L. Magnani (2015), Naturalizing logic

Journal of Applied Logic 13 (2015) 13–36

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Journal of Applied Logic

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Naturalizing logicErrors of reasoning vindicated: Logic reapproaches cognitive science

Lorenzo MagnaniDepartment of Humanities, Philosophy Section and Computational Philosophy Laboratory, University of Pavia, Pavia, Italy

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 May 2014Accepted 5 November 2014Available online 13 November 2014

Keywords:Naturalization of logicAbductionEco-cognitive modelFallaciesPeircean philosophy

A complete revision of mainstream logic is an urgent task to be achieved. This revision will be able to bring logic into a creative rapprochement with cognitive science. This can be achieved by trying to do for logic what over forty years ago Quine and others attempted for epistemology. It is necessary to propose a “naturalization” of the logic of human inference. This paper deals with an examination of how the naturalization process might go, together with some indication of what might be achieved by it. To assist the reader in understanding the naturalization of logic I will take advantage of my own research on the concept of abduction, which vindicates the positive cognitive value of the fallacy of the affirming the consequent thanks to the so-called EC-model (Eco-Cognitive model), and of the recent book Errors of Reasoning: Naturalizing the Logic of Inference(2013) [86], by John Woods. While this paper certainly aims at promoting the research program on the naturalization of logic, it also further advocates the placement of abduction in the research programmes of logic, and stresses to what extent our contemporary philosophical and logical tradition is indebted towards Charles Sanders Peirce, a thinker often praised for his productivity but whose quality and importance are too often overlooked.

© 2014 Elsevier B.V. All rights reserved.

Of the three Universes of Experience familiar to us all, the first comprises all mere Ideas, those airy nothings to which the mind of poet, pure mathematician, or another might give local habitation and a name within that mind. Their very airy-nothingness, the fact that their Being consists in mere capability of getting thought, not in anybody’s Actually thinking them, saves their Reality.

Charles Sanders Peirce, A Neglected Argument for the Reality of God, 1908.

1. Errors of reasoning: Logic reapproaches cognitive science

In this paper I will deal with an examination of how the naturalization process might go, together with some indication of what might be achieved by it. To help the reader in understanding the naturalization of logic I will take advantage of my own research on the concept of abduction and of the recent book Errors

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14 L. Magnani / Journal of Applied Logic 13 (2015) 13–36

of Reasoning: Naturalizing the Logic of Inference (2013) [86], by John Woods, which I think constitutes a major event in logic and philosophy, especially if seen in their relationships with cognitive science. Even if there is quite natural tendency among orthodoxies in the realm of logic not to pay much attention to work done outside their sphere of interest, or to dismiss it out hand when it calls them into question, one would expect the book’s very subtitle to catch the attention of many of the journal’s readers, even if not belonging to the cognitive science area of research. It would be attention well-rewarded by what the subtitle promises. The naturalization of logic is a notable departure from how logic is usually conceived.

It has to be said that the idea of naturalizing logic does not really or completely originate with John Woods. In the modern era alone, it was actively proposed by Dewey [19, vol. 12, p. 27] and sympathetically entertained by Toulmin [81, p. 257], and Finocchiaro [21, pp. 6–7]. Pointing out additional specific recent relevant and effective published work on the collective effort to naturalize logic, arisen over time in cognitive science or AI, I have to cite the new Kowalski’s book Computational Logic and Human Thinking [43], where the 17 chapters each consider a different type of reasoning, also taking advantage of considerations related to the need of the extension of logic. Starting with deductive reasoning on horn clauses, Kowalski considers abduction, induction, planning, nonmonotonicity, decision making, temporal and meta-reasoning and many other forms of reasoning, showing how logical studies related to computer science and AI can be extended to encompass and explain them all. Further, the recent synoptic book Human Reasoning and Cognitive Science [77] certainly adds new insight on the naturalization of logic: both a psychologist and a logician richly show the choice of logical formalisms for representing actual reasoning. There are two interlocking questions: what are the right formalisms to represent how people reason, and what forms do the reasoners themselves bring to the world in order to reason about it? This is an excellent book in cognitive science that logicians can learn some new logic from.

Many other results of the current literature directly or indirectly related to the naturalization of logic need be quoted, such as recent AI oriented research on counterfactual reasoning [15,56,64,68]; moral reasoning [37,67,74,75]; mutual debugging and argumenting [65,66]; objecting [62,63]; preferring [61]; forgetting [3]; updating [2,4,38]; intention recognition and decision making [31,33]. Also, interesting studies related to the evolutionary game theory concerning emergent population norms and emergent cooperative behavior morals represent a new promising area for the naturalization of the logic of agents embedded in populations and groups, and certainly points out central issues which help to go beyond the expressive rigidity of the mainstream received logical tradition [3,30,32,34–36].

In Errors of Reasoning Woods adds new important considerations. He holds a naturalized logic to an adequacy condition of “empirical sensitivity”. This is achieved in three ways. One requires that the logicians familiarize themselves with the data that cognitive science seeks to account for: “At a minimum, the decision to naturalize the logic of reasoning is a decision to take into account well established lawlike results of the cognitive science” [86, p. 62]. A second requires an informed acquaintance with the findings of the best-confirmed of those theories. The third requires a logic’s empirical disconformities with the data and findings of the partner sciences be accounted for, under pain of having to give them up.1 In this perspective we should conclude that “It is not in the general case preferable – indeed it is not smart and not even possible – to upgrade our cognitive targets in ways that favor truth-preservation or experimental/statistical confirmation as general cognitive strategies” [86, p. 198].

A special importance is possessed by this third condition, which leads to view with suspicion (and lots of telling argument) the most prominent justification for hanging on to an empirically false theory. According to that view, it is not the aim of such theories to be descriptively adequate; the goal is to establish rules

1 Indeed the author maintains it is necessary to construct an “empirically sensitive logic”: a logic considered as an “empirically sensitive and epistemologically responsive account of the reasoning practices of beings like us” [86, p. 386].

L. Magnani / Journal of Applied Logic 13 (2015) 13–36 15

that are normatively authoritative for human practice on the ground. First of all naturalizing logic is the rejection of this sort of normative presumptuousness, at least until such time as it might come to have a convincing and non-tendentious defence. In this perspective we can say that a naturalization of logic follows the spirit of research typical of the artificial intelligence (AI) tradition. Woods acknowledges that our best sciences routinely make indispensable use of false idealizations, such as the infinite largeness of populations in population genetics. They are, Woods and Rosales say, “virtuous distortions” [87], and are so when they are paid for by the success of the theory’s observational predictions at the empirical checkout counter. Normatively idealized theories of normatively assessable human performance can’t meet that test, think here of the closure-under-consequence assumption for ideally rational belief-management systems. So the only payment option would appear to be the theory’s doing well at the normative checkout counter. But Woods’ position (in effect) is that in logic no one has much of a clue about how this kind of checkout operation should be run. Pending a sounder and more sure-footed understanding of normative authority, Woods claims that the only option is to handle the problem of empirical discomportment in some other way.

Used to deal of idealized formal systems, the new naturalized logic stresses the priority of attending with care to the actual details of human reasoning on the ground, well in advance of assessments of goodness or badness. Meanwhile, a canny naturalizer should park his entirely rightful interest in goodness and badness in a default rule that is called “Convergence of the Normative on the Normal”. The rule bids the theorist to take it as given in the absence of particular reasons to the contrary, that humans reason well when they reason in the ways that humans normally do reason in the conditions of real life. We have to be careful: the NN -convergence principle is not a safe default for all aspects of human reasoning; its employment here is solely for premiss-conclusion reasoning.2 It counsels us to assess premiss-conclusion reasoning in roughly the same kind of way that we’d check the circulation of a subject’s blood. What this means is that, by and large, a human agent’s premiss-conclusion reasoning is the right way to reason when his conclusion-drawing cognitive equipment is in good working order and, on that occasion working in the right way, operating on good information in the absence of hostile externalities.

The empirical turn pulls logic and cognitive science in the opposite direction from that towards which the well-known mathematical turn – which marked the birth of mathematical logic – pulls. Their respective orientations are, so to say, poles apart. For the past thirty years, the mathematically oriented disciplines have sought a closer attachment to agent-centered, goal-directed, resource-based, time and action systems, in a kind of non-standard cognitive atmosphere, with respect to the ideality established and promoted by classical logic. These additions to one’s base logic are a considerable complication, whose handling the new logic’s formal machinery must be supplemented with new machinery of correspondingly greater complexity, sometimes dauntingly so. Unfortunately these machineries are extremely complicated and baroque, and we have to worry about these heavy-equipment upgrades: the heavier they are, the harder they are to manage and the harder they are managed, the likelier they are to seek the relief of simplification in a fresh array of tailor-made normative idealizations. The empirical turn is an attempt to reverse this expansion of capital assets, by easing up on the idea that it is the theorist’s job to prove theorems. To make an example that is also stressed by Woods, theorem-proving is not demanded for population biology. Why, asks Woods, should it be demanded here?

2 The restriction to premiss-conclusion reasoning is here related to the fact that whenever in the discharge of a cognitive function there is an element of inference discernible in the process, there will be inputs to and outputs of an inferential relation of some kind. As used here, “premiss” names inputs and “conclusion” names outputs. A similar observation can be extended to other kinds of reasoning: for example, as widely believed, to the approaches to uncertainty reasoning based on probability theory – where the normative is taken to be governed by Kolmogorov’s axioms of probability theory. A good example of where the normative (in this sense) and normal do not converge is in human judgment under conditions of uncertainty (following from well-known work by Tversky and Kahneman [82]) (cf. Busemeyer et al. [14]). For dissenting views, see Gabbay and Woods [23], Woods [85], and Woods [86, pp. 478–483].


2. The naturalistic turn in logic and the need of a “third way” reasoning

The new naturalistic approach is particularly appropriate to analyze and discuss some problems that belong to the current epistemological and cognitive debate. A key example is the discussion of “paradigm creep” [86, p. 481], especially as it relates to the importation of mathematical methods into the human sciences of cognition. Woods’ position could be summed up in these words: “Do not for your present purpose employ successful methods”. What this means, less jokingly, is that methods that work well elsewhere should not automatically be supposed to work well here; and should not be used here until their applicability is realistically ascertained. When this requirement is failed, the methods in question can give rise to “paradigm creep”, sustained by a silly inference roughly to the effect that since these methods were paradigms of good methodology for theories of type K, we should give them pride of place in theories of K∗ as well. Here, too, the recurring or persistent problem is the ideal models paradigm, which works smoothly for descriptive science but cannot make the normative cut in a convincing way: again empirically false norms have to be paid for, short of the wholesale indictment of cognitive human performance on the ground. We can look for payment in the ways of nature, in how human practice actually plays out there. But normal practice cannot pay the bill for the false norms of paradigmatic enquiry, which occasions the necessity of a wholesale rejection of them.

Indeed, with human reasoning, especially of the premiss-conclusion sort, it is comparatively rare that the standards of deductive validity or statistico-experimental inductive strength are ever met or in place. Accordingly, new standards for the so-called “third way” reasoning [86, chapter seven] should be found as a mixture of nonmonotonic, default, ceteris paribus, agenda-relevant, inconsistency-adaptive, abductive reasoning, for which neither standard deductive validity nor inductive strength are a good rule of assessment. The best recourse involves a significant restructuring of the varying provisions of families of nonmonotonic logics, crucially including the logic of abduction. Most “right” reasoning is third-way reasoning, which owes its rightness to the meeting of requirements other than deductive validity (or inductive strength).

I have contended few lines above that it is comparatively rare that the standards of statistico-experimental inductive strength are ever met or in place: Bayesianism is extremely popular in contemporary cognitive science, how would the new views on naturalizing logic be applied to Bayesian approaches to cognition? Together with John Woods I reject Bayesianism as a fruitful way of modeling normatively assessable premiss-conclusion reasoning as performed by human individuals in the conditions of real life. A good deal of my case against Bayesianism can be found in Woods [86, chapter two and pp. 75, 80, 142]. The case against Bayesianism and virtually every other normatively idealized approach to normatively assessable cognitive performance can be summed up as follows. As applied to individual human reasoners as they operate in the conditions of real life – in the cognitive economies in which they live out their lives – Bayesianism’s idealized norms cannot be implemented owing chiefly to their computational intractability for beings like us. Some of these norms – e.g. the closure of belief under consequence, are not only false of human practice but transfinitely false of it. No human reasoner performing at his humanly possible best approximates to this ideal in any finite degree. This enormous gap between what the model mandates and the human agent delivers has not to date been satisfactorily explained away. One of the least satisfactory is the thesis that the vastness of this gap just goes to show how bad we are at reasoning. A scepticism this nasty requires a substantial justification, indeed nothing less than a well-muscled demonstrative of the normative authority of the model’s idealizations. To date, nothing remotely like this has been advanced.

Some options are considered in Woods [86, chapter two], all of them bad. In one, it is assumed that the normative authority of the rules arises from these truths (or analyticity) in-the model. Another is that it arises from the necessity that attaches to their mathematical formulation (After all, are not the truths of mathematics necessary?). These arguments are laughable on their face. The third one, while not so silly, is also unsatisfactory. This is the reflective equilibrium demonstration of the normative authority of the Bayesian norms as regards the cognitive performance of the human individual. It provides that norms or


rules are normatively binding on such behavior when they are discernibly reflected in the standard practice of the community at large. But how are such communities at large to be individuated? Are they the man in the street, i.e. all of us? If so, the last thing that they are is that they are in equilibrium with the Bayesian norms. Or are they the community of people who conduct research into human reasoning, i.e. are they Bayesians themselves? If so, we get an odd result. In terms of reasoning behavior these experts are not a jot different from the rest of us. In terms of what they say makes for good reasoning, there is indeed a degree of conformity to their own norms (how could there not be?).

I will better explain below the importance of abduction in the naturalization of logic. Let us anticipate some words about abduction commenting on its relationship with Bayesianism. Why does not the natu-ralizing logician follow the Bayesian lead favored by cognitive scientists who work on abduction? There are two reasons for this omission. One is that Bayesianism lacks a demonstrated (or even plausibly argued) normative legitimacy. The other is that when considering Peirce’s conception of abduction, one of whose key characteristics is that a rationally successful abduction does not raise the objective probability of the hy-pothesis in question and should not raise its subjective probability either. So to impose Bayesian constraints would be to distort Peirce’s abduction, beyond recognition.

Let us come back to the general logico-cognitive problem of naturalizing logic. It refers to the fact that one thing is “consequence-having”, which characterizes the “logical space” pertaining to the traditional concept of “logical consequence” provided by mainstream logic, another thing is “consequence-drawing”, which refers to the “the reasoner’s mind” [86, pp. 24–26].3 Consequence-drawing represents the need of a kind of pragmaticization of consequence-having. Various species of nonmonotonic and abductive logics already afforded the task of accounting for third-way reasoning, but a deeper naturalization should require a significant restructuring of them if they are to become capable of more satisfactorily accounting for conclusion-drawing structural relations of this kind. It is usually occurring that the consequences of a set of premises sometimes fail to be the relevant consequences the cognitive agent ought to draw for its own aims. Woods strongly emphasizes that the conclusion-drawing is constitutively causal and contemplates a cognitive agent X, the information I the agent reasons on, a background database Δ of information available to the agent, a cognitive agenda A of duties for the agent, a conclusion α, obtained after applying the background Δ to I, and a disposition D to answer – if asked – justification requests for α’s being drawn by citing I(Δ) [86, pp. 285–286].

All of normatively presumptive science is put on hold until the normative authority problem is properly sorted out. Naturalizing logic does not simply mean to rejoin and further enrich or amend the whole area of research in agent-based logics, including logics of probabilistic reasoning, theories of belief-change and decision, epistemic and justification logics, fallacy theory, discourse analysis and normative psychology. The aim of vindicating the cognitive status of “errors of reasoning” by extracting their virtues aims at something richer. Indeed, to further depict the actual character of the new naturalization of logic, Woods makes interesting new headway in how to understand defeasible and default reasoning, nonmonotonic consequence relations, autoepistemic and anti-closed world belief-formation, and much else. This new analysis brims with interesting new ideas, including some genuinely novel insights into the structure of presumption and its role in the management of belief. A further highlight is a thoroughly engaging chapter on the transmission of knowledge when one person tells something to another. Also the central problem of abduction – I will discuss below in section 5 – a kind of inference that is fundamental in human and animal life, receives interesting new light and new interesting ideas are proposed.

In summary, naturalizing logic aims at avoiding dogmatic designs on the logic of premiss-conclusion reasoning. Even if provisional and exploratory, this new naturalism unexpectedly applied to logic, delineates

3 “Proposition 3.8. Consequence-Drawing: An agent X draws β as a consequence of α1, ..., αn when (1) his circumstances are such that his belief that α1∧, ...,∧αn causally suffices for his belief that β and his belief-forming devices are in good working order and operating here as they should, and (2) if asked what led him to believe that β, any disposition to reply would be a disposition to cite the α” (p. 100).


an important project. Following the suggestions proposed by Woods there is only one way to find out. It is to establish a working alliance between logic and the (other) sciences of cognition, and see where we have got to forty years hence. Perhaps there are readers of the Journal of Applied Logic who might consider taking me up on the offer.

3. The new logic is agent based

It is well-known that Peirce rejected the possibility of a practical, agent-based, “logic” and consequently – for example – a logic of abductive reasoning in practical contexts. Naturalizing logic overcomes Peirce’s limitations that are stated in the following passage:

My proposition is that logic, in the strict sense of the term, has nothing to do with how you think [. . . ]. Logic in the narrower sense is that science which concerns itself primarily with distinguishing reasonings into good and bad reasonings, and with distinguishing probable reasonings into strong and weak reasonings. Secondarily, logic concerns itself with all that it must study in order to draw those distinctions about reasoning, and with nothing else [60, p. 143].

Peirce adds “In everyday business reasoning is tolerably successful but I am inclined to think that it is done as well without the aid of theory as with it” [60, p. 109].

To illustrate the fact that the new naturalized logic is instead possible and that has to be agent-basedit is useful to start with the case of the logic of abduction, where the naturalization of the well-known fallacy “affirming the consequent” is at play. Gabbay and Woods [24, p. 81] clearly maintain that Peirce’s abduction, depicted as both a) a surrender to an idea, and b) a method for testing its consequences, perfectly resembles central aspects of practical reasoning.

Facing the problem of “reaching” a logic of abduction – and so of the “everyday business reasoning” – Woods [86, chapter eleven] contends the results achieved until now just lead to a formal and somewhat still too idealized descriptions of the envisaged cognitive behavior of the agent performing abductive reasoning. Following the eco-cognitive4 description of abductive reasoning I myself have illustrated in Magnani [49], an abductive human agent can naturalistically be seen in the perspective – typical of the distributed cognition framework, see below – of the role of manipulations of external representations and of the consequent interplay between internal – at the neuronal level – representations and the external ones (out there in the environment). In this framework both conscious and unconscious inferences are important. Gabbay and Woods [24, p. 27–29] seem to agree with me: they indeed stress the function of consciousness and indicate both its narrow bandwidth and its slow processing of information, an extraordinary quantity of information processed by the human system cannot be accessed by consciousness. Spontaneous devices, “unconscious, sublinguistic, inattentive, involuntary, automatic, effortless, non-semantic, computationally luxuriant, parallel, and deep” have to be taken into account [86, p. 23]. Moreover, the bandwidth of natural language is narrower than the bandwidth of sensation, a great quantity of what we know we are not able to communicate one to another. Moreover, a side effect of consciousness is that it suppresses information.

Mainstream logic is clearly historically related to conscious and propositional thinking and it seems to disregard the subconscious and prelinguistic levels of thinking. This fact leads to the following dilemma: rules of logic are thought of as having something to do with how human beings actually think as practical agents, then by and large they are too complex for conscious deployment. On the other hand, unconscious performance or tacit knowledge is a matter of certain things happening under the appropriate conditions and the right order, but it is unlikely to suppose that this is a matter of following rules (an inclination which seems embedded in a considerable part of contemporary computer science): “Given the cognitive goals typically

4 The description of the meaning of this expression will be given below, subsection 5.2.


set by practical agents, validity and inductive strength are typically not appropriate (or possible) standards for their attainment. [. . . ] This, rather than computational costs, is the deep reason that practical agents do not in the main execute systems of deductive or inductive logic as classically conceived” [24, p. 25]. It is a kind of dilemma that the naturalization of logic can clarify. However, the naturalization project asserts that logic provides rules which humans cannot conform their conscious thinking to except for very few exceptions, so that logicality cannot be considered just as a simple matter of following rules: indeed the intervention in reasoning of implicit knowledge sometimes renders performances relatively effortless.

If, as Gabbay and Woods contend, a logic is a formalized idealization of a type of agent, a logical agent, which features of a human agent will a logic of abduction describe? They maintain that a real human agent is a kind of biological realization of a nonmonotonic paraconsistent base logic and surely the strategies provided by classical logic and some strictly related non-standard logics form a very small part of the individual cognitive skills, given the fact that human agents are not in general dedicated to error avoidance like “classical” logical agents. They say: “A formal model is an idealized description of what an abductive agent does. As such, it reflects some degree of departure from empirical accuracy. Thus an ideal model I is distinct from a descriptive model D” (p. 22). Immediately they add that in this logic of a practical agent basic questions of “contextual” relevance and plausibility are central.

Gabbay and Woods describe the features of “real” human thinking agents in the case of abduction in the following way: a human abductive agent certainly operates at two levels, conscious and unconscious,5 and at both levels she engages (or it is influenced by) truth conditions on propositional structures, state conditions on belief structures and their fixation, and sets of rules defined for various argumentative structures, for instance for evaluating arguments. These three capacities cut across explicit and implicit thinking. I also think that many of the most important inference skills of a human agent are endowed with a story which varies with the multiple propositional relations she finds in her environment and which she takes into account, and with various cognitive reasons to change her mind or to think in a different way, and with multiple motivations to deploy various tactics of argument.

Facing the problem of logical modeling this kind of practical (abductive) human agent, related logical systems can be considered mimetic, that is they are “mimetic representations” (nonmonotonic systems seem to “mime” much better than classical logic – they are more psychologically adequate – human beings’ reasoning actual performances).

To make an example, a good mimetic abductive logical agent is embedded in a situation of nescienceand is characterized by the following general distinct levels

– a base logic L1 with proof procedures Π;– an abductive algorithm which deploys Π to look for missing premises and other formulas to be abduced;– a logic L2 for deciding which abduced formulas to choose, which criteria of selection apply, etc. This

logic is related to the specification of suitable problems of plausibility, relevance (topical, full-use, irredundancy-oriented, probabilistic) and economy, making the ideal agent able to discount and select information which does not resolve the task at hand.

The second and the third component together – endowed with what it is called a filtrating power – form the logic of discovery.

I will come back to illustrate the problems related to the naturalization of the logic of abduction in sec-tion 5.2. As for now we can just remember that logical agents which characterize the tradition of mainstream logic certainly incarnate ideals of “good reasoning” , but, such as the few remarks I have just described concerning a naturalized perspective about the logic of abduction suggest,

5 On implicit and unconscious cognition see below the part devoted to the analysis of abduction as perception, section 5.2.


Good reasoning is always good in relation to a goal or an agenda which may be tacit. [. . . ] Reasoning validly is never itself a goal of good reasoning; otherwise one could always achieve it simply by repeating a premiss as conclusion, or by entering a new premiss that contradicts one already present. [. . . ] It is that the reasoning actually performed by individual agents is sufficiently reliable not to kill them. It is reasoning that precludes neither security not prosperity. This is a fact of fundamental importance. It helps establish the fallibilist position that it is not unreasonable to pursue modes of reasoning that are known to be imperfect “Given the cognitive goals typically set by practical agents, validity and inductive strength are typically not appropriate (or possible) standards for their attainment” [24, pp. 19–20, p. 25].

Abduction in the light of classical logic is a fallacy, and so very prone to errors, seen as a kind of imperfect reasoning, but everyone knows how it is fruitful and knowledge-providing for beings-like-us. Human agents, as practical agents, certainly are imperfect hasty inducers/generalizers, bad predictors, and hybrid6 abducers [49, chapter seven], obviously unlike ideal (logical and computational) agents: the naturalization of logic aims at showing the highly poietic and positive side of these “flecks”.

4. Restructuring the fallacies project and the problem of abductive cognition

It can be argued that from Aristotle onwards logic has irremediably mismanaged the fallacies project. Accordingly, if it is thought desirable for logic to have an account of fallacious reasoning – and of its detection, avoidance, and repair – new approaches will have to be found. The naturalization of logic is appropriate to this task.

Following Woods’ “manifesto” of the naturalization of logic, the normative authority claimed by formal models of ideal reasoners to regulate human practice on the ground is, to date, unfounded. This is true of the dominant mathematical models of such things – think here of classical decision theory and Bayesian epistemology – and is equally true of “informal” idealization of them – think here of the pragma-dialectical approach to argument. It is argued here that the valid norms of good premiss-conclusion reasoning are implicit in normal cognitive practice. What about fallacies? The problem is that the so-called fallacies are active both in common sense and scientific reasoning, and indeed fallacies are often very appropriate to reach reliable cognitive results which show a local adaptive effect in everyday life and also long-term adaptive effects in more sophisticated performances, for example through scientific discovery and scientific modeling.

Classical deductive and inductive fallacies like ad baculum, (argument to the cudgel or appeal to the stick) ad hominem (to the man or to the person), ad populum (appeal to the people), ad ignorantiam (appeal to ignorance), ad verecundiam (authoritative argument or appeal to authority), affirming the consequent, denying the antecedent, hasty generalization, equivocation or quaternio terminorum (fallacy of four terms), the gambler’s fallacy and post hoc ergo propter hoc (after this, therefore because of this), have to be restudied. Indeed, reasoning of the premiss-conclusion sort has a pervasive and characteristic presence in epistemic contexts. It is engaged in by cognitive agents to facilitate the attainment of interesting cognitive and rational ends. Accordingly, agent-centered theories of human reasoning should be both empirically sensitive and epistemologically aware. Doing so will require the adjudication of the tension between justificationist and causal theories of knowledge. The verdict here is for causalism. Woods’ general conviction refers to the fact that our mostly doing what we ought to do in reasoning is a case of our mostly succeeding in knowing what we ought to know. This derives from our being cognitive agents which are subjected to natural selection: Peirce would have said that humans are – because of evolutionary reasons – “akin to truth”; the cognitive endowments work properly in various circumstances and the facto permit survival and prosperity. According

6 That is they strongly count on the cognitive resources of their brains and also of their environments.


to a kind of convergence of natural and normative, we can say that “human beings have knowledge, lots of it” [86, p. 86].

The official core topic of the naturalization of logic is the one of logical fallacies: the traditional theory of fallacies is radically wrong. The reason of this extreme negative statement is a complicated and highly revisionary philosophical view of human reasoning. Woods contends that a fallacy is by definition considered a mistake in reasoning, a mistake which occurs with some frequency in actual arguments and which is actually deceptive.7 Traditionally recognized fallacies like hasty generalization and ad verecundiam are considered “inductively” weak inferences, while affirming the consequent is a deductively invalid inference. Nevertheless, when they are used by actual reasoners, “beings like us”, that is in an eco-logical8 and not merely logical – that is “ideal” and abstract – way, they are no longer necessarily fallacies. Traditionally, fallacies are considered mistakes that appear to be errors, attractive and seductive, but also universal, because humans are prone to committing them. Moreover, they are “usually” considered incorrigible, because the diagnosis of their incorrectness does not cancel their appearance of correctness: for example, if, like everyone else, I am prone to hasty generalization prior to its detection in a particular case, I will remain prone to it afterwards. The so-called EAUI conception picks up the initial letters of the adjectives “error”, “attractive”, “universal” and “incorrigible”.

Woods calls this perspective the traditional – even if not classical/Aristotelian – “EAUI-conception” of fallacies: in sum, as I have just mentioned, fallacies are Errors of Reasoning, Attractive, Universal, and Incorrigible. Further, he more subtly observes

first, that what I take as the traditional concept of fallacy is not in fact the traditional concept; and, second, that regardless whether the traditional concept is or is not what I take it to be, the EAUI notion is not a fit target for a theoretically robust account of fallacy. But for the present I want to attend to a slightly different objection of my own: whether the traditional conception or not, the EAUI conception is not a sufficiently clear notion of fallacy to bear the weight of the concept-list misalignment thesis.9 If the EAUI conception is right, it takes quite a lot for a piece of reasoning to be fallacious. It must be an error that is attractive, universal, incorrigible and bad. Fallacy’s five defining features gives to a piece of reasoning five defences against the charge of fallaciousness. Indeed it gives a piece of erroneous reasoning four methods of defence. No doubt this will give some readers pause. How can a piece of bad reasoning not be fallacious? My answer to this is that not being a fallacy is not enough to make a piece of reasoning good. Woods [86, p. 136].

In [53] I have depicted a sharp distinction – after all very intuitive – between strategic and cognitive rationality, and many of the traditional fallacies – hasty generalization for example – call for an equivocal treatment. They are sometimes cognitive mistakes and strategic successes, and in at least some of those cases, it is more rational to proceed strategically, even at the cost of cognitive error. On this view, hasty generalization instantiates the traditional concept of fallacy (for one thing, it is a logical error), but there are contexts in which it is smarter to commit the error than avoid it. In this perspective we can say that we face with a case of “casual” truth preserving feature of fallacies.

Outside the realm of logical models, a view of hypothetical intelligence as consisting in “fast and frugal heuristic” [26–28,69], still confirms that the perspective on strategic rationality I have mentioned above is essential to understanding human (but also some aspects of animal) behavior. In this perspective the heuristics are devices that can solve a class of problems in situations with limited knowledge and time.

7 Of course deception – in so far as it is related to deliberate fallaciousness – does not have be considered to be a part of the definition of fallacy [80].8 That is when fallacies are seen in a social and real-time exchange of information and/or speech-acts between parties/agents.9 “Proposition 1.2a. The concept-list misalignment thesis: Contrary to the traditional concept-list instantiations thesis, the items

on the traditional list are not to be found in the extension of the traditional concept of fallacy” (p. 6.)


In this case intelligence is sometimes viewed in a Darwinian way as an adaptive toolbox that involves an ecological and social view of rationality. Gigerenzer [25] contends that

The ideal of omniscience fuels the many disciplines and theories that envision godlike humans. Much of cognitive science, and Homo economics as well, assume the superiority of a mind with complete, veridical representations of the outside world that remain stable and available throughout a lifetime. The Law of Indispensable Ignorance, in contrast, says that complete information is neither realistic nor generally desirable. What is desirable are partially (not totally) ignorant people. [. . . ] We can prove that situations exist in which a group does best by following its most ignorant member rather than the consensus of their informed majority, and we can prove that a heuristic that ignores all information except for one reason will make better predictions than a multiple regression with a dozen reasons.

According to Woods’ last and more recent observations the traditional fallacies – hasty generalization included – do not really instantiate the traditional concept of fallacy (the EAUI-conception). In this perspec-tive it is not that it is sometimes “strategically” justified to commit fallacies (a perfectly sound principle, by the way), but rather that in the case of the Gang of Eighteen traditional fallacies they simply are not fallacies. The distinction is subtle, and I can add that I agree with it in the following sense: the tradi-tional conception of fallacies adopts – so to say – an aristocratic (ideal) perspective on human thinking that disregards its profound eco-cognitive character. Errors, in an eco-cognitive perspective, certainly are not the exclusive fruit of the so-called fallacies, and in this wide sense, a fallacy is an error – in Woods’ words – “that virtually everyone is disposed to commit with a frequency that, while comparatively low, is nontrivially greater than the frequency of their errors in general”. The book Errors of Reasoning states the so-called cognitive virtue thesis [86, p. 7]: most of the traditional fallacies should not be labelled as errors, but are, on the contrary, virtuous ways of reasoning. Berto [10, p. 303] points out: “Now one expects what Lewis called ‘incredulous stares’: how can denying the antecedent or ad ignorantiam not be logical mistakes? There is no way for ‘If A then B’ and not-A to entail not-B, or for ‘There’s no evidence that not-A’ to entail A, in any logically decent sense of ‘entail’. But according to Woods, much mainstream logic has got the standards of logical decency wrong: he calls, in fact, for a rethinking of what counts as error in human reasoning.” My implicit agreement with the new Woods’ “negative thesis” is clear in the light of the illustration of the general ‘military” nature of language I have described in [50], which I will recall again below: 1) human language possesses a “pregnance-mirroring” function, 2) in this sense we can say that vocal and written language is a tool exactly like a knife; 3) the so-called fallacies, are certainly linked to that efficacious “military intelligence”, which relates to the problem of the role of language in the so-called coalition enforcement, which characterizes all the various kinds of groups and collectives of humans.10

As I have already illustrated, if we see the so-called fallacies in practical agent-based and task orientedreasoning occurring in actual interactive cognitive situations, some important features immediately arise. In agent-based reasoning, the agent access to cognitive resources encounters limitations such as

– bounded information– lack of time– limited computational capacity.11

10 Taking advantage of the conceptual framework brought up by Thom’s catastrophe theory on how natural syntactical language is seen as the fruit of social necessity, its fundamental function can only be clearly seen if linked to an intrinsic moral (and at the same time violent) aim which is basically rooted in a kind of military intelligence [79]. Thom says language can simply and efficiently transmit vital pieces of information about the fundamental biological oppositions (life – death, good – bad): it is from this perspective that we can clearly see how human language – even at the level of more complicated syntactical expressions – always carries information (pregnances) about moral qualities of persons, things, and events. Such qualities are always directly or indirectly related to the survival needs of the individual and/or of the group/coalition.11 We have seen in the previous section that, on the contrary, logical systems, which Gabbay and Woods consider a kind of theoretical/institutional (“ideal”, in my terms) agent, is occurring in situations characterized by more resources and higher cognitive targets.


Some aspects are typical of agent-based reasoning and are all features which characterize fallacies in various forms and can consequently be seen as good scant-resource adjustment strategies. They are:

1. risk aversion (beings like us feel fear!),2. guessing ability and generic inference,3. propensity for default reasoning,4. capacity to evade irrelevance, and5. unconscious and implicit reasoning.12

Woods also contends that in this broader agent-based perspective one or other of the conditions I have described at the beginning of this section remain unsatisfied, for example: i) fallacies are not necessarily errors of reasoning, ii) they are not universal (even if they are frequent), iii) they are not incorrigible, etc. Paradoxically, fallacies often successfully facilitate cognition (and hypothetical thinking, for example in the case of abductive cognition) (Abundance thesis), even if we obviously acknowledge that actually beings-like-us make mistakes (and know it) (Actually Happens Rule). If we take into account the role of the so-called fallacies in actual human behavior, their cognitive acts show a basic, irreducible, and multifarious argumentative, rhetorical, and dialectic character. These cognitive acts in turn clearly testify that cognition can be successful and useful even in the presence of bounded information and knowledge and, moreover, in the absence of sound inferences. In this perspective, deeper knowledge and sound inferences loose the huge privileged relevance usually attributed to them by the intellectual philosophical, epistemological, and logical tradition. “Belief” seems sufficient enough for human groups to survive and flourish, as they do, and indeed belief is more “economical” than knowledge as at the same time it simulates knowledge and conceals error.

The anti-intellectual and naturalistic approach to logic advanced by Woods’ agent-based view is nicely captured by Proposition 5.5a, which illustrates the concept of epistemic bubble: “A cognitive agent is in an epistemic bubble with respect to proposition α if he is in a k-state13 with respect to α and the distinction between his knowing that α and his experiencing himself as knowing it is phenomenally inapparent to him in the there and now” [86, p. 162]. Hence, we know a lot less than we think we do. Moreover, it is fundamental to stress that, when epistemic bubbles obviously change, the distinction between merely apparent correction and genuinely successful correction exceeds the agent’s command and consequently the cognitive agent from his own first-person perspective favors the option of genuinely sound correction. In sum, detection of errors does not erase the appearance of goodness of fallacies.

This Humean skeptical conclusion is highly interesting because it shows the specific and often disregarded very “fragile” nature of the “cognitive” Dasein14 – at least of contemporary beings-like-us. I also consider this conclusion fundamental in the analysis of fallacies from the point of view of what I have called “military intelligence” (cf. footnote above 10). A basic aspect of the human fallacious use of language regarding “military” effects is – so to say – the softness and gentleness which the constitutive capacity of fallacies to conceal error – especially when they involve hypothesis guessing – can grant. Being constitutively and easily unaware of our errors is very often intertwined with the self-conviction that we are not at all aggressive in our performed argumentations. Human beings use the so-called fallacies because they often work in

12 See below, in the following section, the part devoted to the role of inference in perception.13 A k-state is a special case of saturated end state. A cognitive human agent is in a k-state with respect to α when he experiences himself as knowing that α. K-states are s-belief-states. An s-belief is an agenda closing “ belief”: “Indeed, we quest for knowledge, but settle for belief. We settle for belief when from the first-person perspective the belief is a saturated and agenda-closing end-state” [86, p. 158].14 I am using here the word Dasein to refer to the actual and concrete existence of the cognitive endowments of a human agent. It is a German philosophical word famously used by Martin Heidegger in his magnum opus Being and Time. The word Daseinwas used by several philosophers before Heidegger, with the meaning of “existence” or “presence”. It is derived from da-sein, which literally means being-there/here, though Heidegger was adamant that this was an inappropriate translation of Dasein.


a positive vital way: but when they are eco-cognitively fruitful, we cannot call them fallacies anymore. I contend that in this case we find ourselves inside a kind of moral bubble,15 that is very homomorphic with the epistemic bubble. Unawareness of our error is often accompanied by unawareness of the (potential or actual) deceptive/aggressive character of our speeches (and behaviors). Implicitly agreeing with my perspective, Woods is pretty clear when acknowledges that the “abusive ad hominem” – that is ad hominemwhen exploited in moral/violent cognitive settings related to the specific need of an individual in the framework of a coalition enforcement – is not a fallacy in the traditional EAUI sense of the term [86, p. 446].

Woods also stresses that although a cognitive agent may well be aware of the embubblement thesis and may accept it as true, the phenomenological structure of cognitive states precludes such awareness as a concomitant feature of our general cognitive awareness, and, consequently even when an agent X is in a cognitive state S in which he takes himself as knowing the embubblement thesis to be true, S is immune to it as long as it is operative for X. In short, a skeptical conclusion derives that errors are unavoidable, their very nature lies embedded in their concealment; that is, in an epistemic bubble, any act of error-detection and error-correction is subject in its own right to the concealing of error.

In a sense, there is nothing to correct, even when we are aware of the error in reasoning we are performing. Analogously, there is nothing to complain about ourselves, even if in some sense we are aware of the possible deceptive character of the reasoning and hypothetical cognition we are performing. The kind of “awareness” that has a priority and that is stable is about the fact we are contending our opinions, which are endowed with an intellectual value simply because they are ours. Moreover, these opinions are often endowed with an intrinsic moral value because they fit some moral perspective we agree with as individuals – a perspective that we usually share with various groups we belong to. Errors, and so deception and aggressiveness, tend to be a constitutive “occluding edge” of agent-based linguistic acts, and consequently they are not recognized or felt by the subjects that commit them, but only by others, in some cases because they are negatively affected by them or because they present ideal and sophisticated criteria of reasoning. It is from this perspective that we can also grasp the effective importance reserved by humans for so-called “intuition”, where they simply reason in ways that are “typical” for them, and “typically” justified for them.

Finally, we can conclude that the putative distinction between a merely apparent truth and a genuine truth collapses from the perspective of first-person awareness, i.e., it collapses within epistemic bubbles. Hence, truth is “fugitive” because one can never attain it without thinking that one has done so; but thinking that one has attained it is not attaining it and so cognitive agents lack the possibility to distinguish between merely apparent and genuine truth-apprehension. It can be said that fallibilism in some sense acknowledges the perspective above and, because of its attention to the propensity to guess (and thus also to abduce) and to error-correction, it does not share the error-elimination paroxysm of the syllogistic and mainstream logical tradition.

If humans are so inclined to disregard errors it is natural to especially devote to the so-called fallacious reasoning a kind of natural, light military role, which becomes evident when more or less vital interests of various kinds are at stake. In this case arguments that embed fallacies can nevertheless aim at 1) defending and protecting ourselves and/or our group(s) – normally, human beings belong to various groups, as citizens, workers, members of the family, friends, etc. – groups which are always potential aggressive coalitions; 2) attacking, offending and harming other individuals and groups. Here, by way of example, it is well-known that gossip takes advantage of many fallacies, especially ad hominem, ad baculum, ad misericordian, ad verecundiam, ad populum, straw man, and begging the question.16

15 Extensively described in Magnani [50].16 More considerations on the moral role of gossip are given in chapter three of my book [48], in Bardone and Magnani [9] and Bertolotti and Magnani [11].


5. The fallacy of affirming the consequent naturalized: The eco-cognitive model of abduction (EC-model)

We have to say that the rich research on abduction already available in the fields of logic, cognitive science, philosophy, and artificial intelligence, has already rehabilitated the cognitive importance of the fallacy “affirming the consequent” (abductive reasoning corresponds to this fallacy in the light of classical logic), traditionally taken as the mistake of having a conditional and its consequent, and from this deriving the antecedent. When reframed in the spirit of the naturalization of logic this fallacy becomes a form of abduction endowed with a positive cognitive value, in most of the real-life reasoning contexts in which it occurs, included diagnosis and creative processes. It can exhibit what some writers have called “material validity”,17 in this case to refer to the fact that an invalid form provides a cognitive good semantic outcome. In the last two subsections I will depict a naturalization of the fallacy of the affirming the consequent, which illustrates the cognitive virtues of abduction, taking advantage of my EC-model (Eco-Cognitive Model).

5.1. Is abduction ignorance-preserving?

As I have illustrated in my book on abductive cognition [49, chapter two], following Gabbay and Woods’ contention, it is clear that “[. . . ] abduction is a procedure in which something that lacks epistemic virtue is accepted because it has virtue of another kind” [24, p. 62]. For example: “Let S be the standard that you are not able to meet (e.g., that of mathematical proof). It is possible that there is a lesser epistemic standard S′ (e.g., having reason to believe) that you do meet” [86, p. 370]. Focusing attention on this cognitive aspect of abduction, and adopting the naturalized logical framework centered on practical agents I have described in the previous sections, Gabbay and Woods [24] contend that abduction, when emancipated by the fallacious character which classical logic assigns to it, can be basically seen as a scant-resource strategy, which proceeds in absence of knowledge and presents an ignorance-preserving (or, better, an ignorance mitigating) character. Of course “[. . . ] it is not at all necessary, or frequent, that the abducer be wholly in the dark, that his ignorance be total. It needs not be the case, and typically isn’t, that the abducer’s choice of a hypothesis is a blind guess, or that nothing positive can be said of it beyond the role it plays in the subjunctive attainment of the abducer’s original target (although sometimes this is precisely so)” (p. 370). In this perspective, abductive reasoning is a response to an ignorance-problem: one has an ignorance-problem when one has a cognitive target that cannot be attained on the basis of what one currently knows. Ignorance problems trigger one or other of three responses. In the first case, one overcomes one’s ignorance by attaining some additional knowledge (subduance). In the second instance, one yields to one’s ignorance (at least for the time being) (surrender). In the third instance, one abduces and so has some positive basis for new action even if in the presence of the constitutive ignorance.

From this perspective the general form of an abductive inference can be symbolically rendered as follows. Let α be a proposition with respect to which you have an ignorance problem. Putting T for the agent’s epistemic target with respect to the proposition α at any given time, K for his knowledge-base at that time, K∗ for an immediate accessible successor-base of K that lies within the agent’s means to produce in a timely way,18 R as the attainment relation for T , � as the subjunctive conditional relation, H as the agent’s hypothesis, K(H) as the revision of K upon the addition of H, C(H) denotes the conjecture of Hand Hc its activation. The general structure of abduction can be illustrated as follows (GW-schema)19:

17 The concept of material validity is illustrated in [12], as a case of a semantically valid inference, which instantiates an invalid syntactic form.18 K∗ is an accessible successor of K to the degree that an agent has the know-how to construct it in a timely way; i.e., in ways that are of service in the attainment of targets linked to K. For example if I want to know how to spell “accommodate”, and have forgotten, then my target can’t be hit on the basis of K, what I now know. But I might go to my study and consult the dictionary. This is K∗. It solves a problem originally linked to K.19 That is Gabbay and Woods Schema.


1. T !α [setting of T as an epistemic target with respect to a proposition α]

2. ¬(R(K,T )) [fact]3. ¬(R(K∗, T )) [fact]4. H /∈ K [fact]5. H /∈ K∗ [fact]6. ¬R(H,T ) [fact]7. ¬R(K(H), T ) [fact]8. If H � R(K(H), T ) [fact]9. H meets further conditions S1, ..., Sn [fact]

10. Therefore, C(H) [sub-conclusion, 1–9]11. Therefore, Hc [conclusion, 1–10].

It is easy to see that the distinctive epistemic feature of abduction is captured by the schema. It is a given that H is not in the agent’s knowledge-set. Nor is it in its immediate successor. Since H is not in K, then the revision of K by H is not a knowledge-successor set to K. Even so, H � R(K(H), T ). So we have an ignorance-preservation, as required (cf. Woods [86, chapter eleven]).

[Note: Basically, line 9. indicates that H has no more plausible or relevant rival constituting a greater degree of subjunctive attainment. Characterizing the Si is the most difficult problem for abductive cognition, given the fact that in general there are many possible candidate hypotheses. It involves for instance the consistency and minimality constraints.20 These constraints correspond to the lines 4 and 5 of the standard AKM schema of abduction,21 which is illustrated as follows:

1. E

2. K /� E

3. H /� E

4. K(H) is consistent5. K(H) is minimal6. K(H) � E

7. Therefore, H.Gabbay and Woods [24, pp. 48–49]

where of course the conclusion operator � cannot be classically interpreted].22Finally, in the GW-schema C(H) is read “It is justified (or reasonable) to conjecture that H” and Hc is

its activation, as the basis for planned “actions”.In sum, in the GW-schema T cannot be attained on the basis of K. Neither can it be attained on the

basis of any successor K∗ of K that the agent knows then and there how to construct. H is not in K: H is a

20 I have noted (cf. Magnani [49, chapter two, subsection 2.3.1], and above in this paper) that, in the case of inner processes in organic agents, this sub-process – here explicitly modeled thanks to a formal schema – is considerably implicit, and so also linked to unconscious ways of inferring, or even, in Peircean terms, to the activity of the instinct [57, 8.223] and of what Galileo called the lume naturale [57, 6.477], that is the innate fair for guessing right. This and other cognitive aspects can be better illustrated thanks to the alternative eco-cognitive model (EC-Model) of abduction I will sketch below, subsection 5.2.21 The classical schematic representation of abduction is expressed by what Gabbay and Woods [24] call AKM-schema, which is contrasted to their own (GW-schema), which I am just explaining in this subsection. For A they refer to Aliseda [5,6], for K to Kowalski [44], Kuipers [45], and Kakas et al. [42], for M to Magnani [47] and Meheus [55]. A detailed illustration of the AKM schema is given in Magnani [49, chapter two, subsection 2.1.3].22 The target has to be an explanation and K(H) bears Rpres [that is the relation of presumptive attainment] to T only if there is a proposition V and a consequence relation � such that K(H) � V , where V represents a payoff proposition for T . In turn, in this schema explanations are interpreted in consequentialist terms. If E is an explanans and E′ an explanandum, the first explains the second only if (some authors further contend if and only if) the first implies the second. It is obvious to add that the AKM schema embeds a D-N (deductive-nomological) interpretation of explanation, as I have already stressed in Magnani [47, p. 39].


hypothesis that when reconciled to K produces an updated K(H). H is such that if it were true, then K(H)would attain T . The problem is that H is only hypothesized, so that the truth is not assured. Accordingly, Gabbay and Woods contend that K(H) presumptively attains T . That is, having hypothesized that H, the agent just “presumes” that his target is now attained. Given the fact that presumptive attainment is not attainment, the agent’s abduction must be considered as preserving the ignorance that already gave rise to her (or its, in the case for example of a machine) initial ignorance-problem. Accordingly, abduction does not have to be considered the “solution” of an ignorance problem, but rather a response to it, in which the agent reaches presumptive attainment rather than actual attainment. C(H) expresses the conclusion that it follows from the facts of the schema that H is a worthy object of conjecture. It is important to note that in order to solve a problem it is not necessary that an agent actually conjectures a hypothesis, but it is necessary that she states that the hypothesis is worthy of conjecture.

Briefly, considering H justified to conjecture is not equivalent to considering it justified to accept/activate it and eventually to send H to experimental trial. Hc denotes the decision to release H for further promissory work in the domain of enquiry in which the original ignorance-problem arose, that is the activation of H as a positive cognitive basis for action. Woods usefully observes:

There are lots of cases in which abduction stops at line 10, that is, with the conjecture of the hypothesis in question but not its activation. When this happens, the reasoning that generates the conjecture does not constitute a positive basis for new action, that is, for acting on that hypothesis. Call these abductions partial as opposed to full. Peirce has drawn our attention to an important subclass of partial abductions. These are cases in which the conjecture of H is followed by a decision to submit it to experimental test. Now, to be sure, doing this is an action. It is an action involving H but it is not a case of acting onit. In a full abduction, H is activated by being released for inferential work in the domain of enquiry within which the ignorance-problem arose in the first place. In the Peircean cases, what counts is that H is withheld from such work. Of course, if H goes on to test favorably, it may then be released for subsequent inferential engagement [86, p. 371].

We have to remember that this process of evaluation and so of activation of the hypothesis, is not abductive, but inductive, as Peirce contended. Woods adds: “Now it is quite true that epistemologists of a certain risk-averse bent might be drawn to the admonition that partial abduction is as good as abduction ever gets and that complete abduction, inference-activation and all, is a mistake that leaves any action prompted by it without an adequate rational grounding. This is not an unserious objection, but I have no time to give it its due here. Suffice it to say that there are real-life contexts of reasoning in which such conservatism is given short shrift, in fact is ignored altogether. One of these contexts is the criminal trial at common law” [83].

In the framework of the GW-schema it cannot be said that testability is intrinsic to abduction, such as it is instead maintained in the case of some passages of Peirce’s writings.23 This activity of testing, I repeat, which in turn involves degrees of risk proportioned to the strength of the conjecture, is strictly cognitive/epistemic and inductive in itself,24 for example an experimental test, and it is an intermediate step to release the abduced hypothesis for inferential work in the domain of enquiry within which the ignorance-problem arose in the first place.

Through abduction the basic ignorance – that does not have to be considered total “ignorance” – is neither solved nor left intact: it is an ignorance-preserving accommodation of the problem at hand, which

23 When abduction stops at line 10. (cf. the GW-schema), the agent is not prepared to accept K(H), because of supposed adverse consequences.24 Hintikka appropriately criticizes this Peircean use of the word “induction”: “I do not think that it is instructive to call such reasoning inductive, but this is a merely terminological matter” [39, pp. 52 and 55].


“mitigates” the initial cognitive “irritation” (Peirce says “the irritation of doubt”).25 As I have already stressed, further action can be triggered – in a defeasible way – either to find further abductions or to “solve” the ignorance problem, possibly leading to what the “received view” has called the inference to the best explanation (IBE).

It is clear that in the framework of the GW-schema the inference to the best explanation – if considered as a truth conferring achievement justified by the empirical approval – cannot be a case of abduction, because abductive inference is constitutively ignorance-preserving. In this perspective the inference to the best explanation involves the generalizing26 and evaluating role of induction. Of course it can be said that the requests of originary thinking are related to the depth of the abducer’s ignorance.

5.2. The EC-model: Towards a logic of abduction in embodied distributed cognitive systems

From a general philosophical perspective (with, and beyond, Peirce) the condition 9. (cf. the GW-schema) is, as Woods himself admits “more a hand-wave than a real condition. Of course the devil is in the details. [. . . ] I myself I am not sure” [84, p. 242]. Obviously consistency and minimality constraints were emphasized in the “received view” on abduction established by many classical logical accounts, more oriented to illustrate selective abduction [47] – for example in diagnostic reasoning, where abduction is merely seen as an activity of “selecting” from an encyclopedia of pre-stored hypotheses – than to analyze creative abduction (abduction that generates new hypotheses).27

For example, to stress the puzzling status of the consistency requirement, it is here sufficient to note that Paul Feyerabend, in Against Method [20], correctly attributes a great importance to the role of contradiction in generating hypotheses, also against the role of similarity, and so implicity celebrates the value of creative abductive cognition. Speaking of induction and not of abduction (this concept was relatively unknown at the level of the international philosophical community at that time), he establishes a new “counterrule”. This is the opposite of the neoposititivistic one that it is “experience” (or “experimental results”) which constitutes the most important part of our scientific empirical theories, a rule that formed the core of the so-called “received view” in philosophy of science (where inductive generalization, confirmation, and cor-roboration play a central role). The counterrule “[. . . ] advises us to introduce and elaborate hypotheses which are inconsistent with well-established theories and/or well-established facts. It advises us to proceed counterinductively” [20, p. 20]. Counterinduction is seen more reasonable than induction, because appro-priate to the needs of creative reasoning in science: “[. . . ] we need a dream-world in order to discover the features of the real world we think we inhabit” (p. 29). We know that counterinduction, that is the act of introducing, inventing, and generating new inconsistencies and anomalies, together with new points of view incommensurable with the old ones, is congruous with the aim of inventing “alternatives” (Feyerabend contends that “proliferation of theories is beneficial for science”), and very important in all kinds of creative reasoning.

Since for many abduction problems there are – usually – many guessed hypotheses, the abducer needs reduce this space to one. This means that the abducer has to produce the best choice among the members

25 “The action of thought is excited by the irritation of doubt, and ceases when belief is attained; so that the production of belief is the sole function of thought” [59, p. 261].26 By illustrating abductive/inductive reasoning of preservice elementary majors on patterns that consist of figural and numerical cues in learning elementary mathematics Rivera and Becker monitor the subsequent role of induction. In performing the abductive task to the general form/hypothesis the subjects referred to the fact they immediately saw a relationship among the drawn cues in terms of relational similarity “[. . . ] within classes in which the focus was not on the individual clues in a class per se but on a possible invariant relational structure that was perceived between and, thus, projected onto the cues” [73, p. 151]. Through the follow-up inductive stage of generalizations the subjects tested the hypotheses just examining extensions (new particular cases beyond what was available at the beginning of the reasoning process). This process was also able to show subjects’s disconfirmation capacities: they acknowledged their mistakes in generating a bad induction, which had to be abandoned, in so far as they were checked as insufficient in fully capturing in symbolic terms a general attribute that would yield the total number of toothpicks in new generated cues.27 I have proposed the dichotomic distinction between selective and creative abduction in Magnani [47].


of the available group: “It is extremely difficult to see how this is done, both formally and empirically. Clause (9) [in the GW-model] is a place-holder for two problems, not one. There is the problem of finding criteria for hypothesis selection. But there is the prior problem of specifying the conditions for thinking uppossible candidates for selection. The first is a ‘cutdown’ problem. The second is a ‘fill-up problem’; and with the latter comes the received view that it is not a problem for logic” (Woods [84, p. 243] emphasis added).

Here we touch the core of the ambiguity of the ignorance-preserving character of abduction. Why?

• Because the cognitive processes of generation (fill-up) and of selection (cutdown) can both be sufficient – even in absence of the standard inductive evaluation phase – to activate and accept [clause (11) of the GW-schema above] an abductive hypothesis, and so to reach cognitive results relevant to the context (often endowed with a knowledge enhancing outcome, as I have illustrated in [51,52]). In these cases the instrumental aspects (which simply enable one’s target to be hit) often favor both abductive generation and abductive choice, and they are not necessarily intertwined with plausibilistic concerns, such as consistency and minimality.

In these special cases the best choice is immediately reached without the help of an experimental trial (which fundamentally characterizes the received view of abduction in terms of the so-called “inference to the best explanation”). Not only, we have to strongly note that the generation process alone can suffice, like it is demonstrated by the case of human perception, where the hypothesis generated is immediate and unique. Indeed, perception is considered by Peirce, as an “abductive” fast and uncontrolled (and so automatic) knowledge-production procedure. Perception, in this philosophical perspective, is a vehicle for the instantaneous retrieval of knowledge that was previously structured in our mind through more structured inferential processes. Peirce says: “Abductive inference shades into perceptual judgment without any sharp line of demarcation between them” [58, p. 304]. By perception, knowledge constructions are so instantly reorganized that they become habitual and diffuse and do not need any further testing: “[. . . ] a fully accepted, simple, and interesting inference tends to obliterate all recognition of the uninteresting and complex premises from which it was derived” [57, 7.37].28

My abrupt reference to perception as a case of abduction (in this case I strictly follow Peirce) does not have to surprise the reader. The problem also usefully relates to the role of unconscious and implicit inferences indicated above at point 5 of section 4. Recent cognitive studies on perception seem to confirm Peirce’s philosophical speculations. Through an interdisciplinary approach and suitable experimentation some cognitive scientists (cf. for example Raftopoulos [70,71]) have acknowledged the fact that, in humans, perception (at least in the visual case) is not strictly modular, as Fodor [22] argued, that is, it is not encapsulated, hardwired, domain-specific, and mandatory.29 Neither is it wholly abductively “penetrable” by higher cognitive states (like desires, beliefs, expectations, etc.), by means of top-down pathways in the brain and by changes in its wiring through perceptual learning, as stressed by Churchland [16]. It is important to consider the three following levels: visual sensation (bodily processes that lead to the formation of retinal image which are still useless – so to speak – from the high-level cognitive perspective), perception (sensation transformed along the visual neural pathways in a structured representation), and observation, which consists in all subsequent visual processes that fall within model-based/propositional cognition. These processes “[. . . ] include both post-sensory/semantic interface at which the object recognition units intervene

28 A relatively recent cognitive research related to artificial intelligence presents a formal theory of robot perception as a form of abduction, so reclaiming the rational relevance of the speculative anticipation furnished by Peirce, cf. Shanahan [76].29 Challenges to the modularity hypothesis are illustrated in Marcus [54].


as well as purely semantic processes that lead to the identification of the array – high level vision” [71, p. 189].30

On the basis of this distinction it seems plausible – as Fodor contends – to think there is a substantial amount of information in perception which is theory-neutral. However, also a certain degree of theory-ladenness is justifiable, which can be seen at work for instance in the case of so-called “perceptual learning”. However, this fact does not jeopardize the assumption concerning the basic cognitive impenetrability of per-ception: in sum, perception is informationally “semi-encaspulated”, and also semi-hardwired, but, despite its bottom-down character, it is not insulated – so to speak – from “knowledge”. For example, it results from experimentation that illusion is a product of learning from experience, but this does not regard penetrability of perception because these experience-driven changes do not affect a basic core of perception.31

Higher cognitive states affect the product of visual modules only after the visual modules “[. . . ] have produced their product, by selecting, acting like filters, which output will be accepted for further processing” [70, p. 434], for instance by selecting through attention, imagery, and semantic processing, which aspects of the retinal input are relevant, activating the appropriate neurons. I contend in this article that these processes are essentially abductive, as is also clearly stressed by Shanahan [76], who provides an account of robotic perception from the perspective of a sensory fusion in a unified framework: he describes problems and processes like the incompleteness and uncertainty of basic sensations, top-down information flow and top-down expectation, active perception and attention.32

It is in this sense that a certain amount of plasticity in vision does not imply the full penetrability of perception. As I have already noted, this result does not have to be considered equivalent to the claim that perception is, so to speak, not theory-laden. It has to be acknowledged that even basic perceptual computations obey high-level constraints acting at the brain level, which incorporate implicit and more or less model-based assumptions about the world, coordinated with motor systems. At this level, they lack a semantic content, so as they are not learnt, because they are shared by all, and fundamentally hardwired.

Human auditory perception should also be considered semi-encapsulated [18]. The human auditory system resembles that of other vertebrates, such as mammals, birds, reptiles, amphibians or fish, and it can be thought to derive from simple systems that were originally strictly intertwined with motor systems and thus linked to the sense of space.33

Hearing, which works in “dark and cluttered” [18, p. 253] environments, is complementary to other senses, and has both neural bottom-up and top-down characters. The top-down process takes advantage of descending pathways that send active information out from a central point and play a part in selectively “listening” to the environment, involving relevant motor aspects (indeed action is fundamental to calibrating perception). The role of hearing in the perception of space is central, complementing multichannel visual information with samples of the acoustic field picked up by the ears: cues to location of source by means of interaural intensity, difference and distance according to cues like loudness are two clear examples of

30 A full treatment of the problem of perception both from a psychological and neural perspective is available in the recent [72]. A recent rich volume that shows the semi-encapsulated character of perception as illustrated by recent cognitive science results is [1].31 Evidence on the theory-ladenness of visual perception derived from case-studies in the history of science is illustrated in Brewer and Lambert [13].32 Cohn et al. [17] propose a cognitive vision system based on abduction and qualitative spatio-temporal representations capable of interpreting the high level semantics of dynamic scenes. Banerjee [8] presents a computational system able to manage events that are characterized by a large number of individual moving elements, either in pursuit of a goal in groups (as in military operations), or subject to underlying physical forces that group elements with similar motion (as in weather phenomena). Visualizing and reasoning about happenings in such domains are treated through a multilayered abductive inference framework where hypotheses largely flow upwards from raw data to a diagram, but there is also a top-down control that asks lower levels to supply alternatives if the higher level hypotheses are not deemed sufficiently coherent.33 The example of a simple hypothetical organism equipped with two fins and two eyes [78] can explain this link between perception and action in the case of vision: “The right eye was connected to the left fin by a neuron, and the left eye to the right fin. When a prey appears within the field of the right eye, a command is sent to the left fin to instruct it to move. The organism then turns towards the prey, and this orientation is maintained by bilateral activation until the prey is reached. Perception in this primitive organism is not distinct from action” [18, pp. 253–254].


the abductive inferential processes performed by hearing that provide substantial models of the scene facing the agent. The whole process is abductive in so far as it provides selections of cues, aggregation of acoustic fragments according to source and an overall hypothetical meaningful explanation of acoustic scenes, that are normally very complex from the point of view of the plurality of acoustic sources. The auditory system of vertebrates which decouples perception from action (motor systems) – still at work together in acoustically rudimentary organisms – enhances economy, speed, and efficacy of the cognitive system by exploiting abstract models of the environment and motor plans.

The digression above about abductive cognition as perception is certainly endowed with an eco-cognitive character, individual human agents, senses, environment, and cognition are all involved. How can we better grasp the complete significance of what I call eco-cognitive model of abduction? As stated above we also need refer to the cognitive science tradition of embodied and distributed cognitive systems: at the of center of my perspective on abductive cognition is the emphasis on the “practical agent”, of the individual agent operating “on the ground”, that is, in the circumstances of real life.

Hence, to better explain my eco-cognitive approach to abduction let me describe some basic concepts regarding distributed and embodied cognitive systems. Early work in distributed cognition was informed by the basic idea that cognition is a socially distributed phenomenon, one that is situated in actual practices. The theory contends that cognitive processes generally are best understood as situated in and distributed across concrete socio-artifactual contexts. The received theories in cognitive science emphasize an internalism that relegates to a lower edge the role of external representations (and so of the correspondent cognitive delegations to various areas of the external environment) and problem solving in collaborative contexts.

The new theoretical view criticizes the traditional accounts of cognition, emphasizing instead the role of concrete social and artifactual contexts. At the same time a kind of ecological perspective stresses the role played by the agent-environment interaction. For example, in current collaborative work environments, we find humans and artifactual technologies together preserving and manipulating representational states, very often to the aim of solving problems. The theory of distributed cognition is motivated by the idea that such complex systems perform authentic cognitive processes and that the cognitive features and properties of these kinds of socially, materially and temporally distributed systems differ from those of the agents that act in them.

The theory of distributed cognition was proposed by Edwin Hutchins to present a new analysis of problem solving processes in real work settings, and to supply a new framework for cognitive science generally. In his seminal study Hutchins [40] describes how agents use tools and instruments (and so external cognitive representations) to produce, create, manipulate, and maintain representational states. Hutchins contends that the cognitive properties of the distributed cognitive system depend on the physical and “material” properties of the external representational media in which they are applied. The theory of distributed cognition does not destroy the concept of individual cognition, even if eco-cognitive aspects are emphasized. The aim is the analysis of cognition as distributed across people and artifacts, and of its strict reference to the interplay of how both internal and external representations.34

It is in the theoretical framework I have just described that my eco-cognitive approach to abduction has to be seen. The backbone of this approach can be found in the manifesto of my EC-model of abduction in Magnani [49]. In all its contexts, from the most abstractly logical and mathematical to the most roughly empirical, I always emphasize the eco-cognitive nature of abduction. Reasoning is something performed by cognitive systems. At a certain level of abstraction and as a first approximation, a cognitive system is a triple (A, T, R), in which A is an agent, T is a cognitive target of the agent, and R relates to the cognitive resources on which the agent can count in the course of trying to meet the target-information, time and computational capacity, to name the three most important. My agents are also embodied distributed cognitive

34 On this interplay and on the role of external representations as material anchors for conceptual blends see also the more recent [41].


systems: cognition is embodied and the interactions between brains, bodies, and external environment are its central aspects. Cognition is occurring taking advantage of a constant exchange of information in a complex distributed system that crosses the boundary between humans, artifacts, and the surrounding environment, where also instinctual and unconscious abilities play an important role. This interplay is especially manifest and clear in various aspects of abductive cognition.35

It is in this perspective that we can appropriately consider perceptual abduction as a fast and uncontrolled knowledge production, that operates for the most part automatically and out of sight, so to speak. This means that – at least in this light – GW-schema is not canonical for abduction. The schema illustrates what I call “sentential abduction” [49, chapter one], that is, abduction rendered by symbols carrying propositional content. It is hard to encompass in this model cases of abductive cognition such as perception or the generation of models in scientific discovery (cf. Magnani [51]). My perspective adopts the wide Peircean philosophical framework, which approaches “inference” semiotically (and not simply “logically”): Peirce distinctly says that all inference is a form of sign activity, where the word sign includes “feeling, image, conception, and other representation” [57, 5.283]. It is clear that this semiotic view is considerably compatible with my perspective on cognitive systems as embodied and distributed systems: the GW-Schema is instead only devoted to illustrate, even if in a very efficacious way, a subset of the cognitive systems abductive activities, the ones that are performed taking advantage of explicit propositional contents. Woods seems to share this conclusion: “[. . . ] the GW-model helps get us started in thinking about abduction, but it is nowhere close, at any level of abstraction, to running the whole show. It does a good job in modelling the ignorance-preserving character of abduction; but, since it leaves the Si of the schema’s clause (T ) unspecified, it makes little contribution to the fill-up problem” [84, p. 244].

In a wide eco-cognitive perspective the cutdown and fill-up problems in abductive cognition appear to be spectacularly contextual.36 I lack the space to give this issue appropriate explanation but it suffices for the purpose of this study to remember that, for example, one thing is to abduce a model or a concept at the various levels of scientific cognitive activities, where the aim of reaching rational knowledge dominates, another thing is to abduce a hypothesis in literature (a fictional character for example), or in moral reasoning (the adoption/acceptation of a hypothetical judgment as a trigger for moral actions). However, in all these cases abductive hypotheses which are evidentially inert are accepted and activated as a basis for action, even if of different kind.

It might seem awkward to speak of “abduction of a hypothesis in literature,” but one of the fascinating aspects of abduction is that not only it can warrant for scientific discovery, but for other kinds of creativity as well. We must not necessarily see abduction as a problem solving device that sets off in response to a cognitive irritation/doubt: conversely, it could be supposed that esthetic abductions (referring to creativity in art, literature, music, etc.) always arise in response to some kind of esthetic irritation that the author (sometimes a genius) perceives in herself or in the public. Moreover, not only esthetic abductions are free from empirical constraints in order to become the “best” choice: as I have shown in [51], many forms of abductive hypotheses in traditionally-perceived-as-rational domains (such as the setting of initial conditions, or axioms, in physics or mathematics) are relatively free from the need of an empirical assessment. Similarly, in empirical science abducing conventions favors and increases knowledge even if these hypotheses remain evidentially inert – at least in the sense that it is not possible to empirically falsify them. Consequently abduced conventions are evidentially inert but knowledge-enhancing at the rational level of science.

35 It is interesting to note that recent research on Model Checking in the area of AST (Automated Software Testing) takes advantage of this eco-cognitive perspective, involving the manipulative character of model-based abduction in the practice of adapting, abstracting, and refining models that do not provide successful predictions. Cf. Angius [7].36 Some acknowledgment of the general contextual character of these kinds of criteria, and a good illustration of the role of coherence, unification, explanatory depth, simplicity, and empirical adequacy in the current literature on scientific abductive best explanation, is given in Mackonis [46].


Furthermore, in science we do not have to confuse the process of abducing models with the process of abducing fictions: the recent epistemological conundrum concerning fictionalism presents to us the epis-temic situation in which the models abduced by scientists reveal themselves not to be “airy nothings” at all, and certainly different in their gnoseological status from literary fictions. Scientific models instead play fundamental “rational” knowledge-enhancing roles: in a static perspective (for example when inserted in a textbook) scientific models can appear fictional to the epistemologist, but their fictional character disappears if a dynamic perspective is adopted. Abduction in scientific model-based reasoning is not a sus-picious process of guessing fictions.37 The same could be said of moral judgements: they are eco-cognitive abductions, inferred upon a range of internal and external cues and, as soon as the judgment hypothe-sis has been abduced, it immediately becomes prescriptive and “true,” informing the agent’s behavior as such.

Assessing that there is a common ground in all of these works of what could be broadly defined as “creativity” does not imply that all of these forms of creativity are the same, contrarily it should spark the need for firm and sensible categorization: otherwise it would be like saying that to construct a doll, a machine-gun and a nuclear reactor are all the same thing because we use our hands in order to do so!

In summary, the example of logical and eco-cognitive research on abduction is certainly exemplar of the fruitfulness of a wide approach to “good reasoning”, which can favor a unexampled root to a new logic of abductive cognition, in the spirit of the naturalization of logic. It clearly shows that traditional logicians uninterested in abduction and in similar forms of third-type reasoning appear exaggeratedly “skeptic about good reasoning. They violate what we might call the maxim of logical generosity toward reasoning” [86, p. 519].

6. Conclusion

The status of logical systems is very controversial: taking advantage of the recent book Errors of Rea-soning: Naturalizing the Logic of Inference, written by John Woods, and of studies concerning abduction, I have proposed a revision of mainstream logic able to bring logic into a creative rapprochement with cog-nitive science. This is achieved by doing for logic what has been already attempted for epistemology, that is a “naturalization” of the logic of human inference. Naturalizing logic needs an agent-based approach, a reassessment of the cognitive status of fallacious reasoning and the adoption of a full and sophisticated eco-cognitive framework. To help the reader in understanding the naturalization of logic I have also illus-trated how the cognitive value of the well-known fallacy of the affirming the consequent (that is abduction, in the light of classical logic) can be vindicated. Abduction is not necessarily an ignorance-preserving kind of cognition. To confirm this conclusion I have taken advantage of my eco-cognitive model (EC-model) of abduction which clarifies that, through abduction, knowledge can be enhanced, even when abduction is not considered an inference to the best explanation in the classical sense of the expression, that is an inference necessarily characterized by an empirical evaluation phase, or an inductive phase, as Peirce called it.

As the very last few words, it should be said that if on the one hand this paper was aimed at promoting the research program on the naturalization of logic, on the other hand it also pursued the aim of stressing the importance of abduction in the good research programmes of logic. And finally, the paper worked toward the secondary but ever-present goal of celebrating the specifically valuable heritage of Charles Sanders Peirce in our contemporary philosophical and logical traditions: whereas C. S. Peirce’s importance is usually acknowledged, this acknowledgment often turns into a lip-service as Peirce is regarded as a mad creative genius, and his specific and ground-breaking contributions to philosophy and logic are often unjustly overlooked.

37 The problem of the knowledge enhancing role of conventions and models in science is analyzed in Magnani [52].


Acknowledgements

For the instructive criticisms and precedent discussions and correspondence that helped me to develop my analysis of the naturalization of logic and/or abductive cognition, I am indebted and grateful to John Woods, Atocha Aliseda, Luís Moniz Pereira, Paul Thagard, Woosuk Park, Athanassios Raftopoulos, Michael Hoffmann, Gerhard Schurz, Walter Carnielli, Akinori Abe, Yukio Ohsawa, Cameron Shelley, Oliver Ray, John Josephson, Ferdinand D. Rivera, to the two reviewers, and to my collaborators Tommaso Bertolotti, Selene Arfini, and Simone Pace.

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