A hierarchical framework for concepts in physical geography

Abstract

The word concept is widely used in physical geography but seldom defined. Developing from an earlier proposal of concept types in geomorphology, this paper considers a structure for categorising concepts in physical geography in the light of sciences and philosophy more generally. It reviews where our concepts derive from, and their relation to kinds, universals and categories, whilst also indicating the lack of an agreed clear distinction between them. Because an unstructured diversity of concepts has previously been proposed in physical geography by different authors, a new provisional hierarchy is constructed. This is cognisant of specific developments in a range of disciplines, including formal concept analysis, lattice theory and hierarchy theory. A ‘concept of concepts’ hierarchy of six categories is proposed in which multidisciplinary (superordinate, contextual meta-concepts) and fundamental, operational and ancillary categories provide a 6 × 5 framework. This enables attention to be focused on stimulating conceptual underpinnings that can be tested at different levels in future learning, teaching and research. This can support the formation of knowledge structures and monitoring procedures that keep in step with ways that are characterising other disciplines.

Keywords

Concepts kinds universals categories physical geography trends structure of learning

I Introduction

When considering making concepts more explicit for geomorphology it was suggested that ‘Allusion to concepts in geomorphology is a paradox – frequently mentioned but seldom explicitly analysed’ (Gregory and Lewin, 2015). Our previous paper proposed a system structure for geomorphological understanding. Attention to concepts throughout physical geography is now particularly timely in view of recent internal trends, reflected in a detailed benchmarking review of UK physical geography (Thomas et al., 2017), and also external trends in science education and multidisciplinary developments, with Bocking (2015) arguing that concepts are ubiquitous in scientific work and necessary to organise and communicate knowledge, classify landscapes and regions, and control and conserve nature.

Styles of learning and teaching in higher education (HE) are also changing rapidly. As syllabi and what is taught at many levels in physical geography evolve, greater awareness of the conceptual foundations of physical geography seems essential. New approaches including concept-based teaching and learning (Erickson, 2012), ‘geocapabilities’ (e.g. Fargher, 2018; Solem et al., 2013) and ‘powerful knowledge’ (Maude, 2016, 2018) all prominently involve concepts. Confronted by different lists of concepts is confusing for students who could benefit from a more explicit statement of concepts and their relationships. In addition to supporting the learning experience for students in HE, a more explicit understanding of concepts can facilitate research and the identification of new directions such as connectivity (Wohl, 2017). We argue that the development of a more explicit understanding of concepts in physical geography, for both learning and research, needs attention to the way in which concepts are currently presented, in physical geography and more generally, and some reflection on where concepts derive from, including their philosophical and scientific background in the context of an evolving framework of concepts. At a time when knowledge, or at least information, is expanding at a terrific rate, with possible over production of articles that Lane (2016) has warned about, our proposal for a concept hierarchy framework can be very timely – so that the direction in which physical geography is now being driven at different levels can be better understood. We suggest that much of the present physical geography literature is driven by empirical work for which the conceptual underpinnings are unstated. Any readership that is wider than the few experts on individual topics may be unable to see how, or indeed if, broader knowledge is being advanced, and where the work fits into discernible patterns of knowledge at different levels. We believe that there is a need to balance the large, and in many ways admirable, amount of empirical and case study research and technical and methodological developments that dominate current literature.

II Concepts in physical geography and the sciences

The term ‘concept’ has been in general use in publications from the 1860s and even earlier, appearing more frequently between 1940 and 1980, and continuing significantly to the present day (Figure 1(a)). Specifically in branches of physical geography, the term concept has been employed frequently since 1950 (Figure 1(b)), as in book titles in climatology (Bonan, 2016; Crowe, 1971) and in geomorphology (Bierman and Montgomery, 2013; Gregory and Lewin, 2014; McCullagh, 1978). In the development of pedology, concepts have been traced to provide a frame of reference from which pedologists could evaluate potential scientific contributions to a rapidly changing world (Bockheim et al., 2005). In their Dictionary of Concepts in Physical Geography, Huber et al. (1988) covered 100 major concepts under 12 major topics. Huggett (2010) also adopted an alphabetical approach in providing explanations for 99 concepts, selected ‘to provide extended definitions of concepts and terms that are central to discourse within physical geography and its many branches’. Huggett did not define concepts but used three criteria when choosing the 99 ‘terms’ (employed synonymously with concepts?): first, that they are germane to physical geography as a whole (e.g. energy); second, they are central to a branch of physical geography (e.g. natural selection); third, there are important concepts from other disciplines that play a starring role in some aspect of physical geography (e.g. plate tectonics). Both Huber et al. (1988) and Huggett (2010) include a range of types of concept in their lists. Bierman and Montgomery (2013) in their book Key Concepts in Geomorphology did not define concepts, although their final chapter list resulted from the work of 10 geomorphologists meeting at the National Science Foundation (NSF) in April 2008, with input from 60 geomorphologists at the cutting edge, teaching geomorphology workshop in July 2008. At plenary sessions of that workshop, discussions focused on general issues such as ‘How do we help students visualise important concepts in geomorphology?’, and ‘How can we best integrate geomorphology concepts into courses in the core geoscience curriculum?’

Figure 1.

Frequency of citations of concept (a) and of geomorphological, biogeographical and climatological concepts (b) derived from Ngram viewer.

In physical geography so-called ‘concepts’ have commonly been imported from, or used in compatibility with, other disciplines, mainly sciences. Some concepts, such as complexity (e.g. Temme et al., 2015), connectivity (Wohl, 2017) and sensitivity (Bracken et al., 2015; Fryirs, 2017; Harrison, 2009; Knight and Harrison, 2013; Phillips, 2016), have been internally developed within sub divisions of physical geography, often as variants of more generally applied ones. But the word has been used at different levels and in a variety of contexts. ‘Concept’ as an expression may signify general scientific terms (e.g. systems, energy, power) or generalities (permanency of natural laws). But ‘concept’ has also been applied to dimensions (space, time, scale), to perceptions (environment, landscape, nature), to states (equilibrium, complexity), to processes (e.g. energy flows), to conditions (e.g. thresholds), to influences (e.g. climate, complexity, human activity, inheritance, geological structure), to explanations (e.g. uniformitarianism), to change or trends (e.g. evolution) or to combinations of these (e.g. distinctive imprint resulting from process assemblages). Concepts have also been stated as including aspirations (sustainability, obligations to the future) and even specific sub-field approaches (climatic geomorphology). Concepts have therefore been used throughout physical geography in a great diversity of ways: at one extreme including paradigms, the overarching approaches or practices within the discipline that have received considerable attention, and at the other very specific ideas such as the soil catena. However just as clarification of fundamental paradigms progressed the discipline over the last six decades, it is now timely in view of the rapid growth of knowledge with a doubling rate of 1–2 years to explicitly identify the big ideas or key concepts that underpin the discipline and its branches to further facilitate learning and research. Furthermore, throughout physical geography, as is echoed in several physical and earth sciences, there is no standardised or even broadly agreed use of terms, although the spectrum of subjects denoted as concepts may be understandable in view of the range in philosophical understandings of ‘kinds’, ‘universals’ and ‘process philosophy’ as indicated below.

The fact that ‘concept’ is seldom defined, and has therefore been used loosely in a general, non-specific way – often overlapping with hypotheses, theories, laws, principles or even paradigms – may explain why the number of concepts proffered by different authors ranges from 3 to 10 in geomorphology alone (Gregory and Lewin, 2015: Table 2), and why there is no agreement about what concepts are, and which are the most important. More broadly, the Royal Geographical Society (RGS) identified seven high level concepts (place, space, scale, interdependence, physical and human processes, environmental interaction and sustainable development) as large themes seen to be underpinning the study of geography, identifying what learners need in order to make progress in their understandings. Alternative expressions employed include ‘conceptual bases’ (Chorley et al., 1984); common ‘core themes’, arising from an interdisciplinary workshop sponsored by NSF on developing key questions and integrative themes for advancing the science of human–landscape systems (Wohl et al., 2014); and eight core themes in contemporary physical geography identified from 13 current textbooks (Day, 2017). Other sciences show similar awareness of the need to pronounce on essential fundamentals, although there is no agreement on how they are described. Thus in physics, Rovelli (2014) uses ‘lesson’ as the term to describe his seven subjects (relativity, quantum mechanics, cosmos architecture, particles, quantum gravity, probability and black holes, ourselves), but are these not also concepts? Other terms used include big ideas (Harlen, 2015) and key ideas or canons (as employed by Lester King, 1953, and cited by Inkpen, 2018).

The key question, ‘What are the concepts that lie at the very core of geography?’, is posed by Clifford et al. (2009: xiii). They affirm that geography, like other disciplines, needs to establish its key foundation elements, especially in the context of new approaches to learning and teaching. Gregory and Lewin (2014) did not critically discriminate between the many meanings of the term, or how they might be organised and their framework structured, but defined ‘key concepts’ in relation to geomorphology as ‘those abstract ideas, general notions or units of knowledge that are vital to the development of a reliable science’ (Gregory and Lewin, 2014: 2). Harvey (1969: 19) had clarified how mental constructs require recognition of connections between sense perceptions (percepts), mental constructs and images (concepts) and linguistic representations (terms) but also scrutinised how meaning has been ascribed to similar terms and concepts (Harvey, 1969: 301). He identified ‘ostensive definition’ (Harvey 1965: 301), that is, conveying meaning through examples, as when a word is ascribed to an object, citing Caws (1965) who proposed this form of definition. In view of the range of applications of concept and of the types that have been recognised, especially with the advent of formal concept analysis (FCA; see below) as a methodology of data analysis, information management and knowledge representation (Sumangali and Kumar, 2017; Žáček et al., 2017), an extended definition is desirable and this is provided below.

The importance of concepts is widely acknowledged in education and at pre-HE levels where concepts have been identified in examination syllabi and in science education (Chang et al., 2010). Harlen (2015: 45–46) proposed big ideas in science education and noted that these are echoed by developments in many countries including France and the USA asserting that: ‘The goal of science education is not knowledge of a body of facts and theories but a progression towards key ideas which enable understanding of events and phenomena of relevance to students’ lives’. If such key ideas are current in earlier stages of education then they should be reflected in HE and in research. The ability of students in team-based learning (TBL) to engage in concept-based learning has been evaluated in physics and environmental sciences (Parappilly et al., 2015), and concept based teaching and learning has provided a focus in the international baccalaureate (Erickson, 2012). Implementing big ideas to advance teaching and learning is suggested by Chalmers et al. (2017) to be achieved by three types of big ideas: within-discipline big ideas, cross-discipline big ideas, and encompassing big ideas. Concepts seen as essential tools nevertheless require cautious and critical reflection (Bocking, 2015); they will be affected by cultural background and have often been influenced by more pragmatic approaches to complement earlier academic ones, as in the case of pedology (Calzolari and Filippi, 2016). Although not all concepts will prevail indefinitely, some becoming ignored and others rejected, education experts agree that disciplines do require basic fundamental beliefs however they are described. The epistemic ascent required to convert large amounts of data into processable knowledge requires hypotheses, theories, and models (Vetere, 2009). It is the concepts held that reveal most clearly the imaginative and creative innovation drivers present in any science.

For all such reasons, greater awareness of the conceptual foundations of physical geography seems appropriate at the present time. This concerns not so much method or reasoning, but rather what lies behind such procedures at different levels, using approaches and entry points understood to be interesting and useful, and that are then followed through using satisfying methods and available technologies. Concepts can provide the framework as to what can, and perhaps should, be academically studied as much as how. At a time when issues like globalisation and environmental change in the broadest sense are being examined, the things that physical geography is structured and moved to study are ripe for scrutiny.

III Where do our concepts derive from?

The term ‘concept’ may have originated in the mid-16th century from the Latin conceptum ‘something conceived’, coming thence to be defined as a general notion or idea (e.g. the concept of evolution), something developed in the mind as an abstract or generic idea which may be generalised from particular instances. Dictionary or Wikipedia definitions (Table 1) usually involve the notion that concepts are general, and possibly, abstract ideas. An obvious source of definitions is philosophy. The German philosopher Arthur Schopenhauer (1788–1860) suggested that concepts are ‘mere abstractions from what is known through intuitive perception’, and linked concepts to perception by focusing on how the world appears to us, also suggesting that every concept has a range, an extension or a sphere (Schopenhauer, 1818/19). Concept spheres may overlap. Although concept spheres do not seem to have persisted as an applicable idea, concepts have featured prominently in philosophy with many succinct definitions offered (Table 1) and, as ‘constituents of thoughts’, have been the subject for much debate (Zalta, 2017), partly because they occasion deeply opposing approaches. There is thus extensive discussion in philosophy, reflected in other disciplines including psychology and biology. The definition of concepts as ‘abstract ideas, general notions or units of knowledge that are vital to the development of a reliable science’ could be qualified by adding ‘because they are the units of thought, and the constituents of beliefs and theories (Carey, 2009) that organise and communicate knowledge’. They encompass a great range of ideas so that it has been suggested that, for many, philosophy itself is essentially the a priori analysis of concepts (Margolis and Laurence, 2014).

Table 1.

Definitions of concepts and associated terms.

Source	Definition
Dictionary definitions
A general idea or understanding of something (The Free Dictionary); something conceived in the mind (Merriam-Webster); An abstract or generic idea generalised from particular instances (Merriam-Webster); an abstract idea representing the fundamental characteristics of what it represents. […] Arise as abstractions or generalisations from experience or the result of a transformation of existing ideas (Wikipedia)
Philosophy contributions
Arthur Schopenhauer (1788–1860)	Concepts are ‘mere abstractions from what is known through intuitive perception’.
Bruner et al. (1967)	Concepts are the mental categories that help us classify objects, events, or ideas, building on the understanding that each object, event, or idea has a set of common relevant features. A concept is an idea of something formed by combining all its features or attributes which construct the given concept. Every concept has two components: Attributes: features that one must look for to decide whether a data instance is a positive one of the concept. A rule: denotes what conjunction of constraints on the attributes will qualify as a positive instance of the concept.
Jackson (1998)	If philosophy is primarily about concepts and concepts can be investigated from the armchair, then the a priori character of philosophy is secured.
Murphy (2002)	‘Concepts are the glue that holds our mental world together.’ ‘I try to use the word concepts to talk about mental representations of classes of things and categories to talk about the classes themselves.’
Prinz (2004)	‘Without concepts there would be no thoughts. Concepts are the basic timber of our mental lives.’
Novak and Canas (2006)	Define concept as a perceived regularity in events or objects, or records of events or objects, designated by a label. Concept maps are graphical tools for organising and representing knowledge
Carey (2009)	‘Concepts are mental representations.’ ‘Concepts are units of thought, the constituents of beliefs and theories….’
Margolis and Laurence (2014) and Zalta (2017)	Concepts are the constituents of thoughts: they are mental representations as psychological entities, or concepts are abilities that are peculiar to cognitive agents, or concepts are Fregean senses identified with abstract objects rather than with mental objects and states. Concepts are at the centre of current disputes in philosophy. For many, philosophy is essentially the a priori analysis of concepts, which can and should be done without leaving the proverbial armchair.
Geography contribution by Harvey (1969)
Harvey (1969: 117–127)	Geographers in the past have developed ‘concepts’ and ‘principles’ to facilitate explanation and to justify the way in which they organise a particular set of facts. Concepts used by geographers include (1) derivative: developed by reference to concepts from other disciplines; (2) indigenous within geography, e.g. the region.
Definition adopted in this paper
Abstract ideas, general notions or units of knowledge that are vital to the development of a reliable science; because they are the are units of thought, and the constituents of beliefs and theories that organise and communicate knowledge, they encompass a great range of ideas so that it has been suggested that philosophy is essentially the a priori analysis of concepts

Endeavouring to isolate key elements from a very extensive literature shows that kinds, universals and categories are pertinent to the way in which thinking about concepts has developed. One definition of ontology, the branch of philosophy that deals with the nature of being, is a set of conceptual categories in a subject area or domain showing their properties and the relations between them. A main task of philosophy described by Berlin (2013) is ‘to uncover the various models and presuppositions – the concepts and categories – that men bring to their existence and that help form that existence’. Whereas Bruner et al. (1967) described concepts as mental categories (Table 1), Spirikin (1983) saw categories as ‘extremely general, fundamental concepts reflecting the most essential, law-governed connections and relationships of reality’, the forms and stable organising principles of the thought process, the results of generalisation. Category theory has been shown to relate to the foundations of mathematics (Muller, 2001).

Metaphysics, embracing ontology, is the branch of philosophy concerned with being and with other general features of reality. This includes ‘universals’. Some earlier logical-positivist philosophers, like Ayer (1946), used ‘metaphysics’ to define things transcending the physical world, in contra-distinction to the verifiable nature of philosophical statements. Dealing with the most fundamental concepts, the theory that universals are concepts existing in the mind has been taken as the definition of ‘conceptualism’. Particularly pertinent are the ideas of A.N. Whitehead (1861–1947) who concluded that all objects should be understood as fields having both temporal and spatial extensions, and that it is process rather than substance that should be taken as the most fundamental metaphysical constituent of the world (Whitehead, 1929). His process philosophy, that basic reality is processual rather than static, has found widespread application (Whitehead, 1967), in ecology for example, and as the basis for environmental ethics (e.g. Cobb, 1971). Whitehead’s process philosophy argues that ‘there is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us’ (Mesle, 2009). Universals are what particular things have in common, namely characteristics or qualities. Three major kinds of quality recognised are: types (e.g. mammals), properties (such as short or long) and relations (as in ‘close to’). In philosophical terms, some have considered these as independent of human perceptions, others as mental constructs. ‘Conceptualism’, as a philosophical tenet, embraces universals as thoughts or ideas in, and constructed by, the mind.

Scientific disciplines have divided the particulars they study into kinds, which are groupings or orderings that do not depend on human identification, therefore reflecting the structure of the natural world rather than the actions of human beings (Zalta, 2017). Natural kinds were introduced into natural analytic philosophy by W.V.O. Quine (1908–2000) (Quine, 1969). Essentialism concerning natural kinds has three main tenets: first, all and only the members of a kind share a common essence; second, this essence is a property, or a set of properties, that all the members of a kind must have; and third, a kind’s essence causes other properties associated with that kind. Like concepts, kinds are not readily agreed because questions raised include whether natural kinds genuinely are ‘natural’, and what the properties are that might be essential for kind membership. Kinds have been identified in the sciences but in the social sciences their definition is more problematic. Discussion of natural kinds is suggested by Stanford and Kitcher (2000) to have emerged from an attempt to understand aspects of the world around us, not only in looking for common causal mechanisms in particular cases but also in trying to integrate cases into a coherent global framework. Kinds have continued to engage the interest of philosophers including Slater (2015) who posed questions of their definition, their role in science and metaphysics, and the categories that count as natural kinds; and Beebee and Sabbarton-Leary (2011) who provided a collection of essays on natural kinds and natural kind terms. It has been contended by Piccinini and Scott (2006) that, in the concepts’ literature, a common presupposition is that concepts constitute a singular natural kind so that they sub-divide concepts. Although the details of such philosophical discussions are not appropriate here, awareness of them confirms the general lack of uniformity of definition that exists. Held (2017) has argued that philosophers and psychologists have long believed that mind-dependent/human (or social) kinds are not natural kinds and so drew attention to the challenge by Richard Boyd, to widespread acclaim in the philosophy of biology where the natural-kind status of species taxa has been debated. Boyd (1991) proposed that any human/mental kind can in principle be a natural kind, without physical reduction of its properties, as long as it constitutes a homeostatic property cluster (HPC) kind and so can be studied by way of the causal mechanisms that, he theorises, underlie all natural kinds.

Recent accounts have included proposals for multiple distinct kinds of concepts, with plurality of concepts for each category (Rice, 2016) or different kinds of concept whereby categories, substances and types of events are represented by hybrid concepts made of several parts (Machery, 2010). Following extensive debate some psychologists have advocated doing without concepts although Hampton (2010), in a review of Machery (2009), argues that cognitive science still needs the notion of ‘concept’ even if it proves to be multifaceted and hard to define satisfactorily, and that eliminating the term from theories will hinder rather than promote scientific progress. Harnad (2009) comments that our vocabulary is rife with instances of the word ‘concept’, and that to a first approximation it means idea, but he progresses to preview how we can ‘do without concepts’ and concludes that what takes their place is in an innate and mostly sensorimotor category – detectors progressively supplemented by verbal category representations composed of grounded category names describing further categories through propositions (Harnad, 2010). Other developments have included applications such as concept mapping (Table 1); such conceptions of terms, if not their definitional methods, are very similar to those of words as lexemes in linguistics, or Dawkins’ idea of ‘memes’ in biology (Lewin, 2016).

Beyond ostensive definition, the great diversity in usage of the word concept may have arisen because in philosophical terms there has been a lack of agreed clear distinction between ‘categories’, ‘universals’, ‘kinds’, and ‘concepts’. The present disparity in geographical usage of ‘concept’ could better be comprehended by recognising the spectrum of kinds, universals, categories and concepts that have come into use from elsewhere. Richards and Clifford (2011) suggest that the philosophical issue is whether the categories and the associated classificatory structures are ‘real’ (i.e. are ‘natural kinds’), or are convenient mental constructs used to impose some degree of regularity on the apparently diverse character of surface forms in landscape. Thus, is the landscape naturally constructed of discrete entities for which we require names – drumlins, cirques, barchans, yardangs, inselbergs, etc. – or is it simply a continuous three-dimensional surface, to some of whose topographic attributes we arbitrarily assign these names? Many common lexical terms are clearly conceptual, whether named physical objects (Lewin, 2016), or time-division names that are useful and meaningful; they are a matter of good judgment and convenience for general application. They are also defeasible, that is, liable to revision as new evidence or opinions emerge, as the history of Quaternary nomenclature shows (Gibbard and Lewin, 2016). Across the sciences, other terms, like chemical elements for example, may not be so debatable, though the ‘real’ nature of phenomena like gravitational attraction may continue to give rise to debate. These kinds of conceptual debate would aid understandings if they were much more widespread, if concepts were explicitly recognised, and also if they could be systematically ordered.

Although there may therefore be no very clear distinction between kinds, universals, categories and concepts, there is general implicit agreement that concepts are of several types and that they can be recognised as covering things brought into play at different levels of enquiry. Disciplines should endeavour to agree about, or at least debate, their key concepts, fundamentals or big ideas. An explicit hierarchy of concepts should also enable progress to be made. In identifying such a hierarchy it is not easy to produce entirely exclusive categories, but the proposal outlined below does highlight the importance of applicability levels in physical geography for recognising and using the types of ‘concept’ available. The subdivisions identified are also compatible with the notion of concept spheres as suggested by Schopenhauer. The great variety evident in usage in physical geography is understandable in the context of philosophy – with its universals, categories, kinds and concepts – whilst a process philosophy involving complex systems may give a clue as to why such a broad spectrum of concepts has been specified and found to be useful at different levels.

IV A hierarchy of concepts

Our basis for a provisional hierarchical structure arises from the range of definitions in use by earlier authors in other science areas (Table 1), and from possible philosophical differences between ‘kinds’, ‘universals’, ‘categories’ and ‘concepts’. When attempting a provisional hierarchy structure we have also considered the ways in which a diverse range of concepts has hitherto been identified throughout physical geography. We have to be aware of concepts as presented at pre-HE levels of education and also in philosophy and other disciplines, and we attempt to be consistent with them as far as possible. We suggest categories that may have future implications for research, learning and teaching and for examining in physical geography.

It is specifically a hierarchy of concepts that has been considered explicitly and implicitly in many disciplines, so that in biological study the concept of function level has been explored (Farnsworth et al., 2017). It has further been suggested that concepts, which play a central role in many human intellectual activities, can originate in interactions with the world prior to being lexicalised, or in the language, only to become grounded or fully defined later on (Sloutsky and Deng, 2017). It has also been proposed that they can have three characteristics: a base, a representing part, and the linkage between them (Kuznetsov and Kuznetsova, 1998). FCA has been employed as a methodology of data analysis, information management and knowledge (Žáček et al., 2017). Because large amounts of data require mathematical models to analyse patterns and trends, Sumangali and Kumar (2017) show how FCA can be used for knowledge discovery from data processing (KDD) and from computing and systems analysis. Lattice theory which dates from 1940 led to the development of concept lattices, formalised conceptual structures; this then prompted use of FCA as a mathematical tool for analysing data and formally representing conceptual knowledge (Ben Yahia and Konecny, 2017). There are many related strands such as consideration of lattice theory in mathematics returning to the origin of the lattice concept in the 19th century. This attempts to formalise logic, where a fundamental step was the reduction of a concept to its ‘extent’ (Wille, 1982). The concept lattice is a research area for concepts and concept hierarchies in computing (Mao, 2017) and concept lattices have been used in FCA to construct a hierarchy of concepts (Butka et al., 2018). Hierarchy theory is likewise able to conceptualise complex ecological systems as composed of relatively isolated levels each operating at a distinct time and space scale (O’Neill et al., 1989). This also characterises many physical systems.

Concepts therefore, have been, and need to be, widely recognised as of several types occurring at levels of investigation. They can be analysed by FCA and lattice theory with concept hierarchies evolved in different areas, including one embracing 32 concepts based on four main areas, and developed for describing quality issues of research practice (see Figure 5 in Mårtensson et al., 2016). In the philosophy of science, the frame model is similarly being applied to represent and analyse scientific concepts and change (Kornmesser, 2016, 2018). In physical geography, a category-tight hierarchy is not easy to construct even qualitatively; it also cannot (like most defeasible ideas) be ‘final’ because it has to allow for the inclusion of new concepts in the same way that resilience has been advocated and elaborated as a significant incoming concept in geomorphology (Thoms et al., 2018). The Anthropocene (Brown et al., 2017) has similarly been noted as an innovative concept which is interpreted differently across the branches of physical geography and between different authors. Other concepts such as river sensitivity, characterised as a lost foundation concept have been resurrected and developed (Fryirs, 2017). Another example is that of transport capacity (Wainwright et al., 2015).

A provisional hierarchical structure is attempted in Table 2, conceived to apply either to physical geography as a whole or to one of its component branches, and constructed to embrace approaches to the discipline and the breadth of ideas that concepts represent. Concepts are visualised in relation to six application categories (we emphasise that the categories themselves are also concepts) including systems, subjects for research investigation, processes, and change over short and longer time scales. In addition to these four, anthropogenic impacts are now so significant and concept-dependent that they merit inclusion as a fifth category; environmental management has become so important that it is also included as a sixth category. These six provide one axis for a framework in which concepts can also be structured. The other axis involves the breadth of context in which concepts figure. As concepts enumerated for any discipline or sub-discipline relate to those in other disciplines, some concepts are multidisciplinary and so these constitute the first two columns of Table 2. Of these some are very broad, the equivalent of what have been termed superordinate concepts in psychology and education. Concepts can be perceived at superordinate, basic and subordinate levels of abstraction (e.g. Sadeghi et al., 2015) and they have also been subdivided in cognition studies into ‘mass’ superordinates and ‘count’ superordinates (Wisniewski et al., 1996). However the first group of multidisciplinary concepts, here termed superordinate can, for example, include the over-arching concepts recognised by the RGS as discussed earlier (place, space, scale, interdependence, physical and human processes, environmental interaction and sustainable development). It should be remembered that these terms are conceptual, and, like space and time in physics, may be interpreted differently as knowledge evolves. Other multidisciplinary concepts include contextual ones that are similar to the highest order ‘concept spheres’ of Schopenhauer (see above), and are related to several discipline groups in academic study. Multidisciplinary concepts may include meta-concepts which have been seen as the mind’s generalised representation of one or more concepts (Erickson, 2012), and as employed in relation to integrated, cross-disciplinary water-resources management (Lenton, 2010), large data sets (Tran, 2013), modelling communities (Van Der Linden et al., 2014; Tingting et al., 2016), personal knowledge management (e.g. Schmitt 2016), business management (Gavrilova and Alsufyev, 2015) and student-centred learning in HE (Klemenčič, 2017).

Table 2.

A provisional concept hierarchy for physical geography (concepts included are examples, not a comprehensive listing).

	Concepts
	Multidisciplinary meta-concepts (Big ideas that are used in several sciences)		Physical geography
	Superordinate Environment related	Contextual Discipline related	Fundamental Foci and frameworks for research investigations (Overarching disciplinary fields)	Operational Associated particularly with analysis of process dynamics, testable theories, classifications, and subfield designation	Ancillary Often related to analysis during research investigations, and benefiting from quantitative analysis procedures in related sciences
1. Systems	Uniformity Permanency of natural laws General systems theory Entropy	Ecosystems Ecotone	Geosystems Nutrient systems	Open and closed system operations Cycles Energy and material flow controls Land systems Sediment cascades	Equilibrium state identity Complexity analysis Threshold recognition Steady state definition Feedbacks
2. Subjects (for research investigation)	Space Environment Nature Topography Morphology Soil Organisms Taxonomy Rocks/ minerals Glaciers Deserts	Physical environment Earth spheres Place Genetics Habitat Region Life zones	Physical environment Landforms Soil profile Catena Plant community Carrying capacity Ecological niche Ecoregion Soil landscapes Karst	Landform evolution models Experimental procedures, e.g. hardware models Concepts used in numerical modelling	Morphological unit Geomorphons Genetic form nomenclature Sediment transport ‘laws’
	Concepts
	Multidisciplinary meta-concepts		Physical geography
	Superordinate	Contextual	Fundamental	Operational	Ancillary
3. Processes	Force Energy/energy flow Resistance Cause and effect Cycles (hydrological, biogeochemical) Erosion/deposition Weather Precipitation Evapotranspiration General circulation of atmosphere and oceans	World climates Tectonics Endo/exogenetic forces Isostasy/eustasy Mass and water balances Microclimate Homeostasis Plant Succession Natural selection Extinction Carrying capacity Biological community Pedogenesis Catastrophe theory Radiation balance	Landforming process assemblages Drainage basins Morphoclimatic zones Climatogenetic zones Bioclimate Local climate (topoclimate) Mass balance Microclimate Solar forcing Speciation Succession Vicariance	Power Zonality Magnitude and frequency Bioaccumulation Energetics Erosion rates Jet stream Hadley cell Coriolis effect Aerosols	Efficiency Least action principle Exhaustion effects Sediment transport equation parameters Flow resistance equation concepts Tracer usages Acid rain Albedo calculation El Nino Southern Oscillation
4. Change and dynamics	Time Geological timescale Evolution Sea level change Climate change (especially Quaternary) Global change	Continental drift Plate tectonics Desertification Gaia hypothesis Uniformitarianism Catastrophism Gradualism Actualism Neocatastrophism Global warming Global dimming	Landform evolution Geochronology Island biogeography, theory of Refugia	Steady, graded and cyclic time Reaction time Recovery time Complex response Rate laws Sensitivity Dating techniques Genetic modification	Step functional change Multicyclic or compound landscapes Palimpsest Inheritance Multiple equilibria states Disequilibrium Forcing functions Metamorphosis identity Adaptation Equifinality Ergodicity
5. Anthropogenic relationships	Cultures Civilisations Pollution	What is natural? Ecological footprint Technosphere Environmental ethics	Human impact Anthropocene	Anthropic force Noosphere Homosphere	Artefacts Technofossils
6. Environmental management	Global climate change Sustainability Environmental ethics Natural resources Conservation	Global warming Land evaluation Ecological engineering Ecosystem services Sustainable development Econoclimate Recycling Renewable energy Heat islands	Landscape Management Environmental stewardship Design with Nature Hazards Disasters Landscape ecology Water resources Environmental perception	Adaptive management Hard or soft engineering Restoration targets Natural flood management	Flood flow modelling parameters and relationships Soil erodibility measures Slope stability models

Physical geography may be a member of such groups and there is a need for cross-disciplinary understanding of concept usage. ‘Fundamental’ or key concepts are then suggested to be those that relate to the whole basis of research objectives and learning intentions, providing the ‘Big Issues’ and study imperatives internal to physical geography today. These are the foci for physical geography research investigations. Deriving from fundamental key concepts, ‘operational’ concepts are those necessary in, and arising from, undertaking individual investigations of fundamental concepts; they often relate to dynamics, and may be regarded largely as elements arising from a process philosophy for models of understanding. They include concepts basic to the construction of particular study projects or programmes. Finally there are ‘ancillary’ concepts, or lower-level ones that have to be incorporated into models of understanding to make them work. These have in many instances been adopted or adapted as quantitative equations from other disciplines, as for example in riverbank erosion or sediment transport equations for geomorphology, derived from engineering, that are dependent upon stream power and grain size rather than incorporating complex resistance estimates.

Table 2 thus provides a 6 × 5 framework to accommodate the great diversity of concepts that have been identified in physical geography. The examples included are selective but have been tested against the content of Huber et al. (1988) and Huggett (2010). However any such framework has to be provisional for many reasons: for example philosophical debate continues about natural kinds and defeasible ones, and the ones identified can change. The concepts used in the lower contextual rows may also overlap with, or be duplicated by, entries in the upper ones (e.g. culture, global warming). Fundamental concepts may be expressed in different ways so that human impact and landscape management could be perceived as variations of a single fundamental concept. Finally, new analytical techniques may lead to fresh concepts being imported from other disciplines over time, especially at operational and ancillary levels, or they may be developed during research programmes. However, what this 6 × 5 structure does is provide a basis for rationalising and exploring the concepts already in use, and it enables understanding of why a diversity of concepts has previously been proposed by different authors, and where and why they can be used at different levels.

V Conclusions

Our judgement is that the practice of physical geography, driven especially by striking technological developments in recent years, is structurally on the change. Scientific methods, as applicable in physical geography, have been reviewed and broadly accepted as they have evolved in concert with such developments. Concepts, on the other hand, are still frequently cited but not used consistently or embraced sufficiently in educational curricula. In physical geography, as in some other sciences, many have been loosely and implicitly accepted, rather than being analysed for their origin and value. It is also now increasingly acknowledged that what are sometimes referred to either as ‘big ideas’ or ‘fundamentals’, should be identified and debated as they can provide the inspirations and stimuli for progressing research and learning. A provisional hierarchical structure is offered in Table 2, and this may reduce the confusion that can arise for students of the discipline confronted by sets of completely different, and unordered and unanalysed, lists of concepts. There remains plenty of room for constructive debate as to which examples should be placed where in the table.

Global concerns are increasingly being addressed by new multi-disciplinary or multi-skilled groups at research levels which no longer fit easily within what were once modular teaching frameworks on a field-by-field basis. Conceptual ideas transferred across disciplines may be miscomprehended or changed along the way. There are also now more applicable skills and methods, as in remote sensing and geographical information systems, which are relevant right across physical geography. From a student perspective, the technical demands of enquiry at research frontiers are difficult to absorb and to be stimulated by, but the conceptual ideas behind the new research are both exciting and inspiring and these may provide entry points for learning. We have suggested here a new provisional framework for recognising and understanding such conceptual underpinnings, with concepts forming underlying elements for both research and teaching that need greater attention at different levels. These can then be exemplified and their value tested in learning, teaching and research. Physical geography is being advantageously reconceived, and there is a need for its wider research and learning frameworks and structures to be recognised, beyond the level of methods and techniques, to keep in step with the way that is currently characterising other disciplines.

Footnotes

Acknowledgements

The authors gratefully acknowledge the help of Lyn Ertl (University of Southampton) for preparing the figure and two anonymous referees for their helpful comments.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

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