Spatial Opposites
U. Savardi
Verona University, Italy
I. Bianchi
Macerata University, Italy
M. Kubovy
Virginia University, USA
Spatial Opposites
The study of opposites as a cognitive structure has been more or less exhausted
in contemporary psychology, within the study of pairs of antonyms (Croft &
Cruse, 2004; Cruse, 1986, 2000; Fellbaum, 1998; Jones, 2002; Lyons, 1977;
Muehleisen, 1997; Murphy, 2003; Willners, 2001).
Different classifications have been proposed:
-Gradable opposites (e.g. large/small), defined as qualities that can be
conceived of as 'more or less' (e.g. fairly large, very large); the scale or
dimension associated has a mid interval (e.g. if something is neither
large nor small, it is medium size);
-Complementary opposites (e.g. dead/alive) characterized by the fact
they divide a conceptual domain into two mutually exclusive
compartments, so that “what does not fall into one of the compartments
must necessarily fall into the other" (Cruse 1986, p. 198; see also
Palmer, 1976; Carter, 1987; Jackson, 1988). These are sometimes called
contradictory or simple binary opposites (Kempson, 1976);
- Reversive opposites (Lehrer & Lehrer, 1982, Egan, 1968): “adjectives
or adverbs which signify a quality or verbs or nouns which signify an act
or state that reverse or undo the quality, act, or state of the other”
(Egan 1968, 27a). E.g. tie/untie, enter/leave.
- Directional opposites (Lyons, 1977; Cruse, 1986): pairs such as in/out or
clockwise/anticlockwise, which are related to opposite directions on a common
axis.
- Relational (Cruse 1986; Palmer, 1976; Leech 1974) or relative (Egan 1968) or
conversive opposites (Lyons 1977): pairs which imply a relationship where one
of them cannot be used without suggesting the other, such as parent/child and
teacher/student.
Cruse (1986) also proposed defining two further classes of “near opposites”:
- "impure" opposites, i.e. opposites which include a more elementary opposition
within their meaning: “Giant:dwarf can be said to encapsulate the opposition
between large and small (but this opposition does not exhaust their meaning);
likewise, shout and whisper encapsulate loud and soft, criticize and praise
encapsulate good and bad..." (Cruse 1986, p. 198);
- pairs that are only weakly contrasted because of "the difficulty in establishing
what the relevant dimension or axis is" (Cruse 1986, p.262). E.g. work/play,
town/country.
• OBSERVATION 1: In these classifications, structural criteria (see the
distinction between gradable and complementary opposites) coexist with
semantic (e.g. reversive opposites, impure opposites) pragmatic (e.g.
weakly contrasted opposites) and even logical (e.g. relational opposites)
criteria.
• OBSERVATION 2: Despite the fact that very specialized taxonomies have
been developed, this high level of descriptive specialization leaves
researchers with too many questions when confronted with the everyday
use of opposites. And this seems to be the cause of the recent need to
look afresh at the cognitive structure of ‘opposites’, moving towards new
approaches in semantics (Muehleisen, 1997; Jones, 2002), linguistics
(Paradis & Willners, 2006) and even in brain sciences (Kelso & Engstrom,
2006).
Our goal:
We propose a new approach to the study of the “internal structure of
opposites” based on what Kubovy (2002) called phenomenological
psychophysics. (This could go beyond the simplistic distinction between
gradable and complementary opposites).
Our methods “are phenomenological: they rely on the reports of
observers about their phenomenal experiences. They are also
psychophysical: they involve systematic exploration of stimulus spaces
and quantitative representation of perceptual responses to variations in
stimulus parameters.” (Kubovy and Gepshtein, 2003, p. 45).
General Hypothesis:
the structure of opposites can be defined metrically and
topologically, based on direct estimates and descriptions of the
characteristics of three components: the two poles and the
intermediates.
Why using spatial opposites?
Since our intuition is that the analysis of the cognitive structure
of contraries that we propose is grounded in perception. Since
perception of space is recognized to be almost exclusively the
result of automatic processes, we considered space a suitable
domain to start with.
Study 1: A Metrical analysis
Goal: to determine how observers think we should partition an interval () into
two regions: one to which a property () applies and a complementary region to
which the opposite property () applies.
E.g.: it is likely that we think that the scope of large things is greater than the
scope of small things. Therefore, the interval between small and large (see
Figure) should be partitioned into two unequal intervals,  and ¯.
We do not mean that we encounter more large than small objects in an
everyday environment. Nor do we mean that we encounter more types of
large objects than small ones.
The question is rather how to put these objects or types of objects into a
finite number of bins ( -experience bins).
The problem is closely related to the statistical problem of determining how
to assign continuous data to bins in a histogram.
-experience bins
Consider two ants: one large, the other small. Since you can readily tell
that one is bigger than the other you would say that they differ in size.
If, however, you were asked whether there was a qualitative sizedifference between them, taking into account the range of all object
sizes, from the smallest thing you can see (say, a grain of sand) to the
biggest thing you can see (perhaps a tall and wide rock wall that
exceeds your visual field), you might choose to place them in the same
size-experience bin. On the other hand, you might decide that because
there is a qualitative size-difference between the size of ants and the
size of butterflies or nuts, they belong in different size-experience bins,
whereas you might assign butterflies and nuts to the same sizeexperience bin.
Once the concept of -experience bins is clear, it is not difficult to take
the next step which is to estimate the number of  -experience bins
referring to one property, to the opposite property, and to the
properties perceived as intermediates.
Method
•
Participants: 45 undergraduates (Industrial Design at the University of
Milan) randomly assigned to ten groups of four and one group of
five).
•
Procedure: Each group was given a sheet of 37 labelled scales. Each
scale consisted of two stacked bars. The distance between the endpoints (10 cm), represented the whole range of variations in between
the two poles. They were asked:
1. to draw a vertical boundary between opposites in the upper bar, in
order to express the proportion referring to one property (-bins) and
the proportion referring to the opposite property (¯-bins).
2. to draw in the lower bar two vertical boundaries, on either side of the
boundary drawn in the upper bar, to indicate the range of experiences that are neither  nor ¯.
Results:
From the responses we computed the data in Table 1.
We performed non-metric Multidimensional Scaling on the values of asym2, m, lln,
rrn, and asym3, and obtained an excellent two-dimensional solution (non-metric fit, R2
= 0.99)
Dimension 2 contrasts pairs with
lower values of asym2 (top) and pairs
with high values of asym2 (bottom).
•
Dimension 1 contrasts asymmetrical pairs with a very small fraction of
neither  nor ¯ (on the left) with less asymmetrical pairs having an extended
fraction of G covered by intermediates (on the right).
Study 2: A topological analysis
From the results from study 1 it is not possible to recognize further
differences between the pairs that may remain hidden behind the
proportional indexes used.
For example, dense–sparse and wide–narrow are close in study 1.
However, to be maximally dense (e.g., a set of dots; passengers on a
bus) means that when the elements are packed as densely as
possible, adding dots will not change the texture—we have reached a
saturation point (in topology this is called a closed interval). This is
not the case for wide: we can perceive a road as being very wide, but
there is no maximum width (in topology this is called an open
interval). A point, in topology, is treated as a degenerate interval.
This captures the structures of properties consisting of a single
experience-bin (like closed, or still).
Method
 Participants: 54 undergraduates (Industrial design at the University of Milan),
divided in 18 groups of 3.
 Procedure: The 37 spatial pairs were randomly presented in a table.
Participants were asked to make the following distinctions:
a) for the two poles, the distinction
between single experiences (point, P) and
ranges of experiences (intervals) and, in
the latter case, between closed intervals
(i.e. having a “final state”, showing the
property at the maximum possible
degree) and open intervals (i.e. where this
“final” state is not identifiable);
b) for the intermediates, the distinction
between the existence or non–existence of
properties which are “neither one pole nor
the other”. If these properties existed,
participants were then asked to
distinguish between single experiences (P)
and intervals (I).
Results
We performed a Correspondence Analysis on the frequency table of the 37 pairs x
24 series of triples. This produced a two-dimensional solution.
n
r
p
If we divide the map into four
quadrants, we note that:
- the n pairs fall in quadrant II
(upper left)
- the p pairs straddle the
boundary between quadrants I
and IV,
- the r pairs form a rough
diagonal line running from
quadrant I to III.
Joint Analysis
In order to describe the pairs both metrically and topologically, we took the four
pairs of coordinates obtained in Studies 1 (nmMDS) and 2 (CA), and submitted
them to nmMDS (fig. on the left) and hierarchical clustering (Fig. on the right).
Resulting
classification
CPC (: closed interval; neither  nor ¯: point; ¯: closed
interval).
PIP (: point; neither  nor ¯: interval; ¯: point)
ONP (: open interval; neither  nor ¯: none; ¯: point)
OIC (: open interval; neither  nor ¯: internal; ¯: closed
interval)
PIP
ONP
CPC
OIC
CPC
PIP
ONP
OIC
Conclusions
• The studies presented have shown that the proportional extension of
the two poles and the intermediates can be defined by participants
with high accuracy, and that accurate metrical classifications can be
identified.
• These metrical classifications are further enriched when considering
topological aspects regarding the nature of the three components
making up each pair.
• The combination of both metrical and topological aspects lead to a
new system of classification.
We consider that the approach which was applied to the case
of spatial opposites may be extended to the study of the
opposites in whatever domain.
We are aware that a systematic validation of these spatial
structures in different groups of languages is necessary. We
are however inclined to expect that these structures will be for
the most part generalized, if they describe, as we believe, the
result of perceptual and cognitive processes that are somehow
pre-linguistic.