferences, including its
important component of the economy of research, which is consistent with FEP and
its corollary process theory of active inference, or so do we argue. The success of
such a merger would be, as presented here, evidence for the naturalised account of
Variational Free Energy which is at issue in the Free Energy Principle (FEP) is an
information-theoretic measure that sets an upper bound on the marginal likelihood
or evidence of one’s own existence. Karl Friston and coauthors have stated FEP in
its new guise (Friston et al., 2006; Friston, 2010), while the principle itself has its
roots in Hermann von Helmholtz’ research on the neurophysiology of perception
and even in the ideas of Immanuel Kant (Swanson, 2016). The general insight is
that the organism actively garners evidence for its own existence (Hohwy, 2014). In
addition to its connections with the Bayesian Brain Theory and Predictive Coding,
FEP is also receives strong theoretical support from theoretical biology. This is
because its theoretical framework is developed along the lines of autopoiesis in
biology. For, in order to state in non-equilibirum steady state with its environment,
the organism must regulate its internal entropy. This has been formally
characterised in terms of Markov blankets. The Markov blanket of a node consists
of its parents, its children, and co-parents of its children, and the blanket itself is
divided into active states and sensory states. Markov blankets state conditional
independence between the organism’s external states (in Sebeosque terms,
described from the endosemiotic perspective) and internal states (described from
the exosemiotic perspective). This speaks directly to the idea of active inference,
given that regulation of the entropy of internal states takes place via the interaction
between sensory states and active states of Markov blankets. Active states minimise
free energy and thus define the optimisation protocol for model evidence. Active
states are not directly influenced by external states, and they are conditionally
independent of external states but can be affected by sensory states that are
independent of internal states. In living forms, active states have the capacity of
changing the external states.
According to recent interpretations of FEP, the dynamical interaction of living
systems and the external world under active inference can be interpreted
semantically, (Ramstead et al., 2020) by assuming that sensory states are
meaningful representations of the reality. This is especially the case if we assume
that the development of Markov blankets by Friston (now yclept Friston blankets,
cf. Bruineberg et al., 2020), unlike their original characterisation in works of Judea
Pearl on probabilistic causal networks (Pearl, 1988), admit of a realist interpretation
of the relationship between the organism and the environment. While the role of the
concepts of Markov blanket (and Pearl blankets) in many treatments of the free-
energy principle is an instrumentalist one – or as in Peirce’s even stronger terms
concede to a nominalist interpretation of their meaning – Friston blankets are realist
not only in the non-instrumentalist sense but also in the sense of being non-
nominalist entities: the modal terms of references to real possibilities (such as what
is conceivable, or produced by imagination, or anticipatorily related to the future
states of affairs) are used in making sense of the key aspects of the theory. As we
will argue in this paper, FEP has been put at the centre of a viable picture of an
organism’s insights into the consequences of its action and its ability to choose the
best or most efficient strategies that contribute to the fulfilment of best possible
Without insisting on any ultimate accuracy of our interpretation, we observe that
there is a promising similarity between the seminal ideas behind FEP and some of
Peirce’s foregoing and prefatory remarks. Moreover, as observed already in von
Helmholtz’ early research, perception is a form of inference. Peirce would talk on
“our senses as reasoning machines” (R 1101, in NEM 2:1114–1115; cf. R 831).
One can restate these ideas in contemporary terms of living systems inferring in
enactive and embodied manners: their model of the active inference can change the
external states. What is more, they can change the external states in an
anticipatory manner (Chiffi et al., 2020). The model of active inferences
accommodates conditional expectations (likelihoods of the hypothesis on evidence)
of what the future states would or could be like, given the evidence accumulated in
their model, but also occasionally venturing beyond the mere data that such models
have harvested at any particular gradient of time. Not only are there expectations
about future states; organisms can actually find better ways of choosing the policies
that satisfy the fulfillment of their expectations in the future. The conclusion of
active inference is a conjecture about the feasibility of adopting certain strategy
profiles that the organism entertains over time integrals. Expressed in the linguistic
form of our natural language, the anticipatory conditional states that, “If I were to
exist in the next state, then I would display certain classes of properties…” Such
statements now involve reference to real possibilities of what would, could, or
might be the case in the states of affairs that are conceivable for the agent. This
analysis has been backed up by a viable evolutionary story in the context of FEP.
Active Inference in the Light of Abduction
Peirce’s notion of abduction concerns the agent’s faculties of conjecture-making
under a system of (weak) beliefs and their revisions that the agent is able to garner
in a given situation or model of its environment. In science, Peircean abduction can
be likened to what the logic of discovery of scientific hypotheses looks like, with
the cautionary remark than no full assimilation is to be had of Peircean abduction to
IBE, that is, to inference to the best explanation (Pietarinen, 2015). Though Peirce’s
search for the logical notion of abduction was an ambitious work-in-progress
throughout his life, his late formulations after 1903 are those he was most satisfied
with. Yet those later notions have been in the secondary literature the least
We take as our model of comparison Peirce’s 1905 formulation of abduction and its
proposed inferential schema. In brief, the schema captures “Reasoning from
surprise to inquiry” (Ma & Pietarinen 2016, 2017; LF 3). As such, it portrays
retroduction: “given a (surprising) fact C, if A (subjunctively) implies C, then it is
to be inquired whether A plausibly holds”. Like abduction elsewhere in his
writings, this late schema begins with an observation of a surprising fact or event
(or, as in experimental research is usually the case, an event class), and through a
conditional major premise concludes in a ‘co-hortative’ mood which Peirce termed
“the investigand”, namely that something of imperative importance ought to be
done, initially aroused by curiosity that leads to the formulation of a question. Ma
and Pietarinen (2016: 74) state this in the following terms:
The important discovery is that … the conclusion is presented in a
kind of interrogative mood. But the interrogative mood does not
merely mean that a question is raised. In fact, it means that the
possible conjecture A becomes the subject of inquiry: the purpose is
to determine whether that A is indeed plausible or not. Peirce termed
such mood “the investigand mood”. Hence abduction can be viewed
as the dynamic process toward a plausible conjecture and,
ultimately, toward a limited set of the most plausible conjectures.
Peirce wanted to characterise abduction (retroduction) in ways that would avoid
earlier conflations of it with induction (and with IBE, see e.g. Seth 2015 for an
example of this persistent conflation). He also desired to achieve a more nuanced
expression of its logical, linguistic and semiotic forms than was possible with the
rough sketch of it in his 1903 Harvard Lectures (Pietarinen, 2020). For one, Peirce
added the ‘investigand mood’ to qualify how abduction’s conclusion is to be
asserted (and to strengthen it away from concluding merely possibilities, the ‘may-
bes’; on this see Chiffi and Pietarinen, 2020). He then further classified that mood
in his late semiotic schemas of the classification of the signs that included a number
of speech-act modalities (Bellucci, 2017; Pietarinen, 2006). Unfortunately, that
rough sketch from 1903 has dominated the secondary literature to date, while the
later forms, especially those of 1905–1907 and occasionally beyond, have eluded
Peirce also sought to embed the important qualities of the economy of research (as
non-epistemic values) into its logical form (Chiffi & Pietarinen, 2017, 2019). We
will take up the issue of the economy of research in the next section; currently, the
three main conceptual transitions from active to abductive inferences that we
propose are as follows (A-C).
(A) The boundaries of organisms characterised as Markov blankets – or rather
their realist interpretation as Friston blankets – have a markedly Peircean,
irreducibly triadic form. The boundary itself is a mediator between the
agent’s external and internal states. It provides the form of how information
flows from external to internal states, with the resulting changes in the
‘belief’ system of the agents concerning its hypotheses, which as Peirce
notes are accepted “on probabtion” (CP 6.525, 1913), namely on what the
external changes may turn out to be in the future. We map this idea onto a
conceptualisation of the entity’s boundaries as Friston blankets. This
restatementallows us to regiment the agent’s beliefs about the environment
and to model the mechanisms of updating such beliefs. Now the inverse
influence takes place in another triadic form associated with the blanket
triad, namely the agent’s active states now mediating between the sensory
states and the external states. Active states influence and modify the external
states in this way, through the input from sensory states. Importantly, the two
triads are interlocked through their external states, forming a continuous
merger of two triads into one, along the lines of how interpretants are
mediating signs in another triad of signs in Peirce’s semiotics (until, that is, a
habit-change occurs and the process of semiosis terminates on final or
ultimate logical interpretants). In this way, the concept of Friston blanket
receives a full, intensional meaning: there is thirdness which is exhibited not
only in sensorimotor loops between agents and environments (which would
be Peirce’s secondness or degenerative thirdness), but between agents,
environments, and the projections of what those looped relationships might
look like in the future. By speaking of the intensional meaning of Friston
blankets, we propse an initial expansion on the extant semantic interpretation
of FEP; future research is needed to explore the proposal further.
Essentially, it is this realist interpretation of Friston blankets which agrees
with the triadic forms of signs in Peirce’s equally realist philosophy of
science. It in fact does so the strong sense of realism, namely what Peirce
termed ‘scholastic’ realism, as will be referenced below. In this way, we can
preliminarily argue how some of the most potent cross-disciplinary modern
approaches to life sciences (namely FEP and Friston blankets) and the
pioneering theory of semiotics, Peirce’s theory of signs, can be made to
increasingly agree with each other at the fundamental theoretical and
conceptual senses of agreement.
What is more, we receive a broadening of the core idea of Friston blankets in
its interpretation of random variables (within the orthodox Bayesian
probabilities conceived as degrees of belief), into a stochastic notion that
may appear in various guises: empirical, elementary, complex or objective
random variables, among others (see Mumford, 2000). Peirce’s frequentist
view articulated them from the perspective of tychism: randomness (and
random variables in particular) are the real phenomenon of the world,
embedded into the patterns of objective relationships to be revealed by the
analysis of the logic of science. An important addendum is also to note that,
although FEP has commonly been related to the family of Bayesian theories,
this is no theoretical necessity: its formal framework may be construed in
terms of statistical frequencies, or else incorporated into an entropy-based
framework altogether (see Mani 2018b for details), thus easing the tensions
when facing a forced choice between frequentism or Bayesianing on this
(B) In order to count as an inference proper, there need to be leading principles
of reasoning which constrains and guids the agent’s reasoning processes.
Without such leading or guiding principles, the model would capture at most
non-deliberate, instinctive and random thought-associations between mental
events, not the premise-conclusion-bound ratiocination taking place in
embodied reason (Bellucci & Pietarinen, 2017). The leading principles of
abduction are, for Peirce, that the nature is explainable, that is, it is possible
to find out what the law-like principles are that govern the behavior of the
processes in the reality. The nature is explainable, in turn, because the mind
has evolved in attunement with nature over the long, evolutionary and
cosmological history of the development of the universe. In general, the
leading principles as such habits of reasoning constitute the scaffolding upon
which the justification of a particular class of such inferences is justified
(Bellucci & Pietarinen, 2020).
Now, what is the leading principle of active inferences, then? How do we
ascertain that they account for the phenomena as inferences? Active
inferences track gradient flow of information valued as its surprisal quantity.
Surprisal is another name for free energy, which is the (negative) log
probability of an outcome. A fish out of water finds itself in a surprising
state (Friston, 2010). Such surprises need to be avoided. This means that the
organism is better to remain in non-equilibrium steady states by mitigating
the presence of surprisal, say, by looking for their hidden causes from the
observed effects. This speaks directly to the idea of gradient flow, because it
means that in order to survive the organism must remain in a limited number
of states. And this, in turn, speaks directly to the Peircean idea of habits of
action as decision rules by which the ranges of possible states of information
are constrained and updated.
The justification of active inference is thus the justification of abduction,
too: the fact that the mind of an organism is a semiotic factory of signs that
has evolved in affinity with its environment sufficiently justifies a reliance
on that form of inference. In this view, an organism is not a rule-following
machine whose behavior emerged from following the instructions of its
genetic blueprint. Rather, it is the error-correcting and reaching-out for some
new and emergent homeostatic set-points that constitute the driving
methodologies of living systems. There has to be generalisability in its habits
of action: when something goes awry, the genomic blueprint is not the
primary place to look for advice or solution protocols. What organisms are
particularly good at is to not only predict the states of their environment but
to predict (or to ‘conceive’ and ‘imagine’, again in the appropriately
downregulated sense of these terms) themselves as inhabiting those future
environments: that is, to minimise the delta-error or discrepancy between
what their configurations are now and what they remember them to have
been or expect them to become in the future in terms of an abductively
guided guesswork. The latter takes place together with the help of the
modalities of what can be conceived and imagined in various parts of the
organism’s neural, perceptual and cognitive systems. There needs to be,
again, some proper scaling-down of the meanings of ‘mentality’ and
‘consciousness’ here, given the presence of a range of organisms that can
display a great variety of multi-scale behaviour. The references to “mentality
of organisms” is just a Peircean “sop to Cerberus” (R 318, 1907) to make the
goal and purpose-driven endeavours of living beings better understood.
In Peirce’s works, the affinity of the mind with the evolutionary history of
the universe may nevertheless be appreciated in the sense of his thesis of
synechism, which Peirce once expressed in the panpsychism-resounding
terms borrowed from Friedrich von Schiller, such as that “matter is effete
mind” (CP 8:106, 1891) which is “hidebound with habits” (CP 6:158, 1892).
Construing Friston blankets in terms of triadic relationships (signs-objects-
interpretants) leads to unexplored semantic possibilities; as here argued a
semiotic explication of some such age-old ideas that have a marked
synechistic flavor, namely what it means that organisms and their sub-units
may ‘blend’ into their environment, which we explicate by the presence of
interrelated triadic structures. The mediated (or represented) distinction
between the internal (neuronal-cognitive-perceptual) and external
(situational) states is, in turn, mediated (or represented) by a mediated
relation between active and sensory states. This speaks to the idea of Friston
blankets instantiating conditional independencies between internal and
external states of the complex system.
(C) In formal expressions of abductive schemas of inference, it is important to
interpret the second, major premise in non-indicative conditional form. FEP
typically portrays the existential imperative as an indicative conditional (“If I
am to exist, then I better display certain properties”). To get abduction going,
however, the generalisation of the schema’s major premise to subjunctives
becomes a useful, and a nearly evident manoeuvre for an agent to entertain
and perform. In the generative model, its state representations should reflect
the corresponding generalisation, and have I say to myself: “If I were to
exist, then I would need to display certain properties”. This speaks directly to
the general insight behind FEP, namely the main tenet that organisms are in
the business of finding evidence for their own existence, not necessarily in
actu but also in terms of what could, would or might constitute such
evidence in the future states of affairs.
Thus in any individual case of abduction, in which some surprisal quantity Y
(free energy) is given as the minor premise, the second premise is to be
reformulated as a subjunctive conditional: “If X were to be the case, then the
cessation of Y would be the matter of course”. From this, the abductive
conclusion is conjectured as practical guidance: “Let me see to it that X is to
be part of my generative model”. Generative models are sets of the
likelihood of data given their causes (Friston, 2010). From the perspective
FEP, cognition and perception commence from generative models that are
formed at the top levels of the computational architecture of cognition and
perception, and perception mainly consists of the attempt at explaining away
the data in generative models by minimising the discrepancy between
generative models and actual inputs at different levels of the hierarchy. In
other words, cognition and perception consist of minimising prediction errors
(aka surprisal) and thereby enhancing the fit between the expectations and
their target systems. Or, as expressed in the “investigand” mood: “Is X part
of my generative model? Let me investigate!” In other words, the agent’s
(weak) belief of X about its external states is incorporated into that agent’s
generative model as a conclusion of these inferences.
The importance of (C) is that we can now recover a realist position on FEP
through abductions of this sort: models are conceived as real possibilities
that could, would or might be the case in the future. Those possibilities are
part of the objective reality in the same sense in which the possibility of
raising my hand or rolling six on the throw of the dice is real, even when the
time comes such eventualities do not come to pass. Peirce epitomised his
version of realism as “the possible is what can become actual” (R 288, 1905;
Pietarinen, 2008) and came to advocate this version in his mature philosophy
as the proper pragmatistic (or “scholastic”/“scotistic”) restatement of realism
(Lane, 2019; Pietarinen, 2014).
This viewpoint is, we believe, readily implicit in the FEP’s definition of
internal states, which encode beliefs that concern less the actualised actions
as such, but the consequences of actions than an actor can entertain, conceive
and anticipate when exploring and experimenting upon the representations of
its internal states concerning the environmental states. Indeed the pragmatist
meaning of beliefs is, in the fashion of the Bain–Peirce original formulations,
“that upon which one is capable of acting”. That phrase, generalised into any
organism’s habits of acting in certain ways in certain kinds of environments
– including its own sub-units acting in the organism as the environment –
now largely exhausts the meaning of beliefs in the philosophy of action
conceived in the pragmatist spirit.
Such anticipatory and action-based, non-propositional (weak) beliefs are now
included in the agent’s self-description of its generative model, prompting
movement from external to blanket states. In other words, beliefs upon which
an agent is prepared to act are the ‘density morphisms’ that produce the
generative model, arrived as a free-energy functorial from external changes
(variational density morphism) to such models.
The above argumentative cores (A)-(C) are the main elements involved in our view
on the allegiance between the nomenclatures of active and abductive inferences:
first, the presence of non-degeneratively triadic relations, the utilisation of leading
principles of abductive reasoning, and its subjunctive conditional formulations.
Abduction in the Light of Active Inference
It is common in the secondary literature to conceive abduction as occurring in two
parts or in two kinds: as generative abduction and as selective abduction (Magnani,
2001; Niiniluoto, 2018). While this distinction may facilitate understanding of such
inferences as ampliative – the only mode of inference that is able to produce new
ideas, as Peirce aptly emphasises (CP 5.171, 1903) – it is important to remember
that Peirce never distinguished more than one kind of abduction. He did distinguish
two kinds of deduction (logical analysis and demonstration), and three (and
sometimes even nine, see e.g. R 905) kinds of inductions, but none of those of
abduction, which indeed was the ‘firstness’ of the three classes or stages of
reasoning, namely abduction, deduction and induction, performed in this order
according to Peirce’s mature views.
There is a sense of abduction being retroductive, inverse reasoning from effects to
causes. This is not unlike what transpires in practical syllogisms, generating novel
hypotheses about the causes of some observed phenomenon to instruct action.
Under FEP, perception consists of inverse reasoning within an optimisation problem
by ‘asking the right kind of a question’ about the hidden causes of sensory states.
The questioning takes place in terms of probing, experimenting and interrogating
the environment, perhaps influencing it by ‘niche constructions’ of various sorts,
and letting those constructions (both epigenetic and other environmental contexts
and stressors) talk back to the actor by changing its habits of reasoning and
behavior accordingly. By so doing, changes in the organism’s model of its external
states are accomplished precisely in order to move towards non-equilibrium steady
states by self-organisation and self-assembly (Da Costa et al., 2021; Parr & Friston,
Selective abduction is, by some contrast, a sampling process that selects those
hypotheses among a range of possible ones that have the greatest evidential value.
In typical abductive cases in which strong evidence is not forthcoming or evidence
remains inconclusive, this means converging to the least expected free energy, to
use the terms of FEP. Let us thus briefly explicate what ‘expected free energy’ here
means. Some organisms are capable of purposeful and intentional action. When
stated in terms of FEP, this means that an organism can form generative models that
not only include expectations about its sensory inputs, but can also accommodate
expectations about the various outcomes of action in the world (Friston et al.,
2013). Technically, such organisms possess generative models that have temporal
depth or richness. They can in principle create policies or action profiles that result
in the emergence of the most efficient or economical outcome in the world in ways
that minimise their expected free energy. This is because actions that are the most
cost-efficient or economical minimise the expected free energy the most
expediently. Friston and his colleagues have provided detailed accounts of the
relationship between the temporal depth of a model and purposefulness and
intentionality of an organism (Bruineberg & Rietveld, 2014; Friston, 2018).
While there is a temptation to see the two, generative and selective abduction, as
two different kinds of abductive inferences, there is a sense in which this distinction
is not about two different kinds of abductive inferences governed by different kinds
of leading principles. The two descriptions in fact are just two facets of the same
underlying meaning of abduction, explicated by the same schema and guided by the
same leading principle. Here we find it useful to restate the case for this in terms of
the FEP framework. The crux is that the role of internal states is to both (i) infer
causes of the sensory data and (ii) generate appropriate forms of interactions with
one’s surroundings. Both roles presuppose semantic content in the hypothetical
states of any one phenotype (far-from-equilibrium steady states).
Accordingly, we can now recover our restatement of the schema of ‘abductive
active inference’ to look like as follows:
(1) Y, a surprisal, is experienced.
(2) If X were to be the case, then cessation of Y would be the matter of course.
(3) Therefore, let us see to it that/there is reason to suspect that X (to “believe-
X” about external states) is to be part of the generative model.
To meaningfully ascribe meaning to the key terms involved in this schema, such as
“would-bes”, “matters of course”, “antecedents of hypotheticals” and “beliefs”
presupposes that those terms are non-vacuous and have well-defined semantic
values. Given that inferring causes is to solve an actual inverse problem about the
world (as well as about possible worlds such as the future states of affairs or
moments of time), these terms do need sound referential content. Hence the ideas of
semantics and intentional mental states are presupposed to have presense in the
living beings’ solution protocols. At the same time, what is important is that the
interpreter downregulates the meaning of these loaded terms of ‘semantics’,
‘intentions’ and ‘mental states’ – perhaps gradually and continuously – according to
the ongoing discovery of organisms’ multi-scale properties and their subunits that
can exhibit habits of action and faculties of active inference.
At any event, minimisation of variational free energy can be construed as a
conjectural result of such abductions. The inference of hidden causes as antecedents
of hypotheticals and the conclusion that prompts minimisation of negative free
energy are actions that take place at once. One does not wait for the other to
materialise first. Indeed, the variational FEP is the unificatory expression of
abduction in our proposed naturalised context. It does not presuppose the
(erroneous) distinction between the presence of two kinds of abductions. The two
processes (generation and selection of hypotheses on probation) weld into one
strategy or action profile of any entity that has sufficient functional integrity and is
following the prescribed existential imperative.
The Economy of Research and its Free-Energy
At this point there remains one final task to do, which serves to qualify the previous
argument a little further. The apparent difference in the two ways of seeing (or the
two facets of) abduction is explained by noticing that the generative facet of
abduction is strongly correlated with the qualities of the economy of research. The
question concerns how to arrange the selection from the great variety of hidden
causes that would serve the agent best in carrying out its existential, self-organising
and enactivist imperatives.
Now the economy of research and the scientific account of expectations in
hypothesis-formation and conjecture-making are the centrepieces of Peirce’s theory
of science. These notions may be naturalised in terms of the FEP-based account of
the organism’s action on the basis of the expected epistemic values and the control
states that represent the hidden causes in the world. These will be explained briefly
in this section. According to Peirce’s original paper of 1876 on the economy of
The doctrine of economy, in general, treats of the relations between
utility and cost. That branch of it which relates to research considers
the relations between the utility and the cost of diminishing the
probable error of our knowledge. Its main problem is, how, with a
given expenditure of money, time, and energy, to obtain the most
valuable addition to our knowledge. (W 4: 72, 1879)
Peirce argues that not nearly all hypotheses are worth pursuing. The mechanisms of
abduction endowed upon us through evolutionary development are devised
precisely in order to provide a logical grip on how to demarcate promising
hypotheses from disappointing ones with minimal energy expended on such
There are a couple of delicate issues involved in carrying out such tasks in the
desired expedient fashion, while avoiding unintentional corrosion of the process. In
order to produce fruitful scientific theories that are both novel and can
accommodate new predictions, we must be able to specify what new patterns of
relations between classes of phenomena are expected to arise. Singular
observational data are of much lesser value. Moreover, as scientists tend to
demarcate some hypotheses as worthy of further testing and scrutiny under
fundamental uncertainty, that is, on the basis of their promise to yield experimental
results in the future. What matters as to the value of such untested hypotheses is
thus both the interconnectedness of evidence, often sparse, between the number of
guesses that had to be made when drafting those hypotheses, and the expected
novelty and gain, should those hypotheses be on the right track. This attempt at
reducing uncertainty about the future outcomes of scientific research by expediting
the inquiry is explicated by Peirce under the single rubric of abduction. Indeed
abduction is the type of reasoning “that creates hypotheses to account for the
surprising facts by guessing” (Chiffi et al., 2020: 2). Here scientific guesses refer to
peculiar kinds of sampling processes concerning concerning open-ended future
states of affairs.
The process of coping with uncertainty through abduction can further be explicated
in terms of FEP’s account of future-oriented mechanisms of demarcating effective
strategies or policies from inefficient ones. As we explained above, organisms with
temporally deep models can form insight into possible outcomes of their actions. As
such, these organisms tend to purposefully form policies that aim at minimising
expected free energy. FEP thus provides a viable account of how some organisms
possess the capacity to infer and select the policy that, if consistently pursued, will
contribute to effectively minimising the expected free energy (Chen et al., 2019;
Friston et al., 2015; Ramstead et al., 2019).
Technically, the notion of ‘economy’ figures prominently in the minimisation of
variational free energy. As noted, the story goes as follows: the imperative to self-
evidence is met by inference and learning to minimise free energy, where free
energy is an upper bound on negative log evidence. The log evidence and (negative)
surprisal are the same thing. This means that minimising surprise is equivalent to
maximising model evidence. A fish that avoids being out of the water can maximise
evidence for the existence and thus maximise its survival. Crucially, log evidence
can always be decomposed into accuracy minus complexity. This means that
minimising surprise is equivalent to providing an accurate account of the sensorium
that minimises complexity. Interestingly, acting to minimise expected surprise can
also be associated with minimising expected complexity (known as risk in
economics and in Bayesian statistics), while at the same time minimising expected
inaccuracy (also known as ambiguity). In other words, when minimising expected
free energy there are epistemic and pragmatic components to any choice; namely,
risk and ambiguity. The epistemic part means that much of our behaviour is about
seeking information and reducing uncertainty; that is, reducing instances of
expected surprise (Hohwy 2013; Friston et al. 2012; Hohwy 2013). Risk is
particularly interesting because it is the expected complexity which scores the
computational complexity cost of any model or hypothesis. In this sense, an
‘economic’ sampling of the environment is exactly the minimisation of expected
Peirce proposed the qualities of incomplexity (simplicity), breadth and caution as
the characteristics of the economy of scientific hypothesis-making (EP 2:109,
1901). The general question is that given a set of prima facie plausible hypotheses
produced in a given research project, and given the allocation of capita that can be
invested in their further pursuit (fiscal, cognitive or otherwise), which of the many
projected hypotheses should disqualify from being submitted to severe and
expensive test? To mitigate risks, the quality of incomplexity (absence of
complexity, or simplicity) recommends that because few hypotheses are expected to
be optimal in any case, they should at least “give a good leave” (EP 2:110). Any
promising hypothesis slated to be refuted in the future should at least set an
example of a good conduct to be followed, by attempting as large a ‘break’ as
possible from it. That would increase the likelihood that new hypotheses are
discovered from it. Breadth gestures at unification: those hypotheses are to be
favoured which are extendible in the sense of covering more ground under slightly
different perspective or minimally adjusted boundary conditions – or could even
explain unexpected phenomena in some wholly new domains, as occasionally
happens in cross-disciplinary innovation eco-systems. Caution is the economic
quality of avoiding diminishing marginal returns by skillfully breaking down big
questions into series of small questions that can be answered within reasonable
limits of investment in it. For example, questions that are broken down to binary
yes-no questions (such as succeeding in the exact definition of the null hypothesis),
one is at once logarithmically reducing the size of the search space.
In the corresponding fashion, not all policies that the organism it fit to pursue
would maximise its survival (just as not all hypotheses would lead to fruitful
scientific theories). Stated technically, not all outcomes of actions are desirable
from an evolutionary perspective. Thus organisms must be able to choose the right
policies that provide an adequate future-oriented basis for reliable action-guiding of
their beliefs. Organisms must entertain beliefs that are reliable guides to action,
given diverse consequences of their actions. Policies that could maximise the
organism’s survival are derived from optimal error minimisation mechanisms in the
future (see Ramstead et al., 2019: 7).
It follows that the evolutionary basis of optimisation of the organism’s expected
value of policies contributes to the project of naturalising Peirce’s conceptions of
abduction, expectation, and the economy of research. This is so because – stating
the situation somewhat metaphorically – natural selection favours organisms that
pursue strategies that lead to the minimisation of the expected free energy
effectively over organisms that fail to do so. Such organisms draft optimal and
precise models of the future states of affairs of the world on the grounds of their
expected reservoir of free energy. The models are optimal in the sense that they
effectively decrease the discrepancy between expected values and the control states.
Fit organisms are those that rely on strategies that successfully minimise the
discrepancy between generative models’ prediction and the hidden causes of
sensory data. Successful minimisation results in optimisation of future-oriented
inferences on expectations of such organisms and decreases the uncertainty and
ambiguity involved in those inferences. If no uncertainty and ambiguity remains,
the inference would indeed be the securest of all, namely an expression of (non-
The reliability of the organism’s probabilistic inferences and the choice policies that
maximise survival rely on one another, as “inferences about policies depend upon
inferences about hidden states and vice versa” (Friston et al.,, 2013: 2).
Evolutionary considerations lead to a realist understanding of the reliability of
strategies that an organism pursues to maximise its survival effectively. In this
sense, future-oriented inferences of organisms that can maximise their survival are
anchored to the real world, involving semantic values in their interrogations of
Nature and in the solution protocols that attempt reverse-engineering the presence
of her hidden causes.
To be fair, and as briefly noted at the beginning of this paper, there are also
instrumentalist interpretations of FEP and its ingredients such as Markov blankets
(Baltieri et al., 2020; van Es & Hipolito, 2020) (for analysis see Beni, 2021). But
our faith (for want of a better word) in realist credentials of FEP has its roots in the
pragmatist optimism (or rather in its active meliorism) about the gains from the
alliance between evolutionarily useful processes that contribute to maximising
survival on the one hand, and a veridical representation of features of the real world
on the other (see Beni, 2019: Ch. 7; 2020). In other words, this optimism is in line
with the pragmatist proclivity of this paper, committed to no higher tribunal for
accrediting the veracity of models than their practical success in maximising the
enduranceof the species of which an organism alone is only a servant. If this
pragmatist approach to realism displeases the elevated taste of one who looks for
some staunch metaphysical criteria, let a thousand flowers bloom.
The proposed naturalisation of abduction is inspired both by Peirce’s original
writings on abduction as well as by the contemporary research of FEP, whose
corollary process theory is known as active inference. In his writings Peirce
developed upon the Hegelian idea that “nature syllogizes”, witnessed by evolution’s
tendency towards the increasing generalisation of laws of nature (RLT: 197; R 439,
1898). We rather interrogate and exclaim: “Does some fact correspond to the
claim that nature syllogizes? Well, let us investigate!” What is more, while nature
may or may not syllogize as the matter of course, organisms do syllogize naturally.
That is, they perform active inferences, as these are inferences from effect to
causes. In doing so, agents invoke the variational principles of free energy and the
economy of what it means to be an active inquirer of the world. Active inquirers
solve problematic situations in which they find themselves when engaging in a host
of embodied, enactive, active inferences. Their conjectured conclusions influence
their external states, while the external states also talk back to them, forming
feedback loops and enabling homeostasis to form.
Thus the inspiration and motivation for the present study thus derives just as well
from Peirce’s student and colleague John Dewey as well as from other classical
pragmatists in that lineage (Menary 2016). Indeed our proposal has its ultimate
roots in the doubt-belief “action-first” epistemology, which we find articulated
already in Peirce’s teachings from the 1870 s. In that early account, changes in
habits of action arise from the irritation of doubt (i.e., an element of FEP’s
surprisal), which is deprivation of those habits. Replacement of doubt with habits of
actions (beliefs) is induced, that is, not achieved by abduction alone. After all,
abduction preserves the ignorance and the doubt-status of an agent with merely a
promise of a future attainment of belief to replace suspicion on the matters of
course. Testable predictions are, in turn, those drawn by deduction, while the
testing itself is carried out by induction.
One should also not forget the early formulations of the extended-mind arguments
and their influence on scholars such as Dewey by the early physiologists and
anatomists who observed the behaviours induced on decapitated frogs and their
abilities on engaging in bodily habits of reasoning. Their findings were presented in
the Metaphysical Club meetings at Johns Hopkins University in the early 1880 s
which Peirce actively chaired (Pietarinen & Chevalier, 2015). One might even take
the recent findings such as the regenerative capacities of flatworms (Bischof et al.,
2021; Fields & Levin, 2021) as modern representatives of those venerable lines of
research that continue on the pragmatist trajectory that commenced with
philosophical and semiotic implications of the early sciences of physiology and
anatomy, and which see substructures such as bodily tissues and organs capable of
habit-change potentials and even reasoning and decision making. For what the large
cell units are able to do is to deform the possible action-space for its subunits by
altering the space of what is possible (pragmatistically, what can become actual) in
line with the global body plan. In modern terms, this deformation and switching off
certain degrees of freedom (that is, the reduction of uncertainty and ambiguity) can
happen under our interpretation through the execution of FEP as the ‘leading
principle’ of active abductive inferences.
More needs to be said to receive a more comprehensive, or even partially
satisfactory, conceptual consolidation between FEP and active inferences on the one
hand, and Peirce’s theory of semiotics, pragmatism, biosemiotics, and the logic of
science, on the other. Among them is the conceptual nature and role of ‘group
agency’ in which individual states, goals, desires and expectations diluted into that
rough and co-evolving memory depository in reference to which the FEP-led
abductive reasoning processes then strive to attain an agent’s target states.
Focussing on the allegiance between the two nomenclatures of active and abductive
inferences seems, however, to be the proper place where such a larger project could
entertain its beginnings.
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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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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.
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.
The reference R is to Peirce (1967) by the Robin manuscript number. The reference NEM is to Peirce
(1976) by volume and page number.
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).
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).
Some notable exceptions include Bellucci (2018); Hookway (2003); Kruijff (2005); Niño (2007);
Bellucci and Pietarinen (2020); Pietarinen (2020).
The reference LF is to Peirce (2019–2021) by volume number.
Reference CP is to Peirce (1931–1958) by volume and paragraph number.
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).
We thank the reviewer on 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.
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).
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
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).
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.
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.
The reference EP is to Peirce (1998) by volume and page number.
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).
The reference RLT is to Peirce (1992).
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.
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’.