Keynotes (alphabetical order)

José Ferreirós – Concepts of number and external representations

Hanne de Jaegher – Linguistic bodies

Daniele Moyal Sharrock – From Deed to Word: Wittgenstein’s kink-free Enactivism​​

Other speakers (alphabetical order)

Katja Abramova – A more enactive alternative for pantomime in language evolution

Michael Ardoline – Shapes in the Sand: Geometry and Aristotelian Realism as Grounds for an Enactive Account of Mathematics

Arthur Bakker – Accounting for mathematical learning from embodied and enactivist perspectives

Regina Fabry – Enculturation and Embodied Literacy

Matthew Harvey – Starting fresh: Not language, but phases of vocal activity

Jasper van den Herik – The Ontogenetic Origins of Content through Metalinguistic Mastery

Max Jones – Looking at Numbers Affordances, Attention, and Arithmetic

Julian Kiverstein & Erik Rietveld – An Ecological-Enactive Approach to Language in Conversation

Guido Löhr – Towards an Embodied Theory of Abstract Words and Numbers

Karim Zahidi – What is Proof that Man may know it, and what is Man that he may know of it?

José Ferreirós Concepts of number and external representations

In this talk I shall review recent work in cognitive science about mathematical cognition, in particular on the “number sense” (Dehaene 2011) and related ideas, in order to argue that the available evidence does not support the hypothesis of an innate concept of number. In point of method, historical and archaeological evidence must be combined with cognitive science if we are to reach some clarity about the interpretation of available experiments. We shall review evidence that number concepts do not emerge in materially simple cultural environments (Overmann 2013), and that the emergence of abstract ideas of number has been slow and gradual. Number representations seem to depend on the availability of symbolic means, i.e. external representations such as tallies, body parts, or numerals. Similar considerations apply to the case of geometric knowledge, where the relevant symbolic means are maps, figures or diagrams (Giardino 2016). All of this supports the viewpoints of embodied cognition and enactivism, pointing to basic cultural-technical practices of counting as the ground from which arithmetic concepts have emerged (Ferreirós 2016).

Hanne de Jaegher Linguistic bodies

How can we go from embodiment to language?

I will present elements from an ongoing project, a book being written as we speak by Ezequiel Di Paolo, Elena Cuffari, and me, called Linguistic Bodies. One motivation for the book is the current gap between embodiment and language: How do we go from neural activations, perception-action loops, sensorimotor contingencies, sense-making, and so on, to utterances, dialogues, self-directed speech, narratives and texts?

Our attempt to cross this abyss takes place in two phases. First, we develop an increasingly sophisticated understanding of precarious, self-identifying forms of agency, from organic, over sensorimotor, to intersubjective agency. In a second phase, we start from the primordial tension in intersubjective agency—participatory sense-making—between individual self-maintenance and the self-maintenance of social interaction processes. Using a dialectical model, we show how this pervasive tension in interactions engenders increasingly complex forms of social agency and co-regulations. In this way, we propose to fill in the conceptual void between embodiment and language.

Towards the (provisional) end of this model, we arrive at linguistic bodies: open, interdependent, self-contradictory intersubjective agents who dynamically navigate the primordial tension of participatory sense-making. Linguistic bodies incorporate acts and ways of speaking and incarnate the voices, gestures, styles and perspectives of others in their own ways. Linguistic agency develops both individually and constitutively socially, such that linguistic bodies emerge, tethered but displaced, at once anchored and distanced from and oriented towards their own and others’ organic and sensorimotor agencies and the community.

Daniele Moyal Sharrock From Deed to Word: Wittgenstein’s kink-free Enactivism​​

In their most recent book, Evolving Enactivism: Basic Minds Meet Content (MIT 2017), Dan Hutto and Eric Myin claim to give a complete and gapless naturalistic account of cognition, but it comes with a kink. The kink being that content-involving cognition has special properties found nowhere else in nature, making it the case that minds capable of contentful thought differ in kind, in this key respect, from more basic minds. With the help of Ludwig Wittgenstein and John V. Canfield, I will argue that the emergence of language (the use of words, symbols, representations) is an extension of action and not therefore due to some novel or unnatural properties or features that would in any way arrest or divert continuity. The enactive account of cognition is kink-free both in its basic and non-basic manifestations: there is simply no kink to mind.

Katja AbramovaA more enactive alternative for pantomime in language evolution

This paper examines a popular trend of postulating that gestures have played a crucial role in the emergence of human language. Language evolution is frequently understood as a transition from a system, in which signals (whether vocal or manual) have fixed meanings and are used asymmetrically by senders and receivers, through specific cognitive and neurological changes, to a system, in which signals are (1) flexibly referential, i.e., can stand for a variety of ideas and (2) intersubjective, i.e., can be used equally in production and comprehension with any member of the community. The function assigned to gestures in gesture-first theories is to provide a first version of the more advanced open-ended communication in the form of spontaneous pantomimes that initiates a subsequent expansion of this system, its conventionalization and eventually a switch to the vocal modality. In the present paper I examine a particular theory that claims that pantomime was enabled by changes within the system of complex action recognition and imitation. I argue that while the theory is promising, the notion of a pantomime it employs, presupposes two sophisticated abilities that themselves are left unexplained: symbolization and intentional communication. I point out two ways to remedy the situation, namely, constructing a leaner understanding of pantomime or supplementing the theory with an explanation for the emergence of these abilities. In this paper I pursue a third option: identifying an alternative mechanism that can lead to a suitably complex language precursor while avoiding pantomime and its problematic cognitive bases altogether. This mechanism is ontogenetic ritualization, a well-known process responsible for the development of gestures in non-human primates. I outline the possibility that when placed in appropriate socio-cultural circumstances, in which complementary actions around objects are required, this process can lead to signals that are modestly referential and intersubjective.


Grice, P. (1957). Meaning. The Philosophical Review, 66(3), 377–388.

Maturana, H. (1970). The Biology of Cognition. BCL Report 9.0. Biological Computer Laboratory, Department of Electrical Engineer, University of Illinois.

Maturana, H.R. (1978). Biology of Language: The Epistemology of Reality. In G. Miller and E. Lenneberg (Eds.), Psychology and Biology of Language and Thought: Essays in Honor of Eric Lenneberg (pp. 27-63). New York, NY: Academic Press.

Maturana, H. & Varela, F. (1987). The Tree of Knowledge. Boston and London: Shambhala New
Science Library.

Moore, R. (2015). A common intentional framework for ape and human communication. Current
, 56(1), 70-71.

Moore, R. (2016). Gricean communication, joint action, and the evolution of cooperation. Topoi. An
International Review of Philosophy
, 1–13.

Scott-Phillips, T. (2015). Speaking our minds. Houndmills: Palgrave Macmillan.

Sperber, D., & Wilson, D. (1995). Relevance: Communication and cognition. Oxford: Blackwell.

Villalobos, M., & Abramova, E. (2016). Two senses of ‘recursion’ in Maturana’s theory of language:
A necessary distinction. Presentation at the First International Conference on Language and
, June 1-3, Clermont-Ferrand, France.

Michael Ardoline Shapes in the Sand: Geometry and Aristotelian Realism as Grounds for an Enactive Account of Mathematics

The embodied and enactive approaches to cognition have a particular challenge to meet when brought to bear on the more abstract abilities of the mind. The highest of these challenges may be an embodied account of mathematics which adequately explains its apparent universality, its consistency, and its formal abstraction. A first attempt to meet this challenge was undertaken by Lakoff and Núñez in their book, Where Mathematics Comes From. While their attempt has provided valuable tools for an embodied account of mathematics and set the stage for future work on the subject, I will show that there are fundamental flaws with both their conclusions as well as the methodology and presupposition which leads to these conclusions. First, it is necessary to give an overview of the account which Lakoff and Núñez use to provide an embodied account of mathematics, namely through mental abilities such as subitizing, and rigorous cognitive metaphors which bootstrap from embodied practices to formal systems. This paper will then proceed by developing three prongs of a critique of Lakoff and Núñez’s work, and providing a brief suggestion for a body of work which addresses the issue better. The prongs of this critique against Lakoff and Núñez can be summarized as such: their account is ahistorical which is evinced by beginning with contemporary set-theoretical formulations of various branches of mathematics, it is insufficiently embodied in that it does not take into account the tools and cultural practices which make mathematics possible, and their application of embodied metaphor occludes the process of formalization at the heart of mathematics. Careful attention to the various branches of geometry provides the tools to rectify the flaws in Lakoff and Núñez’s work in that geometry is the most obviously materially and environmentally engaged form of mathematics, and that Euclidean geometry is the oldest case of mathematical formalization (so we may easily infer it is also the simplest and therefore a proper starting point for an embodied account of mathematics). With this completed, I will then suggest an overarching research program within which the further study of embodied mathematics should be undertaken. Ultimately, I will argue that an updated Aristotelian realism about mathematics, the claim that mathematical forms are necessarily embodied, provides just such an overarching paradigm to investigate the cognitive genesis of mathematics.

Arthur BakkerAccounting for mathematical learning from embodied and enactivist perspectives

Accounting for mathematics learning is a challenge for embodied and enactivist nonrepresentationalist approaches. How can something as abstract as proportional reasoning be explained? How is it learned, and how might it be taught? What role might interactive educational technology play in this didactical process? In this contribution we intend to focus on the fundamental questions raised in our project on embodied design of proportional reasoning and illustrate learning progressions with empirical data (eye-tracking, action-logging, video of reasoning).

Our research in mathematics education is inspired by arguments from embodied-cognition and enactivist theory and moves towards multidisciplinary approaches that take into account the role of socioculturally framed and motivated sensorimotor interaction in problem solving. Eye tracking bears exciting new methodological affordances when combined with other data, such as handmovement logging and audio–video recording of multimodal utterance. Such data can assist in inferring the sensorimotor schemes students develop and deploy as they engage in manipulation problems. For the past several years, we have been investigating an empirical context centered on a multitouch-screen tablet application called the Mathematics Imagery Trainer so as to understand systemic factors leading to students developing task-effective bimanual coordination presumed to underlie proportional reasoning. Using eye-tracking technology together with hand logging and
thinking-aloud data we have investigated the micro-processes by which task-oriented sensorimotor interaction with the trainer gives rise to proportional reasoning.

We report on findings from a succession of empirical studies centered specifically on variants of this educational tablet application. Analyzing the emergence of bimanual kinesthetic patterns, we demonstrate that students achieved the enactment of these task-effective movements by way of inventing attentional anchors—perceptual structures organizing goal-oriented motor action. With reference to a database of over 100 students in primary and prevocational education, we show how students come to focus their attention on mathematically relevant areas of interest, and how they progress from incorrect, low-level strategies to high-level strategies when solving the proportional tasks. We present interactions between the sequence of sensorimotor schemes and the developed sequence of solution strategies. We will also report on students applying their newly acquired proportional knowledge to solve post-test problems in related mathematical domains such as scaling geometrical shapes proportionally.


Abrahamson, D. (2009). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27-47.

Abrahamson, D. (2014). Building educational activities for understanding: An elaboration on the embodied-design framework and its epistemic grounds. International Journal of Child-Computer Interaction, 2(1), 1-16.

Abrahamson, D., Shayan, S., Bakker, A. & Van Der Schaaf, M. (2016). Eye-Tracking Piaget – Capturing the Emergence of Attentional Anchors in the Coordination of Proportional Motor Action. Human Development, 58(4-5), 218-224.

Duijzer, C. A., Shayan, S., Bakker, A., Van der Schaaf, M., & Abrahamson, D. (2017). Touchscreen tablets: Coordinating action and perception for mathematical cognition. Frontiers in Psychology, 8(144).

Regina Fabry Enculturation and Embodied Literacy

Many cognitive processes are shaped by our acquisition of cognitive practices such as reading, writing, or mathematics. Cognitive practices are evolutionarily recent, embodied interactions with writing systems, number systems, and other epistemic resources in our cognitive niche. The acquisition of cognitive practices during ontogeny is a matter of enculturation.

Enculturation is associated with significant changes of the organization and connectivity of the brain and of the functional profiles of embodied actions and motor programs. Learning driven plasticity (LDP) is a potent principle governing ontogenetic brain development, according to which structural changes in brain areas lead to new neuronal functions. LDP is constrained by the functional biases of certain cortical units that contribute to the emergence of new neuronal connections. This assumption is supported by empirical evidence suggesting that certain brain areas are reused to contribute to distinct, yet functionally related neuronal circuits. This component of LDP is especially important in cases of enculturation. This is because it helps explain how cognitive practices have become possible, given that there was not sufficient evolutionary time for the development of dedicated brain areas.

LDP is complemented by learning driven bodily adaptability (LDBA). This principle captures the idea that new ways to bodily interact with epistemic resources are established in the course of enculturation. LDBA guides the ontogenetic trajectory of skilled motor action in concert with LDP. The resulting development of new motor patterns and action routines is constrained by the overall morphology of human bodies and their constitutive parts.

The present account of enculturated cognition is committed to the view that cognitive practices are embodied and distributed across the brain, the rest of the body, and the cognitive niche. The cognitive niche is the incrementally, trans-generationally structured socio-cultural environment that provides human organisms with epistemic resources for the completion of cognitive tasks. The assumption here is that our understanding of LDP and LDBA needs to be complemented by considerations of the embodied interaction with the cognitive niche. Since cognitive practices are socio-cultural phenomena, their acquisition is in itself a socio-culturally sculpted process. This process is characterized by scaffolded learning, which can be defined as a systematic process of novice-expert interaction in the cognitive niche.

The acquisition of reading and writing are paradigm examples of enculturation. Drawing on a wealth of empirical evidence, I will show that these deeply transformational processes are consistently associated with LDP and LDBA on a sub-personal level of explanation. Explicit instruction in the embodied interaction with writing systems is necessary for becoming literate. On personal and suprapersonal levels of explanation, I will suggest that reading and writing instruction are good examples of scaffolded learning in the cognitive niche.

In sum, enculturation is a complex phenomenon that requires the synthesis of several explanatory components targeting the cerebral, the extra-cerebral bodily, and the socio-cultural dimensions of cognitive practices. This approach promises to provide us with new insights into the complex developmental processes that lead to literacy.

Matthew HarveyStarting fresh: Not language, but phases of vocal activity

The primary challenge for embodied and enactive approaches to language is not any poverty or inadequacy of the approaches, but their acceptance of a structuralist conceptualization of language. That conceptualization – on which language is either primarily a medium for conveying content or a formal structure for communicative behavior – is in fact a metaphorical description of the phenomenology of a few narrow and hyper-literate varieties of linguistic activity. Embodied and enactive approaches to language have been constrained by the limitations this conceptualization imposes, such as the idea that language must have repeating structural units, the idea that these units must in some sense be substrate-general (i.e., across neuromuscular, auditory, acoustic, graphical, and phenomenal substrates), and the idea that speech is an activity whose organization and nature are fundamentally attributable to the activity of individual organisms.

This paper proposes an alternative conceptualization of linguistic phenomena, with the goal of aiding scholars in developing new ways of explaining them and accounting for them. The first move is to leave behind all notions of duality of patterning, arbitrariness, and semantics; the second is to choose a loose set of features that characterize certain human-environment dynamical systems. These features are tendencies rather than requirements: to involve vocalization, to be inter-bodily (i.e., “social”), to involve extremely dextrous and refined sensorimotor coordination, to depend upon the close regulation of attention, and to be organized on multiple timescales (especially including intra-utterance, conversational, and ontogenetic timescales). If bodily activity that shares these characteristics is “linguistic activity”, then the temporal organization of linguistic activity – and the means and mechanisms underlying that organization – form the core of a new way of approaching language.

Given this starting point, the lived experience of linguistic phenomena on the part of both participants and observers can then be explored in terms of the sensorimotor skill involved, and especially in enchronic-scale regulatory effects like anticipating and controlling upcoming actions or events, as well as through the study of affective coordination, traditional phenomenological investigation, and the study of genres, speech communities, and other parameters that factor into the creation of specific context-types for the occurrence of linguistic activity.

The paper will highlight just one possible way of building on this basic position. Linguistic activity of any kind displays phase transitions in the dynamics of the system composed of the participants and their physical environment. Some of these phrase transitions are well understood, such as the relation between individual cycles of vocal fold contraction and perceived voice quality. Others are less well understood, and many of these have been ignored by linguistics either because they are inter-individual (rather than present in the speech of a single speaker) or don’t have obvious grammatical or semantic effects or motives. These include transitions between intonation units that stretch across speakers, between affectively-defined modes of vocalizing, between different periodicities of coordination between vocal tract closures and head movements, and many others. Investigation of these types of phase transitions, as well as investigation of their phenomenal consequences as mentioned above, will provide a new way of understanding what happens in situations involving human language.

Jasper van den HerikThe Ontogenetic Origins of Content through Metalinguistic Mastery

Some utterances and inscriptions can be correct or incorrect (or, true or false), in which case they have content. Sensitivity to content is crucial to a wide variety of human practices. Traditionally, cognitive science claimed that cognition is necessarily contentful and aimed to provide a reductionist account of mental content (e.g. in terms of biological functions). In contradistinction, radical embodied approaches to cognition deny that cognition is always and everywhere contentful (Hutto & Satne 2015), opting for construing basic cognition in terms of world-involving instead of world-representing processes (Varela, Thompson, & Rosch 1991; Gibson 1979). This raises the question: how do contentful forms of cognition emerge from non-contentful forms?

In this paper I give an answer to this question on the ontogenetic timescale by proposing a two-stage developmental account of content-sensitivity – which I understand as a sensitivity to the content of other’s as well as one own’s behaviour and attitudes.

In the first stage, a child’s normative similarity responses are ‘calibrated’ by a caregiver, so that the child responds appropriately to culturally salient aspects of her world (Williams 2010), such as emotions, social situations, but also shapes, colours, &c. This calibration can be explained through the education of attention (Reed 1995) and relies on the normative and cognitive structuring of the initiate learning situation by the caregiver: in first instance, the actions of the child are completely dependent for their meaning on the caregiver. However, by being treated as if she is already competent, a child can gradually grow into her role as participant in her communities practices (Rączaszek-Leonardi 2016). The initiate learning situation is in first instance a non-epistemic context: it is aimed at coordinating behaviour in culturally appropriate ways, not about getting things right.

In the second stage the child becomes a master of contentful practices. I argue that content-sensitivity stems from the child’s growing affinity with metalinguistic practices (talking about talking) that can similarly be explained through calibration, only now with respect to verbal aspects of the child’s world (Taylor 2013). Her growing metalinguistic competence allows the child to construe (verbal) responses of others as expressions of their perspective on the world, perspectives that can be correct or incorrect. This realisation allows for a novel kind of reflexivity: as her attention is educated to the affordances of linguistic behaviour, she becomes able to relate to other people’s relation to the world, and ultimately, to herself as a subject of a perspective on the world. Note that the two stages, although analytically separable, will in practice be intertwined.

What does this mean for the nature of content? In contradistinction to traditional accounts, that see content as the objective value of decontextualised symbols, we see content-sensitivity as a repertoire of social skills. Although the normative similarity responses form a necessary ground for the development of content-sensitivity, they do not fully determine content: content is always determined – provisionally and defeasibly – by the interacting individuals themselves.

Max JonesLooking at Numbers Affordances, Attention, and Arithmetic

Recent evidence from the cognitive sciences suggests that humans possess some capacity for numerical perception. This capacity seems to be incompatible with both traditional views about the metaphysical status of numbers and with traditional approaches to perception. However, as Kitcher (1984) suggested, ecological psychology (Gibson, 1979, Chemero 2009) offers an alternative approach that can explain our access to number in terms of perceiving affordances, arguing that “mathematics is an idealised science of universal affordances” (p. 12). Kitcher’s own proposal is incompatible with available evidence about the nature of numerical perception, as a result of focusing on a too coarse-grained notion of the affordances relevant to number. However, it is possible to remedy this situation by understanding numerical perception in terms of affordances related to sequential attention.

This more fine-grained ecological approach also has the potential to explain certain aspects of more offline numerical cognition. There is a wealth of evidence to support a close association between the system for directing visuospatial attention and systems involved in numerical/arithmetical cognition (e.g. neural proximity (Gillebert et al. 2011), various spatial-numerical association effects (Dehaene et al. 1993; Fischer et al. 2003, 2004), spatial/numerical neglect (Zorzi et al. 2002), eye movements during offline numerical cognition (Loetscher et al. 2011, Hartmann 2015)). Moreover, in line with the premotor theory of attention, there is a wealth of evidence to suggest that the systems for overt visuospatial attention may also be involved in covert, nonvisual, and even cognitive attention (Findlay & Gilchrist 2003; Rizzolatti & Craighero 2010). Taking this evidence together, and on the basis of the ecological approach to numerical perception, I will present the hypothesis that offline/abstract numerical/arithmetical cognition is, in part, based on simulated sequential attention.

In more detail, perceiving number involves seeing opportunities for enumeration, i.e., affordances of sequential attention; while thinking about number involves simulating enumeration (either overtly or covertly), and both are supported, in part, by systems that govern visuospatial attention. Although somewhat speculative, this proposed hypothesis offers a possible explanation of how mathematical thought can become abstract and detached from immediate reality, perhaps even in the absence of mathematical symbols. By using our attention system to simulate enumerative actions we can explore a merely simulated landscape of numerical affordances.


Chemero A. (2009) Radical Embodied Cognitive Science, MIT Press

Dehaene S. et al. (2003) ‘Three Parietal Circuits for Number Processing’, Cognitive Neuropsychology, 20(3–6)

Findlay J. & Gilchrist I. (2003) Active Vision: The psychology of looking and seeing, Oxford University Press

Fischer M. et al. (2003) ‘Perceiving numbers causes spatial shifts of attention’, Nature Neuroscience, 6(6)

Fischer M. et al. (2004) ‘Oculomotor Bias Induced by Number Perception’, Experimental Psychology, 51(2)

Gibson J. (1979) The Ecological Approach to Visual Perception, Psychology Press

Gillebert C. et al. (2011) ‘Lesion evidence for the critical role of the intraparietal sulcus in spatial attention’, Brain, 134(6)

Hartmann M. (2015) Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition?’, Cognitive Processing, 16(1)

Kitcher, P. (1984) The Nature of Mathematical Knowledge, Oxford University Press

Loetscher T. et al. (2010) ‘Eye Position Predicts What Number You Have in Mind’, Current Biology, 20

Rizzolatti G. & Craighero L. (2010) ‘Premotor Theory of Attention’, Scholarpedia, 5(1)

Zorzi M. et al. (2002) ‘Neglect Disrupts the Mental Number Line’, Nature, 417

Julian Kiverstein & Erik RietveldAn Ecological-Enactive Approach to Language in Conversation

We argue that the concept of enaction as a non-representational mode of cognition doesn’t only apply to basic sensorimotor ways of engaging with the environment but also to language–based activities people engage in when engaged in conversation with each other. We will focus our paper on the enactive account of conversation as presented in an innovative recent paper by Cuffari, Di Paolo and De Jaegher (2015). They take language use to be form of social agency in which linguistic forms of meaning are made in interaction with others. We are very much on board with their project of developing a non-representational account of conversational abilities. Skilled action whether it is found in riding a bicycle or having a conversation is best understood in non-representational, enactive terms. However we will argue their account presupposes much that this is essential to the success of a nonrepresentational explanatory programme that deals with skilled action in cognitive science. By stressing the co-construction of linguistic meaning through social interaction, we will argue they miss the “sociomaterial” reality of language. They fail to take into account the constraints on enactive sensemaking that come from the sociomaterial environment to which members of language-speaking communities are always attuned. We will show this failure can be remedied by making the enactive theory more ecological. The result is an ecological-enactive approach that is able to do justice to both the material reality of language as an integral aspect of the landscape of affordances, and to the importance of social interaction.

Guido Löhr Towards an Embodied Theory of Abstract Words and Numbers

According to embodied and enactive theories, perception, action and context are crucial to language and mathematics (Barsalou, 1999; Fischer, 2001; Vigliocco, et al., 2004; Pulvermüller, et al. 2005; Borghi & Binkofski, 2014). The main objection to embodied theories has been that they cannot explain concepts that are, by definition, detached from perception, i.e., abstract concepts, such as TRUTH or DEMOCRACY and mathematical concepts (Dove, 2009; 2011; 2016; Machery, 2006; 2007; 2016). For embodied theories of language this means that they can only explain the use of concrete, but not of abstract words and sentences. This objection however is rarely spelled out in detail and is usually merely taken for granted. I introduce a distinction between epistemic and semantic accounts of concepts to the debate of concept empiricism and show that if we understand embodied theories of concepts as providing empirical testable, epistemic theories of how we actually think, and not a semantic account of concepts (how to individuate concepts), the bjection from abstract concepts can be dealt with.

I first argue that we should distinguish between three kinds of objections from abstract concepts: one is semantic and two are epistemic. According to the first, perception/action/context (p/a/c) cannot fix the reference of abstract words and numbers, i.e., cannot fully account for their meaning (semantic). According to the second, p/a/c cannot explain how we acquire abstract concepts, i.e., how we establish a causal-historical link to abstract kinds or how we acquire the knowledge that determines the reference of the respective concept (epistemic). According to the third, p/a/c cannot explain how we apply our concepts (epistemic). The latter two are empirical and epistemic questions because they involve questions of how people actually use their knowledge as opposed to how symbols get their content. Concept empiricism offers at least a plausible hypothesis of how we acquire and apply our abstract concepts even if perceptual symbols may not exhaust their meaning.

Reducing concept empiricism to an epistemic account does no harm to embodied theories of concepts, which are explicitly empirical theories and supported by empirical evidence of context and embodiment effects (Barsalou, 1999). Their contribution does not necessarily need to be assessed on semantic grounds. Once a distinction between semantic and epistemic accounts of concepts is in place and once we see that embodiment theories provide an epistemic theory of concepts we can see why abstract concepts pose no particularly serious conceptual problem to concept empiricism.


Barsalou, L. W. (1999). Perceptual symbol systems. Behavioral Brain Sciences, 22:577–660.

Borghi, A. M. and Binkofski, F. (2014). Words as Social Tools: An Embodied View on Abstract Concepts. Springer.

Dove, G. (2009). Beyond perceptual symbols: a call for representational pluralism. Cognition, 110:412–431.

Dove, G. (2011). On the need for embodied and dis-embodied cognition. Frontiers in Psychology, 1.

Dove, G. (2016). Three symbol ungrounding problems: Abstract concepts and the future of embodied cognition. Psychonomic bulletin & review, 23(4), 1109-1121.

Fischer, M. (2001). Number processing induces spatial performance bias. Neurology, 57(5), 822– 826.

Machery, E. (2006). Two Dogmas of Concept Empiricism. Philosophy Compass, 1(4):398–412.

Machery, E. (2007). Concept empiricism: A methodological critique. Cognition, 104(1), 19-46.

Machery, E. (2016). The amodal brain and the offloading hypothesis. Psychonomic bulletin & review, 23(4), 1090-1095.

Pulvermüller, F., Hauk, O., Nikulin, V. & Ilmoniemi, R.J. (2005). Functional interaction of language and action: a TMS study. European Journal of Neuroscience, 21 (3), 793-797.

Vigliocco G, Vinson DP, Lewis W, and Garrett MF. (2004) Representing the meaning of object and action words: The featural and unitary semantic space hypothesis. Cognitive Psychology, 48: 422e488,

Karim ZahidiWhat is Proof that Man may know it, and what is Man that he may know of it?

The growing literature in the domain of mathematical cognition focuses mainly on basic mathematical (numerical and geometrical) competences. But central to mathematics is a set of metamathematical ideas that guide mathematical practice. Understanding mathematical practice from a cognitive point of view thus requires that cognitive science engages with our ability to participate in practices that involve these metamathematical concepts. In this talk I will focus on a metamathematical core concept, i.e. the concept of PROOF. With respect to this concept the challenge for cognitive science is to explain how humans are in a position to produce and understand mathematical proofs. While it may be premature to expect empirically well-grounded theories for this competence and draw philosophical lessons from them, some prior reflection on what a mathematical proof is, might be useful to avoid the Platonic pitfalls that have plagued some of the cognitive science literature on basic mathematical competences. In this talk I will argue that PROOF is a social kind. In particular, I will argue that the acceptance of an argument by a community as proof is constitutive for its status as proof. My argument will be based on Wittgensteinian ideas concerning normative phenomena, supplemented with examples from the history of mathematics. The upshot for a cognitive science of mathematics is that in order to get a grip on proof practices, it should focus on the social infrastructure of these practices and the competences needed to navigate this infrastructure. Enactivism, so I will argue, is particularly well-suited for this task.