Keynotes (alphabetical order)

Sorin Bangu (University of Bergen) – Wittgenstein and the Genealogy of Mathematical Necessity

Dorit Bar-On (University of Connecticut) – Crude Meaning, Brute Thought

Glenda Satne (University of Wollongong & Universidad Alberto Hurtado) – Linguistically scaffolded Minds: Transformation and Continuity​

Roy Wagner (E.T.H. Zürich) – The concrete practice of abstraction​

Other speakers (alphabetical order)

Inês Hipólito unfortunately had to cancel. Instead, Erik Myin will give a presentation.

Ruben Baakman – Symbols and Representational Content: Connecting Symbolic and Representational Capacities in Cognition

Daan Dronkers – What is mathematics that the enactivist might know it?

Jasper van den Herik – An Ecological-Enactive Account of Language: Attentional Actions and Reflexivity

Inês Hipólito Erik Myin – Radical Enactive Computation and Logic

Max Jones – Numerals and Neural Reuse

Julian Kiverstein & Erik Rietveld – Scaling-Up Skilled Intentionality to Linguistic Thought

Victor Loughlin – Going Wide: Enactivism and Wittgenstein

Chauncey Maher & Zed Adams – Targets, Contents, and Words

Markus Pantsar & Regina Fabry – The Cognitive Role of Embodied Symbol Manipulation in Mathematical Problem Solving

Jean-Charles Pelland – Grasping numbers without our hands

Antonio Scarafone – Enactivism and usage-based approaches to language acquisition.

Karim Zahidi – Doing without public representations

Sorin Bangu Wittgenstein and the Genealogy of Mathematical Necessity

Dorit Bar-On Crude Meaning, Brute Thought

I address the question what sense to make of the idea that there can be thought prior to language (both in ontogeny and among nonlinguistic animals). I begin by juxtaposing two familiar and influential philosophical views, due to Paul Grice and Donald Davidson. These philosophers share a broad, rationalist perspective on language and thought, but they endorse conflicting theses on the relation between them. (Roughly, whereas, on the Gricean view, thought of an especially complex sort is a precondition of linguistic meaning, on the Davidsonian view, there can be no genuine thought without language.) I argue that both views present us with unpalatable alternatives concerning our understanding of the natural origins of objective thought and meaningful language. Drawing on what I take to be key insights from Grice and Davidson, I propose several desiderata for an intermediate position concerning ‘brute thought’. I argue briefly that leading representationalist and anti-representationalist views do not satisfy all these desiderata. I then turn to certain forms of nonlinguistic communication of the sort of which both prelinguistic children and languageless animals are capable – viz., expressive communication. I propose that a proper appreciation of the character and function of expressive communication can help point the way to the desired intermediate position.

Glenda Satne Linguistically scaffolded Minds: Transformation and Continuity

Roy Wagner The concrete practice of abstraction

The notion of abstraction is most often explained in terms of subtraction: we inductively extract the common features of a set of concrete phenomena, or analyze them conceptually to derive essential features. Subtracting everything that’s not common or essential, we arrive at the abstraction. Sometimes this subtractive process involves idealizations: we exclude features common to all relevant phenomena in order to generate new mathematical entities, such as the exclusion of “thickness” in the definition of a Euclidean line.

Against this common narrative of abstraction, I would like to suggest a different approach, according to which abstraction is a cumulative practice of selective translations between various concrete modalities. My argument will rely on research from math education, cognitive science and history of mathematics.

The first source is the work of Luis Radford and his colleagues on middle school teaching of algebraic representations. According to this research, generalization and abstraction do not arise simply from subtracting something from concrete representations, but by correlating diagrams, words, gestures and rhythms. I interpret this work as showing that abstract algebraic reasoning depends not on extracting a common symbolic core of the above, but on the ability to move between the different representations in controlled ways without committing to any of the specific representation.

In order to provide this story with a cognitive-theoretical underpinning, we must move away from representational-cognitivist approaches, which assume that the brain transforms concrete stimuli into abstract computational symbols, to embodied and enactivist approaches. Here I will follow the approach of Vincent Walsh, who argues for the existence of a space-time-magnitude unit in the brain (instead of distinct modules for each), and of Walter Freeman III, who argues that cognition is reflected in large scale coordination of various brain parts related to different kinds of sensory modules. In either case, the synchronization or correlations between the different modules is not supposed to be perfect, so it does not extract the common denominator of the various modules involved.

Given this theoretical grounding, I will move on to historical examples. The first example will be Euclidean geometry. According to Reviel Netz, Euclidean reasoning is based on a highly formulaic textual apparatus and on drawing lettered diagrams. My point is that these are not separate-and-complementary mechanisms, as reflected, say, in the now popular distinction between exact and co-exact attributions. Instead, I argue that Euclidean reasoning requires intermittent translations between text and diagram that obfuscates the distinction between exact and co-exact. This does not mean that a valid Euclidean piece of reasoning is one where every textual inference can be replaced by a diagrammatic one and vice versa (which would define the “geometrical” as the common denominator of text and diagram, in line with a subtractive approach). Instead, I claim that Euclidean reasoning involves a less rigid correlation between diagram and text, and a specific training on when we may neglect one and focus on the other.

This example will be my paradigm for explaining mathematical abstraction: a correlation of several modalities of representation, which is neither the common denominator of all those modalities, nor an exclusive division of labor between them. These modalities may include more than one kind of textual representation (different languages or calculi). I will demonstrate this in the context of early Arabic and European algebra, early 19th century infinitesimal calculus and/or modern matrix theory.

Ruben Baakman Symbols and Representational Content: Connecting Symbolic and Representational Capacities in Cognition

Hutto and Myin’s “Radically Enactive, Embodied account of Cognition” (REC) claims that basic cognition, such as basic perceiving, imagining or remembering, involves no representational content. Instead, human beings learn to engage with representational content only through the participation in Symbolic Sociocultural Practices (SSPs), such as natural languages. Even though REC conceives of content as inextricably linked to SSPs, both REC and its opponents treat the question of how content in SSPs ought to be understood as secondary and dependent on the question of whether a contentless account of basic cognition is viable. Bringing the former question to the foreground and investigating what makes SSPs special in their own right provides a different perspective on what makes contentful cognition in SSPs possible. Taking up this strategy, I explore what role symbols could play in getting from contentless basic cognition to contentful cognition in SSPs. First, I reconstruct REC’s notion of representational content as content governed by correctness conditions that are external to both the representation and the representation’s reference. Second, building on a distinction between (1) iconic, (2) indexical and (3) symbolic referential relations, I argue that only symbolic referential relations could be governed by the kind of external correctness conditions required for representational content. Third, I argue that it is the public nature of a symbol that enables the symbol to become the object of sociocultural practices in which external correctness conditions are brought into existence, developed and sustained.

Daan Dronkers What is mathematics that the enactivist might know it?

A common allegation against enactive approaches to cognition is that, although they might account for some forms of cognition in non-representational terms, there are domains in which enactivism is bound to fail. One of those domains is thought to be mathematics: since its objects are taken to be abstract, it seems obvious that any account of mathematical cognition must involve mental representations of them. After all, abstract objects are notoriously difficult to interact and engage with, so it is difficult to see how they can become (rather than just be) the content of mathematical cognition. In particular, following Hutto and Myin’s brand of radical enactivism, it is hard to see how basic minds can meet abstract mathematical content. In this paper, I argue that this reasoning shows not the defeat of enactivism, but instead that accounts of mathematical cognition cannot be separated from their (presupposed) answers to the question what mathematics is. My main objective is to show that there is an account of mathematics that supports the enactive approach to mathematical cognition. To formulate such an account, instead of taking the traditional approach concerned with the static products of mathematics, I take inspiration from E-approaches to cognition and look at the dynamic processes of mathematics. However, rather than settling for some form of constructivism, as seems to be customary for E-accounts of mathematics, I argue that formalism should be the enactivist’s preferred philosophy of mathematics, because it allows for direct interaction with its content without the need for representation.

Jasper van den Herik An Ecological-Enactive Account of Language: Attentional Actions and Reflexivity

We have ways of talking about non-linguistic behaviour and ways of talking about linguistic behaviour, but ‘what we lack is a satisfactory vocabulary for describing the intermediate steps’ Davidson (1975: 11). In this talk I propose a way of talking about these intermediate steps. Building on the ecological definition of attention as the selective openness to the field of affordances in relation to a task or goal (Gibson & Rader, 1979; Rietveld & Kiverstein 2014), we can understand early infant communicative behaviour and animal communicative behaviour in terms of attentional actions: a repeatable form of behaviour performed to indicate an aspect of the current situation to someone in order to achieve something (Van den Herik 2018). An attentional action do not represent, but should be understood as an ostensive (vocal) gesture. Ostension does not only attract attention to a thing, it attracts attention in a particular way because it operates as an ‘operator of reminiscence’ (Bottineau 2010: 283), linking the present situation to previous situations. In this way, attentional actions can contribute to the formation of what Millikan (1998) calls natural conventions.

Human language goes beyond attentional actions because it is reflexive (Harris 1998; Taylor 2000): we do not only attract attention to aspects of our environment, but to attentional actions themselves. Reflexive attentional actions enable us to explain how human linguistic behaviour emerged. By bringing in a metadimension to communicative behaviour, reflexive attentional actions enable communicators to ostend attentional actions themselves. On phylogenetic and sociogenetic timescales, reflexive attentional actions provide the necessary normative force to explain the emergence of language, thereby foregoing the need to ground this normativity in the normativity of mental representations or a language of thought. On ontogenetic timescales, a child’s development of language can be understood as learning to be sensitive to, and perform, attentional actions and reflexive attentional actions. Crucial here is that caregivers construe the child’s behaviour in metalinguistic terms, a fact that enables the child to gradually grow into her role of competent languager.

Erik Myin Radical Enactive Computation and Logic

According to the Radical Enactive/Embodied approach to Cognition and Intelligence (REC), defended By Hutto & Myin, basic cognition is conceived of as dynamically unfolding embodied interaction with worldly offerings. Cognition, including perception, is intentional, in that it targets specific objects and aspects of the environment, but it does so without involving either contentful representation or computation. REC does not deny that content involving or computational cognition exists—but only when cognition is scaffolded by normative shared practices such as the use of a language.

In this talk, I will detail how the REC story works for computation. In this story, computation isn’t the basis of cognition, but a product of some forms of cognition, and there is no valid reason for assuming that brains compute, even if brain activity can be computationally modelled. In the end I’ll hint at how REC can deal with logic.

Max Jones Numerals and Neural Reuse

Menary (2015) has argued that the development of our capacities for mathematical cognition can be explained in terms of enculturation. Our ancient systems for perceptually estimating numerical quantities are augmented and transformed by interacting with a culturally-enriched environment that provides scaffolds for the acquisition of cognitive practices, leading to the development of a discrete number system for representing number precisely. Numerals and the practices associated with numeral systems play a significant role in this process.

However, the details of the relationship between the ancient number system and the discrete number system remain unclear. This lack of clarity is exacerbated by the problem of symbolic estrangement and the fact that unique features of how numeral systems represent require our ancient number system to play a dual role.

These issues highlight that Dehaene’s (2005) neuronal recycling hypothesis may be insufficient to explain the neural mechanisms underlying the process of enculturation. In order to explain mathematical enculturation, and enculturation more generally, it may be necessary to adopt Anderson’s (2010, 2014) theory of neural reuse.

According to the neural reuse approach, sophisticated cognitive capacities, such as discrete numerical cognition, are supported by transiently assembled neural coalitions that are recruited on the fly, rather than dedicated neural systems that are solely shaped by neural plasticity. This neural recruitment is, in part, determined by the cultural affordances of external representations, such as numerals.

Julian Kiverstein & Erik Rietveld Scaling-Up Skilled Intentionality to Linguistic Thought

In earlier work we’ve proposed a conceptual framework for ecological-enactive cognitive science: the Skilled Intentionality Framework (SIF). But SIF in common with other ecological and enactive approaches faces a scaling-up problem when it comes to explaining higher-order cognitive capacities. Higher-order cognition seems to require explanation in terms of rule-like operations carried out on internal mental representations. SIF proposes to think of cognition across the board including so-called cases of “representation-hungry cognition” in terms of skilled practical engagement with affordances. “Higher-order” cognition is argued to be just another variety of skilled action in which individuals coordinate their activities to the many affordances their ecological niche makes available.

In this paper we show how the human ecological niche makes available affordances that can be exploited for purposes of discursively structured thinking. First we take up an objection that the affordances of the human ecological niche are restricted to those aspects of the environment that are specified by law-based information. Such a view of affordances would imply that linguistic practices cannot make available affordances. The environment doesn’t contain information that specifies all the things people can do with language. We aim to clear the way for a more expansive view of the affordances of the human ecological niche. This we do by defending the SIF view of the human ecological niche as a socio-material environment whose material aspects are intermingled with, and inseparable from human social life. We show how language and the historically and concretely situated activities speakers engage in with words cannot be separated.

We will make our argument through a discussion of Wittgenstein’s example of the language game of the builders. Many interpreters of Wittgenstein have argued that what the builders are doing should be thought of as best on a par with animal signaling. Brandom for instance has argued that what the builders are doing cannot constitute a discursive practice because they cannot be said to be making assertions. He has argued that for any activity to count as linguistic it must have the force of a content-carrying assertion in which the speaker is saying something that can either serve as or stand in need of reasons. We will argue in agreement with Williams that what the builders are doing with words counts as linguistic activity, while agreeing with Brandom that what the builders are doing shouldn’t be thought of as the making of assertions. There is a primitive form of normativity in play that governs the builder’s activity and that suffices to count what they are doing as linguistic. It follows from our reflection on the builders that not everything people do with language is a matter of making content-involving assertions. This raises the question of how people get into the business of making assertions. While this is really the topic of another talk, we will suggest that this activity can likewise be thought of in terms of skilled engagement with the affordances of language. The upshot of our argument will be a view of linguistic thought as made possible by the activities people perform as members of their linguistic communities some of which should be thought of as “truth-telling practices”. People live their lives surrounded by and immersed in language. The human environment is an “enlanguaged” environment.

Victor Loughlin Going Wide: Enactivism and Wittgenstein

Opponents to enactivism have objected that enactivist accounts fail to reveal what constitutes cognition. This is because histories of interactions with environments only reveal the causes of cognition. If we seek to determine the constituents of cognition, so the objection goes, then we need to examine what is happening now inside the agent.  

Many authors have identified a link between later Wittgenstein and enactivism. I claim that if enactivists were to endorse this link, then they could challenge the previous objection. 

This objection can be formulated in terms of a Process View of Cognition (PV). Accordingly, what constitutes cognition are accompanying processes, where ‘accompanying processes’ means ‘subpersonal processes ongoing at some moment’. Once we endorse PV, then historical explanations are only causal. 

For Wittgenstein, it is the full range of human behaviours that reveals our mental lives. The term ‘behaviour’ here includes the non-mediative link between our use of psychological concepts and behaviourial criteria. This link ensures that it is the surrounding norm governed practices and contexts that make any activity cognitive. 

If Wittgenstein is correct, then PV is false. The non-mediative link entails there is nothing ongoing at some moment that makes an activity cognitive. If PV is false, then the objection can be challenged. Enactivists can claim that any account of what is happening now only explains cognition to the extent that such an account references surrounding norm governed practices and contexts. Historical explanations are thus constitutive. I will develop this point by considering a ‘wide’ account of dreaming.

Chauncey Maher & Zed Adams Targets, Contents, and Words

There is currently a wide range of views on the relationship between language and thought. At one end is the standard view, widely held in cognitive science: the external manipulation of symbols in a public language mirrors internal manipulation of symbols in a language of thought (Von Eckardt 2012, Bermudez 2014). At the opposite end is the maximally enactivist view: public language constitutes the representational capacities of individuals, enabling them to engage in genuine representation at all (Sellars 1956, Brandom 1994, Hutto and Myin 2017). Nearer the center is the minimally enactivist view: public language supplements inner representations, extending them in new and significant ways (Clark 2006, Sterelny 2010).

We argue for a new version of minimal enactivism. To do so, we critically engage with Hutto and Myin’s version of maximal enactivism, which holds that there is a sort of nonlinguistic “basic cognition” that is wholly non-representational and which allows animals to engage with objects without in any way characterizing them. We critique this position from two angles. First, their account of “basic cognition” conflates two distinct aspects of representational abilities; carefully separating them lets us see how there are nonlinguistic animals that can both target objects and characterize them as being specific ways. Second, we argue that the external manipulation of symbols in a public language cannot constitute the representational capacities of individuals, because such external symbolic activity presupposes the representational ability to interpret others’ intentions (Sperber and Wilson 1995, Scott-Phillips 2014). Combining these critiques, we argue that public language supplements inner representations by enabling a capacity to characterize things in an open-ended variety of ways.

Works Cited

Bermudez, J. L. (2014). Cognitive Science (2nd ed.). New York: Cambridge University Press.

Brandom, R. (1994). Making it Explicit. Cambridge, MA: Harvard University Press.

Clark, A. (2006). Language, Embodiment, and the Cognitive Niche. Trends in Cognitive Science, 10(8), 370-4.

Hutto, D., & Myin, E. (2017). Evolving Enactivism. Cambridge, MA: MIT Press.

Scott-Phillips, T. (2014). Speaking Our Minds. New York: Palgrave Macmillan.

Sellars, W. (1956). Empiricism and the Philosophy of Mind. In Minnesota Studies in the Philosophy of Science (Vol. I, pp. 253-329). Minneapolis: University of Minnesota Press.

Sperber, D., & Wilson, D. (1996). Relevance: Communication and Cognition (2nd ed.). New York: Wiley-Blackwell.

Sterelny, K. (2010). Minds: Extended or Scaffolded. Phenomenology and the Cognitive Sciences, 9, 465–481.

Von Eckardt, B. (2012). The Representational Theory of Mind. In K. Frankish, & W.
Ramsey (Eds.), The Cambridge Handbook of Cognitive Science. New York: Cambridge University Press.

Markus Pantsar & Regina Fabry The Cognitive Role of Embodied Symbol Manipulation in Mathematical Problem Solving

Proponents of embodied and enactive cognition describe symbol-integrating cognitive processes in mathematics as socio-culturally distributed and embodied practices that are acquired in the course of enculturation (Hutto, Kirchhoff, & Abrahamson, 2015; Hutto, Myin, Peeters, & Zahnoun, in press; Menary, 2013, 2015). These accounts emphasize the importance of skilful embodied interactions with cognitive tools (e.g., numerical symbol systems) in the cognitive niche. However, the specific properties of these interactions and their precise cognitive role have remained largely underdetermined. The purpose of this talk is to help close this gap. Considering cases of mathematical problem solving, we will show that the embodied manipulation of symbols in space makes an indispensable contribution to the completion of cognitive tasks. We will focus on two important ways in which embodied symbol manipulation actively contributes to mathematical problem solving. First, the spatial arrangement of lines and symbols, e.g., on a piece of paper, reduces the complexity of arithmetical and algebraic problems and breaks them down into easily computable steps. Second, the active manipulation of mathematical problems through eye movements often plays an indispensable role in solving equations and validating proofs.

The upshot is that the active embodied engagement with cognitive tools is an integral component of mathematical practices, which lends direct support to accounts of embodied and enactive cognition. This perspective on the embodied dimension of mathematical cognition has important implications for research in cognitive science that aims at developing models of enculturated problem solving.

Jean-Charles Pelland Grasping numbers without our hands

Despite the tremendous progress made in the study of numerical cognition in recent years, an important question remains: given the precision and size limitations of our innate numerical systems, how do we manage to develop arithmetically-viable numerical content? To explain how we bridge this content gap, many have adopted a form of externalism about cognition, emphasizing the important role played by extracranial objects and symbols in the historical and ontogenetic development of arithmetic. In this talk, I argue that this externalist approach is incomplete. To make my case, I focus on Lambros Malafouris’ brand of externalism, Material Engagement Theory (2013).

Combining elements of enactivism and embodied cognition, Malafouris (2010) argues that the manipulation of clay tokens was essential to the development of arithmetical practices in ancient Sumeria. On this view, the development of manual accounting techniques that led to the abstract representation of precise quantities of objects shows that material engagement with cultural artefacts is a necessary precursor to an abstract representation of number.

Against this, I claim that manipulating tokens for accounting purposes presupposes possession of the content PRECISE QUANTITY, whose origin is left unexplained in externalist approaches. I argue that Malafouris, like other externalists, cannot give a full account of the initial development of numerical content by inquisitive individuals in a numeral-free environment. I illustrate the limitations of externalist accounts by appealing to difference-making features of explanations (Clark 1998; Sterelny 2010) and applying these to anumeric cultures like the Piraha and Mundurucu.

Antonio Scarafone Enactivism and usage-based approaches to language acquisition

In the last three decades, the psychologist and primatologist Michael Tomasello has developed and championed a usage-based approach to linguistics and language acqusition. Contrary to the main tenets of the Chomskyan tradition, usage-based theorists conceive of language as essentially tied to the communicative functions that it serves, and as not requiring any innate Universal Grammar. Tomasello has been importantly inspired by Wittgenstein’s later conception of language, and it might be tempting to think that his usage-based approach can open up an enactivist way to think about language acquisition.

In this paper I argue that since Tomasello employs an intentional-inferential model of communcation to describe prelinguistic children’s communicative interactions, his proposal is prima facie at odds with Wittgenstein’s later conception of language and linguistic competency. While Wittgenstein conceives of the acquisition of a first language as consisting in acquiring irreducibly practical abilities, Tomasello’s Gricean model of communication apparently requires pre-linguistic children to have, and be able to acquire, propositional knowledge about others’ propositional attitudes. Correlatively, Tomasello’s cognitivist conception of the understanding of others seems at odds with radically enactivist theories of cognition.

On a more positive note, I also argue that Wittgenstein, the enactivists and Tomasello might be fruitfully reconciled. A functionalist reading of communicative intentions (Richard Moore), together with a complementary account of expressive communication (Dorit Bar-On), can play the relevant explanatory role in a usage-based theory of language acquisition, and they would both be in accord with Wittgenstein’s later philosophy and the main tenets of the enactivist program.

Karim Zahidi Doing without public representations