On the notion of abstraction in systemic functional linguistics

ion is to take a distance from the concrete world. Abstraction coincides with (or is a close variant of ) generalisation. Abstraction is information hiding. Abstraction is to keep relevant aspects and to disregard irrelevant ones.ion is information hiding. Abstraction is to keep relevant aspects and to disregard irrelevant ones. Abstraction is a kind of reformulation or approximationion is a kind of reformulation or approximation Due to this multi-valance, it is important to make certain what is meant by the term’s use on a case-by-case basis. Otherwise, misunderstandings concerning the nature of this theoretical notion may arise, and any inexplicitness may hinder the successful application of theoretical notions to real-life cases. This article argues that although the term abstraction has been applied to all three of the theoretical dimensions mentioned, the specific nature of the term differs in each case. Proceeding from a discussion of abstraction from other academic disciplines, this investigation will focus on the following aspects of abstraction that seem most relevant for functional linguistics: (1) abstraction as linked to the idea of ‘mere omission’ (c.f. Jones 2005: 174), (2) abstraction as generalisation, and (3) abstraction as decontextualisation. Using these factors as criteria, it is possible to show how stratification, delicacy, and instantiation differ from and are alike to each other in these regards. In doing so, it is hoped that a deeper and clearer understanding of these crucial theoretical notions will be achieved. The rest of the article is organised as follows: Section 2 provides a discussion of the methodology taken in this work, namely that making a comparison with the use of abstraction in other disciplines can aid our understanding of the term in SFL. It will also address some potential criticisms that may be levied against this approach. Section 3 gives an overview of the facets of abstraction mentioned above. Section 4 discusses the relevant theoretical dimensions in SFL, and investigates the meaning of abstraction in each case. It concludes with the main finding of this study, by giving a typology of the different kinds of abstraction found in systemic theory. Section 5 returns to the notion of stratification, because, as will be shown, this dimension does not map on well to the factors previously discussed. Section 6 concludes the work and points towards further potential avenues of research. Systemic functional linguistics and the (other) sciences Abstraction is considered one of the fundamental concepts in scientific practice (Godfrey-Smith, 2009: 46). Physicists’ equations, chemical symbols, and mathematicalion is considered one of the fundamental concepts in scientific practice (Godfrey-Smith, 2009: 46). Physicists’ equations, chemical symbols, and mathematical Williams et al. Functional Linguistics (2017) 4:13 Page 3 of 22 descriptions all involve some degree of abstraction in their creation. As such, the nature of this process has attracted discussion from those working in the philosophy of science, whose aims include investigating the reasoning implicit in the creation of scientific models. Crucial to the work presented here is a comparison of how abstraction is defined in other disciplines, mainly from the mathematical and physical sciences, with how the term has been used by SFL practitioners. Before commencing with this enterprise, there are potential criticisms with this approach that need to be addressed. Halliday (1992a. [2005]) argues that the objects of scientific study and linguistic study may be of a different type; although there may be some similarities in systems of all kinds, there will undoubtedly be features particular to each discipline. If the subject matter is indeed different, then the question remains whether any comparisons of theoretical terms can prove useful. Secondly, he argues that philosophy of science produces a highly idealised viewpoint, far removed from the daily practices of scientists as they carry out their work. As such, linguists can learn from scientists, if linguists so wish, by observing scientists actually going about their work, and not “studying the models constructed in the name of philosophy of science” (ibid: 200). Drawing upon the work of such writers, then, may be less useful than it may at first seem. This paper takes the view, however, that although it cannot be assumed that theoretical notions do transcend discipline boundaries, neither can the possibility be dismissed out of hand. As mentioned, abstraction has already been compared in various subjects, and certain regularities have been argued for. If: (a.) the processes that are involved are linked to general properties of human cognition, as has been argued for by Barsalou (2003, 2005) and Martinez and Huang (2011), and (b.) these same capacities are utilised to some degree in all human academic endeavour, as seems reasonable to assume, then there is good reason for thinking that some comparison may prove beneficial, regardless of any purported differences in the systems under study. Additionally, far from models being constructed “in the name of philosophy of science”, idealised models are more often than not constructed by scientists themselves on the basis of experiments performed and observations made. For instance, the abstract, idealised objects which dominate physics are not created by or for the sake of philosophers; they are created so that scientific practitioners can allow their observations to lead to predictions that hold in a wider set of cases. The aim of philosophy of science, or at least the part which interests us here, is therefore to study the kinds of processes involved in the construction of such models. As one example, Cartwright (1983) discusses the difficulties in linking mathematical laws in physics with the real world, by highlighting the problems of marrying the certus paribus foundations of physical description with the multitude of causes which may act to produce a certain effect in reality. Her argument is, briefly, that generalised laws in physics do not state facts about how ‘real’ objects behave, but instead how theoretical objects behave within models, which are usually highly idealised. Regardless of whether Cartwright’s views are correct, and there have been many replies to her arguments, the important issue for this piece is that scientific models, which would include theoretical constructs such as laws, far from being constructed “in the name of philosophy of science” are more often than not constructed by scientists in the name of science. Indeed, this is much a part of their profession as the rigorous, methodological procedure that is the hallmark of Williams et al. Functional Linguistics (2017) 4:13 Page 4 of 22 scientific experimentation. The role for those interested in investigating scientific practice is then to enquire into the processes involved for its creation, instead of creating models for their own sakes. This would hold for theoretical constructs in a more socially-orientated theory such as SFL, as it would for the more mathematically orientated disciplines. With these potential criticisms addressed, it is now possible to outline the different meanings that have been associated with abstraction in other disciplines. The different aspects of abstraction Abstraction as ‘mere omission’ion as ‘mere omission’ The term abstraction has a rich history in the context of Western thought; φαίρεσις (abstraction) is discussed in both Aristotle’s Analytica Posteriora and Metaphysics, with Cleary (1985) arguing that the underlying meaning in his use of the term is subtraction, or the leaving out of detail. Bäck (2014:2) also describes φαίρεσις as “focussing on an aspect, typically the central one [...] while ignoring the remaining ones.” A further historical example comes from Frege’s (1884) discussion of abstract objects in mathematics, dubbed the way of negation by Lewis (1986), which involved defining abstract objects as those which lack certain features possessed by their concrete counterparts: spatial and temporal extension, and causal powers. In all of these accounts, there are common themes of omission: either abstract descriptions ignore features, or lack certain properties found in more concrete examples. From a more modern perspective, Jones (2005) provides a means of distinguishing between two related concepts: abstraction and idealisation. On his account, abstraction involves “mere omission” (ibid: 174), or the omission of truth. Idealisation, on the other hand, is an assertion of a falsehood; it involves claiming that a phenomenon has certain qualities which it in fact does not, or vice-versa. As an example, Jones (ibid: 181–184) considers a model used to predict and explain the trajectory of a ball fired from a cannon. The final resting place of the ball is determined by considering factors such as the angle of trajectory, the force with which the ball is fired, and the effects of gravity. He points to several idealisations and several possible abstractions in models of this kind. Idealisations include: supposing that the ground is flat, that the force of gravity on the ball is equal at all points, and that gravity is the only force affecting the ball after its initial velocity, ignoring factors such as air resistance. Abstractions highlighted include: the colour of the ball, the material constituting it, the ball’s internal structure, and its temperature. He argues that in the first list of properties, the modeller is proposing a falsehood, whereas in the latter case she is simply being quiet on certain issues (ibid: 183–184). For example, the abstraction of remaining silent about the colour of the ball is different to an explicit assertion that “the ball has no colour”. Compare this to representation of the ground on something like a straight x-axis on a graph. This is an explicit assertion of a fact that we know not to be the case, and this therefore has an impact, however minor, on the predictions made by the model. This idea of remaining silent without proposing a falsehood is the definition of a “mere omission”. This view of abstraction has influenced Godfrey-Smith’s (2009) discussion of abstraction in evolutionary biology. He describes abstraction as ignoring detail, whereas idealisation involves an act of imagination; scientists imagine a phenomenon to be different to how we know it to be in reality, which is a clear parallel of Jones’ proposal. Williams et al. Functional Linguistics (2017) 4:13 Page 5 of 22 As presented above, all explicit misrepresentations count as idealisations, and every omission of a truth counts as an abstraction. However, these characterisations would cast the net too wide. There would be certain false ascriptions that we would not want to properly count as idealisations, but instead as mistakes. Phlogiston, a postulated constituent of combustible objects believed to exist in the 17 and 18 centuries, acts as an example of an error in a model (Jones, 2005: 186). Additionally, there may be cases where a researcher remains silent on certain issues that are, in fact, crucial to understanding the system under study. In this case, then we may not want to call such omissions abstractions. The notion of relevancy provides a good way of narrowing down the definitions. Cartwright (1989: 187) and McMullin (1985: 258) both argue that abstraction only occurs in cases where irrelevant facts about the system under study are omitted. We can see links here as well to one of the meanings of abstraction identified by Saitta and Zucker (2013), through the link to the retention of relevant information, and by extension, the omission of irrelevant information. Jones (op. cit.: 190) alters this perspective slightly, by arguing that the term can refer to the omission of relevant factors, but only in cases where this occurs on some idealised basis, that is, factors that seem irrelevant in the model, whereas in the real case they are not. With these subtleties in mind, this work will define one facet of abstraction as the omission of irrelevant information, but not in cases where this amounts to an explicit misrepresentation of the system (which would be called an idealisation). Abstraction and generalisationion and generalisation Another common idea associated with abstraction is that it involves the retention of common features between objects. Again in Aristotle, a potential consequence attributed to this process was the discovery of a universal, which he defined as “that which is common to many individuals” (Coniglione 2004: 60). Lewis (1986) defines his way of abstraction as forming categories by means of comparing a number of experienced objects and only focussing on similarities. This means of comparing and focussing on similarities will, in this work, be taken to be indicative of the process of generalisation. Generalisation is important to many disciplines, and many discussions of abstraction often involve or imply it. For instance, Ferrari (2003: 1226) writes: A good share of mathematicians regard abstraction mainly as generalization. The following definition is taken from Wells’s (2002: p. 17) online glossary of mathematics: An abstraction of a concept C is a concept C’ that includes all instances of C and that is constructed by taking as axioms certain statements that are true for all instances of C. Above, it can be seen that: (a.) abstraction is explicitly linked to the notion of generalisation, and (b.) this process is defined as a set of statements that hold for all members of a particular group of objects. On Ferrari’s own account, part of abstraction (but not the only aspect) can be conceptualised as increased inclusion. For instance, the concept of QUADRILATERAL is considered to be more abstract than that of the concept SQUARE, because the former not only contains all instances of the latter but also others such as RECTANGLE and RHOMBUS. Therefore, it has as content the aspect that is common to all of these geometrical shapes, while not including the differences between them. In this regard, it generalises over them. Williams et al. Functional Linguistics (2017) 4:13 Page 6 of 22 Mitchelmore and White (2004) name this variant of abstraction empirical abstraction, and discuss its application in the learning of mathematical concepts. They highlight three examples of concepts that children need to become proficient with: addition, angles, and rate of change. In all of these cases, the authors outline a pedagogical strategy whereby students first encounter the relevant mathematical concepts in exemplar settings. After repeated experience of the same concept in a variety of individual settings, children are then able to notice the similarities, and thus grasp the abstract mathematical concept. Mitchelmore and White link this process to the account of abstraction given by Skemp (1986), who describes it as “an activity by which we become aware of similarities [...] among our experiences” (ibid: 21, cited in Mitchelmore and White, op cit: 332). It should be noted that although generalisation has been discussed so far in terms of the retention of common features, certain accounts of the process have allowed for a slightly weaker reading. Instead of an account of generalisation in terms of necessary and sufficient conditions (e.g. an object x is a QUADRILATERAL if and only if it is a geometric shape with four sides), Ponsen et al. (2010: 6), in a discussion of computer science, allow for “a weaker definition of generalisation [that] states we have good evidence that all [objects] behave in a similar way.” There is a shift here from absolute criteria to a more fluid notion: generalisation is a process that groups certain entities because they are highly likely to exhibit certain features. Undoubtedly, there are similarities between the processes of generalisation and omission. In choosing to generalise and focus upon the similarities, it is necessary to leave other properties out (since if two objects shared exactly the same set of properties, they would count as the same object). One might be tempted to think, therefore, that generalisation and omission are simply labels that refer to the same underlying process, but simply from differing perspectives. However, this work takes the perspective that although they are closely related, they should properly be kept apart. We argue that: (a.) the two terms are not co-extensive, i.e. that there are cases where only one of the terms can be properly applied, and (b.) the notion of relevancy is part of the meaning of omission, but not of generalisation. Such justification is important, because below in §4 these terms will be used as separate criteria in our discussion of theoretical dimensions in SFL. For the first point, consider the minimum number of individuals (defined here in its broadest sense to include everything from concrete objects to abstract theoretical constructs) that each of the processes operates over. From the above characterisation of generalisation, it is clear that the process must operate over at least two individuals, for means of comparison. Furthermore, the representation that arises out of generalising stands for all of the individuals that were part of the comparison process. The same cannot be said for the related process of mere omission. Instead, omission involves reducing the number of features used to describe a minimum of one individual. This would still hold in cases where another object was used for comparison in order to hypothesise what features are irrelevant, and therefore should be omitted. The consequence is that the representation of the individual that resulted would not hold for the one used for comparison. Note the differences here between the two processes, where, for generalisation, the representation stands for all involved individuals. Secondly, recall the notion of relevancy, which was argued to be important in the case of feature omission above. Generalisation is only the retention of common Williams et al. Functional Linguistics (2017) 4:13 Page 7 of 22 properties, with no regard to whether those properties that remain are relevant or not. It is of course hoped that the generalised properties will be relevant, but this is not guaranteed by the process of generalisation itself. Strictly speaking, generalisation is ‘blind’ to the notion of relevancy: it can only arise out of serendipity. Furthermore, properties that may be omitted during an abstraction may indeed be ones that are common to all of the individuals. For instance, in Jones’ example, such a model could have been formed by comparing the flights of cannonballs that were all red in colour. Although this property would be common to each individual situation, it could still be the target of the omission process if there was good reason to believe that it is an irrelevant feature of the situation. Therefore, we believe we are justified in keeping these terms as separate possible aspects of abstraction, and therefore they will be discussed separately when we turn to theoretical dimensions in SFL. Abstraction and Decontextualisationion and Decontextualisation The final aspect to be discussed is the idea of decontextualisation. Some accounts of abstraction highlight a detachment of specific observations and events from their immediate context. For instance, consider Roth (2012: 95, emphasis added): Science is a successful endeavour because its concepts are applicable to a wider range of phenomena the less they are tied to the specifics of any context, and representations become more inclusive and abstract the less [sic] contextual parameters they include. Noss et al. (2002: 206) discuss a similar view in terms of what they dub “a traditional view of abstraction.” On this view, abstraction is seen to be an “essential property extracted from a situation, but not contained in it,” and “deemed ‘apart’ from, even above, the situation of its genesis” (ibid). This idea of abstractions not being tied to any particular situation is intuitive. After all, when we consider, say, an equation denoting a physical law, or an economic trend, there is not one specific context or situation that is attached to those abstract objects, even the situation(s) that first led to their creation. Instead, they have transcended such specific situations which are thought to hold for all past, present, and (possible) future situations where the circumstances they describe hold. A concrete theoretical object, then, is one that is directly linked to one particular situation. If we were to create a representation of a particular individual, such as an equation that describes a particular relationship in a particular moment, then this is contextualised. Decontextualised, and thus abstract, theoretical objects are those for which this precise link to a particular situation does not hold. As with the previous section, it can be difficult to ascertain where two proposed different facets of a concept really should be counted as such. Therefore, it is again necessary to show how decontextualisation is distinct from both omission and generalisation. On face value, there seems to be an immediate distinction to be made between decontextualisation and omission. Omission, defined as omitting features of a system in its description, does not entail a form of decontextualisation; the description, after all, is still representing the original case. Of course, these more abstract descriptions can later be used to cover other situations than the original one. However, such Williams et al. Functional Linguistics (2017) 4:13 Page 8 of 22 extension is not integral to the omission process; it is instead a further kind of abstraction taking place upon an already abstracted object. In the case of generalisation, a similar situation emerges. Given the previously discussed definitions, generalisation simply involves a comparison of two or more objects. Again, this does not entail any decontextualisation. It is possible for someone to provide a description of two objects directly in front of her. That description is then directly linked to that situation; it is general, but contextual.