Review of Philosophy and Psychology
https://doi.org/10.1007/s13164-023-00720-x
A Pattern Theory of Scaffolding
Albert Newen1
· Regina E. Fabry2
Accepted: 3 December 2023
© The Author(s), under exclusive licence to Springer Nature B.V. 2023
Abstract
In recent years, philosophers have developed accounts of cognitive and affective
scaffolding to describe the contribution of environmental resources to the realization of mental abilities. However, an integrative account, which captures scaffolding
relations in general terms and across domains, is currently lacking. To close this
gap, this paper proposes a pattern theory of scaffolding. According to this theory,
the functional and causal role of an environmental resource for an individual agent
or a group of agents concerning a mental ability in a situational context can be specified by multiple conditions that a scaffold can satisfy. On this view, scaffolds can be
described in terms of patterns of relevance-weighted, gradually satisfied scaffolding conditions. The resulting theory will be applied to cases of mathematical cognition to demonstrate its plausibility and feasibility. The pattern theory of scaffolding,
it will be shown, has important implications for research on embodied, embedded,
extended, and enactive (4E) cognition.
1 Introduction
In the last two decades, increasing evidence has been collected that demonstrates
the relevance of physical and social environmental components for mental abilities
and their realizations (Clark 2008; Menary 2010; Newen et al. 2018). The starting
point are cognitive systems with minimal flexible behaviour that is based on cognitive processes (Newen 2017). The relevant mental abilities involve basic mental
processes (in a wide sense) like spatial orientation, social interaction, and emotion
Albert Newen and Regina E. Fabry contributed equally to this article.
* Regina E. Fabry
regina.fabry@mq.edu.au
Albert Newen
albert.newen@rub.de
1
Institut für Philosophie II, Ruhr Universität Bochum, Universitätsstr. 150, 44801 Bochum,
Germany
2
Department of Philosophy, Macquarie University, Sydney, NSW 2109, Australia
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A. Newen, R. E. Fabry
recognition. For example, spatial cognition of blind people is usually only realizable with a white cane, blindfolded people can learn to navigate with a so-called
magnetic belt (Kaspar et al. 2014). Furthermore, complex abilities like decisionmaking (Walter 2017) and mathematical cognition (Fabry 2020; Menary 2015) are
also shown to be influenced by environmental factors. In the philosophical literature, one of the most widely discussed examples of environmentally influenced
mental abilities motivated the extended mind thesis (Clark and Chalmers 1998;
for discussions, see Menary 2010). In this example, Otto employs his notebook to
remember the location of the Museum of Modern Art in New York. The discussion of this example triggered an extensive debate about a metaphysical notion of
extendedness (see, e.g., Adams and Aizawa 2001; Aizawa 2010; Kirchhoff 2015;
Menary 2010). According to this metaphysical notion, extending the mind by
including external resources would be metaphysically constitutive of a mental ability. Following Sterelny (2010), Arango-Muñoz (2013) and others, we suggest a
shift from the metaphysical to an epistemic-pragmatic perspective with the aim to
develop a systematic theory, which enables us to account for various influences of
environmental resources on mental abilities.
How can we adequately describe, from a general, epistemic-pragmatic perspective, the role of environmental components for the realization of a mental ability?
Here, the central claim is that a theory of scaffolding is the most fruitful framework. As we will argue in detail in Section 5, this perspective allows us to characterize classical extended mind cases as borderline cases of scaffolding (see also
Sterelny 2010). While previous research has contributed to a better understanding
of scaffolding relations, we are still lacking a theoretical framework which allows
us to characterize a minimal common ground for all cases of scaffolding. Some
important contributions to research on cognitive scaffolding highlight relevant general features of scaffolds while neglecting others (e.g., Sterelny 2010; Sutton 2016).
More recent suggestions are much more elaborate, but are too detailed for a general
theory of scaffolding, because they focus on affective scaffolding (e.g., Colombetti
and Krueger 2015; Coninx and Stephan 2021; Saarinen 2020). Consequently, they
integrate many features of an individual agent, e.g., the agent’s intention to use a
scaffold or the mineness of a scaffold. In many cases, however, a group of agents
qualifies also as a relatum in a scaffolding relation (Sterelny 2010). For a general
theory of scaffolding, we will show, we need to describe how scaffolds are typically used in a specific situation to realize mental abilities. This insight allows us
to develop, for the first time, a general framework to characterize scaffolds for both
cognitive and affective abilities. Although some aspects can already be found in the
relevant literature (esp. Varga 2019), we will argue that our account also differs significantly from previous proposals and has a wider descriptive range.
The resulting pattern theory of scaffolding consists in the claim that the role of
an environmental resource for an agent concerning a mental ability can be specified by multiple conditions that a scaffold can satisfy. Accordingly, we understand
‘scaffolding’ as a basic notion for the characterization of a mental ability with a
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A Pattern Theory of Scaffolding
multifactorial characterization of the scaffold.1 The multiple conditions are not
meant to characterize necessary and jointly sufficient conditions, since we think
that this classical definitional aim does not fit to the variety of scaffolds and their
functional and causal roles. Furthermore, these conditions can all be satisfied
gradually and they can be of varying relevance to characterize a scaffold. Thus, we
will propose that we can describe a scaffold used by an agent for a mental ability
in a situation with a pattern of relevance-weighted, gradually satisfied scaffolding
conditions. For this reason, we call the outcome of our considerations a pattern
theory of scaffolding (for similar approaches, see Gallagher 2013; Newen 2018).
We thereby present an account that describes core conditions not as defining but as
constraining conditions for scaffolds. Furthermore, we will argue that our account
can be understood as an intermediate position between radical claims about the
extended mind (Clark and Chalmers 1998), on the one hand, and classic internalistic causal explanations of the mind (Adams and Aizawa 2001), on the other hand.
To develop our pattern theory of scaffolding, we proceed as follows: we start with
a working definition of scaffolding and characterize the central components (Section 2). To distinguish scaffolding relations from unimportant environmental influences, we anchor the characterization of the components in a general background
account of causal relations relevant for realizing a mental ability. To adequately capture scaffolding relations, we specify scaffolding conditions which can be satisfied
in a variety of ways (Section 3). We will then apply our pattern theory scaffolding to
cases of mathematical cognition (Section 4) because basic mathematical abilities are
widespread (e.g., counting, arithmetic) and crucially rely on scaffolds. Our theory
is in an optimal position to adequately capture a wide range of cases. Finally, we
describe central features and advantages of our account (Section 5).
2 Towards a General Characterization of ‘Scaffold’ and ‘Scaffolding’
Let us start with a working definition: A scaffold is an environmental resource that
contributes non-trivially to the manifestation of a specific mental ability of an agent
in a given situational context. The contribution of such a resource presupposes that
there is an interaction of the agent with the resource while realizing the mental ability. This means that it is not the external resource per se that is a candidate for a scaffold but the resource standing in an interactional relation to the agent in a situation.
1
In what follows, we adopt a Wittgensteinian family resemblances approach to the notion of ‘scaffolding’. Accordingly, we suggest that ‘scaffolding’ refers to “a complicated network of similarities overlapping and crisscrossing” (Wittgenstein 2009, § 66). Previous philosophical research has shown that
family resemblances approaches leads to a better theoretical understanding of various mental phenomena, including pain (Coninx 2023a), the emotions (Newen et al. 2015), and mind-wandering (Seli et al.
2018). We assume that a family resemblances approach is more conducive to understanding the role of
environmental resources for mental abilities than the development of a set of necessary and sufficient
conditions for the ascription of ‘scaffolding’ to a certain phenomenon. Our approach is compatible with
the view that the concept of ‘scaffolding’ has a probabilistic structure. However, this view remains underspecified. The important progress consists in spelling out the central conditions for scaffolding relations.
We are grateful to an anonymous reviewer for pressing us on this issue.
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A. Newen, R. E. Fabry
More precisely, the concept of ‘scaffold’ is specified by a relation of an environmental resource to
i. an agent
ii. a mental ability
iii. a situational context
The environmental resource can be fruitfully characterized as a specific type
of agent-external entity that is used or reorganized to enable, support, enhance, or
regulate a certain mental ability. Drawing on previous research, we can specify the
relata of scaffolding in more detail.
i.
Agent
A background assumption of our theory of scaffolding is that we can draw a
prototypical distinction between an agent and the environment. We are aware that
this is not a rigid distinction, but we can explicate a sufficient distinction with an
example: A blind person walking with a white cane is an agent and the white cane
is a typical scaffold for the ability to spatially navigate in a situation. Why is the
human being the agent and not the human being together with the white cane?
While navigating, it may be useful to describe the human being and the white cane
as an integrated agentive unit (Merleau-Ponty 2012), but if we look at the whole
profile of mental abilities, we notice that a human being can feel, memorize, think,
or communicate without relying on the white cane. Given this rich mental profile of
the agent and the fact that the white cane is involved only in the application of one
specific cognitive ability (i.e., spatial navigation), it is much more fruitful to identify the human being as the agent and the white cane as a part of the environment,
which can be systematically and reliably used.2
Previous research has largely focused on individual agents that enter a scaffolding
relation. However, as Sterelny (2010) notes, the numerical unit of analysis can range
from individuals to small-scale groups to entire cross-generational populations
depending on the relevant situational context (see below). Accordingly, we develop
our approach in such a way that it can be used for the analysis of both individual
and group agency. We presuppose that an agent or a group of agents is one of the
relata. In contrast to Varga (2019), we exclude for conceptual reasons sub-personal
2
An anonymous reviewer pointed out that the agent-environment relation may be more fluent than the
example rehearsed in the main text suggests and that it can be, under certain conditions, a case of soft
assembly (Clark 1997), for example when the relationship between an agent and a prosthetic limb is at
issue. We agree that a prosthetic limb can be considered as a candidate of an environmental resource
that becomes, over time, part of the agent for several reasons: (a) the prosthetic limb is used almost all
the time; (b) for a large variety of activities; and (c) is thus probably even more intensely integrated into
the body schema than the white cane; and (d) the replacement of the prosthetic limb by another, slightly
different resource is usually connected to a need of intense learning to reestablish the integration into the
body schema. Thus, we think there is a cluster of criteria to distinguish pragmatically the agent and the
environmental resource. Furthermore, although we focus on human agents in this article, our account is
explicitly open for artificial agents, including autonomous cars and robots.
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A Pattern Theory of Scaffolding
sensory-motor processes as proper candidates for relata (which he describes as a
case of intrasomatic scaffolding).3
ii. Mental ability
Previous research on scaffolding has distinguished between cognitive and affective domains (Saarinen 2020; Sutton 2016). Within these domains, we can distinguish
between various cognitive abilities (e.g., remembering, problem-solving, reasoning, perceiving) and affective abilities (e.g., having or recognizing emotional episodes, moods,
affective personality traits) that can be scaffolded. In this paper, we offer a general framework of scaffolding that can be applied to both cognitive and affective abilities. For the
ease of exposition, we will explore mathematical cognition as a test case (Section 4).
iii. Situational context
The role of an environmental resource for a mental ability is strongly dependent
on the way it is applied in a situation. Thus, we need to characterize situationally relevant causal features concerning the environmental resource. For a general theory of
scaffolding, the challenge lies in focussing on those aspects that are typically playing
an important role in the rich causal network underlying the realization of a mental
ability. First, we want to exclude irrelevant factors as well as general background
factors which are not specific to the mental ability under investigation. Second, we
want to abstract from causal factors which may be relevant, but too specific to the
token case. Third, we sometimes are not able to describe adequately the relevant
causal factors as part of the underlying causal network, but can only constrain them,
e.g., by characterizing certain implementation conditions. To meet these challenges,
we now proceed as follows: first, we will clarify the general framework of causal
relations for scaffolds, thereby excluding causal background conditions, which are
too general to be relevant for any informative characterization of scaffolds (Section 2.1). Second, we will describe a variety of scaffolding conditions, which can
help constrain the identification of typically relevant causal factors (Section 3).
2.1 The Framework of Causal Relations for Scaffolds
We aim to characterize the candidates of environmental resources that can be scaffolds by describing the causal network, which is relevant for the realization of a mental ability. A central constraint is that the causal role of a potential scaffold for an
agent’s mental ability should be distinguished from trivial causal background conditions. Sufficient oxygen is a trivial background condition because a lack of oxygen
not only decreases the typical mental ability of memorizing items, for example, but
3
One reason to call the conceptual adequacy of ‘intrasomatic scaffolding’ into question comes from
considerations on parsimony: According to Varga (2019), neural reuse theory (Anderson 2015) and
empirical research based on Lakoff and Johnson’s (1999) conceptual metaphor theory, e.g., Williams and
Bargh (2008) and Zhong and Leonardelli (2008), lend support to the idea that embodied processes nontrivially contribute to cognitive processes. However, it remains unclear why ‘intrasomatic scaffolding’
needs to be introduced as a new conceptual category to interpret and contextualise empirical findings that
can be accommodated equally well by already existing conceptual frameworks in embodied cognitive
science (Anderson 2015; Chemero 2009).
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A. Newen, R. E. Fabry
all mental and behavioural aspects of the living system. On this basis, we can start to
characterize non-trivial background conditions. For example, stress is a non-trivial
background condition of memorizing items, which systematically influences performance: little stress increases, while intense stress decreases memory performance
(Wolf et al. 2016); there are more detailed reports on the nuanced effects of stress
on the memory system (Wolf 2019). Behavioral abilities like running, by contrast,
may not be influenced so intensely by stress and running can even be a method to
decrease intense stress (Fuchs and Klaperski 2018).
Another heuristic criterion to distinguish non-trivial background conditions is that
they typically have a special influence on specific, but not all mental abilities. Stress
strongly influences memory, emotion recognition, etc., but does only minimally influence, if at all, the visual perception of objects.4 We think that there is no clear-cut distinction between trivial and non-trivial background conditions, but assume a continuum with
some paradigmatic cases as starting and end points. For biological agents, the trivial conditions include homeostatic functions (e.g., breathing, body temperature) which must be
well-regulated, i.e., having enough oxygen, being not extremely hungry or tired, having
no extreme body temperature in relation to the acceptable range. Thus, causal conditions
which have the central functional role to keep a living organism in stable conditions (e.g.,
homeostatic processes to control body temperature) are trivial background conditions of
mental abilities since they are enabling life and thereby indirectly also mental abilities
but not any specific mental ability. In contrast, non-trivial background conditions of a
mental ability are more specific causal background conditions typically fulfilling two criteria. First, they specifically influence mental abilities while not influencing basic behavioural dispositions in the same way. Second, they have a systematic influence on some,
but not all mental abilities. Interesting candidates of nontrivial background conditions for
many mental abilities include social and cultural background conditions, e.g. a propensity for cultural learning and general linguistic capacities (Heyes 2018). Since we are not
aiming at a detailed theory of causal networks but a general theory of scaffolding, these
coarse-grained characterizations are sufficient to continue with the description of nontrivial causal conditions enabling an ability.
For our purposes, we can benefit from the additional distinction between triggering and structuring causes of an event (Dretske 1988). Structuring causes are
non-trivial conditions, which normally need to be implemented to enable a specific
cause to trigger an event in a situation; the latter is the triggering cause. Concerning the ability to memorize the chemical formulas of many substances during an
oral exam, for example, the structuring cause could be a moderate level of stress
while the triggering cause could be the question of the examiner.5 Let us transfer this to a case involving an environmental resource, for example, the white cane
which enables a blind person to spatially navigate a certain environment. The white
4
Some influence of stress on the neuronal realization of perception is reported. For example, Arnsten
(2015) shows that there is more bottom-up driven processing associated with perception under stress due
to weakened neuronal activations in the prefrontal cortex in contrast to situations without stress, but this
is a comparably minimal modification of perception.
5
We accept that the distinction between triggering and structuring causes involves metaphysical as well
as epistemic constraints, but leave it open what exactly these factors are and how they are weighted.
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A Pattern Theory of Scaffolding
cane would be described as the scaffold. The structuring cause involves sufficient
sensitivity for the vibrational feedback of the stick, an ability of spatial imagination,
etc. The triggering cause would be the use of the white cane in a typical way when
walking. Against this background of excluded trivial background conditions, we
can already characterize the scaffold more generally as a structuring cause, while a
specific use of the scaffold can be a triggering cause of a mental ability.
A further specification of the causal role of a scaffold can be labelled as the
directionality of the causal relation. The causal dependence relation between the
scaffold, understood as a triggering cause, and the ability can be uni-directional or
bi-directional (Krueger 2020; Saarinen 2020). In cases of uni-directional scaffolding, the scaffold (e.g., the white cane) influences, but is not influenced by, the relevant mental ability (e.g., spatial navigation). Bi-directional scaffolding is realized
when the scaffold and the relevant mental ability mutually influence each other over
time, i.e., when the realization of a mental ability modifies the relevant scaffold or
its causal involvement. In the next step, we will capture general scaffolding conditions, which help constrain descriptions of the causal role of a scaffold for a mental
ability.
3 Specifying Scaffolding Relations: Scaffolding Conditions as Causal
Constraints
In order to specify the causal role of scaffolds for the realization of mental abilities, we need to develop a set of conditions that help specify scaffolding relations.
These scaffolding conditions should be neither too general nor too specific to enable a general account of scaffolding. For example, the distinction between material and social scaffolds is too general (Krueger 2020; Sutton 2016; Varga 2019).
While this distinction is intuitively reasonable, it would require further qualifications. Thus, we will not consider this distinction in detail when developing relevant scaffolding conditions. The features of ‘individualization’ or ‘entrenchment’,
for example, are too specific for a general characterization of a scaffold (Coninx
and Stephan 2021; Saarinen 2020; Sterelny 2010), as they would only be applicable to some, but not all cases of scaffolding relations. We concede that a detailed
causal profile of a token mental ability is of course useful for some analyses, but
it is too specific for current purposes.
We propose to introduce six conditions that help characterize scaffolding relations that realize a mental ability in a certain situation.
In each case, the scaffolding relation as defined above (i-iii) can be further
characterized by
a)
b)
c)
d)
a temporal condition;
a competence condition;
a purpose condition;
a format condition;
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A. Newen, R. E. Fabry
e) an access condition;
f) a use condition.
In what follows, we will specify each condition and refer, where appropriate, to
cross-connections between these conditions.
a) Temporal condition: Determining a timescale
This condition helps us characterize the relevant situational context by specifying the timescale on which a scaffolding relation of interest is realized. Previous
research has suggested to distinguish between synchronic and diachronic realizations of scaffolding relations (Griffiths and Scarantino 2009; Saarinen 2020). Sutton (2016) proposes a more fine-grained distinction between phylogenetic, culturalhistorical, ontogenetic (diachronic) and occurrent (synchronic) timescales. We adopt
this fine-grained distinction of four timescales (see also Coninx and Stephan 2021).
Note that scaffolding relations on phylogenetic and cultural-historical timescales
always concern a certain population of agents. Scaffolding relations on ontogenetic
and occurrent timescales can comprise an individual agent or a group of agents.
Selecting the relevant timescale of recruiting an environmental resource is often
connected to a description of the directionality of the causal relationship. For example, the cumulative cultural evolution of a scaffold can be described as a case of bidirectional dependence on a cultural-historical timescale. This means that an environmental resource and the relevant mental ability that is scaffolded by it mutually
influence each other across cultural history. On an ontogenetic timescale, we may
identify a bi-directional causal relationship if the use of an environmental resource,
which causally triggers a mental ability, modifies properties of the environmental
resource.
b) Competence condition: Contexts of acquisition and application
Scaffolding relations are in part determined by the agent’s level of competence in
a certain domain. Initially, the notion of ‘scaffolding’ referred to socially conveyed
guidance and support structures that help novices acquire a new skill, e.g., problemsolving (Wood et al. 1976). However, subsequent research has emphasised that environmental resources enter scaffolding relations, relative to a certain mental ability,
at all levels of competence, ranging from novice and advanced skills to expertise in
the relevant domain (Clark 1997; Varga 2019). In any given case, the competence
condition can help specify the relevance of the environmental resource, given the
agent’s current mental abilities and the characteristics of the situational context.
c) Purpose condition: Single versus multi-purpose environmental resources
The purpose condition specifies the scope of application of a certain environmental resource that enters a scaffolding relation. We can distinguish between specialpurpose and multi-purpose resources. Special-purpose resources are, by their very
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A Pattern Theory of Scaffolding
(socio-culturally shaped) design, limited to the manifestation of specific mental
abilities. For example, a compass indexes geographic north and thereby exclusively
contributes to spatial orientation (Heersmink 2013). Multi-purpose resources can
contribute to the manifestation of various different mental abilities across situational
contexts. For example, given a certain level of literacy, linguistic symbols can contribute to reasoning (Dutilh Novaes 2020; Harris 2009) or narrative practices (Fabry
2018).
d) Format condition: Non-representational and representational environmental
resources
To introduce this condition, we start with a focus on features of environmental
material resources. Recently, Colombetti (2020) has suggested to adopt Heersmink’s
(2013) taxonomy of cognitive artefacts to enrich our understanding of the various
kinds of material resources that contribute to scaffolding relations. At the most general level, Heersmink (2013) distinguishes between non-representational (ecological)
and representational artefacts.6 Non-representational artefacts contribute to cognitive and affective processes in virtue of their structural (spatial, temporal) properties. Building on Peirce’s (1935) semiotic analysis, Heersmink (2013) differentiates
between three different kinds of representational vehicles: icon, index, and symbol.
An icon (e.g., a map) bears a strong structural isomorphism to the represented object
(e.g., a landscape). An index (e.g., a thermometer) bears a causal relation to at least
some properties of the represented object (e.g., the current room temperature). A
symbol (e.g., a numeral symbol) relates to the represented object (e.g., a natural number) by virtue of norms that constrain its socio-culturally shared use.
Icon, index, and symbol are not mutually exclusive categories. Some environmental resources, e.g., diagrams, are both iconic and symbolic in that at least some
of their elements are isomorphic to the object they are representing, while other elements relate to the representational object in virtue of normative constraints. Other
resources can be used as either iconic or symbolic representations, for example in
the case of transitive and intransitive counting (Benacerraf 1965). In cases of transitive finger counting in various cultures (Bender and Beller 2012), extended fingers stand in an isomorphic relationship to the counted objects (e.g., three apples),
thereby iconically representing their cardinality. In cases of intransitive counting,
extended fingers symbolically represent the ordinality of natural numbers.7
6
In contrast to Heersmink (2013) and Colombetti (2020), we wish to include environmental resources
into our considerations that are not artefacts in the strict sense of the term (i.e., human-made, culturally
evolved material objects). Having said this, we think that Heersmink’s (2013) taxonomy is helpful for
categorising those environmental resources that are artefactual in kind.
7
An anonymous reviewer raised concerns about the assumption that fingers, as body parts, can be
described as environmental resources in the context of finger counting practices. We agree that the role
of fingers, in this particular context, is a borderline case: one may want to classify it as a case of embodiment. But fingers, as body parts, are manipulated during finger counting in ways that follow environmentally established, normatively constrained, and socially shared cultural practices. Accordingly, in the case
of finger counting, fingers can satisfy the scaffolding conditions we are developing in this section. We
return to this point below in Section 4.
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A. Newen, R. E. Fabry
Note that the distinction between representational and non-representational
resources can also be applied to characteristics of the real-time, face-to-face communicative interaction between agents. For example, gestures can be iconic if they
complement the oral communication of a particular embodied action (GoldinMeadow and Alibali 2013; McNeill and Levy 1982). They can be symbolic if they
metaphorically represent the linguistic meaning of an utterance (McNeill and Levy
1982). Batonic gestures are non-representational in that they emphasise the temporal
structure of an utterance (Feyereisen et al. 1988).
In sum, a distinction between non-representational and representational (iconic,
indexical, symbolic) environmental resources is fruitful for specifying how objects
or actions contribute to scaffolding relations.8
e) Access condition: Finding, constructing, and being forced to use environmental
resources
There are three different sub-conditions under which an environmental resource
can be accessed in a certain situational context: it can be found in a situation, constructed by the agent(s) or it can be forced upon the agent(s) by others.
The use of environmental resources by nonhuman animals is often realized with
resources (e.g., tools) that are just found in the environment (Seed and Byrne 2010;
Visalberghi et al. 2017). The construction of environmental resources can also be
discovered in nonhuman animals (Shumaker et al. 2011), but it seems especially
common in human culture: we are creating, for example, maps, diagrams, and mathematical statements. In human culture, we are often forced to use certain environmental resources to realize cognitive abilities according to conventional rules. For
example, a teacher may insist that a child calculates with pen and paper instead of
using a calculator. This aspect may also include cases in which someone is manipulated to accept a certain ideology by being enforced to read only very selective
material (Haq et al. 2020). The latter case illustrates that scaffolds do not only
have positive effects for the agent, but can be also systematically used to control
or manipulate their mind (Coninx 2023b; Slaby 2016; Timms and Spurrett 2023).
Thus, we distinguish three types of access to scaffolds: finding resources, constructing resources, and being forced to use certain resources.
So far, we have mainly focused on the agent(s) on ontogenetic and occurrent
timescales and we have illustrated the access for an individual. However, many
environmental resources in human culture like symbol systems, folk narratives, or
songs are not just created by one individual, but are the product of cumulative processes of innovation by groups of agents across generations on a cultural-historical
timescale (Fabry 2017). The products of group-level innovations on a culturalhistorical timescale, in turn, influence the creation of environmental resources on
ontogenetic and occurrent timescales. In cases of resource innovation and creation,
8
To prevent any misunderstandings: This notion of representational tools concerns publicly available
signs and the way they are used. We are not discussing mental representations and their role. Our account
of scaffolding is neutral concerning the debate whether or not some mental abilities can only be adequately characterized by postulating mental representations.
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A Pattern Theory of Scaffolding
the developed resource and the relevant mental ability stand in a bi-directional
causal relationship, where the resource influences and is influenced by the relevant
mental ability.
f) The use condition: Availability and reliability
The characterization of scaffolding presupposes that the relevant environmental resource satisfies minimal requirements of availability and reliability (Saarinen
2020; Sterelny 2010; Sutton 2016). More precisely, for each aspect, there is a continuum that allows us to describe that use condition in more detail. Availability ranges
from single via multiple to permanent use of a scaffold when realizing a certain ability. It also includes the aspect of gradual ease of access: in the case of a white cane,
it has to be picked up each time the blind person leaves her apartment in contrast to
fingers used for basic counting. While the white cane can be misplaced, forgotten,
stolen, etc. (without noticing), fingers being part of the body are different in these
respects: they exemplify the most intense form of availability for the agent by being
part of it. Reliability ranges from minimal to strong reliability of a scaffold in enabling or supporting the ability.9
Let us summarize the six conditions of scaffolding relations: A scaffold used by
an agent to realize a mental ability in a situation can be characterized by a temporal,
competence, purpose, format, access, and use condition. If we capture a scaffolding
relation by applying most or all of these conditions, we arrive at a profile of scaffolding that is epistemically fruitful. It allows us to describe the causal role of the
environmental resource for a certain mental ability without making any problematic
metaphysical assumptions. We can thereby specify our description of the causal profile of the realization basis of a token mental ability. Note that we are not claiming
that each of the six conditions is always relevant to the same degree or even relevant
at all. Our pattern account indicates that these six conditions can be weighted differently relative to the specific case under consideration.
We will now apply this framework to cases of mathematical cognition. To do
this, we will show that the scaffolding conditions can help us specify the causal and
functional roles of scaffolds for the realization of mental abilities in the mathematical domain.
4 Application of the Pattern Theory of Scaffolding: the Case
of Mathematical Cognition
In this section, we will consider examples from the domain of mathematical cognition to illustrate the epistemic advantages of our pattern theory of scaffolding. However, it should be noted at the outset that the specification of scaffolding relations
9
A minimum of availability and reliability is a presupposition for an environmental resource to be a
scaffold. Concerning reliability, the minimum presupposition is that the resource is not functionally inadequate, e.g. a calculation machine which is broken or wrongly programmed. Variation of the use condition concerns only the scale above that minimum.
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A. Newen, R. E. Fabry
is relevant for understanding various cognitive and affective abilities. Mathematical
cognition can serve as an important test case of our pattern theory of cognitive scaffolding, because it has a wide range of applications from rather concrete cases of
counting objects in the world to abstract mathematical practices, including complex
arithmetic and the development of mathematical proofs. These practices are usually
enabled by the engagement with certain environmental resources. These resources,
we will argue in this section, serve as scaffolds for agents’ mathematical abilities.
Humans and many non-human animals are evolutionarily endowed with abilities
in quantity approximation and subitizing. Quantity approximation concerns the estimation of the quantity of items in a collection (Ansari 2008; Dehaene 2011; Emerson and Cantlon 2015). Subitizing refers to the intuitive identification of the quantity
of ≤ 4 items in a collection (Dehaene and Cohen 1994). On cultural-historical and
ontogenetic timescales, quantity approximation and subitizing precede counting and
qualify as proto-arithmetical abilities (Pantsar 2019). The cultural-historical, ontogenetic, and occurrent possibilities for mathematical cognition beyond these protoarithmetical abilities depend on the innovation, creation, and recruitment of environmental resources (Beller et al. 2018). In what follows, we will consider fingers, clay
tokens, Hindu-Arabic numeral symbols, and diagrams as examples of resources that
scaffold mathematical abilities.
As human body parts, fingers qualify as natural objects (access condition) and
multi-purpose resources (purpose condition), which are often recruited as scaffolds
for counting. The specific properties of finger counting systems vary across cultures
(Bender and Beller 2012; Everett 2017; Overmann 2018). While fingers are parts of
the human body, their recruitment in the service of socio-culturally shared counting
practices shows that they can take on various functional roles, some of which fulfil
the conditions for scaffolding developed in Section 3. As we show in this paragraph,
this is indeed the case if fingers are recruited and manipulated in the situational context of counting practices.10 In all their variability, finger counting systems make
nontrivial causal contributions to numerical cognition on cultural-historical, ontogenetic, and occurrent timescales. As already noted above, fingers can represent natural
numbers either iconically or symbolically, depending on their causal contribution to
transitive or intransitive counting, respectively (format condition). In many contemporary socio-cultural communities, fingers can be a scaffold for counting during the
acquisition of numerical competence on an ontogenetic timescale (temporal condition). While it is debated whether or not finger counting is “an obligatory prerequisite for the development of numerical cognition” and arithmetical abilities (Bender
and Beller 2012, p. 176; italics in original), there is evidence suggesting a systematic
“functional relationship” between subitizing, finger gnosis (the recognition and identification of individual fingers in response to tactile stimulation), finger counting, and
arithmetical skills in 5- to 7-year-old children (Noël 2005, p. 415). At the very least,
finger counting can help novices understand the base-10 system used in various cultures, the cardinality principle and the ordinality principle of natural numbers, and
the relationship between quantities and numeral words (Bender and Beller 2012). It
10
We are very grateful to an anonymous reviewer for pressing us on this point.
13
A Pattern Theory of Scaffolding
thus provides a uni-directional causal contribution to numerical abilities. On a cultural-historical timescale (temporal condition), expert finger counting may have been
a “precursor technology” for innovations at the group-level, including resources that
scaffold counting and arithmetic (Overmann 2016, p. 48), such as clay tokens.
Clay tokens were special-purpose environmental resources for counting and simple arithmetical operations (purpose condition). They were innovated in Mesopotamia between ~ 10,000 and ~ 1,000 BC (Overmann 2016, 2018) (access condition).
As representational resources (format condition), they prevalently served a symbolic
function by establishing norm-governed correspondence relations between grouped
tokens and quantities. While it is difficult to draw inferences from the archaeological
record to the level(s) of competence associated with the recruitment of clay tokens,
we may assume that clay tokens were relevant for counting and arithmetical abilities
in novice, advanced, and expert accountants (competence condition). As impressions
in clay envelopes, spatial configurations of clay tokens may have been a precursor of
the Mesopotamian cuneiform system (~ 3,000 BC), the first recorded numeral symbol system (Donald 1991; Ong 2012). This could imply that clay tokens and agents’
numerical and arithmetical abilities stood in a bi-directional causal relationship,
mutually influencing each other across cultural-historical time (temporal condition).
Numeral symbol systems are important environmental resources that scaffold
mathematical abilities. While the scope of application varies, ranging from timekeeping to algebra, numeral symbol systems can be categorized as special-purpose
resources that enable and support the exact, symbolic representation of number
(purpose condition). On a cultural-historical timescale, numeral symbol systems
are group-level, multi-generational innovations (Fabry 2017) (temporal and access
condition). The history of these systems can be described as a “material-social feedback loop” (Everett 2017, p. 224), where agents’ socially distributed mathematical
abilities and the scaffolding resources used in support of these abilities have stood
in a bi-directional causal relationship. Numeral symbol systems are crucial environmental resources for everyone engaging in algebra and other complex mathematical
practices, ranging from novices to experts (competence condition). To characterize
the format condition, we need to have a look at specific aspects.
Generally, numeral symbol systems have two properties that can help us understand
how they can scaffold mathematical abilities. First, numeral symbols are, in principle,
de-phonetized representations of numbers (De Cruz 2008). That is, they can be manipulated independently from the phonetic structure of the corresponding numeral words.
Second, numeral symbols are de-semantified: they can be manipulated independently
from the semantic content of the representandum (Krämer 2003). That is, mathematical operations (e.g., the application of the partial products algorithm) can be carried out
independently from the numerical value represented by certain numeral symbols. The
de-semantification of numeral (and operational) symbols leads to an independence “of
representation and operation” (Krämer 2003, p. 531; see also Dutilh Novaes 2013, 2014).
Numeral symbol systems are powerful environmental resources for mathematical
cognition, at least in part, in virtue of their de-phonetization and de-semantification.
On the one hand, they are concrete physical structures that can be manipulated in
space, e.g., on a piece of paper (Fabry & Pantsar, 2021). On the other hand, they are
abstract, symbolic representations that can be manipulated independently from their
13
A. Newen, R. E. Fabry
phonetic and semantic relata (format condition). In what follows, we will illustrate
these general observations by considering key characteristics of the Hindu-Arabic
decimal numeral system.
This system is organized according to the place-value principle: the magnitude
of a symbolically represented number (> 9) is determined not only by the value of
the composite digits, but also by their spatial arrangement (Dehaene 2011; Jones
2020; Knops 2020). In the following example, the value of each digit (2, 5, 7, 9)
is determined by its place in the symbolic arrangement:
9257, 5972, 2579, 7259, 5729
The understanding and application of the place-value principle is crucial for becoming
a competent arithmetician in cultural communities that employ the Hindu-Arabic system
on an ontogenetic timescale (temporal condition) (Fabry 2020). For novice, advanced,
and expert mathematicians, this numeral symbol system is a powerful resource for the
visualization and spatialization of mathematical statements and mathematical knowledge on an occurrent time scale (temporal condition) (Krämer 2014a). Historically, its
cumulative innovation has led to the symbolic representation of arithmetical operations
(e.g., +, −, ×, ÷), as well as the acceptance of negative integers, irrational numbers, and
complex numbers as mathematical objects (De Cruz and De Smedt 2013). On a culturalhistorical timescale (temporal condition), these symbolic innovations have scaffolded the
manifestation of genuinely new, or increasingly complex, mathematical operations.
Focusing on Clark’s (1998) conception of ‘scaffolding’, Larvor (2020) recently
argued that the crucial role of symbolic representation for mathematical practices
cannot be adequately described in terms of scaffolding. On his view, the concept
of ‘scaffolding’ suggests that numeral symbols, operators, and algebraic expressions would merely simplify mathematical tasks. However, “[m]athematics is full
of cognitive tasks that would not exist without the notations and representations
that create the environment in which those tasks present themselves” (Larvor 2020,
p. 3754). We agree with this claim and argue that his criticism does not apply to
our pattern theory of scaffolding. Our formulation of the temporal, competence,
purpose, format, access, and use conditions, as explicated above, leave room for
the idea that symbolic representations not merely simplify mathematical tasks, but
enable and advance mathematical abilities. In turn, the resulting abilities help shape
and re-shape mathematical knowledge through the innovation and creation of new
modes of symbolic representation. In these cases, the scaffolding resource and relevant mathematical abilities stand in a bi-directional causal relationship.
These considerations are also relevant for fully appreciating the crucial role of
symbolic scaffolds for arithmetical abilities in advanced and competent agents on
an occurrent timescale (temporal condition). In the case of arithmetic, Jones (2020)
argues, “[t]he regimented numerical and spatial structure of numerals is more than just
a handy representational tool, as it enables procedures, such as ‘long addition’ or ‘long
division’, which allow us to carry out calculations that would be extremely difficult, if
not impossible, with our natural cognitive capacities alone” (p. 3666). Indeed, while
competent arithmeticians do engage in mental arithmetic, which seemingly obviates the relevance of occurrent scaffolding, working memory limitations render more
13
A Pattern Theory of Scaffolding
complex arithmetical operations that are not scaffolded by numeral symbols and operators unfeasible (Imbo et al. 2007). In a large number of cases, then, symbolic representations uni-directionally influence the occurrent realization of arithmetical abilities.
The upshot is that numeral symbol systems in general, and the Hindu-Arabic system in
particular, provide a crucial resource for the innovation, transmission, and application
of mathematical abilities on all levels of competence on cultural-historical, ontogenetic, and occurrent timescales.
Diagrams are another key example of environmental resources that scaffold mathematical abilities. To a first approximation, diagrams can be defined as “cognitive tools
that are meant to spatially display information in order to improve memory and promote inference” (Giardino 2017, p. 500; italics in original). According to this definition,
diagrams are environmental resources for representing mathematical facts and relations
between mathematical statements and thereby contribute to mathematical reasoning.
Krämer (2016) goes one step further by arguing that diagrams are resources that enable
unique forms of reasoning and problem-solving in mathematics and other domains. On
Krämer’s (2014b) view, “[k]nowledge is not only represented, transmitted and disseminated through the diagrammatic; it is produced and expanded by it” (p. 3). Accordingly,
diagrams are assumed to play an important epistemic role by visualizing and spatializing mathematical statements or solutions to mathematical problems. They open up new
possibilities for acquiring and generating mathematical knowledge through the configuration of lines, points, and symbols in two-dimensional space (Krämer 2016).
From the perspective of our pattern theory of scaffolding, diagrams are multi-purpose environmental resources that enable mathematical reasoning and problem-solving, but also crucially contribute to epistemic processes in other domains, including
mechanics (Heiser and Tversky 2006), chemistry (Stieff 2011), and medicine (Grant
and Spivey 2003) (purpose condition). As already noted, diagrams can be both iconic
and symbolic (format condition). However, in the domain of mathematics, the components of diagrammatic representations are mostly symbolic in that they relate to
abstract mathematical objects and their relations in norm-governed ways. Diagrams are
the product of innovation and creation and can be disseminated, transmitted, and transformed within and across generations (access condition). While diagrams can support
novices in acquiring mathematical knowledge, for example knowledge about the multiplication table (Krämer 2014b), diagrams continue to scaffold mathematical abilities in
advanced and expert mathematicians (competence condition). These scaffolded mathematical abilities, in turn, can lead to modifications of diagrammatic resources themselves, either on an ontogenetic timescale (in the case of creation) or a cultural-historical timescale (in the case of innovation) in virtue of a bi-directional causal relationship
between agents’ abilities and environmental resources (temporal condition).
As an example for the epistemic role of diagrams in expert mathematics, consider
the diagrammatic proof of the geometric series theorem. This theorem states that
1 1 1
1
1
+ + +
+
+⋯=1
2 4 8 16 32
The proof of this theorem can take a diagrammatic form (Brown 2008; Giardino
2017) (Fig. 1).
13
A. Newen, R. E. Fabry
Fig. 1 Diagrammatic proof of
the geometric series theorem.
Adapted from Fabry & Pantsar
(2021)
The diagram scaffolds the insight that the represented sequence equals 1. Expert
mathematicians can also gain this insight by conducting or understanding a formal proof (Fabry & Pantsar 2021). However, the diagrammatic proof scaffolds the
application of expert mathematical abilities by transforming the problem space into
configurations of lines and symbols, thereby facilitating visuo-motor and spatial
abilities that contribute to mathematical cognition. The specific epistemic status of
diagrammatic proofs, especially in comparison to formal proofs, is debated in philosophy of mathematics (Fabry & Pantsar 2021). At the very least, they can scaffold
the creation and understanding of formal proofs (Tennant 1986). Ultimately, this
example illustrates that diagrams scaffold mathematical abilities not only in novice
and advanced mathematicians, but also enable and support mathematical reasoning
and problem-solving in expert mathematicians (competence condition).
Specific environmental resources, we have shown in this section, scaffold abilities in the mathematical domain. The temporal, competence, purpose, format and
access conditions can help specify the contribution of fingers, clay tokens, numeral
symbol systems, and diagrams to the acquisition and application of mathematical
abilities (Table 1).11 Vice versa, our discussion of specific examples demonstrates
that the plausibility and feasibility of these conditions are supported by theoretical
considerations and empirical evidence.
11
The use condition is not explicitly characterized because in all cases of mathematical cognition, as
well as in the case of the white cane, we do observe a rather high level of availability and reliability; for
other scaffolds this need not be so, although there is a tendency to develop scaffolds into the direction of
intense availability and reliability.
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A Pattern Theory of Scaffolding
Table 1 Overview of environmental resources that scaffold mathematical cognition (fingers, clay tokens, numeral symbols, diagrams) and spatial navigation (white cane)
Scaffolds
Temporal condition
Competence condition
Purpose condition
Format condition
Access condition
Fingers
Ontogenetic
Novice
Multi-purpose
Iconic or symbolic
Natural
Clay tokens
Cultural-historical
Novice to expert
Special-purpose
Symbolic
Innovated
Numeral Symbols
Cultural-historical to occurrent
Novice to expert
Special-purpose
Symbolic
Innovated
Diagrams
Cultural-historical to occurrent
Novice to expert
Multi-purpose
Iconic or symbolic
Innovated
White cane
Occurrent
Novice to expert
Special-purpose
Ecological
Innovated
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A. Newen, R. E. Fabry
5 Features and Advantages of the Pattern Theory of Scaffolding
Our starting point was the observation that we often have to include components that
are going beyond the brain and body in order to adequately describe the manifestation of cognitive abilities. These ‘external’ components are part of a wider causal network, which includes all relevant causal components underlying a mental phenomenon. This involves the inclusion of structuring and triggering causes of an event and
the exclusion of general background conditions. The external components are normally part of the structuring causes of an event, e.g., the white cane, while the triggering causes are systematically based on specific uses of this external resource, e.g.,
the sensorimotor information given by using the white cane in a situation. The central
claims of the pattern theory of scaffolding are the following: first, an environmental
resource can be fruitfully characterized as a scaffold if it is used to enable, support,
enhance, or regulate a certain realization of a mental ability. Second, it does this as a
part of the relevant causal network underlying this realization, i.e., as a triggering or
a structuring cause. Third, we can constrain our description of the causal and functional role of the scaffold for the typical realization of a certain ability by specifying
six scaffolding conditions. Fourth, we propose our theory as a pattern theory of scaffolding. This means that the multiple scaffolding conditions can all be realized gradually and they can be of varying relevance to characterize a scaffold. Thus, we characterize the causal role of an environmental resource for a mental ability in a situation
with a pattern of relevance-weighted gradually realized scaffolding conditions.
What Do we Gain by Such a Characterization of Scaffolding Relations? First, we
receive a fruitful comparison of different types of environmental resources as causally relevant for a mental ability, for example, different mathematical resources and
ecological resources such as a white cane. Second, since we characterize the causal
relevance and role of environmental resources for a mental ability, our account can
be understood as an enrichment of a causal characterization of mental phenomena.
However, our view is opposed to narrow internalistic accounts, according to which
only internal brain mechanisms can be part of the relevant causal network (e.g.,
Craver 2007). Third, by integrating the scaffolding conditions as constraints on the
causal and functional roles of the relevant environmental resource, our characterization of environmental resources avoids running into a speculative metaphysics
of unclear influences of the resource on the mental ability. The scaffolding conditions help us constrain the causal role of environmental resources and describe the
degree of relevant agent-scaffold couplings.
What are the Advantages of Our Pattern Theory Compared to Alternative Theories of
Scaffolding? So far, there has been no general systematic and integrative theory of
scaffolding. Part of the reason is a pervasive conceptual distinction between cognitive
scaffolding and affective scaffolding. Accordingly, previous work has focused on the
role of environmental resources for the realization of either cognitive abilities (e.g.,
Sterelny 2010) or affective abilities (e.g., Coninx and Stephan 2021; Saarinen 2020).
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A Pattern Theory of Scaffolding
We suggest a general theory of scaffolding as a minimal common ground, which then
can be enriched and modified into specific accounts depending on the relevant target
phenomenon and specific research questions. Thus, we highlight some advantages of
our theory over these systematic and elucidating accounts. Under the label of trust,
for example, Sterelny (2010) considers parts of our access condition. However, his
proposal lacks the purpose, format, and competence conditions. Saarinen’s (2020)
and Coninx and Stephan’s (2021) accounts share our aim to systematize and taxonomize scaffolding relations and suggest to take the temporality and the causal directionality of scaffolding relations into consideration. However, they focus on the scaffolding of affective abilities and highlight features that are ascribed to an individual
agent and their particular mindset. A couple of examples should suffice to establish
this assumption. First, following Sterelny (2010) and Colombetti and Krueger (2015),
Coninx and Stephan (2021) and Saarinen (2020) suggest the feature of individualization: how well is the scaffold adapted to our individual needs? Second, Coninx and
Stephan (2021) propose mineness as an important feature of scaffolding relations. On
their view, this feature “captures how closely the scaffold is integrated into one’s selfnarrative” (Coninx and Stephan 2021, p. 50). While these features are of interest for
characterizing the full scope of scaffolding relations relative to a certain individual
agent, they are too specific to describe the role of a scaffold for the same mental ability across individual agents.12 Since these features focus on the individual, they cannot capture the causal roles of scaffolds for a group of agents at various timescales.
By definition, the notions of mineness and individualization are applicable to an individual agent, not a group of agents. For this reason, their descriptive scope is too
limited to accommodate all cases of scaffolding relations.
The time is ripe for an integrative account of scaffolding that helps specify the
causal influence of environmental resources on cognitive and affective abilities on
a general level. One reason is that it might prove unfeasible to clearly distinguish
between cases of cognitive and affective scaffolding as is presupposed by existing
accounts. For example, the same environmental resource can scaffold both cognitive
and affective abilities (Fabry 2021a; Saarinen 2020). An integrative theory can help
explore the commonalities and differences of the relevant realizations of cognitive
and affective abilities. Accordingly, our account proposes scaffolding conditions as
constraints on the relevant causal network, such that we can informatively describe,
using those conditions, the general causal and functional roles of a certain environmental resource for the relevant cognitive and affective abilities.
12
Let us illustrate this point with an analogy to speech act theory. Speech acts are mainly characterized by an illocutionary role (e.g., a promise) and a propositional content (e.g., that the speaker will visit
you the next day). In addition, speech act theory distinguishes the perlocutionary effect on the addressee
of the utterance. For example, someone can be flattered or frightened by the same promise. The perlocutionary effects of the token promise on each individual are certainly interesting, but they seem to be
secondary to the type of speech act. By analogy, we think that our pattern theory focuses on the central
aspects of the type of scaffolding relation in abstraction from its effects on the individual agent. However,
this strategy still allows for the possibility that those can be integrated if the aim is to describe the role of
a scaffold for a specific agent and their relevant mindset in detail.
13
A. Newen, R. E. Fabry
Finally, there is a specific conceptual benefit of the pattern theory of cognitive
scaffolding in the context of 4E accounts: It allows us to reduce the classical distinction of 4E concepts to 3Es, namely keeping embodiment and enactment while
substituting embeddedness and extendedness by the new pattern notion of environmental scaffolding (scaffolding, for short) (see also Stephan 2018). This can only be
outlined here: From a birds-eye view, just relying on the starting distinction between
an agent and the environment in relation to an ability, the concepts of embodiment
and enactment are highlighting the relevance of certain features of the agent for
the realization of the ability, namely that bodily features beyond the brain are causally relevant for the ability (some form of embodiment) or that a certain activity or
disposition of the agent is causally relevant for the ability (enactment). A scaffold
enters the picture if we rely on environmental resources to realize an ability. In the
classical 4E approach, we describe an ability as being embedded for an agent by a
scaffold s if s is an (extra-agential) environmental resource that is causally relevant
but not constitutive for the ability; an ability is extended for an agent by a scaffold s
if s is an (extra-agential) environmental resource which is constitutive for the ability.
Why is it explanatorily fruitful to substitute these notions of being extended and
being embedded by the notion of being environmentally scaffolded? We will address
each aspect in turn. Substituting being extended by being environmentally scaffolded
is a consequence of adopting an epistemic-pragmatic perspective on environmental
resources, which has at least four clear advantages. First, the notion of extending the
mind has led to various metaphysical or metaphysically loaded discussions about the
coupling-constitution fallacy (e.g., Adams and Aizawa 2001; Aizawa 2010; Menary
2006) and the cognitive bloat problem (e.g., Allen-Hermanson 2013). While these
discussions are interesting in their own right, we do not think that they necessarily lead to a better empirically informed understanding of the role of environmental resources for the realization of mental abilities. In other words, we can keep
the intuitive idea of extendedness without inheriting the problematic features of a
metaphysical interpretation.13 Second, leaving aside metaphysical considerations
on the potential diachronicity of extended mental assemblies (e.g., Kirchhoff 2015),
the extended mind hypothesis is exclusively concerned with organism-environment
coordination dynamics on an occurrent timescale (Fabry 2021b). By contrast, our
epistemic-pragmatic theory of scaffolding can operate on phylogenetic, cultural-historical, ontogenetic, and occurrent timescales. As we exemplified in Section 4, this
leads to a more encompassing, while conceptually and descriptively constrained,
understanding of the contribution of certain environmental resources to the realization of mental abilities. Third, work on the extended mind focusses on the relationship of an individual agent to certain kinds of environmental resources. By contrast,
our pattern theory of scaffolding is well-equipped to cover scaffolding relations
between both an individual agent and a group of agents and a certain environmental
resource. Finally, even with a modified understanding of extendedness, we would
13
One reviewer highlights that one may insist that the metaphysical relation of being constituted by is
essential for describing mental phenomena. While we accept this perspective, we are not committed to
sharing it. For those taking this perspective, our epistemic-pragmatic proposal of scaffolding can still be
seen as an instrument for producing fruitful descriptions of mental phenomena.
13
A Pattern Theory of Scaffolding
cover only a rather limited range of environmental resources. By contrast, our framework is able to accommodate a wide array of heterogeneous, causally relevant external resources, which may or may not satisfy the special conditions of extendedness.
Together, these four reasons strongly suggest that cases that have been widely discussed by extended mind theorists can be more fruitfully described as special cases
of environmental scaffolding – this has been first suggested by Sterelny (2010).
Why do we propose to substitute the notion of being embedded by the notion
of being environmentally scaffolded? As pointed out by Menary (2015), commitments to embeddedness can come in various strengths, ranging from weak
assumptions compatible with internalism (Rupert 2004) to strong assumptions
compatible with the extended mind thesis (e.g., Clark 2008) and cognitive integrationism (Menary 2007). This indicates that the notion of embeddedness is used
in a very unspecific way. Furthermore, it lacks any additional characterizations
that would be needed to identify, describe, and compare different functional roles
of rather heterogeneous external resources. By contrast, our alternative account
consists in characterizing the role of an external resource for a mental ability by
its gradually increasing role in a causal network in a systematic way. The latter
is exactly what we offer by describing a profile of scaffolding relations for each
scaffold. Starting with some basic causal relations, we can add specific relevant
causal constraints by describing the scaffolding conditions and thus enable more
specific descriptions of the typical realization of a mental ability by an agent in a
situation. We think of embeddedness and extendedness as the endpoints of a rich
gradual spectrum of agent-ability-scaffold relations. The intensity of such a relation is characterized by the scaffolding conditions. Intense scaffolding relations
(high level concerning the aspects of the use condition, temporal continuity on
an occurrent timescale, special purpose, etc.) would be usually classified as cases
of extendedness. Our use condition includes the often-discussed aspects of a high
degree of availability and reliability. By contrast, moderate agent-ability-scaffold relations (moderate level concerning the availability and reliability aspects
of the use condition, moderate temporal continuity on ontogenetic or occurrent
timescales, multi-purpose, etc.) would be usually classified as cases of moderate
embeddedness (cf. Menary 2015). Most importantly, our gradual theory of scaffolding allows for a variety of intermediate cases. Let us highlight three features
of our account.
(i) The application area of a mental ability influences the status of a scaffold. For
example, fingers are a scaffold for counting, but not for any complex mathematics.
(ii) The same external resource can change its role over time. For example, fingers are an important resource at the early developmental stages of numerical
cognition but cease to play any relevant role for arithmetical abilities beyond
the initial learning phase. They are normally substituted by numerals.
Such changes for the same scaffold (as mentioned in ii) can in principle be
observed for all scaffolding conditions. Since many scaffolds have a stable functional and causal role, at least for some period, our classification remains useful.
13
A. Newen, R. E. Fabry
Finally, recall the following theoretical assumption, introduced in Section 2:
(iii) We characterized a scaffold only relative to an agent, a mental ability and a
situational context.
This allows us to leave aside problematic aspects of the extended mind debate: for
us, it does not make sense to ask the question whether, for example, the white cane
is part of the mind of a blind person. It is reasonable to describe the white cane as a
scaffold for the ability of spatial orientation when it is used in a situation. We can of
course describe different types of such applications, but it seems to be a superfluous
metaphysical debate whether the white cane is part of the mind of a blind person per
se. Our pattern theory, and its application in Section 4, comes with an open invitation to other researchers to apply our theory to other cases in cognitive and affective
domains in their future work.
6 Conclusion
To adequately describe the role of external resources for the realization of mental
abilities, we have offered a systematic theory of scaffolding. A core aspect of this
pattern theory is the characterization of scaffolding conditions. The six scaffolding
conditions we developed above are chosen to be general enough to enable descriptions of various scaffolding relations in both cognitive and affective domains. Furthermore, the scaffolding conditions can best be understood as constraints on the
relevant causal network. The multiplicity of combinations of scaffolding conditions leads to a large variety of patterns of scaffolding relations. With our theory,
we can integrate the usually highlighted paradigmatic cases of embeddedness and
extendedness without the need to enter any metaphysical debates on the distinction
between causation (or high causal relevance) and constitution. Consequently, we
offer a general framework of scaffolding, which substitutes the 4E framework by a
3E framework for the study of embodied, enacted and environmentally scaffolded
phenomena.
Acknowledgements We are grateful to Sabrina Coninx, Roy Dings, Gabriele Ferretti, Maja Griem,
Alfredo Vernazzani, and Wanja Wiese for their helpful and constructive feedback on an earlier version
of this paper.
Funding Newen’s work on this paper has been financially supported by the German Research Foundation
in the context of funding the Research Training Group “Situated Cognition” (GRK 2185/1). (Gefördert
durch die Deutsche Forschungsgemeinschaft (DFG), Projektnummer GRK 2185/1.)
Fabry’s work has been funded by a Postdoctoral Research Fellowship granted by the Ruhr Universität Bochum and a Discovery Early Career Research Award granted by the Australian Research Council
(DE210100115).
Declarations
Conflict of interest None
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A Pattern Theory of Scaffolding
References
Adams, F., and K. Aizawa. 2001. The bounds of cognition. Philosophical Psychology 14 (1): 43–64.
https://doi.org/10.1080/09515080120033571.
Aizawa, K. 2010. The coupling-constitution fallacy revisited. Cognitive Systems Research 11 (4): 332–
342. https://doi.org/10.1016/j.cogsys.2010.07.001.
Allen-Hermanson, S. 2013. Superdupersizing the mind: extended cognition and the persistence of cognitive bloat. Philosophical Studies 164 (3): 791–806. https://doi.org/10.1007/s11098-012-9914-7.
Anderson, M. L. 2015. After phrenology: neural reuse and the interactive brain. MIT Press.
Ansari, D. 2008. Effects of development and enculturation on number representation in the brain. Nature
Reviews Neuroscience 9 (4): 278–291.
Arango-Muñoz, S. 2013. Scaffolded memory and metacognitive feelings. Review of Philosophy and Psychology 4 (1): 135–152. https://doi.org/10.1007/s13164-012-0124-1.
Arnsten, A.F.T. 2015. Stress weakens prefrontal networks: molecular insults to higher cognition. Nature
Neuroscience 18 (10): 1376–1385. https://doi.org/10.1038/nn.4087.
Beller, S., A. Bender, S. Chrisomalis, F.M. Jordan, K.A. Overmann, G.B. Saxe, and D. Schlimm. 2018.
The cultural challenge in mathematical cognition. Journal of Numerical Cognition 4 (2): 448–463.
Benacerraf, P. 1965. What numbers could not be. The Philosophical Review 74 (1): 47–73. https://doi.
org/10.2307/2183530.
Bender, A., and S. Beller. 2012. Nature and culture of finger counting: diversity and representational
effects of an embodied cognitive tool. Cognition 124 (2): 156–182.
Brown, J.R. 2008. Philosophy of mathematics: a contemporary introduction to the world of proofs and
pictures, 2nd ed. New York: Routledge.
Chemero, A. 2009. Radical embodied cognitive science. Cambridge, Mass: MIT Press.
Clark, A. 1997. Being there: putting brain, body, and world together again. Cambridge, Mass: MIT Press.
Clark, A. 1998. Magic words: how language augments human computation. In Language and thought,
ed. P. Carruthers and J. Boucher, 162–183. Cambridge, UK: Cambridge University Press.
Clark, A. 2008. Supersizing the mind: embodiment, action, and cognitive extension. In Embodiment,
action, and cognitive extension. Oxford: Oxford University Press.
Clark, A., and D. Chalmers. 1998. The extended mind. Analysis 58 (1): 7–19.
Colombetti, G. 2020. Emoting the situated mind: a taxonomy of affective material scaffolds. JOLMA:
The Journal for the Philosophy of Language Mind and the Arts 1 (2): 215–236. https://doi.org/10.
30687/Jolma/2723-9640/2020/02/004.
Colombetti, G., and J. Krueger. 2015. Scaffoldings of the affective mind. Philosophical Psychology 28
(8): 1157–1176. https://doi.org/10.1080/09515089.2014.976334.
Coninx, S. 2023a. The notorious neurophilosophy of pain: a family resemblance approach to idiosyncrasy
and generalizability. Mind & Language 8 (1): 178–197. https://doi.org/10.1111/mila.12378.
Coninx, S. 2023b. The dark side of niche construction. Philosophical Studies. https://doi.org/10.1007/
s11098-023-02024-3.
Coninx, S., and A. Stephan. 2021. A taxonomy of environmentally scaffolded affectivity. Danish
Yearbook of Philosophy 1–27. https://doi.org/10.1163/24689300-bja10019.
Craver, C.F. 2007. Explaining the brain: Mechanisms and the mosaic unity of neuroscience. Oxford:
Oxford University Press.
De Cruz, H. 2008. An extended mind perspective on natural number representation. Philosophical
Psychology 21 (4): 475–490.
De Cruz, H., and J. De Smedt. 2013. Mathematical symbols as epistemic actions. Synthese 190 (1):
3–19. https://doi.org/10.1007/s11229-010-9837-9.
Dehaene, S. 2011. The number sense: how the mind creates mathematics, 2nd ed. Oxford: Oxford
University Press.
Dehaene, S., and L. Cohen. 1994. Dissociable mechanisms of subitizing and counting: neuropsychological evidence from simultanagnosic patients. Journal of Experimental Psychology: Human
Perception and Performance 20 (5): 958.
Donald, M. 1991. Origins of the modern mind: three stages in the evolution of culture and cognition.
Cambridge, Mass: Harvard University Press.
Dretske, F. 1988. Explaining behavior: reasons in a world of causes. Cambridge, Mass: MIT Press.
Dutilh Novaes, C. 2013. Mathematical reasoning and external symbolic systems. Logique & Analyse
221: 45–65.
13
A. Newen, R. E. Fabry
Dutilh Novaes, C. 2014. Formal languages in logic: a philosophical and cognitive analysis. Cambridge, UK: Cambridge University Press.
Dutilh Novaes, C. 2020. The dialogical roots of deducation: historical, cognitive, and philosophical
perspectives on reasoning. Cambridge University Press.
Emerson, R.W., and J.F. Cantlon. 2015. Continuity and change in children’s longitudinal neural
responses to numbers. Developmental Science 18 (2): 314–326.
Everett, C. 2017. Numbers and the making of us: counting and the course of human cultures. Harvard
University Press.
Fabry, R.E. 2017. Cognitive innovation, cumulative cultural evolution, and enculturation. Journal of
Cognition and Culture 17 (5): 375–395. https://doi.org/10.1163/15685373-12340014.
Fabry, R.E. 2018. Enculturation and narrative practices. Phenomenology and the Cognitive Sciences
17 (5): 911–937. https://doi.org/10.1007/s11097-018-9567-x.
Fabry, R.E. 2020. The cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturated arithmetical cognition. Synthese 197 (9): 3685–3720. https://doi.org/10.1007/
s11229-019-02238-1.
Fabry, R. E. (2021a). Narrative scaffolding. Review of Philosophy and Psychology. https://doi.org/10.
1007/s13164-021-00595-w
Fabry, R.E. 2021b. Limiting the explanatory scope of extended active inference: The implications
of a causal pattern analysis of selective niche construction, developmental niche construction,
and organism-niche coordination dynamics. Biology & Philosophy 36: 1–26. https://doi.org/10.
1007/s10539-021-09782-6.
Fabry, R.E., and M. Pantsar. 2021. A fresh look at research strategies in computational cognitive science: The case of enculturated mathematical problem solving. Synthese 198 (4): 3221–3263.
https://doi.org/10.1007/s11229-019-02276-9.
Feyereisen, P., M. Van de Wiele, and F. Dubois. 1988. The meaning of gestures: what can be understood without speech? European Bulletin of Cognitive Psychology 8 (1): 3–25.
Fuchs, R., and S. Klaperski. 2018. Stessregulation Durch Sport Und Bewegung. In Handbuch Stressregulation Und Sport, ed. R. Fuchs and M. Gerber, 205–226. Cham: Springer.
Gallagher, S. 2013. A pattern theory of self. Frontiers in Human Neuroscience 7: 443.
Giardino, V. 2017. Diagrammatic reasoning in mathematics. In Springer handbook of model-based
science, ed. L. Magnani and T. Bertolotti, 499–522. Cham: Springer.
Goldin-Meadow, S., and M.W. Alibali. 2013. Gesture’s role in speaking, learning, and creating language. Annual Review of Psychology 64: 257–283.
Grant, E.R., and M.J. Spivey. 2003. Eye movements and problem solving: guiding attention guides
thought. Psychological Science 14 (5): 462–466.
Griffiths, P., and A. Scarantino. 2009. Emotions in the wild: the situated perspective on emotions. In
The Cambridge handbook of situated cognition, ed. P. Robbins and M. Aydede, 437–453. Cambridge, UK: Cambridge University Press.
Haq, H., S. Shaheed, and A. Stephan. 2020. Radicalization through the lens of situated affectivity.
Frontiers in Psychology 11: 205. https://doi.org/10.3389/fpsyg.2020.00205.
Harris, R. 2009. Rationality and the literate mind. Routledge.
Heersmink, R. 2013. A taxonomy of cognitive artifacts: function, information, and categories. Review of
Philosophy and Psychology 4 (3): 465–481.
Heiser, J., and B. Tversky. 2006. Arrows in comprehending and producing mechanical diagrams. Cognitive Science 30 (3): 581–592. https://doi.org/10.1207/s15516709cog0000_70.
Heyes, C. 2018. Cognitive gadgets: the cultural evolution of thinking. Harvard University Press.
Imbo, I., S. Duverne, and P. Lemaire. 2007. Working memory, strategy execution, and strategy selection in mental arithmetic. The Quarterly Journal of Experimental Psychology 60 (9): 1246–1264.
https://doi.org/10.1080/17470210600943419.
Jones, M. 2020. Numerals and neural reuse. Synthese 197 (9): 3657–3681. https://doi.org/10.1007/
s11229-018-01922-y.
Kaspar, K., S. König, J. Schwandt, and P. König. 2014. The experience of new sensorimotor contingencies by sensory augmentation. Consciousness and Cognition 28: 47–63. https://doi.org/10.1016/j.
concog.2014.06.006.
Kirchhoff, M.D. 2015. Extended cognition & the causal-constitutive fallacy: in search for a diachronic
and dynamical conception of constitution. Philosophy and Phenomenological Research 90 (2):
320–360. https://doi.org/10.1111/phpr.12039.
Knops, A. 2020. Numerical cognition: the basics. London, New York: Routledge.
13
A Pattern Theory of Scaffolding
Krämer, S. 2003. Writing, notational iconicity, calculus: on writing as a cultural technique. MLN 118 (3):
518–537.
Krämer, S. 2014a. Mathematizing power, formalization, and the diagrammatical mind or: what does computation mean? Philosophy & Technology 27 (3): 345–357.
Krämer, S. 2014. Trace, writing, diagram: reflections on spatiality, intuition, graphical practices and
thinking. In The power of the image: emotion, expression, explanation, ed. A. Benedek and K.
Nyíri, 3–22. Frankfurt am Main: Peter Lang.
Krämer, S. 2016. Figuration, Anschauung, Erkenntnis: Grundlinien Einer Diagrammatologie. Berlin:
Suhrkamp Verlag.
Krueger, J. 2020. Schizophrenia and the scaffolded self. Topoi 39 (3): 597–609. https://doi.org/10.1007/
s11245-018-9547-3.
Lakoff, G., and M. Johnson. 1999. Philosophy in the flesh: the embodied mind and its challenge to western thought. New York: Basic Books.
Larvor, B. 2020. Why ‘scaffolding’ is the wrong metaphor: the cognitive usefulness of mathematical representations. Synthese 197 (9): 3743–3756. https://doi.org/10.1007/s11229-018-02039-y.
McNeill, D., and E. Levy. 1982. Conceptual representations in language activity and gesture. In Speech,
place, and action, ed. R.J. Jarvella and W. Klein, 271–295. Hoboken, New Jersey: John Wiley & Sons.
Menary, R. 2006. Attacking the bounds of cognition. Philosophical Psychology 19 (3): 329–344. https://
doi.org/10.1080/09515080600690557.
Menary, R. 2007. Cognitive integration: mind and cognition unbounded. Basingstoke, New York: Palgrave Macmillan.
Menary, R. 2010. The extended mind. Cambridge, Mass: MIT Press.
Menary, R. 2015. Mathematical cognition: a case of enculturation. In Open MIND, eds. T. Metzinger and
J.M. Windt, 1–20. MIND Group. https://doi.org/10.15502/9783958570818
Merleau-Ponty, M. 2012. Phenomenology of perception (trans: Landes, D.A.). Routledge & K. Paul.
Newen, A. 2017. What are cognitive processes? An example-based approach. Synthese 194 (11): 4251–
4268. https://doi.org/10.1007/s11229-015-0812-3.
Newen, A. 2018. The embodied self, the pattern theory of self, and the predictive mind. Frontiers in Psychology 9: 2270. https://doi.org/10.3389/fpsyg.2018.02270.
Newen, A., L. De Bruin, and S. Gallagher. 2018. 4E cognition: Historical roots, key concepts, and central
issues. In The Oxford handbook of 4E cognition, ed. A. Newen, L. De Bruin, and S. Gallagher,
3–15. Oxford: Oxford University Press.
Newen, A., A. Welpinghus, and G. Juckel. 2015. Emotion recognition as pattern recognition: The relevance of perception. Mind & Language 30 (2): 187–208. https://doi.org/10.1111/mila.12077.
Noël, M.-P. 2005. Finger gnosia: a predictor of numerical abilities in children? Child Neuropsychology
11 (5): 413–430.
Ong, W.J. 2012. Orality and literacy: the technologizing of the word. London, New York: Routledge.
Overmann, K.A. 2016. The role of materiality in numerical cognition. Quaternary International 405:
42–51. https://doi.org/10.1016/j.quaint.2015.05.026.
Overmann, K.A. 2018. Constructing a concept of number. Journal of Numerical Cognition 4 (2): 464–
493. https://doi.org/10.5964/jnc.v4i2.161.
Pantsar, M. 2019. The enculturated move from proto-arithmetic to arithmetic. Frontiers in Psychology
10: 1–15. https://doi.org/10.3389/fpsyg.2019.01454.
Peirce, C.S. 1935. Collected papers of Charles Sanders Peirce, ed. C. Hartshorne, P. Weiss, and A.W.
Burks, Volume 1–8. Cambridge, Mass: Harvard University Press.
Rupert, R.D. 2004. Challenges to the hypothesis of extended cognition. Journal of Philosophy 101 (8):
389–428.
Saarinen, J.A. 2020. What can the concept of affective scaffolding do for us? Philosophical Psychology
33 (6): 820–839. https://doi.org/10.1080/09515089.2020.1761542.
Seed, A., and R. Byrne. 2010. Animal tool-use. Current Biology 20 (23): R1032–R1039. https://doi.org/
10.1016/j.cub.2010.09.042.
Seli, P., M.J. Kane, J. Smallwood, D.L. Schacter, D. Maillet, J.W. Schooler, and D. Smilek. 2018. Mindwandering as a natural kind: a family-resemblances view. Trends in Cognitive Sciences 22 (6):
479–490. https://doi.org/10.1016/j.tics.2018.03.010.
Shumaker, R.W., K.R. Walkup, and B.B. Beck. 2011. Animal tool behavior: the use and manufacture of
tools by animals, 2nd ed. Baltimore: Johns Hopkins University Press.
Slaby, J. 2016. Mind invasion: situated affectivity and the corporate life hack. Frontiers in Psychology, 7.
https://doi.org/10.3389/fpsyg.2016.00266.
13
A. Newen, R. E. Fabry
Stephan, A. 2018. Critical note: 3E’s are sufficient, but don’t forget the D. In The Oxford handbook of 4E
cognition, 1st ed., ed. L.C. de Bruin, A. Newen, and S. Gallagher, 607–619. Oxford University Press.
Sterelny, K. 2010. Minds: extended or scaffolded? Phenomenology and the Cognitive Sciences 9 (4):
465–481. https://doi.org/10.1007/s11097-010-9174-y.
Stieff, M. 2011. When is a molecule three dimensional? A task-specific role for imagistic reasoning in
advanced chemistry. Science Education 95 (2): 310–336. https://doi.org/10.1002/sce.20427.
Sutton, J. 2016. Scaffolding memory: themes, taxonomies, puzzles. In Contextualizing human memory:
an interdisciplinary approach to understanding how individuals and groups remember the past, ed.
L. Bietti and C.B. Stone, 187–205. London, New York: Routledge.
Tennant, N. 1986. The withering away of formal semantics? Mind & Language 1 (4): 302–318.
Timms, R., and Spurrett, D. 2023. Hostile scaffolding. Philosophical Papers 1–30. https://doi.org/10.
1080/05568641.2023.2231652
Varga, S. 2019. Scaffolded minds: integration and disintegration. Cambridge, Mass: MIT Press.
Visalberghi, E., G. Sabbatini, A.H. Taylor, and G.R. Hunt. 2017. Cognitive insights from tool use in nonhuman animals. In APA handbook of comparative psychology: perception, learning, and cognition,
eds. J. Call, J.M. Burghardt, I.M. Pepperberg, C.T. Snowdon, and T. Zentall, 673–701. American
Psychological Association.
Walter, S. 2017. Précis zu Illusion Freier Wille? Grenzen Einer Empirischen Annäherung an ein philosophisches Problem. Zeitschrift Für Philosophische Forschung 72 (3): 407–412. https://doi.org/10.
3196/004433017821835696.
Williams, L. E., and J. A. Bargh. 2008. Experiencing physical warmth promotes interpersonal warmth.
Science 322(5901):606 LP – 607. https://doi.org/10.1126/science.1162548
Wittgenstein, L. 2009. Philosophische Untersuchungen—Philosophical investigations: The German text,
with an English translation by G. E. M. Anscombe, P. M. S. Hacker and Joachim Schulte (P. M. S.
Hacker & J. Schulte, Eds.; 4th ed.). Wiley-Blackwell.
Wolf, O.T. 2019. Memories of and influenced by the trier social stress test. Psychoneuroendocrinology
105: 98–104. https://doi.org/10.1016/j.psyneuen.2018.10.031.
Wolf, O.T., P. Atsak, D.J. de Quervain, B. Roozendaal, and K. Wingenfeld. 2016. Stress and memory: a
selective review on recent developments in the understanding of stress hormone effects on memory
and their clinical relevance. Journal of Neuroendocrinology, 28(8). https://doi.org/10.1111/jne.
12353.
Wood, D., J.S. Bruner, and G. Ross. 1976. The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry 17 (2): 89–100.
Zhong, C.-B., and G.J. Leonardelli. 2008. Cold and lonely: does social exclusion literally feel cold? Psychological Science 19 (9): 838–842. https://doi.org/10.1111/j.1467-9280.2008.02165.x.
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