Three Classes of Models

Science is a complex collection of cognitive processes, and these pertain namely to perception, conceptualization, categorization, discovery, explanation, justification, and action.

And in science, one model is usually not enough (Green 2013). They are multiple, and their classification becomes necessary. One of the main classes of models has been the mathematical one. Recently, Weisberg (2015), in his taxon­omy, has added a class of computational models and a class of physical models. Inspired by the taxonomy put forth by Dennett, Marr, and Pylyshyn, and by the analysis of many concrete scientific practices in cognitive science, we shall propose a tripartite and more inclusive classification in which we will include many sub-models. Our three main types of models are: (a) formal, (b) physical, and (c) conceptual models. We see these classes as more inclusive and applicable to many other sciences. Cognitive science practices, compared to natural science, usually call upon one or other sub-models of these three main classes of models in building their theories. These three classes reveal finer properties of the internal dynamics of theories of cognition.

In this taxonomy, the functional stance is seen as a sub-type of formal models. The physical stance, often understood as a physical implementation, is here seen as one particular sub-type of physical models. The knowledge or representational stance is one particular type in the class of conceptual models. We shall explore these three classes of models but always in view of questioning the realist and objectivist thesis in the cognitive science context.

4.1 Formal Models in Cognitive Science

Practically all epistemologists suggest that the main if not the ideal classical model to be used in a theory is a formal model.

In the Hilbertian and Carnapian traditions, a formal system is first and overall an axiomatized system of symbols. Its syntax is highly controlled. Strictly speaking, such a formal system of symbols does not need a semantics for its lexicon and formulas. But normally, as it is applied in some particular domain, it will require interpretation. The various formal systems will then be differentiated by the importance given to the syntax or to the semantics. We shall here distinguish two main but related sub-classes of formal models: mathematical models and compu­tational models.

The first class of models is that of mathematical ones. They are used mainly for expressing functional relations or regular dependencies among the entities identified by predicates describing them in the chosen domain of enquiry. For instance, in physics, the algebraic equation F = ma expresses the functional relations between sets of numerical values pertaining to predicates: FORCE, MASS, ACCELERA­TION. And many variants of these mathematical models exist. For instance, in chemistry, they are mainly algebraic, probabilistic, geometric, and diagrammatic; in physics, the models are mostly algebraic, statistical, etc. In artificial intelligence and linguistics, they are mainly logical, algebraic, and algorithmic.

In cognitive science, many sets of mathematical languages are to be found. A first and most classical type of mathematical model have been inspired by the axiomatic and logical systems. In artificial intelligence (Newell and Simon 1976), knowledge is formalized through a set of physical symbols that become for instance predicates, propositions, or arguments, and they are expressed in a variety of notational systems such as frames (Minsky 1974), conceptual graphs (Sowa 2000), micro-worlds (Genesereth and Nilsson 1987), ontologies (Gruber 1993), and are used in different sorts of reasoning: common sense (McCarthy and Hayes 1969), non-monotonic logic (McDermott and Doyle 1980), description logic, semantic networks (Levesque and Brachman 1987), and causal reasoning (Pearl 2000).

Cognitive empirical psychology working on learning processes has explored probabilistic models namely for describing and explaining the evolution and sta­bilization of learning. We may consider for instance Hebb's law which is expressed as a simple linear algebraic equation.

1 P ^wij = p E ^Xi^Xj, Pk =1

Connectionism (Rumelhart and McClelland 1987) has explored linear and non-linear algebra, while Smolensky (1986) has proposed tensor algebra. Hohwy (2014) used Bayesian probability for predictive reasoning. Cognitive linguistics (Langacker 1987; Talmy 2000; Evans 2009) offer topological structures with homomorphisms for the mental lexicon and statements from mental spaces, among other things. Neurosciences also described and explained brain processes with linear and non-linear, dynamic, chaotic, geometrical, and Bayesian systems. Finally, robotics includes a hybrid set of such models. Each choice depends on the functions of their modules and their interaction.

The second class of formal models is that of the computable models. These models are a subset of formal models (not to be conflated with mathematical models) in that they use calculable symbolic systems. A calculable system is one where the manipulation of symbolic expressions (irrespective of meaning) can decide whether a specific expression (equation, formula) belongs or not to the system. Turing (1936) demonstrated that calculability is equivalent to the “com­putation” performed by a physical and mechanical machine called a Turing machine. All calculable systems are computable systems. Later on, they were defined in algorithmic terms (Markov 1960), in productive terms (Post 1936), and in combinatorial terms (Curry and Feys 1958). Von Neumann (1945) has in turn demonstrated that certain physical architectures of computers are a specific sort of concrete Turing machine.

Thus, in a more general formulation, a functional expression of a mathematical system is calculable or computable, algorithmic, etc., if there exists an effective procedure to process inputs and systematically produce results.

In cognitive science, computational models are of the utmost importance. Some claimed (Fodor 2008; Pylyshyn 1984; among others) that cognitive processes can only be described and explained by computational models. But not all cognitivists accepted this thesis. Some connectionists, neuroscientists, and philosophers pre­ferred algebraic, dynamic system models, which they saw as external to the com­putational paradigm of cognitive science for it allowed a reduction of the theory to the physical brain (van Gelder 1997; Brooks 1991).

We wish to replace the ‘computer metaphor' as a model of mind with the brain metaphor as models of the mind (Rumelhart and McClelland 1987:1:75).

Still, following more technical examination^[128] (Davis 1982; Utal 2003) these models remain computational. They even have been developed into the “neuro­computing” field of research (Sejnowski and Churchland 1992).

Computation might be understood as a collection of active recursive functions operating on symbolic list structures. Alternatively, it might be understood as parallel-operating “knowledge sources” reading from, transforming, and writing complex symbolic expres­sions on a “black board” (Nilsson 2007).

As Mundici and Sieg (1993:30) have argued, computational modelling in cog­nitive science modifies the understanding of a scientific law. A law can be defined in a formal way as classically proposed, but computation helps to detail the proof. However, more importantly, when the function is not known, but a sample of its behaviour is observable (i.e. a sample of its extension), learning algorithms can approximate the function. The law then is not necessarily expressed by means of a general expression (i.e. intensionally), but can nevertheless be approximated by means of an algorithmic model like a perceptron, a random forest, or the like.

What happens then to the realist and objectivist thesis in the context of cognitive formal models? The answer to this question is quite direct.

Everywhere, from mathematics to computer science, to physics, to mathematically- formulated portions of chemistry, biology, ecology, and economics (Chaitin et al. 2012).

The non-computability problem indirectly affects the realist and objectivist thesis in cognitive formal models. A solution to this may be to propose adjustments to the system, such as Turing's solution of Oracles or the adding of rules or axioms in the systems. But in doing so, realism or objectivity is not better guaranteed. This only adds more complexity: “Just add new axioms, increase the complexity of your theory” (Chaitin et al. 2012:36). In this perspective, the only solution would be to adjust the system by controlling its semantic and pragmatic interpretation which, however and by definition, is exterior to a formal system. And this addition is subject to all the problems of interpretation and adjustment that are classical in the semantic view of theories.

Still, even staying in the inner structure of the formalisms themselves, it has been shown that they are often riddled with hidden technical formal problems that affect the result's objectivity and truth. For instance, many abbreviation symbols for example: the integral symbol) have presented many problems regarding the manipulation of mathematical symbols (Woodhouse 1803; Koppelman 1971). Another one is the manipulation of variables (Descles 2006). So much that Curry and Feys (1958) have proposed a language without variables: combinatorial logic.

Formal cognitive models do not escape these problems. The multiple conditions for a strict computational model are not that easily met. A typical example is Fodor’s (1983) modular proposition for modelling cognitive operations. This was explored systematically in AI projects such as expert systems, for instance. These types of programs contained specific computable modules. But because they were well-formed, they were seen as interchangeable with other modules in other pro­grams. And it was hoped that they could operate just as well in this new envi­ronment and preserve truthfulness. But this ideal was problematic. Even though the modules, when exported into a new environment, were still formally identical, their semantics may have changed. Adjustments require heuristics or oracles, and this increased the complexity and the risk of non-decidability. It was opening the door for ‘bugs’ (Meunier 2003).

Other problems touch upon the multiplicity and complexity of functions, their sensibility to evolution, their variety among subjects, etc. In other words, the formal models, even if very mathematical and computational, are not exempt of adaptive interventions and their semantics may include biases. This challenges the realist and objectivist ideal in a particular way.

4.2 Physical Models in Cognitive Science

One important problem of formal models is their epistemic distance with causal explanation (Salmon 1984). For instance, the physics equation F = ma does say that F is caused by the multiplication of m by a! Equations do not deliver a complete explanation for the human understanding of a phenomenon. According to the Humean tradition in the philosophy of science (Thagard 2000), a causal explanation is one that allows predictability.^[129] So scientific theory will often include a second class of models: the physical models. They contribute to such causal explanations.

These types of physical models are used regularly in natural science. They are so integrated that often they become transparent as models. But many researchers (Baetu 2013; Rheinberger 1997; Leonelli 2007) have studied examples of these types of models. A typical one is Newton's laws of motion. It has among its formal models the equation or law F = ma. A concrete physical model for this equation takes the form of an implementation in specific and selected physical entities linked by observable causal relations. And this physical model concretely contributes to the semantics of the symbols “F,” “m,” “a,” “=,” and “x” (hidden multiplication symbol) by linking them to a numerical value associated to a concrete mass, a concrete acceleration for an effective force^[130] and operations on these values.

When a many-model implementation is well controlled and systematized, it becomes, in fact, a many-individual physical experiment which can be considered as concrete proof of the formal model. And various statistical analyses will allow the generalization of the variations of a set of experimental numerical values. In other words, we can see experimental implementations of formal equations as physical models distributed over time.

These types of physical models are omnipresent in cognitive science. They define a first class of physical models which Bechtel (2008) and Craver (2016) call causal mechanical models:

Mechanists insist explanation is a matter of elucidating the causal structures that produce, underlie, or maintain the phenomenon of interest (Craver et al. 2016).

The term mechanism is as ubiquitous in psychology, cognitive science, and cognitive neuroscience as it is in the domains of biology to which philosophers have appealed in articulating the account offered above of what a mechanism is (Bechtel 2008:22).

The brain for instance is such a mechanism:

Brain mechanisms, accordingly, are far more likely to be structured and organized in ways particularly suitable to the tasks they must perform (Bechtel 2008:3).

The brain is seen as a causal mechanism constituted by parts that are cells with various levels of organization that form a complex neural structure. Their interac­tions are made of electrochemical synaptic connections. Even if the brain is not a machine mechanism, it constitutes a biological mechanism. Because of this argu­ment, the brain is modelled as a sort of computing machine. But it cannot be seen as an electronic computer. It is a neurocomputing machine. In neural theory, it can thus be seen as a physical mechanical model that instantiates/implements the computable functions given in the formal models.

In this same perspective, it follows that connectionist models are not physical models implementing formal equations. They are formal models: a set of linear and non-linear dynamic algebraic equations. They have effectively been called artificial neural net models and they are used to describe the dynamics of physical neurons.

More examples of physical models are found in other cognitive sciences. A cognitive psychologist may be confronted with sets of data originating from causal experiments where physical neurons of monkeys are actually stimulated these data in turn, can be submitted to learning algorithms (Michalsky 1983; Mitchell 1997) that can approximate the functions describing the causal relations among the data. And a formal model could express this function in an algebraic equation such as for example Hebb's law. In neuroscience, Eliasmith (2003) identifies such regularities in the activation and pathways of physical neurons and offers mathematical dynamic system models to explain these behaviour patterns.

The second class of physical models are strictly speaking computer models. As we have said above, computational models are mathematical or virtual models. Turing (1936) did in fact distinguish a virtual computing machine A and an actual physical machine B. The A machine was a diagrammatic formal computable function. The B machine, a mechanism made namely of a motor, some paper, and ink (often called the “the Turing machine”), instantiated physically the virtual machine A. Its purpose was to concretely and effectively implement the computa­tion of a formal function. A contemporary computer is a B Turing machine with a Von Neumann architecture realized physically in an electronic circuit. It has ef­fective procedures (Copeland 2000) that compute a “computable” function. In this sense, each effective computation by a computer is a physical model implementing formal functions.

Artificial intelligence programs are typically “implemented” in physical causal computer models. Often, these types of physical modelling of “intelligent behav­iors” are called computer simulations. For instance, in simulating vision, a com­puter may receive through its own captor's input signals similar to the ones received by the cones, rods, and iris of the eyes. It then applies to these input signals some computer effective electronic process so as to produce a behaviour simulating an eye seeing something.

A variant of visual simulation is computer-based visual representation often called “visualization.” The “causal” state transitions of the computing operations are projected on a monitor, where they are “illustrated” by colouring pixels in such a way as to be recognized by humans as images or as iconic figures, for instance. In many AI and cognitive sciences, visualization is a part of the proof methodology: For example, an IMR activation visualization uses colour intensity and tone to represent the degree of activation of computational functions translating the impulses in a specific brain area.

In more sophisticated visualization simulations, metaphorical names are given to these simulations. In information retrieval, paths of research may be called maps, or nets (Gentner 1983). Many complex cognitive behaviours (analysis, decision-making, strategies, narration, etc.) are simulated by means of “games.” Complex “electronic machines,” simulating very complex cognitive processes, are called “robots.” They are complex computer instantiations of formal computational models of cognitive behaviours. Technically speaking, robots do not “think,” “decide,” ‘‘desire,” or whatever. No more than there is a real “trash bin” or a real “desk” on the monitor screen.

How do these physical models relate to our realism and objectivity problems? The following argument by Craver (2006) explicitly reveals it. As he well stated:

Constitutive explanations go beyond merely describing the phenomenon. They describe the mechanism responsible for the phenomenon, that is, the mechanism that explains its diverse features^[131] (Craver 2006:153).

As explained when addressing the case of formal models, the physical model contributes to the semantics of formal models. Models are mediators between the formula of the formal models and the physical phenomenon itself. They are proxies (replicas, simulations, implementations) for the phenomenon. As physical entities, they possess observable properties or features. But not all of their properties and features are relevant for a scientific theory. For example, if pushing a billiard ball on a carpet is taken as a physical model, not all the properties and features of this model are relevant for the Newtonian law F = ma. For instance, the colour and the type of marble of the ball are not relevant. A choice must be made, and this choice has criteria. A first one requires that the features chosen must be representable in the formal model. For instance, the mass is representable by “m” in F = ma. But another one is preliminary to this first one. For example, what, technically, is the physical property to be put into correspondence or to be associated with the mass? Is it its weight? Its molecular structure? Is it its electromagnetism? In natural science, instruments and controlled protocols are often the means by which these features are identified as pertinent and to which a numerical value can be associated. And strict observation language is used to express these features. Still, it has been shown that these means imply theoretical commitments on the part of the researchers.

In cognitive science, these problems are also to be found in the physical models. Choices of relevant features must be made. But here, the instruments and obser­vation language cannot be controlled as easily when the physical models require complex interpretative acts. For instance, a computerized physical model may associate to its variables and operations certain physical entities and apply to them effective electronic computing processes. The dynamics of the processes and their results can be associated with some visualizations that are recognizable by scien­tists. For example, a brain scan will “dynamically” represent states of neural acti­vation via the colouring of pixels of a computer monitor. These visualizations are then interpreted as “areas”, “paths”, etc. But these interpretations are committed to complex physical theories and are associated to concepts pertaining to phenomenal and introspective if not cultural accounts, as in the example in the Kanizsa triangle illusion referred to above. I see a circle, triangle, etc. A nice illustrative example of this is the brain scans of nuns in relation to their verbal accounts of their “spiritual experiences”. The activated areas are interpreted as “spiritual areas”. The authors of the study prudently said that these areas could not be identified as “God spots” (Beauregard 2006).

In other words, the semantic and pragmatic role that physical models play by their properties and features will often be influenced in their construction by some paradigmatic theories. In this sense, cognitive science physical models often require many implicit theoretical commitments if not even some tacit personal and cultural influences. This directly challenges the realist and objectivist ideal for the physical models.

4.3 Conceptual Models in Cognitive Science

Scientific research usually starts by an interrogation about a phenomenon. For example: Why do apples fall? Or: Why is there a tide? Why do humans have emotions? How does the brain memorize places? Do neurons learn? The answers to these questions cannot, for example, be given only in the form of equations, physical replica, or simulations of a phenomenon. A scientist usually adds some natural language sentences that for himself or for his epistemic community expresses a conceptualization of the problem and the way he would cope with it. In other words, he presents a conceptual model of the research problem.

Conceptual models share similar purposes with the other types of models. They are also mediators but they are used mainly for understanding, discovering, justi­fying, and communicating the research problem and solution explored in the sci­entific enquiry. They are not always expressed in natural language for they may take various other semiotic forms such as pictures, graphs, or films, all of which have their own ways of expressing conceptual structures. Still, these conceptual models have some specificity.

First of all, conceptual models determine the conceptual framework, the con­ceptual “space” (Gardenfors 2000), conceptual system (Brown 2007), and mental models (Johnson-Laird 1986) that are part of human explicit or tacit knowledge (Polanyi 1967), and through which humans ultimately understand the explanations given in a scientific theory. Secondly, they are heuristic in that they express various formulations of intuitions, hypotheses, and the methodologies upon which the scientific theory rests. Thirdly, they have a communicative role and they are mostly expressed in natural language, meaning the various contents will be shared with different epistemic communities.

These conceptual models are omnipresent in science, so much that they become transparent to the user. And even if they are not as rigorous as other models, they are still models in the strict sense because, as Cartwright says, models are an idealized and simplified representation:

A model is by nature a simplified and therefore fictional or idealized representation, often taking quite a rough-and-ready form: hence the term “tinker toy” model from physics, accurately suggesting play, relative crudity, and heuristic purpose (Cartwright 1983:158).

A classical example explored in natural science is the Copernican theory, by Kuhn (1957). One of the important debates around this theory was not only about the mathematical equations describing and predicting the movement of planets. It was also about the conceptual space in which the formal model was understood. It clashed with the existing religious conceptual spaces.

In cognitive science, a nice example of a transparent conceptual model is to be found in M. Graziano’s introduction to his neuropsychology book Consciousness and the Social Brain. Here is a sample of this introduction:

The brain is composed of neurons that pass information among each other. Information is more efficiently linked from one neuron to another, and more efficiently maintained over short periods of time, if the electrical signals of neurons oscillate in synchrony. Therefore, consciousness might be caused by electrical activity of many neurons oscillating together (Graziano 2013:6).

Here, we are not reading equations or seeing some physical instance or replica of neurons. We are reading sentences that express some concepts specific to a con­ceptual framework built out of past and contemporary cognitive science and other theoretical influences, such as concepts from neuroscience, information theory, control theories, philosophical theories of causes, consciousness, attention, etc. They participate in Graziano’s conceptual models of his theory of consciousness and attention. In fact, they take up some 80% of the book.

Such conceptual modelling is omnipresent in all sciences. We shall explore here three main types that are usually found in cognitive science: (a) the intentional, (b) the observational, and (c) the rhetorical models.

The first type, surely the most classical one, is the representational (Fodor 1981; Pylyshyn 1984) or intentional model. Such a model, says Dennett, explains the systems’ behaviour by ascribing goals to it.

One predicts behaviour in such a case by ascribing to the system the possession of certain information and supposing it to be directed by certain goals (Dennett 1971:224).

This type of model explores and explains cognitive phenomena by grounding them in a principle of rationality, a principle that ultimately allows inferentiality and normativity in the manipulation of representations (Sellars 1948; Brandom 1994).

The practical uptake of specifically representational purport must include normative assessment of states, performances, and expressions—assessment of their specifically representational correctness (Brandom 1994:78).

Finally, these models, even formulated simply as in folk psychology, are the anchors for understanding. For humans, they serve as mediator in the interpretation and the understanding of cognitive phenomena.

A second type of conceptual models is the observational models. They are popular with the empiricists if not the experimentalist scientists:

[E]xperiential data might be conceived of as being sensations, perceptions, and similar phenomena of immediate experience (Hempel 1952:740, 829).

Their aim is to report cognitive experiences as perceived by a cognitive agent. And if used in science, they have to be controlled, instrumentalized, and formalized. But whatever they are used for, they are usually expressed in natural language terms and sentences such as the following examples of first-person experience accounts: I see, I fell, I hear, I listen, I perceive, I touch, I taste, etc.

The sentences built out of these words refer to subjective data and become translated into variables and operations. Often, in some cognitive sciences, the observation may belong to inner experiences as described by an experimental subject. In his brain exploration by direct stimulation, Penfield (1959) could only describe the inner reaction of the subject by the phenomenological sentences and words given by the patient: I see myself with my son, I recall my mother, etc. This type of observational model has been shown to contain complex epistemological and epistemic problems specific to observation languages or even to other types of conceptually explicit semiotic forms such as iconic languages (maps, graphs, etc.).

A third type of conceptual model is a rhetorical conceptual model. In explaining a phenomenon, it explores various types of rhetorical strategies so as to mediate the understanding of complex phenomena. Many philosophers of science (Hartmann 1995; Knuuttila 2011) have underlined the presence of such types of models in science. As Morgan and Morrison say, one main task of models is “fitting together [...] bits which come from disparate sources [...] [including] stories” (Morgan and Morrison 1999:15). To express these problems, conceptual models will take rhetorical forms such as analogies, fictions, and metaphors, if not narration. Lakoff and Johnson (2003) are among those who regard metaphors and analogies as the main underlying process of thinking. They are omnipresent in natural and cognitive sciences.

As Hesse has shown, analogies and metaphors are often used in science to introduce and manipulate various theoretical entities: “most physicists do not regard models as literal descriptions of nature, but as standing in a relation of analogy to nature” (Hesse 1963:2011). A classical example of this is the famous illustrations of the Brownian movement through billiard balls or the atom as a planetary system (Rutherford and Bohr).

Artificial intelligence constantly uses metaphors in presenting its research pro­grams. For instance, the behaviour of a robot cannot be explained only by a list of program lines. Azimo, for example, is presented as “thinking”, “communicating”, “meeting people”, answering questions, etc. Such words referring to human cog­nition are analogically projected onto robots. Metaphors are found to be more “hard” and formal in connectionist models. Many of their concepts are explained in a conceptual model. They are translated in natural language by words such as stimuli, impulses, point of gravity, attractors, stabilization, chaos, or equilibrium, or by sentences such as: Neurons communicate with other neurons. They talk to each other, exchange information.

In cognitive science, one important form that a conceptual model often takes is called pop psychology. Many cognitive behaviours are then modelled through a variety and a mixture of general concepts, analogies, metaphors, and fictions. Concepts such as motivation, beliefs, desires, attention, decision consciousness, will, or temptations are of the sort. They belong to a Judeo-Christian folk philos­ophy of mental processes. For naturalists (Smart 1959; Armstrong 1968; Church­land 1988), such discourse is useless, and it should be discredited and abandoned. It does not belong to a scientific theory or model. They should be reduced to empirical “causal and physical models concepts”.

Dennett (1978) and Fodor (2008) however recognize the role of these folk discourses in science. Analogies, fiction, and metaphors are heuristic means in thinking. We find them at the beginning of research where the explanandum is presented. They reappear at the middle of the research where the explanans are elaborated and inferences are made. And at the end, results of the research are anchored in the conceptual space of the individual or the epistemic community. Some complex mathematical equations are sometimes only understandable by humans if translated into folk-understandable terms such as chaos, bifurcation, emergence, attractors, oracles, if not motivation, will, and communication.

There probably exist other variants of the conceptual models. We have presented only three of them: the intentional models, the observational models, and the rhetorical models. Their difference lies in the content of the conceptual models.

They offer different points of view, emphasize different dimensions of the research problem and therefore determine different conceptual spaces. Theories are intro­duced, illustrated, and ultimately understood by means of conceptual models. They are a necessary part of scientific theory.

How does the conceptual model deal with realism and objectivity? As we may guess, the various conceptual models directly challenge once more the realist and objectivist thesis. They are often taken as proofs by anti-realists of the non-validity of the realist thesis. They are prototypes of the constructiveness inherent to sci­entific theories. Here are a few of the problems these models raise.

A first one pertains to the predicates the conceptual model chose to express the features and properties of the cognitive processes. Where do they come from? Most of them do not originate from the experimental schema or the rigorously controlled instruments. For instance, some of these predicate are in the narrative of personal introspection or cultural analysis. For example, the predicate “mourning” names a specific cognitive experience belonging to a personal or cultural experience. And from a purely lexical semantic point of view this predicat has its own social or cultural connotation. Even with standardized observation criteria, a scientist “ob­serving” the Kanizsa triangle will rely on his introspection of the illusion. Other concepts are part of general culture. For example, the results of Rizzolatti’s (1999) experiments on the brain of macaque monkeys have been translated into conceptual terms such as mirror and neurons, and some of their functions are translated as empathy. If one does not situate the concept of mirror, neurons, or of empathy in their own conceptual space, understanding will be difficult. Hence, because the predicates used in conceptual models are often grounded in subjective first-person experiences (introspection) or shared with third-person reports (culture), pure realism and objectivity in the conceptual model is challenged.

The second problem of the conceptual model pertains to the overall language chosen to express the concept. As said before, the language usually chosen is a natural language and not a formal one. Hence, the model will suffer of the many defects of a natural language. For instance, at the level of syntax, not all sentences or lexemes will be strictly controlled. And at the level of semantic and pragmatics, the various epistemic conventions for building the conceptual models are not always stable and explicit. Ambiguity will be omnipresent, formal rules of inference will not be strictly followed. Generalizations will be fuzzy and modality will be implicit. For instance, when describing the cognitive behaviour of an Alzheimer’s patient, what does it mean to say he is disoriented? Does it mean: losing one’s bearings or not knowing where one is in one’s house? Does it not also imply a normative judgment?

As one may guess, such language directly affects the rigour of science and therefore contravenes to the realist and objectivist thesis.

Let’s conclude by saying that maybe some user may think that the conceptual model is objective and expresses reality, but the language or semiotic forms chosen will often use predicates whose semantics and pragmatics are grounded in sub­jective and cultural conceptual spaces. These predicates suffer from the main defects (but also richness) of all natural semiotic forms: ambiguity, fuzziness, incorrectness in reasoning, etc. The realist thesis is therefore directly questioned in the conceptual models.

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