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 13 Vol.:(0123456789) 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 13 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. 13 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. 13 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). 13 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. 13 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; 13 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 13 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. 13 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. 13 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. 13 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. 13 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 13 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). 13 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.) 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