How does it come about that this arrow➔ points? Doesn’t it seem to carry in it something beside itself? – “No, not the dead line on paper; only the psychical thing, the meaning, can do that.” – That is both true and false.
The arrow points only in the application that a living being makes of it.
Ludwig Wittgenstein,Philosophical Investigations, p. 454
It is impossible to have no viewpoint, at least in the physical sense. As we move around the physical world the angle between our line of sight and various objects to which we attend varies continually. In practice, it is not only the line of sight that is at issue, but the coordinate systems located, so to speak, at various points on our bodies – for example, our limbs, particularly our hands, which are designed to grasp and tweak. But we can have a
‘hearpoint’ also, since we detect direction of sound sources too, if less finely with our ears than with our eyes. Viewpoint is thus, to a certain extent, a misnomer but we shall keep it because line of sight for sighted people is the probably the dominant perceptual modality.
From this premise we can go in various directions, which are not spatial or physical at all. One direction is temporal. For example, it is possible to adopt a ‘view’ of one’s present situation by imagining oneself expecting the present this morning, or last year. English enables us to talk about this by means of its tense system, as when we might say, ‘This time last year, I was expecting to be in New York.’ We can do the same with the future, as we see it at some particular time point, as in ‘On 2 June next year John will have been given his degree certificate.’
But more abstractly, and in fact more commonly, when we say we adopt a viewpoint, we mean something that is neither spatial nor temporal. Idiomatic-ally, in English and other languages, when we speak of our point of view we mean something roughly like ‘opinion’. What is the connection between such an abstract notion as ‘opinion’ and physical viewpoint? The vision-is-cognition metaphor is well known: I see what you mean is metaphorical (Lakoff and Johnson 1980, Sweetser 1990). There are indefinitely many physical viewpoints. Opinions in this sense are complex cognitions dependent on all kinds of cultural factors. But a fundamental ingredient would seem to 15
be the degree to which an individual judges some proposition or set of propositions to be true (or real) or false (or unreal). This is the sense in which the present chapter relates epistemic judgements to spatial and temporal viewpoint. From the next chapter on shall we shall leave the purely spatial almost entirely behind. In the present chapter, however, we review some of the theoretical and empirical work in linguistics that has investigated the language–space interface. This will lay the groundwork on which is built the DST framework.
2.1 Physical space: prepositions, deixis and reference frames1 The geometrical notion of ‘reference frames’ (or ‘frames of reference’) has been important in the study of spatial prepositions, in particular in the precise form used by Levinson (2003). Experimental work has shown the relevance of this approach (Carlson-Radvansky et al. 2002, Carlson 2010). We shall suggest ways in which frames of reference are not only constitutive of spatial meanings in language but can be seen to constitute an abstract space essential for explaining many kinds of non-spatial conceptualisations that language gives us.
For modelling the meanings of spatial prepositions geometry may well not be enough. Coventry and Garrod (2004) review geometric models of spatial prepositions and convincingly argue that these accounts are insufficient alone.
On the basis of experimental evidence they propose that two further kinds of cognitive input to the appropriate understanding and production of spatial prepositions are required: (a) the spatial properties of reference objects themselves and (b) the motor schemas for human interaction with such objects. However, despite the need for supplementation, the geometric com-ponent (whether axial or topological), if not sufficient, seems to remain necessary.
Research into spatial prepositions in general indicates that geometry is essential for their description and, furthermore, that humans use geometries in some form in applying prepositional expressions, filled out, however, by other types of cognitive schemata. As far as DST is concerned, the implica-tion is that geometry is not merely an arbitrary theoretical means of descrip-tion. If humans use geometrical schemas for spatial concepts, it is worth speculating that geometry is involved in abstract representations. Indeed, with regard to all kinds of spatial concepts, this is a key assumption behind cognitive metaphor theory. There is a particular class of prepositions known as ‘projective’ prepositions and it is this class that is of special significant for
1 This section uses parts of Chilton (2005).
the DST because all analytical accounts make use of ‘reference’ frames in one form or another. Reference frames are simply three-dimensional axis systems with the origin located either at ego or some other referent. They are thus intrinsically deictic and by extension intrinsically express ‘point of view’.
For this kind of preposition, we need not only three orthogonal axes but geometric transformations (translation, rotation and reflection) of axes, as we shall see for the spatial expressionin front of. It is this class of prepositions that is especially pertinent to the fundamental conception of DST. Such prepositions are essentially deictic: they depend on the orientation of the speaker and of reference objects in relation to them – and vice versa. Another way of saying this is to say it depends on ‘point of view’, the point of view of the self or of some other object (or person). The reflection transformation can be thought of as representing an ‘opposing’ point of view. Taking terms like
‘point of view’ and ‘opposing’ in a metaphorically abstract sense, we have grounds for speculating that a kind of ‘metaphorical geometry’ may not be irrelevant to understanding a certain range of conceptualising phenomena that arise with many linguistic expressions.
The literature on spatial expressions in language, especially prepositions (and adpositions in general), is abundant and growing and it is not to the point to review it all here (for an overview see Evans and Chilton 2010). While geometrical modelling of spatial semantics is certainly not the whole story, certain geometrical approaches are well established. It is these that ground the abstract spaces of DST and it is these we focus on in this section.
2.1.1 Projective prepositions: egocentric and allocentric
What we have said so far assumes an egocentric and unitary set of axes, but it is well known that the human representations of space operate with multiple axes and can shift from one to the other.2In fact different brain areas appear to be responsible for the different spatial coordinate systems and their transformations (see for example Gallistel 1990, 1999, 2002, Andersen 1995, Colby and Goldberg1999, Burgess2002).
In cognitive linguistics, shifting viewpoints are frequently mentioned and they are fundamental. It is also well known that language enables us to encode a shift from an egocentric speaker’s viewpoint, to an allocentric viewpoint, i.e. there is a shift of deictic centre or geometric origin. Langacker (1995) and van Hoek (2003) go a long way in demonstrating the extent of such phenom-ena in language, using Langacker-style pictorial diagrams. However,
2 Levinson (1996,2003) considers the phenomenon cross-linguistically and has demonstrated also the existence of absolute (geophysical) frames of reference (e.g. in Tzeltal and Guugu Yimithirr).
geometrical ideas and formalisms provide much of what we need in this regard, and more. If we adopt coordinate systems as our basis, then translation of axes, a standard operation, is implicit in the geometric framework, and gives us a natural way to describe viewpoint shift and related phenomena. We might indeed hazard the guess that the viewing organism is computing an analogous operation, and the linguistic coding of such shifts can be repre-sented quite simply as vector spaces in alternate coordinate systems. Familiar cases such as(1)can be handled in this way:
(1) John is in front of the church.
Since some buildings, in some cultures, have an orientation calqued on human orientation,(1)is ambiguous.
The conceptual alternation one may experience in reading(1)corresponds to the switching from a coordinate system centred on the human speaker to one whose origin is positioned on the landmark object (the church) and whose axes are directed relative to it. What is the relation between the two coordin-ate systems? In one of the interpretations of(1), the interpreter is not adopting a viewpoint located at the church; the base coordinate system (based on speaker’s and interpreter’s real-space location) is not actually shifted. This is the egocentric viewpoint, where ego is the speaker, S, who is oriented toward (i.e. is facing) the church andJohn’s position is between the oriented speaker and the church. In an alternative conceptualisation of (1),John is located relative to the church’s orientation – specifically, relative to the church’s ‘front’. This interpretation is an allocentric representation: the centre of the axis system is located at the distal church, not at the speaker S. But the church still remains in the space viewed by the speaker. In the straightforward case, the church itself is located by a vector whose tail is at the origin, S, of the base system, that is, the world as viewed by the speaker.3
However, in many real situations, no such vector can be computed. For instance, one may say ‘Go into the piazza; the statue is in front of the church’, without either speaker or interpreter needing to calculate the orientation and distance of the church’s coordinate system with respect to their own. A shift to an allocentric representation is clearly involved in such an example. Each person has their own reference frame, grounded in their bodily orientation, which moves and turns with them. The point remains that egocentric and allocentric spatial coordinate systems are a natural part of the human cogni-tive equipment and that linguistic expressions cue one or the other depending on contextual factors in the real world of discourse processing. In any event, we should not be limited by the single example of (1). In fact, when
3 Axis systems are in fact anchored at various origins of the human body in spatial cognition: e.g.
eyes, effector limbs.
allocentric spatial viewpoint shifts are constructed in discourse, the object to which axes are shifted are not always in view of the interlocutors and their position relative to the interlocutors may not be known and is not interpreted:
(2) Go to the end of the bridge: the church is in front of you.
We might imagine that something like the following cognitive operations occur during processing of(2). (i) The hearer, H, can locate the bridge in his own mental representation of physical space (egocentric representation). (ii) To understandto the end of the bridge, he then has to initiate an allocentric representation in whichthe end of is defined relative to the bridge, such that the bridge is aligned with a path that has a beginning and end, i.e. a vector whose tail is at the start of the bridge. Note that this arrangement will not be entirely allocentric, since which end of the bridge is selected as the starting point depends on the way the bridge is positioned in the egocentric space represented in (i). Then, (iii), H has to decide the interpretation ofthe church is in front of you. The hearer has now mentally shifted his own (egocentric) axes to the end of the bridge, indeed has aligned his sagittal axis with the structural axis of the bridge itself and the location of the church is given byin front of interpreted relative to the egocentric axis system of H. Presumably, then, understanding(2) requires several representations involving axis shift, and these representations are not only sequential but nested.
The point of these examples is to show how discourse seems to trigger axis shifts from egocentric to allocentric representations of physical space. But shifts of ‘viewpoint’ occur also in the domain of abstract discourse process-ing, as Fillmore, Langacker, Talmy and others have amply demonstrated.
What later chapters of this book aim to do is to show how a projection of these mechanisms may underlie key aspects of semantic processing at the more abstract level that linguistic forms appear to prompt.
2.1.2 Axes within axes and transformation of axes
The notion of transformation will be of importance throughout this book. It should not of course be confused with the term ‘transformation’ as it was used in the early transformational-generative grammar of Chomsky. The sense in which we use it here is taken entirely from geometry, and the claim in DST is that geometrical transformations correspond to cognitively real operations.
We can see this very clearly in the case of spatial terms, such as prepositions, which is why we are spending time on prepositions in this chapter. Spatial conceptualisation is the foundation of more abstract conceptualisations.
As Levinson (2003: 25–34) shows, the terminology can be confusing in that terms such as egocentric, allocentric, relative and deictic are used in the different disciplines (philosophy, psychology and brain sciences, for example,
as well as linguistics) that take an interest in spatial representation in lan-guage. In his own classification of reference frames Levinson discards the terms ‘egocentric’ and ‘allocentric’ but I shall retain them in the sense that will emerge in what follows. One reason for this is that in the study of linguistic constructions in general, many cognitive linguists and developmen-tal psychologists believe that language (and language use) reflects and facili-tates perspective-taking, that is, the conceptual adopting of the viewpoint of another speaking subject. This kind of alternation can be understood, as indeed it is also by Levinson (2003: 44–7, 84–92), in terms of geometric transformation of coordinate systems. Levinson’s important and influential account of linguistic expressions for horizontal spatial directions proposes three main reference frames. These are ‘intrinsic, ‘relative’ and ‘absolute’
reference frames. I shall not be concerned with absolute reference frames, which are coordinate systems whose axes are defined relative to the geographical environment. I shall, however, discuss ‘intrinsic’ and, more extensively, ‘relative’ coordinate systems, combined with the egocentric–
allocentric alternation, while emphasising the role of transformations between different systems.
Levinson uses the term ‘frames of reference’ in his main account of spatial expressions (Levinson2003: 34–56). The term is also used by experimental psychologists. In this book I use also the terms ‘coordinate system’ or ‘axis system’, to make clear the connection with geometry. It is important to note that psychological experiments indicate that geometrical axes and transform-ations are alone insufficient to account for the range of semantic judgements prompted by the projective prepositionsin front of, to the left/right of, over/
under and above/below (Coventry and Garrod2004: 91–112). Investigations show that such judgements also involve the function of located objects, knowledge about both located object and reference object and functional properties of the situation in which such judgements are made. But these findings do not mean that the axis systems are not operative – in fact it appears to be the case that they are a necessary component. Axis systems and their transformations are needed for modelling spatial cognition and spatial lan-guage. I will show in the main part of this book that the geometry needed for projective spatial prepositions is very similar to the geometry that is needed for an insightful modelling of much more abstract conceptualisations related to point of view and non-actual ‘worlds’. We may speculate about the connection between the physical–spatial and the highly abstract mental representations we shall look at – and there are plenty of claims about the metaphorical projection from the spatial to the abstract in cognitive linguis-tics. We need not pursue such speculation at this point.
Let us turn to the details of the geometrical component of the conceptual-isations associated with the projective spatial prepositions. As we have noted
in the previous section, people (and many living creatures) are represented as having intrinsic axes, oriented in the direction of their typical motion.
Vehicles and some kinds of building (though they do not move) are also treated as having intrinsically oriented axes. But not all objects are so treated and in such cases people and their languages exhibit some interesting con-ceptual phenomena that have not always proved straightforward to describe (Levinson2003: 1–23). To see this, let us consider a slightly different version of(1)in(3)below:
(3) John is in front of the tree.
This example will illustrate different conceptual types of what Levinson terms the ‘relative frame of reference’ (Levinson 2003: 44–7, 85–9). The prepos-itional phrase in sentence (3) can be analysed either as Figure 2.1 or as Figure 2.2.
Figure 2.1shows the conceptualisation in which the coordinates are centred on the speaker S; the locandum (the object to be located, here John) is between S and the landmark location. Geometrically, there are two points John and tree, call them p and p0respectively, and these points are such that the distance from S top is smaller than the distance from S to p0. In this
p′
p S
Figure 2.1in front of: analysis (i)
understanding of(3)the pointp is positioned in S’s axis system, i.e. John is positioned relative to S in terms of distance; the point p has to be in this position, to satisfy the meaning of in front of. Thus the coordinates within which this reading of(3)emerges are egocentric coordinates, taking S as ego.
As for John’s coordinate system and orientation, these do not make any difference, though the diagram indicates John in a specific orientation (‘facing’ the tree).4
Turning to the speaker’s orientation, in real life the speaker S of(3)may be facing in any direction (including toward the tree), as suggested inFigure 2.2.
In such a situation, the sentence may be acceptable if John is bodily oriented
‘facing’ the tree. Putting things geometrically, we can truthfully assert(3), if his sagittal axis is a vector with its head located on the vertical axis of the tree and has a length that is variable within relevant limits, but we will not be communicating his precise position in a region around the tree, since trees have no intrinsic ‘front’ (or ‘face’) of their own. What seems to be happening is that John’s axes are ‘projected’ onto the tree, whatever his position around the tree.
Unless the hearer H of (3) can see the situation, H’s mental representation based on the linguistic utterance alone, will be indeterminate – H will not know
S
Figure 2.2in front of: analyis (ii)
4 Geometrically, the orientation of John’s axes relative to S’s axes is definable in terms of the angles between the intersection of axes in the two systems.
exactly where in the region John is positioned, only that he is ‘facing’ the tree.
This is the case however H and S themselves are actually oriented.
What I have described so far is alternative mental representations of the spatial expression in front of and the point is that there are alternative
What I have described so far is alternative mental representations of the spatial expression in front of and the point is that there are alternative