A Peircean account of concepts

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Review Cite this article: Cuccio V, Gallese V. 2018 A Peircean account of concepts: grounding abstraction in phylogeny through a comparative neuroscientific perspective. Phil. Trans. R. Soc. B 373: 20170128. http://dx.doi.org/10.1098/rstb.2017.0128 Accepted: 16 March 2018 One contribution of 23 to a theme issue Varieties of abstract concepts: development, use and representation in the brain. Subject Areas: neuroscience, cognition Keywords: abstraction, concepts, Embodied Simulation, icon, mirror neurons, Peirce Author for correspondence: Vittorio Gallese e-mail: vittorio.gallese@unipr.it

A Peircean account of concepts: grounding abstraction in phylogeny through a comparative neuroscientific perspective Valentina Cuccio1 and Vittorio Gallese2,3 1

Department of Humanities, Social Sciences and Cultural Industries, and 2Department of Medicine and Surgery, Unit of Neuroscience, University of Parma, Parma, Italy 3 Institute of Philosophy, School of Advanced Study, University of London, London, UK VG, 0000-0003-4815-3607 The nature of concepts has always been a hotly debated topic in both philosophy and psychology and, more recently, also in cognitive neuroscience. Different accounts have been proposed of what concepts are. These accounts reflect deeply different conceptions of how the human mind works. In the last decades, two diametrically opposed theories of human cognition have been discussed and empirically investigated: the Computational Theory of Mind, on the one hand (Fodor 1983 The modularity of mind: an essay on faculty psychology; Pylyshyn 1984 Computation and cognition: toward a foundation for cognitive science), and Embodied Cognition (Barsalou 2008 Annu. Rev. Psychol. 59, 617645. (doi:10.1146/annurev.psych.59.103006.093639); Gallese & Lakoff 2005 Cogn. Neuropsychol. 22, 455479 (doi:10.1080/ 02643290442000310); Shapiro 2011 Embodied cognition), on the other hand. The former proposes that concepts are abstract and amodal symbols in the language of thought, while the latter argues for the embodied nature of concepts that are conceived of as grounded in actions and perception. The embodiment of both concrete and abstract concepts has been challenged by many (e.g. Mahon & Caramazza 2008 J. Physiol. 102, 5970. (doi:10. 1016/j.jphysparis.2008.03.004); Caramazza et al. 2014 Annu. Rev. Neurosci. 37, 115. (doi:10.1146/annurev-neuro-071013-013950)). These challenges will be here taken seriously and addressed from a comparative perspective. We will provide a phylogenetic and neurobiologically inspired account of the embodied nature of both abstract and concrete concepts. We will propose that, although differing in certain respect, they both might have a bodily foundation. Commonalities between abstract and concrete concepts will be explained by recurring to the Peircean notions of icon and abductive inference (CP 2.247). According to Peirce, icons are the kind of signs on which abductive inferences rest (Peirce CS 1931 in Collected papers of Charles S. Peirce, Hartshorne C, Weiss P, Burks AW. (eds), 40; Peirce CS 1997 In The 1903 Harvard lectures on pragmatism (ed. A. Turrisi)). It will be claimed that the mechanism of Embodied Simulation (Gallese & Sinigaglia 2011 Trends Cogn. Sci. 15, 512519. (doi:10.1016/j.tics.2011.09.003)) can be described as an icon (Cuccio V & Caruana F. 2015 Il corpo come icona. Abduzione, strumenti ed Embodied Simulation. Versus, n. 119, 93103), and it will then be suggested that on these, basic natural signs rest, both phylogenetically and ontogenetically, the capacity to conceptualize. This article is part of the theme issue Varieties of abstract concepts: development, use and representation in the brain.

1. Introduction Concepts are the constituents of thought. This claim that, at first sight, seems to be trivially true, will reveal, when carefully analysed, the profound disagreement that characterizes the debate on the nature of concepts. In fact, the

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(a) Embodied cognition and the challenge of abstract concepts The understanding of the modality of acquisition and representation of abstract concepts is a real challenge for embodied theories of cognition and, among embodied

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concepts as man and unmarried. We can plausibly elaborate and test a hypothesis about the concept bachelor relying on our previous conceptual knowledge (man and unmarried). However, the hypothesis-testing model cannot be applied to simple concepts (e.g. salty or green) that cannot be reduced to simpler mental symbols. It follows that, if the hypothesistesting model is our best model of concepts learning, simple concepts, that cannot be learned, must be innate. Of course, while, in Fodors view, perceptual experiences cannot ground conceptual learning, they still have a role in the development of our conceptual system. Indeed, analogously to what Chomsky has suggested for the process of the acquisition of language, in Fodors view, perceptual experiences trigger the recovery of innate concepts. More or less, as in the Platonic dialogue, Socrates guides and triggers Menos knowledge of the Pythagorean theorem [13]. As we have already noted, Fodors proposal for Radical Concepts Nativism is considered highly controversial and has been rejected even by supporters of the language of thought hypothesis (see [12] for a discussion). However, the CRTM today is still the dominant approach in the Cognitive Sciences. This is so because it undoubtedly has the great merit to provide powerful explanatory tools that allow to analyse the human mind and to explain some of its aspects, e.g. the productivity of thought, that otherwise would be very difficult to understand. Notwithstanding, in the last years, the CRTM [79,80] has been radically challenged by an alternative paradigm, Embodied Cognition, that is deeply grounded in the Empiricist tradition. Embodied Cognition is today the main competitor, and a very powerful one, for the CRTM. It is worth noting that Embodied Cognition is not a unitary research programme. Currently, there are different accounts of Embodied Cognition (see Shapiro [14] for a discussion) that seem to differ in many respects. However, all these accounts share at least two features: (i) they all reject CRTM and basically deny the idea that cognitive processes are merely computations on amodal symbols; (ii) they highlight the role that our body has in cognition and propose that cognitive processes (e.g. language, reasoning and mind-reading; [15]) are rooted in perception and action systems [1619]. In this view, concepts, too, are rooted in our systems for action and perception [20,21]. This claim is supported by copious empirical evidence, especially after the discoveries of mirror neurons [22,23] and the formulation of the Embodied Simulation theory [2426] that have widely shown the involvement of the sensorimotor system in human cognition (data on mirror neurons and the mechanism of simulation, and their implications for the debate on the nature of concepts, will be discussed in 2). Several objections have been raised to this embodied account of concepts (e.g. [27,28]). The main and most critical is the one related to the bodily foundation of abstract concepts. While the embodied nature of concrete concepts seems to be less controversial and even, for some, intuitively evident, the bodily foundation of abstract concepts seems to be highly controversial and counterintuitive.

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definitions of concept and thought are highly controversial as it is controversial, ultimately, our understanding of what the human mind is and how it works. Philosophers, psychologists and, more recently, also cognitive neuroscientists have been proposing very different accounts of the nature of concepts which, no doubt, reflect different conceptions of human nature. Answering the basic ontological question about what concepts are inevitably forces us to take a stand on traditional issues such as, for example, the dispute between nativism and empiricism. Do we learn our concepts/ideas on the basis of our perceptual experiences, as proposed by classic authors of the British Empiricism such as Locke & Hume [1,2] or do we have innate concepts as proposed by giants in the tradition of rationalism such as Descartes & Leibniz [3,4]? Nativism and empiricism, as radically alternative frameworks, have been modelling the discussion in Western philosophy at least since Plato and Aristotle and are still today the schemas within which much of the philosophical debate is carried out. In the last decades, since Chomsky [5,6] presented his nativist conception of language and Fodor [7] proposed the language of thought hypothesis, nativism has gained momentum in the Cognitive Sciences and has become the mainstream perspective on the debate on the nature of concepts. In Fodors hypothesis, concepts are considered as psychological entities, i.e. mental representations, which combine in a language-like form to produce thoughts. Thus, concepts are the words of our mental lexicon and thoughts are like complex linguistic expressions whose meanings are determined by the meanings of their constituent parts plus the syntactic rules used to combine them (see Frege [8] for the Principle of Semantic Compositionality). According to this hypothesis, concepts, the symbols that constitute our mental lexicon, are abstract and amodal (i.e. their format of representation is such that it allows us to represent every content independently from the sensory modality that could have been involved in its perception). Cognitive processes are considered as computations on these amodal symbols. These are the core tenets of the so-called Computational and Representational Theory of Mind (henceforth, CRTM) that has been and still is the dominant approach in Cognitive Sciences. Radical Concepts Nativism, in Fodors view, is a part of this story, too. Virtually, according to Fodor [7,9], all simple concepts are innate. Although this conclusion has been highly criticized (e.g. [10]) and considered as a proposal that cannot even be taken seriously [11], Fodors argument is far from being completely unsound and, as Laurence & Margolis [12] have suggested, Fodors puzzle poses a real challenge to those who wish to develop a convincing model of concepts learning. Fodors argument goes more or less like this: according to the Empiricist models, we learn a new concept on the basis of our experiences that allow us to elaborate and confirm our hypotheses about the meaning of that concept. In other words, Empiricist approaches contend that concepts learning is based on a hypothesis-testing model. We elaborate, and then empirically test, hypotheses about the meaning of concepts. Thus, concepts learning, in the empiricist account, implies that learners already possess meanings or mental contents related to the concepts they will test and then acquire. But this last claim can be plausibly applied only to complex concepts such as, for example, the complex concept, bachelor, that can be reduced to simpler

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2. Concepts and the brain: Embodied Simulation The notion of abstraction refers to the cognitive processes by means of which general concepts are formed. (It is worth noting that multiple understandings of abstraction are currently discussed in the literature; for review, see Saitta & Zucker [42].) According to this view, abstraction requires the omission of particular features of a given collection of things or state of affairs, while preserving their most relevant commonalities. The distinctiveness of concepts and abstract thought has been considered to be a unique trait of our species, as it has been traditionally related to another human-specific feature: language. According to this perspective, the possibility to entertain conceptual representations would be precluded to species devoid of language [4345]. As previously argued [31], this perspective is highly problematic, because neuroscientific evidence shows that nonhuman primates, that is, creatures devoid of language, show evidence of conceptual-like mapping, although we contend that a full-fledged conceptual system also relies on language in ways that will be further discussed in the rest of this paper. An extensive amount of empirical data has shown that cortical premotor areas in non-human primates are endowed with sensory properties. They contain neurons that respond to visual, somatosensory and auditory stimuli. On the other hand, posterior parietal areas, traditionally considered to associate purely sensory information, in fact, play a major role in motor control. The premotor and parietal areas, rather than having separate and independent functions, are neurally integrated not only to control action, but also to serve the function of constructing an integrated representation of actions together with objects acted on and locations towards which actions are directed. This functional organization supports two important functions: (i) providing coherent frames

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is the role played by language. According to some proposals, it is conceived merely as a clue to access meaning (e.g. [36]), while according to others it has a constitutive role in concept formation (e.g. [37,38]). In 3, we will provide an embodied account of both abstract and concrete concepts coherent with the multiple representation approach. We will propose that, although differing in certain respects, they both might have a bodily foundation and both make use of linguistic information. Commonalities between abstract and concrete concepts will be explained by recurring to the Peircean notions of icon and abductive inference (CP 2.247). According to Peirce, icons are the kind of signs on which abductive inferences rest ([39], CP 296; [40], PPM 276). It will be claimed that the mechanism of Embodied Simulation [24 26] can be described as an icon [41]. It will be suggested that the ability to interpret iconic relationships might have provided, both phylogenetically and ontogenetically, the ground for the acquisition of abstract and concrete concepts. Abductive inferences will be presented as the inferential process on which the ability to interpret icon/Embodied Simulation rests. It will also be claimed that although the ability to conceptualize is philogenetically and ontogenetically grounded in the mechanism of Embodied Simulation, and in our view this holds true for both concrete and abstract concepts, at the same time, concrete and abstract concepts differ in some respect as for their acquisition and representation.

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approaches, very different accounts have been proposed. Basically, as Borghi et al. [29, p. 4] have highlighted, two antithetical attitudes have been observed. On the one hand, there are those that contend that both concrete and abstract concepts are bodily grounded and share, more or less, the same mechanisms and modalities of representations. In this view, the representation of both concrete and abstract concepts recruits brain systems for action and perception (e.g. [30]). According to a stronger version of this claim, concrete and abstract concepts do not differ at all. The discovery of mirror neurons [22] and the development of the Embodied Simulation theory [24 26,31] certainly gave momentum to this approach (see 2 of this paper for a deeper discussion). However, although findings in support of this claim are abundant and coherent, we must admit that they are not sufficient to draw the conclusion that all abstract concepts are grounded in action and perception systems. This is so because only particular kinds of abstract concepts (e.g. metaphorical concepts such as to grasp an idea) have been empirically investigated and have been found grounded in action and perception systems. We are, thus, not legitimated to extend these conclusions to other kinds of abstract concepts such as politics or metaphysics. As Borghi et al. [29, p. 4] have noted, there is a second attitude towards the issue of the embodiment of abstract concepts. There are those that propose that, although concrete and abstract concepts are both embodied, they differ with respect to the neural mechanisms underpinning them and, consequently, with respect to their modalities of acquisition and representation. In this approach, the most influential account is, no doubt, the Conceptual Metaphor Theory (henceforth, CMT; [32]). According to Lakoff & Johnson [32], abstract concepts are mainly the product (the target) of a metaphorical mapping whose source is a concrete concept. Hence, the metaphorical mapping is the mechanism that explains the bodily grounding of abstract concepts. Life is a journey is a classic example of conceptual metaphor where the abstract concept life is structured through and grounded in the physical experience of a journey [20,33]. However, this is not a general rule. While basic spatial concepts (e.g. orientation concepts such as up-down) emerge directly from our sensorimotor experiences, thus no mapping is implied, CMT also considers concrete concrete and abstract abstract mappings ([34], p. 45), although they are, by far, less important. Furthermore, it has been objected that not all abstract concepts can be explained by recurring to metaphorical mapping [29] and that the mechanism of metaphorical mapping is not sufficient to account for the acquisition of abstract concepts [35]. Thus, CMT, although quite influential, seems to provide only a partial solution to the problem of abstract concepts. Among the embodied approaches to cognition that suggest different modalities of representation for abstract and concrete concepts particularly interesting, timely, and increasingly influential, are the so-called Multiple representation theories (for a discussion, see Borghi et al. [29]). Different variants of multiple representation theories are currently discussed. They differ in some respects, but all share the basic idea that concrete and abstract concepts representation relies on both sensorimotor and linguistic information. The degree of involvement of these different sources of information has been differently accounted for and varies in relation to the kind of concept, the context or the performed task. One of the main differences that distinguishes variants of multiple representation theories

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3. A Peircean account of concepts In 1990, in a now widely cited paper, Stevan Harnad firstly described the so-called symbol grounding problem. The

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set by bodily action. For example, when using a verb like to give, they initially apply it only to things that can be literally handed and do not generalize it to nouns like ideas [54]. Even more importantly for the topic being addressed here, neuroscience has demonstrated that humans map some types of abstract conceptual content by means of reuse of cortical networks previously understood as uniquely underpinning sensory-motor processes. Somatotopic motor activation has been observed during the comprehension of abstract and figurative use of language such as metaphors and idioms (e.g. [5557]). The latter study, for example, demonstrated that the primary somatosensory cortex is activated when participants process textural metaphors like he is a smooth talker. Yet, the role of Embodied Simulation in the construction of figurative meaning is still controversial, with contrasting empirical findings (e.g. Lai & Curran [58]). In fact, the activation of Embodied Simulation during metaphor processing has not been consistently replicated (see Cuccio; Cuccio et al. [33,59] for a discussion). As recently argued by Hayes & Kraemer [60], grounding conceptual knowledge in perceptual and motor systems addresses the question of how advanced human intellectual systems, such as language and mathematical reasoning, developed across a relatively short evolutionary time scale. Indeed, it is highly unlikely that the human brain developed within few thousand years a distinct neural system dedicated to processing the type of information central to scientific conceptual understanding. Congruent with this hypothesis are the results of Mason & Just [61], showing that the processing of abstract scientific concepts like algebraic equation representation and energy flow led to the activation of cortical regions traditionally related to sensorimotor cognition, like the dorsal premotor cortex and the primary somatosensory cortex. Wilson-Mendenhall et al. [62] reported increased activation in neural regions associated with social cognition (medial prefrontal cortex, posterior cingulate, orbital frontal cortex and superior temporal sulcus) while participants processed the meaning of convince, and increased activation in regions associated with mathematical processing (intraparietal sulcus and superior parietal cortex) while participants processed the meaning of arithmetic. Another recent example of the relationship between the processing of abstract concepts and the activation of experience-dependent bodily-related cortical regions is provided by the study by Constantinescu et al. [63], showing that the same brain areas that map in a grid-like fashion spatial navigation are also activated when individuals are mentally navigating conceptual two-dimensional knowledge. In summary, despite the preliminaryand partly controversialnature of the empirical evidence on the way abstract concepts are mapped by the brainbody, it seems to us that this perspective might offer an exciting opportunity to further pursue the search for the neurobiological grounding of conceptual knowledge and a better understanding of its evolutionary origin. In the next section, we propose a hypothesis, built upon the Peircean notion of icon, on how Embodied Simulation might offer an empirically based theoretical solution to the problem of bodily grounding concrete and abstract concepts.

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of reference for actions of various types and (ii) providing generalized characterizations of agentactionobject relations that function conceptually [20]. It has been shown that in macaques premotor cortex, there are grasping-related neurons that are activated in relation to the accomplishment of the outcome of grasping, regardless of the movements employed to accomplish the goal [46]. Cognitive abilities like the hierarchical representation of action with respect to a distal goal, the detection of motor goals and action anticipation are possible because of the peculiar functional architecture of the motor system, organized in terms of goal-directed motor acts. It has been proposed that the proper development of such functional architecture probably scaffolds more cognitively sophisticated social cognitive abilities [47]. Goal coding is therefore not only an abstract, mentalist and experienceindependent property, but it appears to be a distinctive functional feature upon which the cortical motor system of non-human primates is organized. Goal-directed motor acts are the nuclear building blocks around which action is produced, perceived and understood. Mirror neurons, multimodal motor neurons originally discovered in the ventral premotor cortex of macaque monkeys [22], extend these properties as they map the same goal-related contentsay, to crack a peanutregardless of who the agent is (e.g. the monkey itself or another observed agent, [23]), regardless of whether the observed action is fully visible or can only be imagined [48] and regardless of the sensory channel (e.g. vision or audition) conveying the content that a peanut has been broken [49]. These results show that in macaques, the action of grasping is neither amodal, nor unimodal, but multimodal. The claim that an action like grasping is multimodal means that it is neurally enacted using neural substrates used for both action and perception, and that the modalities of action and perception are integrated at the level of the motor system itself and not via higher association areas. This argues for generality, meeting one of the conditions identifying concepts [20]. Let us now turn to humans. There is ample evidence that mirror mechanisms for action, emotions and sensations are also present in the human brain [47,50]. This led to the proposal of an embodied approach to intersubjectivityEmbodied Simulation theory [25,31,47]. Embodied Simulation and the related notion of neural reuse provide a new empirically based perspective on intersubjectivity, viewed first and foremost as intercorporeality. Embodied Simulation is conceived of as a non-conscious, pre-reflective functional mechanism of the brain body system, whose function is to model objects, agents and events. The notions of neural exploitation [18,20] and neural reuse [47,51,52] refer to the fact that sensorimotor systems, originally evolved to guide our interactions with the world, once decoupled from the common final motor pathway and dynamically reconnected with other cortical areas, can be put into the service of newly acquired cognitive skills. The newly acquired commitment of sensorimotor neural resources would have allowed the grounding of language and conceptual thought. How do we develop, as humans, conceptual knowledge? Research has shown that humans develop their conceptual knowledge in a gradual fashion, progressively gaining greater power for generalization. Children do not have adult-like semantic or syntactic categories [53], but they initially confine the use of verbs to linguistic contexts compatible with constraints

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In what follows, analogously to what Harnad did, we will develop an account of both abstract and concrete concepts that will be built on the notion of icon. However, contrary to Harnad [64, p. 337], whose purpose was to provide a cognitive theory that could stand on its own merits (any brain level description was considered a different matter), we will provide a description of the embodied nature of abstract and concrete concepts that will be grounded in the mechanism of Embodied Simulation. As already anticipated, in our approach, we will adopt the Peircean (CP 2.247) definition of the notion of icon. Peirce identified three types of signs: icon, index and symbols. The relation of signification that holds between the sign and the object of the sign is differently characterized for each of them. This relation is not, however, intrinsic to what we call sign. It depends on our interpretation. There is no sign independently of an interpreting mind. An Icon is a sign which refers to the Object that it denotes merely by virtue of characters of its own, and which it possesses, just the same, whether any such Object actually exists or not (CP 2.247). An Index is a sign which refers to the Object that it denotes by virtue of being really affected by that Object (CP 2.248). A Symbol is a sign which refers to the Object that it denotes by virtue of a law, usually an association of general ideas, which operates to cause the Symbol to be interpreted as referring to that Object (CP 2.249).

More specifically, the relation of signification that, in the case of icons, holds between the sign and its object is a relation of similarity: an icon is a sign that denotes an object by virtue of its similarity with that object. There is no conventionality in the denotative relation (as it is the case for symbols) nor there is merely a spatio-temporal contiguity between the icon and the object it denotes (as it is the case for indexes). There is, instead, a similarity relation that depends exclusively on the structure of the icon and on its quality (CP 2.92). [. . .] An icon is a representamen of what it represents and for the mind that interprets it as such, by virtue of its being an immediate image, that is to say by virtue of characters which belong to it in itself as a sensible object, and which it would possess just the same were there no object in nature that it resembled, and though it never were interpreted as a sign. [. . .] A geometrical diagram is a good example of an icon. A pure icon can convey no positive or factual information; for it affords no assurance that there is any such thing in nature. But it is of the utmost value for enabling its interpreter to study what would be the character of such an object in case any such did exist. Geometry sufficiently illustrates that (CP 4.447).

We form in the imagination some sort of diagrammatic, that is, iconic, representation of the facts, as skeletonized as possible. The impression of the present writer is that with ordinary persons this is always a visual image, or mixed visual and muscular; but this is an opinion not founded on any systematic examination. If visual, it will either be geometrical, that is, such that familiar spatial relations stand for the relations asserted in the premises, or it will be algebraical, where the relations are expressed by objects which are imagined to be subject to certain rules, whether conventional or experiential (CP 2.778).

Thus, in the Peircean perspective, icons are signs that signify an object neither for a conventional relation to it, as symbols do (words are the best example of symbolic relations), nor for their spatio-temporal contiguity with the object, as indexes do (a classic example is the relation that holds between smoke and fire: the former is always index of the latter), but only in virtue of their own qualities, of their own structure. And, importantly, icons are abstract schematizations of the structural features of what they represent. A portrait of a man iconically represents him, but it does not have blood or bones as its constituent elements. In the same vein, a diagram can represent the trend of sales of a car company but it is not made out of real cars. We propose that the mechanism of Embodied Simulation, presented in the previous section, can be described as an iconic sign. This is so because simulations can be considered as natural signs whose denotative relation depends on their similarity with the objects or events they refer to.1 In fact, simulations are not arbitrary signs, i.e. they are not symbols, nor they can be classified as indexes (they do sometimes also imply a spatio-temporal contiguity with the object or event they refer to, but this is not the norm nor it is an essential feature, as simulation routines can be triggered also by imagined objects, facts and events or even, to a certain degree, by their linguistic descriptions) [26]. Simulation routines are the ground for similarity relations that depend only on the qualities of the simulations themselves, i.e. they depend on structural characteristics of the simulations. Most importantly, as it is the case for icons, simulation routines can be considered filtered signs. In fact, they are not actions or perceptions that a subject is currently carrying out nor are they their exact copies. Simulations are the abstract and schematic enactment of features that identify an action or event, independently of any specific movement or sensory-motor contingency that might be involved in it. To come back to the example briefly sketched in the previous section on the abstract character of the mechanism of simulation, Umilta et al. [46] showed that both macaques ventral premotor and primary motor cortices contain neurons able to code the

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Symbolic representations must be grounded bottom-up in nonsymbolic representations of two kinds: (1) iconic representations, which are analogs of proximal sensory projections of distal objects and events, and (2) categorical representations which are learned and innate feature-detectors that pick out the invariant features of object and event categories from their sensory projections. Elementary symbols are the names of these object and event categories, assigned on the basis of their (nonsymbolic) categorical representations. Higher order (3) symbolic representations, grounded in these elementary symbols, consist of symbol strings describing category membership relations (e.g., An X is a Y that is Z). [64, p. 335].

Peirces observation that geometrical diagrams are ideal examples of icons allows us to make a step forward in our argument and to focus on another of the defining features of iconicity. This relation of signification implies, at the same time, similarity with the object the icon represents and, most importantly, also abstraction. Indeed, as it is evident in the case of geometrical diagrams, icons are already filtered signs that only represent some aspects of their objects, those aspects related to the structure of the objects themselves. This is clearly stated in Peirces writing, especially when he refers to the role of icons in mathematical reasoning. Diagrams, graphs and mathematical models are, in Peirce view, icons of the events they represent (CP 3.362). An icon is, thus, a diagrammatic relation that, according to Peirce, needs to be as skeletonized as possible.

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controversy he drew attention to, with his own words ([64], p. 335), can be summarized in the following question: How can the semantic interpretation of a formal symbol be made intrinsic to the system? In his famous paper, Harnad sketched a tentative solution:

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By contrast, Embodied Simulation theory holds that sensory and motor systems are intrinsically multimodal, responding to and processing information associated with multiple modalities. Empirical evidence showed that even primary sensory areas are not unimodal, as they respond to multiple sensory modalities (e.g. visual areas respond to touch and audition,

[. . .] indexical reference depends upon iconic reference, and symbolic reference depends upon indexical [. . .]. It sounds pretty straightforward on the surface. But this simplicity is deceiving, because what we really mean is that the competence to interpret something symbolically depends upon already having the competence to interpret many other subordinate relationships indexically, and so forth. It is one kind of competence that grows out of and depends upon a very different kind of competence. What constitutes competence in this sense is the ability to produce an interpretive response that provides the necessary infrastructure of more basic iconic and/or indexical interpretations. To explain the basis of symbolic communication, then, we must describe what constitutes a symbolic interpretant, but to do this we need first to explain the production of iconic and indexical interpretants and then to explain how these are each recoded in turn to produce the higher-order forms [67, p. 74].

In this view, the ability to interpret iconic relationships is, both phylogenetically and ontogenetically, the ground for the acquisition of the ability to interpret other more complex form of denotative relation. Any referential relation implied by a concept, independently of being it an abstract or concrete concept, is, both phylogenetically and ontogenetically, dependent on our basic capacity to interpret icons. This means that the mechanism of Embodied Simulation, providing us with categorical schematizations, iconic in their nature, is the conditio sine qua non for the phylogenetic and ontogenetic development of the ability to acquire and represent both

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Presumably, each type of symbol becomes established in its respective brain area. Visual symbols become established in visual areas, auditory symbols in auditory areas, proprioceptive symbols in motor areas, and so forth. [. . .] perceptual symbols are multimodal, originating in all modes of perceived experience, and they are distributed widely throughout the modality specific areas of the brain [16, p. 585].

and tactile areas respond to vision and audition). Let us focus on vision. Vision is multimodal: it encompasses the activation of motor, somatosensory and emotion-related brain networks. All in all, while perceptual symbols theory is based on a rather standard account of perception, the Embodied Simulation approach grounds perception in the action system, putting a lot of emphasis on multimodality, viewed as an intrinsic property of the vast majority of brain areas. As for the commonalities between Embodied Simulation and perceptual symbols theory, what they have in common is certainly the fact that they are both clearly antithetical with respect to semantic hub theories of conceptual representation. In fact, according to the latter, there is a unique brain area equally necessary for processing all types of meaning or concepts (see Pulvermuller [19, p. 458], who also criticizes semantic hub theories). On the contrary, Embodied Simulation theory and perceptual symbols theory contend that concepts and meanings are multimodal (although, as we have seen, they adopt two significantly different notions of multimodality): several brain areas contribute to the processing of both concepts and linguistic meanings. Thus, any occurrence of a simulation routine, in our view, might be considered to have an iconic nature. In our proposal, on these basic natural signs rest, both phylogenetically and ontogenetically, the capacity to conceptualize. In fact, as abstract schematizations, icons/Embodied Simulation are the first and primary sources of categorization at our disposal. The mechanism of Embodied Simulation provides us with categorical schematization of objects, actions, emotions and perceptual experiences. These first and rudimentary categorical schematizations will then be the basis for the formation of concepts. This is so because, in our proposal, we consider iconic relationships as the basis to achieve more complex forms of referential relationships, especially symbolic ones, that might be involved in the relation that holds between concepts and what they refer to. The hierarchical nature of referential relationships has been highlighted by Deacon [67].

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goals (i.e. an abstract schematization) of motor actions independently of the specific movements carried out to reach that goals. In their experiment, a motor simulation of the goal of an observed action (grasping) occurred in the monkeys brain independently of the particular movements involved in the action that the monkey observed (grasping with normal pliers or grasping with inverted pliers where the latter implies an opposite pattern of movements with respect to the former). When describing simulation routines as iconic signs, we acknowledge that the mechanism of simulation has been put in relation to the notion of perceptual symbols elaborated by Barsalou [16]. The mechanism of Embodied Simulation, whose proposal was originally driven by the discovery of mirror neurons [22,23], has been considered by many as the neural implementation of perceptual symbols (see Cuccio [33] for a discussion). However, we submit that Embodied Simulation/icons significantly differ from perceptual symbols. Theoretically, icons are much less demanding and much more plausible notions than symbols. Indeed, as we have seen, icons are natural signs that refer to their objects only in virtue of their own structure, on the basis of which a similarity relation is established. Furthermore, icons are already abstract schematizations and, last but not least, they do not imply any conventional relation. Conventionality is, instead, intrinsically present in the notion of symbol, but not implied by Embodied Simulation. Indeed, it could hardly be claimed that the motor simulation, let us say, of the action of grasping a fork refers to its object (the action of grasping a fork performed by someone else) by virtue of an arbitrary and conventional relation agreed upon between the observer and the observed person. From a neuroscientific point of view, while the Embodied Simulation mechanism is based on the re-enactment of self-generated actions, perceptions and emotions, simulations of perceptual symbols are reactivation of perceptual states. This makes a huge difference. In his 1999 famous paper, Barsalou [16, p. 578] discussed the example of the perceptual symbol of a chair. The perceptual symbol of a chair, in Barsalous account, is the reactivation of the neural areas that underpinned the modal (visual) perception of a chair. According to the Embodied Simulation view, in such a case the simulation also includes the reactivation of the multimodal neural areas underpinning the potential actions we can perform with that object. Furthermore, perceptual symbol theory relies on the notion of multimodality in a peculiar way, which is very different from what proposed by Embodied Simulation theory: according to Barsalou, multimodality is the sum of individual and anatomically segregated different modalities [16,66]. In his seminal paper of 1999, Barsalou argues that:

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recruit this knowledge when we remember our past experiences, when we imagine ourselves engaged in fictive experiences (as we do during the experience of artworks such as paintings, movies, poetry and novels or when we are caught in a daydream), when we plan our future actions (as we do, for example, when we plan to use a tool or, as professional athletes do, when we review in our minds the movements and actions we are going to perform), when we interact with other people and we need to understand their actions, emotions and experiences, and even during the comprehension of linguistic descriptions of facts, actions and events. In all these different contexts, our bodily knowledge, activated through the mechanism of Embodied Simulation, is recruited by different cognitive tasks. In each of them, the cognitive puzzle we need to solve is resolved also through the recall of our background, skeletonized, bodily knowledge. This process can be described as an abductive inference ( probably an automatic abduction; see [41,69] on the role of Embodied Simulation in automatic abductions): the cognitive puzzle (i.e. the facts, stated in the premise of the abductive inference, we need to make sense of ) is resolved through a form of diagrammatic reasoning that is based on the recall of a simulation routine. This knowledge (the simulation routine) allows us to identify the similarity relation, for example, between our past actions and experiences, and the actions and experiences of the people we are observing. Thanks to the identification of this similarity relation, we can, thus, go from the premise of the inference (the actions observed, in this example) to its conclusion (our understanding of those actions). Simulation routines are, in this account, the background bodily knowledge on which the inference is based. They are a model of our own bodily experiences. Thus, our body, in this inferential process, becomes an icon of itself that we use to understand ourselves and others and to obtain new knowledge both on ourselves and others (for a more detailed discussion of this point, see [41]). Interestingly, Peirces notion of abduction is usually considered as the equivalent of the Aristotelian notion of apagoghe (Peirce himself acknowledged this; see CP 1.65 and 7.249). Both inferential processes are, indeed, hypothetical, and both allow us to broaden our knowledge. Furthermore, in his writings, Peirce also refers to the Aristotelian notion of paradeigma (a form of analogical reasoning typical of rhetorical contexts; see CP 1.65), which he defined as a combination of the characters of induction (epagoghe) and retroduction/abduction (apagoghe). Indeed, while in the Prior Analytics (II.24 [78]), Aristotle defined the paradeigma (the exemplum, in the Latin translation) as an inference where the major term is proved to belong to the middle by means of a term which resembles the third (this definition seems to suggest that paradigmatic reasoning is an inference based on an analogy), at the same time, in the Rhetorics (1356b 14-15 [76]) he defined the paradeigma as the transposition of inductive reasoning in rhetorical contexts. Thus, paradigmatic reasoning shares some of the features that characterize the iconic logic of abduction and, at the same time, it also presents characters that typically identify induction. As we pointed out in a previous work [52], for these reasons it seems to be, too, a good model to describe the cognitive role of the mechanism of Embodied Simulation. The paradeigma, among rhetorical argumentations, is that which goes from the particular to the particular, from an exemplary case to the present situation. Argumentation

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concrete and abstract concepts. In this sense, abstract concepts are always embodied in the non-trivial sense that the possession of a sensorimotor system with the characteristics of our own sensorimotor system is the necessary condition for concepts formation, both for the abstract and the concrete ones. However, to claim this role for the sensorimotor system and the mechanism of Embodied Simulation does not equal to underestimate the role of language in the acquisition of concepts. In our proposal, Embodied Simulation is a necessary but not sufficient condition for the formation of a full-fledged conceptual system. To be more precise, we propose that Embodied Simulation, with its iconic character, is a prerequisiteboth phylogenetically and ontogenetically for the acquisition of indexical and symbolic relations. After the acquisition of symbolic referential relations and language, this species-specific modality of representation and epistemic access to the world significantly contributes to the formation of abstract and concrete concepts. Language, in this view, is a necessary condition, too, for concept formation, although its role and degree of involvement might differ depending on the kind of concepts or on the context of use. It is worth noting that, in the light of our proposal, the embodiment of abstract and concrete concepts can be interpreted in two different but not mutually exclusive ways. On the one hand, the expression embodiment of concepts usually refers to the direct recruitment of the sensorimotor system during conceptual processing (e.g. [20]). This is the sense of embodiment most frequently discussed in the current Embodied Cognition debate. On the other hand, the embodiment of concepts also alludes to the phylogenetic and ontogenetic acquisition of the ability to conceptualize (e.g. [18,68]). Having said so, we still need to prove that simulation routines are iconically interpreted in human cognition. In fact, as we know, the iconic character of a sign depends on the interpretation of that sign. Although Embodied Simulation seems to match the defining features that Peirce ascribed to icons, still it is true that, to a certain degree, everything could be interpreted as an icon, depending on the level of abstraction and schematization at which we identify and interpret the similarity relation. It is, thus, a fundamental step in our argument to show that the role of Embodied Simulation in human cognition can be explained in terms of the establishment of iconic relations. To do so, we will resort to the Peircean notion of abduction and to the role icons have in this kind of inference. Abduction is a mode of reasoning (deduction and induction are the other two) whose inferential path is characterized by the fact that it presents facts in its Premise which present a similarity to the fact stated in the Conclusion (CP 2.96). In other words, abduction is an inference based on an iconic relation. The premise is connected to the conclusion through the recall of some background knowledge, the rule in Peircean terms. This latter can be thought of as a diagrammatic model, or icon, on the basis of which we can connect the facts stated in the premise with those stated in the conclusion. The abductive inference has a hypothetical nature: by reasoning on the rule/icon, we can discover new elements about the facts we are observing and hypothesize new solutions. Abductive inferences, thus, make us able to acquire new knowledge. Let us now turn again to the mechanism of Embodied Simulation. In our everyday life, the activation of this mechanism can be considered as the recall of a background bodily knowledge that we recruit in several different situations. We

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us to elaborate its abstract representation. At the same time, the degree of involvement of sensorimotor information varies in these different kinds of concepts. While some concepts are deeply grounded in the sensorimotor system (e.g. grasping or knife), other might have a more evident, or even exclusively, linguistic nature philosophy. In the latter case, both the context of acquisition of the concept and the entities to be categorized are grounded in linguistic practice. These considerations force us to further reflect on language. Language has a twofold role in concept formation and representation. On the one hand, we do have a form of linguistic knowledge, encoded in terms of lexical entries, that is considered to be purely linguistic. Lexical entries, however, are far from being full-fledged concepts. As we recently wrote [70], they are just cues that prompt us to activate our background, encyclopaedic knowledge [71] hence, activating concepts. Encyclopaedic knowledge, on the other hand, is grounded in both linguistic and non-linguistic information. Thus, language acts both as a clue for the access to our encyclopaedic knowledge and as a source of information for our encyclopaedic knowledge, in the latter case together with sensorimotor, perceptual and emotional knowledge. While, in our encyclopaedic knowledge, linguistic and non-linguistic information interact, we propose that the balance between them for every concept, be it abstract or concrete, might not be fixed, but depends on concept usage [70]. As a minor note, lexical entries too have a bodily component. In fact, in addition to semantic processing, motor simulation has been suggested to also contribute to speech perception. Lexical entries are encoded and understood not only as sounds, but as articulatory gestures necessary to speak (see Alvin Libermann and colleagues theory of speech perception: [72,73]; see also Di Cesare et al. [74] for a recent discussion and empirical findings). Linguistic and bodily cognition, in our perspective, afford us diversified modalities of epistemic access to the world. However, as we have seen, linguistic and bodily modalities contaminate one another and are inevitably interwoven. Thus, summarizing, on the one hand, as we have already pointed out, Embodied Simulation seems to play a crucial role in understanding language. The intentionality, the aboutness of our linguistic representations, isin the first place an exapted property of the action models instantiated by the cortical motor system ([17], p. 34; see also [52] for a discussion). On the other, language allows usand in this we are unique among all living speciesto fix and relive specific aspects of our bodily experience. Through language we can crystallize and relive fragments of experiences that are not topical, that is to say are not our experiences now, but become a model (an icon) for understanding ourselves and others. It is exactly this twist we are interested in and it is exactly this twist that we would like to disentangle. In this perspective, probably, we would not have had concepts without language. But this does not diminish the importance of their bodily foundation in our ontogeny and in our phylogeny. And this holds true, in our account, both for abstract and concrete concepts. However, as already anticipated, it is important to acknowledge that, while they both have a bodily foundation, abstract and concrete concepts also differ in significant ways. In the case of concrete concepts, their bodily grounding is more evident, not only in terms of the iconic root of their referential relation but also with regard to their direct recall of the mechanism of simulation. The bodily grounding seems to be less evident when we

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based on the paradeigma does not make a claim for universality. The orator is not bound to offer an exhaustive number of cases justifying a universally valid conclusion. One case is sufficient, provided that it is particularly suitable, and precisely exemplary, in relation to the context in which the argumentative discourse takes place. Furthermore, paradigmatic reasoning presents some of the features of inductive inferences. In fact, as inductive inferences, it is characterized (i) by always proceeding from what is best known and first for us (Aristotle, Analytica posteriora II.19 [77]), or from what is for us most immediate and most easily accessible, being part of our baggage of experiences and knowledge and (ii) by identifying similarities between particular cases (for a deeper discussion, see [52]). Both these features also characterize Embodied Simulation. One condition for the simulation mechanism being enacted is sharing a baggage of (sensorimotor) experiences and knowledge. Embodied simulation is enacted starting from what for us is first, i.e. what for us is known and easily accessible in terms of motor potentialities and experiences. Sharing a repertoire of practices, experiences and sensations is therefore an essential condition, because only by starting from what is well known to us it is possible to identify analogies between our actions and others. We understand the other starting from our own bodily experience, which is what is best known and first for us, again using Aristotles words. On the basis of this knowledge, we identify similar elements in our experiences as well as in those of others. We claim that, for the reasons we have already explained, both the iconic logic of abduction proposed by Peirce and the Aristotelian notion of paradeigma well explain the cognitive role of the mechanism of Embodied Simulation. In our proposal, embodied simulation routines, considered as the instantiation of similarity relations, are the root of our ability to conceptualize, being the ground for any other form of referential relation. And, we think, this claim holds true both for abstract and concrete concepts, whose foundation is, thus, both phylogenetically and ontogenetically, grounded in our bodily experiences. The embodiment of concepts, in phylogenetic and ontogenetic sense (see the distinction between the two meanings of embodiment proposed before), points to the fact that the prerequisites for concepts formation are grounded in our sensorimotor system. Schematic categorizations, provided by simulation routines, are the necessary condition for the development of any other form of referential relation. If we want to explain how we went from Embodied Simulation, and its iconic categorical schematizations, to concrete and abstract concepts, we also need to take into account the role of language. In fact, the ability to conceptualize also relies on the acquisition of language, as already anticipated. More specifically, in our proposal, conceptualization also relies on the ability to give names to categories. This holds true both for concrete and for abstract concepts. While the mechanism is probably the same, what changes is the nature of the entities to be categorized and named. We can categorize and name actions, giving rise to concepts such as running or grasping; we can categorize and name artefacts (knife, ball), sets of artefacts (furniture, vehicle), social and intellectual practices (democracy, fantasy or philosophy) and so forth. In all of these cases, even for the most concrete concepts, a certain degree of abstraction is needed. This process of abstraction is tied to language: to name a category forces

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In the present paper, we provided a phylogenetic and neurobiologically inspired account of the embodied nature of both abstract and concrete concepts. This account is philosophically built on the Peircean notions of icon and abduction that provided us the tools to explain the cognitive role of the mechanism of Embodied Simulation. In our view, Embodied Simulation, defined as an icon, is the first and primary source of categorization at our disposal. Thus, embodied simulation routines phylogenetically provided us with the bodily ground for the possibility of any other referential relation. This does not necessarily lead us to conclude that the mechanism of Embodied Simulation is always recruited during the processing of abstract and concrete concepts. In our account, while this mechanism is very probably always triggered by the activation of concrete concepts, it might not be always elicited by the processing of some abstract ones, but this needs further empirical support.

Data accessibility. This article has no additional data. Competing interests. We declare we have no competing interests. Funding. This work was supported by the Einstein Stiftung Fellowship and by the PRIN grant on Perception, Performativity and the Cognitive Sciences to V.G.

Acknowledgements. Although both authors discussed and designed the article together, 1 and 2 were written by V.G., while 3 and 4 were written by V.C.

Endnote 1

The notion of natural sign is not used here in the terms of Grice [65]. The Gricean definition of natural meaning seems to refer to indexical relations: Those spots mean measles [65, p. 377].

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4. Conclusion

Notwithstanding, we submit that the mechanism of simulation, being our first form of categorization, is the conditio sine qua non for the development of our capacity to establish referential relations. Thus, phylogenetically, both abstract and concrete concepts have a bodily ground. As for the nature of abstract concepts, whose embodied character seems to be more controversial, it is plausible to hypothesize that they do not constitute a monolithic and homogeneous class. There might be, in our view, different kinds of abstract concepts: some of these directly recruit the mechanism of Embodied Simulation, while some others do not. In this approach, contrasting empirical data on the embodied nature of abstract concepts, with empirical findings showing the involvement of the motor system in conceptual processing that have not been consistently replicated, seem to be not really contradictory. Indeed, the apparently conflicting results can be accounted for in the light of the heterogeneity of the class of abstract concepts.

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