報告Linguistic Anthropological Research on
Spatial Cognition in European and Non-European Settings*

Kuniyoshi KATAOKA要旨

認知 （認識） 人類学 に お け る 近年の発展の一端 と し て， 言語 と 空間認知の イ ン タ ー フ ェ イ ス に 関わ る 研究 に 焦点 を 当て， そ の 推進者 の 一人，Stephen Levinson の提唱す る 空間指示枠 （Frames of Reference） の分類と ， 日常生活 に お け る 空間指示 の 可塑性 を 検証す る 。 本論考 で は ，Levinson の 確立 し た 3 種類 の 空間指示枠 （固有的 ‘intrinsic’／ 相対的‘relative’／絶対的 ‘absolute’ 指示枠） の特性 を 概観 し ， お の お の の指示
様式 を代表す る 言語 を類型的 に分類す る 。 ま た， 認識の中心 と さ れ る 人
間主体の （egocentric） 空間認知様式は， 各言語の文化的実践 に 照 ら して， 従来当然視 さ れて き た ほ ど の普遍性が認め ら れな い点 を指摘 し ， 人
間主体で は な い （allocentric） 慣例化 し た空間認知様式が思考 に 及ぼす
影響 を考察す る 。 最後に， こ の よ う な知見に基づ く 談話研究の現状 に触れ， 今後の談話分析の方向性 を 示唆す る 。

Keywords: cognitive anthropology, spatial cognition, intrinsic/relative/absolute frames ofreference
キ ー ワ ー ド ： 認知 （認識） 人類学， 空間認知， 固有的／相対的／絶対的指示枠― 121 ―

愛知大学 言語 と 文化 No. 6

1.

Introduction
This review paper is heavily motivated by a series of recent findings fromcross-linguistic studies on spatial cognition in cognitive anthropology, and aims to confirm
that human spatial cognition may not be so equally monolithic across cultures as has been
generally assumed. This is also a partial report of LSA (Linguistic Society of America)
Linguistic Institute 2001 at The University of California, Santa Barbara, where a classdealing with this issue was first officially taught by Stephen Levinson, Director of Language
and Cognition Group at Max Planck Institute for Psycholinguistics. After a brief overview
of the current investigation into space in cognitive anthropology, I will summarize andcomment on the following points: 1) Levinson’s notions of ‘Frames of Reference’ (hereafter
FoR) and ‘Untranslatability grid,’ and 2) primacy of egocentricity and gravity in theWestern concepts of space, and disclaimers against such a position. Finally, I will advocate
a discourse-oriented approach to spatial cognition as one of the future paths toward the
linguistic study of space.

1.1 Overview: Current Investigation of Space in Linguistic Anthropology
Concepts of space and researchers’ focuses of attention differ according to disciplines.
Traditionally, anthropological research on space has mainly been concerned with kinesics,
place names, symbolic use of space such as sacred/polluted places, social organization,
dwelling/migration patterns, habitus (a system of dispositions), etc. (see Lawrence & Low
1990 for an extensive review). Especially in linguistic and cognitive anthropology, current
interests in space are largely devoted to the studies of language-thought interface in spatial
cognition (e.g., Brown & Levinson 1994; Levinson & Brown 1994; Levinson 1996b,
1996b; Pederson 1995) and spatial mapping in speech and narratives (e.g., Hanks 1990;
Haviland 1993, 1996; Farnell 1995; Bickel 1997).
Findings from these lines of research generally suggest that egocentricity ofperspective-taking based on the human body may have been unduly emphasized inconstructing a framework of spatial cognition. Such an egocentric space may be a default
condition in representing spatial relations in everyday referential practice, but there are also
many cultures that defy such an egocentric framework and employ indigenous, allocentric
spatial anchors for the equivalent practice.

― 122 ―In this sense, previous models ofLinguistic Anthropological Research on Spatial Cognition

anthropological space may have been heavily skewed toward the Western concepts ofspace, and thus can be merely cultural constructs.
There also remains a long-standing question about the extent to which language andcognition can be separated or integrated; a recurrent discussion that has been taken up bysuch scholars as Humboldt, Weisgerber, Sapir, and Whorf—a thesis widely known as‘Sapir-Whorf Hypothesis’ (see Hill & Mannheim 1991).

Currently, some linguistic

anthropologists uphold a neo-Whorfian view (e.g., Lucy 1992) that linguistic influence overcognition will be attested by confirming that, if semantic categories A, B, C. . . are shown to
induce distinctly different responses A’, B’, C’. . . , linguistic representations reflect
culturally and linguistically preferred modes of cognition and interactive patterns. If thiscondition is met, we can assume that languages select and arrange repertoires of particularcognitive styles made available by habitual linguistic use (see also Slobin 1987, 1996;
Gumperz & Levinson 1996; Levinson 1996a, 1996b; Choi & Bowerman 1991; Inoue 1998;
Pederson et al. 1998; Bowerman & Levinson 2000). In other words, a central theme thereis that “linguistic patterns point to some systematic differences in the cognitive style withwhich individuals of different cultures deal with space, and it is these underlying cognitive
specializations that may help us to integrate diverse spatial features within a culture. . .
(Levinson 1996a: 356; also Levinson 1996b).”In short, major topics of the spatial research in current linguistic/cognitive
anthropology are: a) the degree to which the kind of linguistically encoded space correlateswith non-linguistic features of thinking, b) relative demotion of egocentricity andcorresponding emphasis of locally and culturally available frames of reference as humanpotentials for spatial cognition, c) neo-Whorfian findings that culture (or language) may
influence cognitive capacity for language processing and the modes for encoding
communicative intentions; and implicitly, d) relative demotion of verbal competence in
representing spatial knowledge, and complementarily, recognition of other ‘modalities’ ofmind which contribute to spatial cognition. The final point is not yet loudly articulated, but
considering the current resurgence of the studies on gesture and sign language (McNeill
1992, 2000; Armstrong, Stokoe, & Wilcox 1995) and re-evaluation of ‘Molyneux’s
Question’ (Morgan 1977; Eilan 1993; Levinson 1996b)1, there is no reason not to assume
its emergence as a central issue of spatial cognition in linguistic anthropology.
In order to fully investigate these issues, we need a cross-linguistically valid
framework, or a spatial ‘etic’ grid, for decoding spatial perspectives. Below I will delineate― 123 ―

愛知大学 言語 と 文化 No. 6

some basic concepts about a currently widely acknowledged model proposed by Levinson(1996a, 1996b), and point out a branch of research that utilizes the framework.

2.

Frames of Reference and Untranslatability Grid

2.1 Non-coordinate vs. Coordinate
One way of conceptualizing the spatial world we live in is to view it as constitutive of
two types of space: the world metrically perceived and the world topologically perceived,with degrees of integration between the two. The former is characteristic of spatial relationsin terms of disengaged/objective modes of representation, such that actual physical volume,
distance, and orientations in a spatially fixed grid are numerically computed, while thelatter, in terms of engaged/egocentric ways of representing spatial properties, often
measured by psychological and social factors. In other words, they are respectively theworlds based on objective, allocentric modes of representation and on subjective, egocentricones.
Of particular concern in this paper are these two modes of spatial construction, roughly
conceptualized as the ‘coordinate’ system and the ‘non-coordinate’ or ‘deictic’ system.
Although, in fact, the research on the ‘deictic’ system has attracted a lot of attention fromlinguists and anthropologists, I will particularly look at the former ‘coordinate’ systems, anddelineate the current conceptualizations of spatial description of static objects on thehorizontal and vertical planes. (See Kataoka [1998, in preparation], for a more detailed
account of ‘deictic’ systems.)
In order to clarify the spatial relationship between objects by using the coordinate
system, one conceptually ascribes to them such roles as figure (Fg) and ground (Gr) (Talmy
1978, 1983). These terms were originally coined by Gestalt Psychology to represent a
perceptually salient entity (Fg) vis-à-vis the background entity which makes the figure
emerge the way it is (Gr), as typically seen in the figure-ground conversion of the famous‘face or base’ picture. This relation is conceptually equated with that between trajector (Tr)and landmark (Lm) in cognitive linguistics (Langacker 1987), or more generally, referent(Rf) and relatum (Rl) or reference object in philosophy and psychology. The definitions
across these disciplines may be slightly different, but I will take these sets of pairs asconceptual equivalents for the current purpose, and use these sets of terms interchangeably
throughout this paper.

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2.2 Three Types of Frame of Reference in the Coordinate System
Here I will illustrate a functional typology of space proposed by Levinson (1996a),
which classifies whole static spatial arrays in the following way.2 This system is currently
gaining a lot of attention from linguists and psychologists, and is becoming one of thestandard systems in spatial description.

(Note that this is the typological grid for‘linguistic,’ not perceptual, encoding of space.)(1)

No coordinate systems employed (not discussed here):a. prototype deixis: e.g., Figure (Fg) is ‘here’ near speaker.
“The apple is here.”b. contiguity: ‘topological’ relations: e.g., Fg is ‘on’ Gr.
“The apple is on the table.”c. named locations“Jerry went to Woodstock.”(2)

Coordinate systems or ‘frames of reference’ (FoRs) employed:a. Horizontal(i) Intrinsic“The cat is behind the truck.” (one meaning: see Figure 1. i) intrinsic)
The cat (Fg) is at the place contiguous with the intrinsic rear part of thetruck (Gr): the coordinate system based on the ‘truck’(ii) Relative (or deictic)“The cat is behind the truck.” (another meaning: Figure 1. ii) relative)
The cat (Fg) is on the occluded side of the truck (Gr) from the standpoint of
the speaker: the coordinate system based on the ‘speaker’(iii) Absolute 3 (Figure 1. iii) absolute)“Canada is to the north of the U.S.”/ “The cat is to the north of the truck.”
Based on cardinal directions or conventional absolute directions.
b. Vertical
Assumption: the same notions for ‘horizontal’ apply.

i) Intrinsicii) Relativeiii) Absolute

Figure 1. Three types of frame of reference: The cat is (behind/to the north of) the truck― 125 ―

愛知大学 言語 と 文化 No. 6

Here the ‘non-coordinate’ system (1) refers to a system where no angular specification
is provided for the objects related in the spatial array. For example, in describing an object
in ‘deictic’ terms, here in “The apple is here (1. a)” does not include any angularspecification from the speakers, nor does “The apple is on the table (1. b),” which is
described with a ‘topological’ term, on. These are thus instantiations of a non-coordinate
system. A third type of a non-coordinate system is ‘named locations’ (1. c), or place names,
which serves as a context-independent means to identify a particular location by referring toa geographically defined space. Although it seems to be a simple referential practice, this is
not so ideologically unproblematic: see Basso (1990) and Feld & Basso (1996) on place
names, which are ethically, and sometimes morally evaluated. We don’t deal with these
non-coordinate systems here.
In contrast, the ‘coordinate’ system (2) roughly represents a configuration where somekind of angular specification is given, and is comprised of three types of frames ofreference: intrinsic, relative, and absolute. For example, if one says, “The cat is to the(left/right, front/back) of the truck,” the cat is located in a particular space such that it
creates a certain angular configuration to the ground object, the truck, from which theposition of the cat is talked about. To borrow Levinson’s words, you choose “a ground or
landmark object in close contiguity with the object to be located” (Levinson 1996a). Now
let us discuss each type of coordinate system in more detail (Figure 1).
First, the sentence “The cat is behind the truck (2a (i, ii))” is ambiguous. The
ambiguity comes from different frames of reference applied to the spatial array. The
intrinsic relation (2a (i)) is ‘binary,’ or relating two objects/entities in the immediate context(cat and truck), but the relative relation (2a (ii)) is ‘ternary’ because the three entities are
related (cat, truck, and Speaker). Thus, the relative FoR involves the speaker’s viewpoint
distinct from a ground object.
In addition to this ambiguity derived from the choices of FoRs, there is another sourceof complication according to the distinctions among intrinsic (coordinate), relative(coordinate), and deictic (non-coordinate) perspectives. Notice that, when the Ground or
Landmark coincides with the speaker, the ordinary configuration of the context may also be
represented in deictic terms. Thus, for the intrinsic context in 2a (i): “The cat is behind thetruck (intrinsic, binary between cat and truck),” we could also say “The cat is to the right of
the truck (relative, ternary among cat, truck and speaker).” Besides, the speaker could walkup to the truck, climb in, and say, “The cat is behind me/I see the cat behind me (deictic,― 126 ―

Linguistic Anthropological Research on Spatial Cognition

binary between cat and speaker).” In the last case, the spatial grid of an intrinsic FoR and a
deictic perspective are merged into one, allowing the two different systems to refer to thesame figure object, the cat.4 This fact indicates that these two systems are highly fluid, andmay possibly overlap in everyday referential practices.
In the Absolute system, referring practice is more simple, because this FoR only
requires as the anchor the absolute directions such as NSEW, ‘where the sun rises/sets,’‘uphill/downhill,’ ‘upstream/downstream,’ etc., usually based on fixed and stable
geographic features. The relation is always binary between these absolute orientations andthe referent. Thus, for the relative situation in Figure 1 ii), an English speaker could also
describe the cat’s position by saying “The cat is to the north of the truck,” although such an
expression is highly marked and requires a special context.
Other researchers in various disciplines have defined these notions using different
terms as shown below (Table 1). To avoid confusion, I will use Levinson’s static spatial
grid and his terminology as the point of departure.
Table 1. Concepts of spatial perspectives (based on Levinson 1996b, 2001 class notes)
Levinson’s FoRs

Intrinsic

Absolute

Relative

Psycholinguistics

object-centeredenvironment-centeredviewer-centered

Linguistics

intrinsic

deictic

Vision theory,
imagery debate

3D models

2.5D sketch

Cognitive psychology
Visual perception

allocentricorientation-freeegocentricorientation-bound

Levinson’s static spatial grid may also be a source for another type of grid:
dynamic—probably we may conceptualize this as a series of configurations projected fromvarious emergent vantage points. However, an analysis of such changing perspectives isbeyond the scope of this current review, and is discussed elsewhere (Kataoka 2001, in
preparation).

2.3 Untranslatability Grid
In constructing the ‘untranslatability’ grid, Levinson (1996b) aimed to answer what iscalled ‘Molyneux’s question’ (see also Morgan 1977; Eilan 1993), and paraphrased it ascomprising two specific issues: 1) do the different representational systems natively and― 127 ―

愛知大学 言語 と 文化 No. 6

necessarily employ certain FoRs?; 2) if so, can representations in one FoR be translated(converted) into another FoR? Confirming that FoRs cannot freely be converted into one
another, Levinson claims that all mental ‘modalities’ must utilize different FoRs available
according to languages; but those particular FoRs can be adapted to other modalities within
the limited sets of translatable FoRs, suggesting a ‘yes’ answer to Molyneux’s question.
In order to determine the nature of untranslatability, Levinson (1996b) examined
linguistic spatial relations between two physical objects, BOTTLE and CHAIR, in the three
types of FoRs; absolute, relative, and intrinsic. His basic strategy was to map the
possibilities of FoRs in the prescribed spatial configuration, where a bottle is placed in thechair’s front region. Figure 2 summarizes these (un)translatable relationships between
FoRs. For example, if the spatial relation which holds between the bottle and the chair in
the relative FoR is true (i.e., ‘bottle to right of chair’), it will also entail, or ‘translate into,’
the intrinsic FoR (i.e., ‘bottle in front of chair’). However, even if the relation that holds
between the objects in the intrinsic FoR is true, it will not translate into the relation in therelative FoR.

ABSOLUTE

RELATIVE

L
R

N
bottle to North of chairbottle to right of chairbottle in front of chair
INTRINSIC

Figure 2. Untranslatability across FoRs (on the horizontal dimension)― 128 ―

Linguistic Anthropological Research on Spatial Cognition

To recapitulate the basic features of FoRs, the sentence “The bottle is in front of thechair (meaning ‘in the chair’s front’)” represents a ‘binary’ and ‘intrinsic’ relation because
it is the relationship between Figure/referent (bottle) and Ground/relatum (chair). On theother hand, “The bottle is to the right of the chair (seen from where I am)” represents a‘ternary’ and ‘relative’ relation because ‘the bottle’ is spatially related to ‘the chair’ throughthe speaker’s or viewer’s point of view.
These relations represent interesting properties in the possibilities for ‘rotation.’ When
the whole array (chair + bottle) is rotated, only the intrinsic system allows/maintains theoriginal acceptability. When the viewer is rotated, intrinsic and absolute FoRs retain it, andwhen the ground (chair) is rotated, absolute and relative FoRs retain it, exhibiting thefollowing rotation possibilities (Table 2: see Levinson 1996b for more detail).
Table 2. Spatial relations and rotation possibilities
Intrinsic
RELATION
ROTATION

Absolute

Relative

relation:

BinaryBinaryTernary

origin on:

GroundGroundViewerwhole array:

Yes

No

No

viewer:

Yes

Yes

No

ground:

No

Yes

Yes

These relations also lead to highly heuristic consequences in the cultural variability
seen for the preferred uses of FoRs. Levinson (2000, class notes 2001) mentions that, evenif speakers can theoretically use the three FoRs, not all languages use all FoRs to the same
extent as the ordinary means of spatial description. Yucatec (Mayan) speakers use all three,
but English and Japanese speakers usually rely on intrinsic and relative FoRs, while Tzeltal(Mayan) and Hai||om (Khoisan) speakers, on intrinsic and absolute FoRs. Amazingly, there
are speakers who exclusively employ only one FoR, such as Mopan Mayan (intrinsic) andGuugu Yimithirr (absolute). However, as may be expected from the untranslatability grid,
there seems to be a constraint that no (or possibly very few) languages exclusively use only
Absolute and Relative FoRs. These facts tell us that preferred uses of FoRs are skewed
toward either a Relative-Intrinsic or Absolute-Intrinsic combination, and one or all of them,with the Absolute-Relative combination rarely observed as a viable pair (see Figure 2).
Given these findings, there is tremendous diversity in the availability of FoRs acrosslanguages, and universals in spatial cognition seem to exist only as constraints.

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Also, we generally assume that the same three coordinate systems may be applied tothe objects on the vertical plane.

The (over-)determination of verticality in spatialdescription is a common basis for understanding spatial relations. For example, Levinson(1996b: 135) says, “… (T)he perceptual cues for the vertical may not always coincide, butthey overwhelmingly converge, giving us a good universal solution to one axis.” The sameline of conceptualization of verticality dominates in linguistics. Lyons (1977: 690) also
maintains that verticality is “physically and psychologically the most salient of the spatial
dimensions: linguistically,… it is the primary dimension” (see also Langacker 1987: 263–7,
1991: 77 and Dirven & Taylor 1988 for ‘verticality’ per se). Given this framework, we may
be able to identify similar constraints placed on the everyday use of space on the verticaldimension.
However, we may need to reconsider this thesis from a different angle. For instance,
Levinson (Levinson & Brown 1994; Levinson 1996d, 1997) has indicated elsewhere that
common-sense spatial notions, ‘right’ and ‘left,’ may be a cultural construct in the Western
framework of space (to be discussed in more detail in Sections 3.1.–3.3.). If that is thecase, an idea that the three spatial axes converge on the ego-centric perspective may also bea Western intellectual legacy of spatial concepts. Then, what about verticality based on
gravity? Below I will briefly trace these widely shared epistemological concepts of spacethat persist in the Western intellectual tradition.

3.

Primacy of Relative Egocentric Space and Gravity in EuropeanIntellectual Tradition

3.1 Tacit Assumptions
Concepts of space have always been a major issue in the philosophy of humanknowledge and perception, and despite numerous theories on this issue, one common
consensus is that they are basic building blocks of epistemological understandings of theworld (Eliot 1987; Van Cleve & Frederick 1991; Jammer 1993). If one asks, “what is themost stable dimension on the vertical plane?,” the answer seems self-evident. Almost
everyone, on a brief reflection, would say it is the gravitational vertical, or the Absolute(here read as ‘up/down’) FoR. In fact, verticality is distinguished from laterality (left/right)
and anteriority/posteriority (front/back) in terms of its stability of perception—verticality is‘impermeable’ to the agent’s movements. That is, verticality always points to the same

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Linguistic Anthropological Research on Spatial Cognition

direction, like the geographic N-S orientations (Figure 3), leading a hierarchy of conceptual
stability on the horizontal plane: ‘up/down > front/back > left/right.’ The same hierarchy isreported for the ease of accessibility to naming recalled objects in terms of the response
times (Bryant, Tversky, & Franklin 1992: Logan and Sadler 1996).
Up

Back

Left
N

S
Front

Right

Down

Figure 3. Asymmetry of coordinates on the horizontal planeThis legacy of putting undue emphasis on the egocentricity of a referential anchor
point is traditionally dated back to Kantian philosophy, which maintains, based on
Newtonian ‘absolute’ space, that egocentric conceptualization of external phenomena in theworld is the precursor to other kinds of knowledge.5 This egocentricity of spatial perception
is seen in Kant’s early exposition:
In physical space, on account of its three dimensions, we can conceive three planes whichintersect one another at right angles. Since through the senses we know what is outside us
only in so far as it stands in relation to ourselves, it is not surprising that we find in therelation of these intersecting planes to our body the first ground from which to derive theconcept of regions in space. The plane to which the length of our body stands perpendicularis called, in reference to us, horizontal; it gives rise to the distinction of the regions we
indicate by above and below. Two other planes, also intersecting at right angles, can standperpendicular to this horizontal plane, in such manner that the length of the human body isconceived as lying in the line of their intersection. One of these vertical planes divides the― 131 ―

愛知大学 言語 と 文化 No. 6

body into two outwardly similar parts and supplies the ground for the distinction between
right and left; the other, which is perpendicular to it, makes it possible for us to have theconcept of before and behind. (Kant 1991 [1768]: 28–29).

Also assumed by Kant and contemporary cognitive scientists is the primacy of gravity
in spatial perception. Kant, prior to his influential work on ‘incongruent counterparts (e.g.,right and left hands and shapes like ‘_| |_’), is said to have sought “to prove that the very
existence of space is due to gravitational force, and that its three-dimensional character is aconsequence of the specific manner in which gravity acts (Kemp Smith 1991 [1918]: 43).”
This dominance of gravity and egocentricity is assumed to be the criterion for defining thevertical and horizontal planes and still seems to exert a persistent influence on theconceptualization of spatial relations in cognitive science and linguistics. The following
quotes are representative examples of this line of thinking:The extensive apparatus we have to tell us how we are oriented in the gravitational field isprecisely an apparatus to tell us which way is up. Of course, the reason this matters to us is
the pervasive influence of gravity on every aspect of our ordinary actions. So here we havean egocentric axis which is not defined as a natural axis of the body. Of course, there issuch a thing as the long axis of the body, but that is not the same thing as ‘up’ and ‘down’,
which continue to be defined in terms of the gravitational field even if one is leaning at anangle (Campbell 1993: 75).
The up/down axis is determined by our recognizing the direction of the pull of gravity, andis therefore not to be explained in terms of egocentric or anthropocentric predispositions oflanguage users (Fillmore 1982: 36–7).

In cognitive science in general, researchers assume that these concepts are theoreticallyapplicable across languages and thus universal (Miller & Johnson-Laird 1976; Lyons 1977;
Regier 1995; Logan 1995). In most cases, it has been tacitly agreed that the relative,
egocentric FoR defined by gravitational orientation is the default or dominant system, and it
is only when the subjects are ‘instructed’ otherwise or they have difficulty in(re)constructing the perspective under discussion that they come to rely on other frames ofreference.
However, there are studies that indicate this is still an over-simplified view. For
example, Kataoka (2000), based on the actual usage of Japanese vertical terms, ue ‘up’ andshita ‘down,’ proposed that the ‘subjectified’ (Langacker 1991) vertical dimension canconceptually override the actual vertical dimension defined by gravity, suggesting that the― 132 ―

Linguistic Anthropological Research on Spatial Cognition

value placed on the vertical dimension and its dominance in spatial coordination may havebeen overestimated in notional frameworks of space. Probably gravity is the dominantfactor in establishing the absolute (vertical) FoR, but the potential ease/difficulty in staying
in or moving out of the frame may vary across languages, as will the sensitivity andboundedness to gravity in spatial lexical assignment.

3.2 Contextually/Culturally Variable use of Coordinate Systems
The notions of space based on egocentricity and gravity may serve as a default
condition for spatial perception and description. However, habitualized linguistic practice
may induce the speaker to unproportionately utilize certain modes of spatial reference and
FoRs.

Even if speakers cross-linguistically have equivalent words for ‘up/down,’‘right/left,’ and ‘front/back,’ what these terms actually refer to are not exactly the same, orrather, can be quite divergent. To examine this issue, let us take for example the following
encounter situation (Figure 4), in which Viewer (V) and the relatum (Rl; here Tom) standfacing each other. This scene is usually called the ‘canonical encounter’ (Clark 1973).
Here, the referent (Rf; ball) may be differently described according to the point ofreference, which may or may not succumb to cross-linguistic relativization.
Tom (=RI)
ViewerBall (=Rf)

Figure 4. “The ball is to the left/right of Tom.”― 133 ―

愛知大学 言語 と 文化 No. 6

It is a well-recognized fact that English and Japanese rely on the same spatial variables
such that both languages employ a ‘facing,’ rather than an ‘aligned’ perspective like in
Hausa (C. Hill 1975, 1982; Levinson 1996a)—super/subscript ‘R’ refers to the ‘right side’of Rl, Tom:
(3)
English/Japanese
Hausa

V
Rl
( ● R →← R ● )( ● R ――→● R → )‘facing’‘aligned’Thus, in English and Japanese, ‘the ball’ in Figure 4 is described as “The ball is to the leftof Tom,” meaning ‘on Tom’s left’ based not on the viewer’s ‘primary’ coordinate but on
Tom’s rotated, ‘secondary’ coordinate. Whereas in Hausa, ‘the ball’ will (dominantly) be
referred to as ‘to the right of Tom’ based on V’s coordinate.
A more variable use of coordinates ensues when the Rl is a ‘tree,’ which has no
intrinsic orientations.

We now know that English/Japanese, Hausa, and Tamil show

variable possibilities for ‘translation,’ ‘rotation,’ and ‘reflection’ as diagrammed in Table 3(see Levinson 1996a: 370–371; 1996b: 143; Fillmore 1971). The dots represent ‘V’ and‘Rl’, respectively, and the capital letters indicate the positions of Rf and how it will bereferred to (i.e., F(ront), B(ack), R(ight) or L(eft)) when given a matrix sentence “The ballis (in/to the) of the tree.”Table 3. Possibilities of ‘translation,’ ‘rotation,’ and ‘reflection’ onto the secondary
coordinate (tree)
English/Japanese
Hausa
Tamil
(reflection)(translation)(rotation)(V →・

Rl: tree)
L
F ・ B
R

Reflection(V → Rl: tree)
L
B ・ F
・
R

Translation― 134 ―

(V → Rl: tree)
R
F ・ B
・
L

RotationLinguistic Anthropological Research on Spatial Cognition

More confusing is the fact that the possibilities for these operations not only showinter-linguistic but also intra-linguistic variability according to the type and function of thereference object.6 In English/Japanese, for example, what ‘the right’ refers to varies for‘person,’ ‘car,’ ‘desk,’ and ‘tree.’ As we have just seen, the right/left succumbs toprojection for ‘person’ based on his/her secondary coordinate, rather than on V’s primary
coordinate.
For a ‘car,’ which has the intrinsic front/back regions, the judgment of ‘the right’ isambiguous because it may mean ‘the car’s right’ or ‘in the region to the right from the car,where “the right” is found in the viewer’s front view in relation to the car.’ For a ‘desk,’
the situation is similar to the car, but not necessarily the same. Because ‘desk’ has afunctionally defined ‘front’ and ‘right’, even if the speaker does not face the desk, ‘to theright of the desk’ will be more likely to mean ‘the desk’s (intrinsic) right’ rather than ‘to theright from the desk seen from the viewer.’
Finally, for a ‘tree,’ ‘the right’ will always refer to the region defined in relation to theviewer because ‘tree’ does not usually induce rotation in English/Japanese. However, it
may be possible that an object like a tree may be metaphorically identified as a human-likeobject and project the secondary coordinate as for ‘person,’ as seen in Tamil. Thispossibility is highly language-specific.
Tamil speakers also show complex, dialect-dependent variability (Pederson 1993,
1995). The assignment of left/right orientations varies according to the regionally dominantmode of the FoR rotation. Pederson observed that urban Tamil speakers mainly use therelative FoR for everyday spatial expressions, but rural Tamils, in contrast, tend to rely on
the absolute FoR, drawing on the habitual use of spatial reference. This result indicates thatpeople in the rural area tend to suppress the use of ‘right’ and ‘left,’ depending instead on
the absolute directions, whereas other Tamils may use ‘right’ and ‘left’ depending on thebody-coordinates.

Furthermore, preference for particular FoRs may also be cross-linguistically variable even among European languages. For example, Carroll (1993) foundthat English speakers tend to take an ‘objective (or object-centered)’ perspective indescribing physical objects, in contrast to German speakers who are likely to adopt a‘subjective (or viewer-centered)’ perspective for the same task.
There is tremendous variability in terminological transfer even for the verticaldimension terms, which are ordinarily thought to be most resistant to such variation. Oneof the “ego-centric” languages, English, can even fall to such transfer to some extent― 135 ―

愛知大学 言語 と 文化 No. 6(Figure 5). Shepard & Hurwitz (1984) argue for the vertical origin of such horizontally
applied expressions as “Look who’s coming down the street,” meaning “coming closer tothe speaker along the street”—an exception is a metaphorical case like “She walked right up
to me,” where up implies the direction toward a salient and/or important object or place.
They basically maintain that what up can mean in spatial cognition may be conceptually
regulated, constituting roughly a four-stage continuum, ranging from the ‘most
gravitationally conferred upright’ direction (canonical ‘up’) to the ‘most horizontal’
extension of the meaning (‘come down the street’).7

Figure 5. Shepard & Hurwitz’s ‘Vertical Origin of Horizontal Projection’Note: “A schematic illustration that a point B that is further ahead of another point A
on the horizontal ground is also ‘higher’ than that point A from the perspective of thecanonically above-the-ground viewer. Also illustrated is the related fact that a rightturn (toward a point C) projects to the right from the ‘top’ of the line leading into thatturn within the viewer’s egocentric frame of reference (Shepard & Hurwitz 1984:167).”

Although I have so far treated spatial terminology as if it has its own semantic concept,
it often cannot be separated from the orientation and function of the human (and animal)
body. Heine (1997: Ch. 3) proposes that five reference points of deictic orientation
generally come from a limited number of source domains: ‘up’, ‘down’, ‘front’, ‘back’, and‘in’. (He further expounds the chain of grammaticalization of spatial terms from the bodyto space in terms of the following sequence: ‘human body→ back of thing→ rear of thing→― 136 ―

Linguistic Anthropological Research on Spatial Cognition

space behind thing’ (and vice versa).)
According to Heine, there are three major domains as the source models for spatial
orientation: body-part terms (e.g., ‘head’ for ‘up’ and ‘buttocks’ for ‘down’), landmarks(e.g., ‘sky’ for ‘up’ and ‘earth’ for ‘down’), and dynamic concepts (e.g., ‘go’ for ‘front’).
Among these, body-part terms are the major source domain for spatial orientation, which
can also be subdivided into anthropocentric and zoomorphic models (Figure 6). Although
there is some regional variation concerning the preference between the two models, thedominant patterns of the spatial projection of the body-part terms he found are as follows:(a) The zoomorphic model(b) The anthropocentric model

Figure 6. Two major models for projection of body-part terms (Heine 1997: 41, 46)

Based on these models, Heine (1997: 46) states that the “human body in its uprightpositions is not perceived as being absolutely vertical but rather as leaning forward—that is,
the way it is situated when one is running or walking, rather than when one is standing.”
These claims indicate that a human-based, egocentric vertical model is not necessarily auniversal principle for linguistic descriptions, and needs to be mediated with the cultural
basis of grammaticalized spatial cognition. Now, a recurrent question is whether or not
such a linguistically mediated spatial grounding can in return influence spatial cognition
itself—an ever-lasting Humboldtian legacy in the study of language and thought.

3.3 Cognitive Variability Based on Habitualized Language UseGiven the contextual and cultural variability of the frames of reference shown above,
dominance of a relative FoR and gravity are highly contestable. Concerning egocentricity,
recent findings from cognitive anthropology point out its subsequent bias toward― 137 ―

愛知大学 言語 と 文化 No. 6

ethnocentric universalism. Levinson & Brown (1994) showed that Tenejapans exhibit aremarkable indifference to the right and the left, or ‘incongruous counterparts’, which is thesource of Kantian claim for the egocentric basis of spatial perception and his argument
against Leibnizian notion that space is merely a network of relations among material
objects.8
Brown & Levinson (1993) also suggest that language may constrain the cognitive
categories, but not vice versa. In Tzeltal, there seems to be a tendency to avoid a relative,
egocentric FoR, and to describe objects according to their dispositions in space. These
dispositions are largely specified in terms of the ‘shape’ and ‘orientation’ of the referent,
rather than through the projection of point of view onto other relativized ‘origos.’ Thus,
they serve an intrinsic motivation for engendering spatial terms. For example, Tzeltal has
numerous nouns which originated from human body-part terms. The term ‘head’ of ahuman is projected through analogy onto a relatively pointed part of a ‘pear’ in terms of anaxial orientation. Likewise, the cusp of pointy shapes is termed a ‘nose,’ and a hollow
opening on the top part of an object, a ‘mouth’ (Levinson 1994). Therefore, Tzeltal
speakers need to pay utmost attention to the shape information in situ in order to correctly
name things, rather than to ‘what and where’ (cf. Landau & Jackendoff 1993).
A more drastic finding about cognitive differences between speakers ofabsolute-FoR-oriented language and Relative-FoR-oriented language was given by Levinsonand his colleagues (Pederson et al. 1998). In one of their numerous experiments, theyfound a persistent cognitive influence of spatial language in non-verbal tasks. In what theycall ‘Recall Memory Task (Animals-in-a-Row Task),’ they first aligned on a table threekinds of small figures of domesticated animals in a particular order (e.g., pig-sheep-cow,from the subject’s left to right), and asked, without using directional terms, the subjects toremember the scene. After this, they had the subjects turn around 180 degrees to anothertable, on which the two rows of animals were displayed: 1) pig-sheep-cow, or 2)
cow-sheep-pig. They then asked the subjects to choose from the two options what they
thought was the same one they saw before. Since they were turned around 180 degrees
now, if a subject chose the first option (pig-sheep-cow, his/her left to right), it meant that
his/her perspective was based on the relative FoR. On the other hand, if s/he chose thesecond option, the absolute FoR. The result was amazingly clear. Tenajapans (absolute
population) dominantly chose the second, and the Dutch counter group showed the opposite
tendency, as shown in Figure 7.

― 138 ―

Linguistic Anthropological Research on Spatial Cognition

Estimated absolute tendency (%)
Relative
Absolute

Figure 7. Recall Memory Task (Levinson 1996b)

They repeatedly found the same tendency in various experiments such as ‘Recognition
memory tasks,’ ‘Motion-to-path transformation & recognition tasks,’ ‘Transitive inferencetasks,’ etc.

They thus claim that, since the Tenejapan subjects were not given the

instructions in any directional terms, the habitualized linguistic practice in organizing their
spatial world in absolute terms has influenced their cognitive performance in thesenon-verbal tasks designed to test perception, memory, and inference—a clear Whorfian
effect.
In other words, a speaker of a certain language must remember the spatial relations in
the whole array depending on what FoR is predominantly used in his/her language. Just as
Guugu Yimithirr and Hai||om speakers remember things in absolute terms, so do English
and Japanese speakers in relative terms. That is, speakers with different FoRs as theirpredominant coordinates will think differently about spatial scenes and relations. Thisphenomenon consequently requires the ‘absolute-FoR’ speakers to be always aware of their
spatial orientations. Amazingly, the absolute populations such as Guugu Yimithirr and
Hai||om were shown to exhibit extremely accurate ‘dead-reckoning’ skills comparable tohoming pigeons (!), in contrast to Dutch and British English speakers who showed very
weak sensitivity to absolute directions. (Levinson 1996c; see also Widlok 1996)
Although there are no experimental data available for the following, similar absolutesystems are reported to exist in Saulteaux (Hallowell 1955), Truk (Goodenough 1966),
Central Australian Aboriginals (Lewis 1976a, 1976b), and many others. Haugen’s (1957)― 139 ―

愛知大学 言語 と 文化 No. 6

seminal work on Icelandic identifies two types of orientation, complementarily distributed:‘proximate’ (corresponding well with the absolute directions) and ‘ultimate’ (directions
along a line of travel, based on the four quarters of Icelandic geography), and a similareffect is reported for Belhare in Nepal (Bickel 1997). Given this, ego-centricity in spatial
cognition seems only to be a cultural construct of some ‘dominant’ cultures rather than theuniversal principle for spatial perception and representation.

3.4 Innate and Universal?
In neuro-physiology, the biological basis of perception of absolute directions has also
attracted the interest of researchers. Traditionally, images stored in the relative, egocentric
space based on gravity are held to ‘generate’ the absolute, allocentric system, but not viceversa. The counter evidence was soon presented. Tolman (1948) and his colleagues
conducted a series of experiments, in which they familiarized rats with a maze, thenblocked one or more of the paths.

In spite of the contemporary response learningperspective (i.e., the rats would choose a short but incorrect path), they chose a longer path
which correctly led them to the expected goal. This fact suggests that the rats are placelearners, rather than response learners, internalizing the whole schema of the maze. Thisidea has been widely surveyed and most clearly articulated by O’Keefe and Nadel (1978):
Most authors attempt to derive all psychological notions of space from an organism’s
interaction with objects and their relations. The notion of an absolute spatial framework, if
it exists at all, is held by these authors to derive from prior concepts of relative space, built
up in the course of an organism’s interaction with objects or with sensations correlated with
objects.
In contrast to this view, we think that the concept of absolute space is primary and that its
elaboration does not depend upon prior notions of relative space. . . [there] are spaces
centred on the eye, the head, and the body, all of which can be subsumed under the headingof egocentric space. In addition, there exists at least one neural system which provides thebasis for an integrated model of the environment. This system underlies the notion ofabsolute, unitary space, which is a non-centred stationary framework through which theorganism and its egocentric spaces move. (O’Keefe & Nadel 1978: 1–2, cited in Campbell
1993: 76).

O’Keefe & Nadel developed the theory that the organization of the brain may hold aplace for processing spatial information. They assume that it is the hippocampus, which
provides us with an a-priori basis for the Euclidean framework for our conception of the― 140 ―

Linguistic Anthropological Research on Spatial Cognition

outer world. In a sense, this notion is closely analogous to (early) Kantian a-priority ofspace concept (see also O’Keefe 1993). As shown above, Levinson (and his colleagues)(1996c) found that Guugu Yimithirr speakers can make extremely accurate judgments
about allocentric orientations (even after being blindfolded and turned around), in contrast
to the poor performance of the Dutch speakers in the same task. This implies the existenceof biological potentials for the perception of cardinal directions.
However, Levinson & Brown (1994) explicitly oppose the early Kantian view of‘right-left’ asymmetry, which is based on the premise that Newtonian ‘absolute’ space isfundamental for the recognition of the difference, and it exists independent of, and prior to,objects and their sensations. (Note that Newtonian ‘absolute’ space is an entity in its own
right, like a physical space, hence a different notion than Levinson’s ‘absolute’ relation.) In
other words, Levinson accepts human potentials for perceiving ‘absolute’ (not Newtonian)spatial orientations, but declines the possibility of physical universality of space derived
from the anthropocentric dimensions such as right/left.
Finally, one of the most powerful denominators for spatial cognition is assumed to be
the distinction between ‘what’ and ‘where’ systems (Landau & Jackendoff 1993, Landau
1994). Landau & Jackendoff (1993) claim that vocabulary filters out particular information
suitable for a particular language but any language typically draws on spatial representationsof object (what) and place (where), which remind us of a ‘Figure-Ground’ distinction.
However, other researchers have suggested that there exist languages whose ‘where’ system
incorporates more ‘shape’ information than has been proposed by Landau & Jackendoff(1993). As shown above, in Tzeltal, one strictly draws on ‘shape’ via a precise geometricalgorithm for describing locations of objects and mapping body-part terms onto parts of
inanimate objects, rather than through metaphor or the ‘what/where’ system (P. Brown
1991, Levinson 1994).
Also, Choi & Bowerman (1991) and Bowerman (1996) maintain that English andKorean children have specific ways of encoding spatial and movement information from theearliest stages of child language development, rather than constructing the same semantic
mapping in terms of the distribution and sequence for encoding object and place. For
example, Korean children are shown to share with English children the tendency to‘under-differentiate’ referent events—they differentiate less among actions of ‘separation’than among actions of ‘joining’—the semantic structure of the input language constrains its
semantic distinctions of corresponding verbs. Thus, it suggests that object (what) and place― 141 ―

愛知大学 言語 と 文化 No. 6(where) are much more differentially encoded in lexicon in different languages than havebeen assumed.
Recent collaborative work by Levinson’s and Bowerman’s groups has shown
illuminating results in linguistic coding of space (Levinson 2001 class notes; Bowerman &Levinson 2000). Based on comparative semantic studies of adpositions and positional verbs
in various Western (e.g., English, Dutch) and non-Western languages (Korean, Arrernte,
Kilivila, Marquesan, Likpe, Rossel, Inuktitut, etc.), they have started to find vast variability
in encoding spatial semantic notions into these elements. At the same time, highly
systematic, but limited generalizations (or universals, if they can be maintained at all) began
to emerge.
According to their studies, such universals are focused not on the ubiquity of thewhat/where system, but on 1) constraints on the semantic space, 2) attractors in space, and
3) order in which attractors fractionate out.

In other words, adpositional maps andpositional verb distinctions, when compared across languages, respect the sameorganization of space, and do not allow widely different distributions of spatial elements.
They are just differentially preferred and bundled up to be realized as adpositions andpositional verbs for particular spatial configurations.

In this sense, languages areconstrained in terms of their possible ways of cutting up space. Besides, although the mostwidely observed concepts, IN and ON, are not adpositional universals—e.g., Tzeltal
preposition fails to distinguish them—languages have certain spatial ‘attractors’ that tend to
be coded first before other adpositions or positional verbs are derived, in such a way thatcolor terminology evolves on an implicational hierarchy.
Given these findings, linguistic universalism based on innateness, or more precisely,
formal linguistic universals modeled on the limited introspective data and the negligence ofthe different mappings of semantic properties, do not seem to hold for many of the
non-Western languages.

4.

Concluding Remarks
The research findings above show that general notions of space, which have been

conceptualized as stable in both perspective-taking and cognitive categories, need to begiven more culturally and linguistically flexible accounts, and that universals (orconstraints) seem to emerge from those vastly variable ways of representing space through― 142 ―

Linguistic Anthropological Research on Spatial Cognition

language, which may in turn influence cognitive performance of humans. All these suggest
other possibilities of local logic of space than those of the Western one for putting space
into actual use in various linguistic contexts. The most important clue to such local logic
lies in the habitualized referential practice most compatible with the indigenous spatial
world. Such an approach provides us with an immense possibility in expanding ourunderstanding about how the spatial world around us is constructed, and how it can
influence our thought and behavior.
Finally, as an addendum, there are currently various linguistic anthropologicalapproaches that aim to explicate the covert relationship between language and space. Suchstudies include, for example, the socio-centric referential practice in Yucatec Maya (Hanks
1990, 1992), the action-centered representation of space in Plains Sign Talk (Farnell 1995),
a narrative/discourse analysis of spatial experience (Payne 1984, Mondada 1996, Kataoka
2000, 2001), conversation analysis of negotiated spatial arrangement (Goodwin 1995;
Nishizaka 2001), mental spaces (Fauconnier 1994; Rubba 1996), and gesture and spatial
mapping (McNeill 1992, 2000; Kita 1993; Haviland 1993, 1996, 2000; Armstrong, Stokoe,& Wilcox 1995; Emmorey & Reilly 1995), to name only a few.
As most efficiently represented in Haviland’s studies (1993, 1996, 2000), there is an
emergent need for, and a heuristic value in, discourse-oriented approaches that investigate
cognitive consequences of particular FoRs used in everyday language. Culturally inscribedspatial knowledge not only affects our cognitive performance but also predominantly guides
our linguistic and non-linguistic coordination of the body and the verbal performance. We
have recently seen more of such analyses coming onto the center stage of discourse analysis
and psychological experiments of space conducted in new contexts using non-Western
informants. Also, a growing number of researchers have come to recognize that spatial
knowledge and imagery are heavily utilized in speech, serving as guiding principles for
spatial orientations, arrangements, and calculations.
Orientations and objectives of these studies vary, but I firmly believe that theseapproaches have a tremendous potential in revealing the mysteries of the indigenous
knowledge of people (whether it is space, color terminology, kinship terms, or nounclassification), and for that purpose, collaboration and exchange of ideas, methods, andfindings from relevant fields will eventually provide us with a better understanding andmore acceptable theories of the mind.

― 143 ―

愛知大学 言語 と 文化 No. 6* Acknowledgement: This review article and some of my studies cited here are supported by
Grant-in-Aid for Scientific Research (C) (2), (No. 12610566). I also thank Mr. Michael Depoefor his careful reading of the final manuscript.
1

2

3

4

5

William Molyneux was a Dublin lawyer, and a friend and correspondence of John Locke.
Locke mentions his question in his Essay, and the question is “whether a blind man, on
recovering the use of his sight and being presented with a cube and a globe before his eyes,
would be able to name them correctly. In other words, would the experience he had gained bytouching these objects enable him to name them correctly when they were placed before his
eyes? (Morgan 1977: 6).” Molyneux’s answer was ‘No,’ to which Locke also agreed: they
upheld a notion, ‘No innate Principles in the Mind.’ On the other hand, Eilan (1993) and
Levinson (1996b: 157) answered ‘Yes,’ suggesting that other (cognitive) modalities have thecapacity to adopt or adapt to other frames of reference, enabling cross-modal (or ‘amodal,’rather than modality-specific) mappings.
It seems that the non-coordinate system in Levinson’s spatial array is roughly equivalent to
the first and second stages of Piaget’s developmental sequence of children’s spatialconception, and his coordinate system, to the third, Euclidean space (Piaget 1956: summarizedin Pinxten 1976).
Three Developmental stages of space are:1. from birth until two years (0–2): sensorimotor or perceptual space, with ‘topological’segmentation; no representation, no symbolization
2. from two until seven/eight years (2–7/8): ‘topological’ space concept; representation andsymbolization of the ‘topological’ notions gradually develop
3. from seven/eight until twelve/thirteen (7/8–12/13): systematic and parallel elaboration ofthe ‘projective’ and ‘Euclidean’ system; even here, the basic notions of ‘projective’ space
are genetically slightly primary to those of ‘Euclidean’ space.
(See Appendix A for detailed explanations of ‘topological,’ ‘projective,’ and ‘Euclidean’spaces.)Levinson’s notion of ‘absolute’ space is distinct from Newtonian absolute space, the concept
which is more widely acknowledged. Newton’s concept is abstractly based on theastronomical location of the universal center of gravity as the reference point. Apparently, theabsolute directions based on this universal center constitute vertical orientations and may or
may not coincide with the ‘absolute’ directions defined by the Earth’s geomagnetic
orientations (compass directions) or indigenously established absolute directions on thehorizontal plane (see Jammer 1993: Ch 4).
Levelt, in one of his classic studies on spatial descriptions (Levelt 1982), defined intrinsic interms of this merging of the speaker’s perspective with that of the moving entity’s in a given
experimental environment. Instead, he preserved the use of relative only for the speaker’s
objective perspective, which covers the whole schema of motion events. In other words, it is adistinction between an object-centered or a viewer-centered perspective. Levinson (2001 classnotes) recently proposed a more refined, four-way criterion for distinguishing the perspective
taken, 1) ground (deictic or non-deictic), 2) origo based on ground or viewpoint, 3)
coordinate system, and 4) the type of coordinate system.
Kant’s theory of space evolved chronologically from ‘space as absolute’ through ‘space as― 144 ―

Linguistic Anthropological Research on Spatial Cognition

intuitive’ to ‘space as mind-dependent’ (Van Cleve & Frederick 1991: viii). Our discussion
utilizes Kant’s first treatment of the topic.
6 An interesting example is seen in Noda (1987), who reports a diachronic change of tate/yoko
perception among older and younger generations of the Japanese. Tate and yoko of a object isdefined along the sagittal line of the speaker and the perpendicularly traversal line to thesagittal line, respectively. Japanese basically allows two types of writing directions:traditionally, vertically from top to bottom and from right to left, and more contemporarily,
horizontally from left to right and top to bottom (like English). Thus, shown a tilted rectangle(like a letter pad), younger generations, who are more accustomed to the Western style ofwriting, tend to associate the longer sides of the rectangular with tate, while older generations,the shorter sides with it.
7 It should be noted that their distinction between ‘metaphorical’ and other rather cognitively
motivated extensions from the vertical and the horizontal is not always so clear. They
consider ‘the direction toward a significant reference object or location’ as the only case of a‘metaphorical’ one: e.g. “She walked right up to me.” However, what is generally
conceptualized as metaphorical extensions may not necessarily be metaphorical in every
culture (Levinson 1994).
8 Kant claims that space is endowed with a reality of its own. He observed that the intrinsic
relations that apply to the right hand is similar to those found for the left hand, and yet thatthe right hand cannot substitute for the left hand. If this difference cannot be explained as
being merely the appearance of different relations with respect to each other (and it can’t,
because we cannot put a right-handed glove on the left hand), we must postulate different
dispositions in terms of absolute space (see Van Cleve & Frederick 1991 for detailed
discussions).

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