Degree and Scalarity - Université Bordeaux Montaigne

1
Journée Agrégation Option C – « L’expression du degré » - Bordeaux 24/01/2014
Catherine MOREAU - Université Bordeaux Montaigne – (CLIMAS EA 4196)
Degree and Scalarity
Introduction
The notion of degree raises a problem of terminology, as the notion of “division into degrees”
is usually designed not only as gradation but also as scalarity. The same confusion occurs
concerning the terms gradable (in French: grad(u)able) and scalar.
Both notions seem to be intimately linked.
The term scalarity does not exist in the OED (Oxford English Dictionary) but you find scalar:
designed as “pertaining to a graduated scale » or « A set or series of graduations [used for
measuring distances, registering the height of a liquid, mercury, etc., or determining amounts
or quantities by inspection] ».
You find the term gradation, defined as « a scale or series of degrees » and the term gradable,
“capable of being classified by grade”.
Such definitions show that degrees are concerned with reference to a scale and with the
process of grading. This has been made obvious in the litterature since Sapir (1944) first
introduced the term scale in his study on the expression of gradation.
Quirk & al. state that degree adverbials are concerned with “the assessment of gradable
constituents in relation to an imaginary scale.”1 They can be amplifiers (I badly want a drink),
diminishers (she helped him a little) or express measure (More than, sufficiently).
In Quirk & Greenbaum degree terms are “thought of as having values on a scale” 2 and they
can be modified by adverbs which convey a degree of intensity.
It has been made clear in Quirk & al. that the term “intensifier” does not refer only to an
increase in intensification: “it indicates a point (relatively low or high) on an abstractly
conceived intensity scale”3 which they apply to gradable verbs. It is Bolinger’s position as he
uses the term intensifier “for any device that scales a quality, whether up or down or
somewhere between the two”.4
1
R. Quirk & al. (1985: 485).
2
R. Quirk & Greenbaum (1973: 160).
3
R. Quirk & al. (1985: 589).
4
D. Bolinger (1972: 17).
2
Kennedy refers to “the structure of the (ordered) set of degrees-the scale itself”5, which adds a
notion of hierarchy to scalarity. As a result of this idea of progressive series, a scale is
considered to be oriented.
There seems to be a strong link between gradability and scalarity (reference to a scale).
Therefore to understand the way degree is construed, a focus on grading and scaling is
required.
1. Grading and scaling
It is now a common assumption that for a predicate to be gradable, it needs to correspond to
some measurement scale.
1.1.
Grading.
Grading is the process of ordered measurement that applies on gradable terms. Rivara states :
“Est gradable une propriété que l’on peut posséder à divers degrés”. 6
Traditionally, gradability is thought to be a property of a select class of adjectives. This is
easy to see for a predicate like tall which is intimately linked to the measure of height.
In semantics, the term gradable has been associated to adjectives and also to determiners,
adjectives, nouns and some adverbial expressions. For adjectives, like for instance villain,
there seems to be no single measure available. Still, such adjectives are gradable:
He is an utter villain means: “he is very villainous”.
Consequently we may posit that gradability is a property that holds for any term that
can be measured in degrees.
The process of measurement may be carried out explicitely or implicitely.
1.1.1. Explicit grading.
Grading is explicit in adjectives which accept degree modification (very, extremely), and
inflectional or analytical comparatives and superlatives (-er, -est, more, the most).
In that case the degree can be questioned (How far is it?) or indicated by means of a degree
adverb (it’s very nice of you; it’s rather serious).
1.1.2. Implicit grading.
Grading is implicit when there are no specialized degree markers to predicate over degrees.
1.1.3. Explicit vs. implicit.
-
-
Rivara (1993), in his key-notion of semantic scale, introduces quantification. He
distinguishes numeral quantification (like this parcel weighs 6 pounds) and evaluative
quantification (like it is very heavy) predicating over degrees.
This distinction is in accordance with Sapir (1944)’s distinction between two
processes:
5
C. Kennedy & L. McNally (2005: 352)
6
R. Rivara (1993 : 40)
3
o the psychological process of quantification by implicit grading by using terms
which grade only by implication. They occupy positions on a scale of values of "more" and
"less": four is implicitly less than five in an ordered set; a foot is more than an inch.
This is said to be based on perceptions of what Sapir calls “envelopment”. He considers that
“This feeling is an illusion” mainly because “grading which is implicit in these terms is not
formally indicated”7.
o the process of explicit grading by implicit quantification 8which is carried out
by using terms which grade explicitly: more, less, very…
- Huddleston & Pullum refer to the same process of “grading by implication” 9when
they distinguish the “plain (/positive) grade” from the “term comparison” and the “set
comparison”. For instance, the plain grade in This book is interesting does not express
comparison on its own (it is not degree modified like this book is more / (the) most
interesting), yet it involves some comparison with the standards of the set to which the term
belongs (books). A possible gloss is: ‘this book is interesting [as far] as books go’.
1.1.4. Gradability and scalarity.
Kennedy (1997) 10 goes further when he states that there is NO systematic correspondence
between scalarity and gradation:
- he shows that some scalar adjectives are not gradable:
e.g.: universal is a scalar property as it refers to the upper part of the associated scale, but it is
not gradable as it cannot be degree modified (*very universal).
- in the same way he points out that gradable adjectives comparing for grades (less, as,
more/-er) are no longer gradable:
e.g.: heavy (G) comparing for grade (heavier) is no longer gradable because it can’t be degree
modified (*very more simple).
YET they do not lose their scalar property: although they do not refer to a precise
point on the scale, they still refer to an oriented scale.
It could be inferred from this that there is no need being gradable to refer to a scale,
although gradability seems to be more common than non-gradability in this respect.
1.2.
Scaling.
Gradable terms refer to a continuous scale along which they are located. This is obvious in
faster and faster, as it describes a continuous growth on the semantic scale of /speed/.
On this semantic scale, it can be referred to located terms or to scalar change11.
7
E. Sapir (1944 : 93).
8
Ibid. (1944 : 95).
9
R. Huddleston & G.K. Pullum (2002: 1161).
10
P. Hadermann (2007).
11
R. Huddleston & G.K. Pullum (2002)
4
1.2.1. Scalar location.
Simple location on a scale is expressed by:
- be with a NP as predicate complement (= un attribut):
the price is £10; the temperature is 10°)
- or a special verb (cost, weigh, measure) taking a measure complement:
it costs £10; it weighs over 12 kilos; the table measures 6 foot by 4.
1.2.2. Scalar change.
What is called ‘scalar change’ involves a change in value along some scale – increase or
decrease.
The extent of change is expressed:
- in the same way as spatial extent using NPs and PPs (he walked three miles, from the
pub to his door / it was extended by 5 acres).
- but it does not involve change in physical location:
Cigarette has gone up another 20 centimes; the temperature fell by 10°; the average mark
rose from 9 through the psychological barrier of 10 to a record level of 15
although the term (cigarette, temperature, average mark) moves along the scale.
There are various ways of expressing scalar change:
- through overall extent (another two dollars)
- or the source (from 9)
- or the goal (to a record level of 15)
- it may even include a path (through the psychological barrier of 10).
2.
Scale and gradient
2.1.
Typology of scale structures12
Kennedy13 has developed a typology of scale structures, which is a significant parameter
of variation in the meaning of gradable adjectives. The point is whether a scale is ‘open’
(it does not have maximal or minimal values or both, like long, expensive, old) or
‘closed’ (it has minimal and maximal values, like full, closed, invisible).
The difference between them is made by maximizers and modifier half.
-
a totally open scale has neither a minimal nor a maximal value like the scale of
/height/:
o Maximizers are incompatible with this scale:
Her brother is completely *tall/*short is a contradiction because maximizers entail
that the end of the scale has been reached and there are no endpoints to be reached.
The same goes for minimizers.
12
C. Kennedy & McNally (2005) and Paradis 2001.
13
C. Kennedy & McNally (2005: 352).
5
o Degree modifier half is incompatible as well :
*The rope is half/mostly long; *A 7-year-old cat is half/mostly old; *That car was
half/mostly expensive are contradictions because the midpoint of the scale has to be
calculated relative to a minimum and a maximum value.
-
a lower closed scale has a minimal but no maximal element.
Ø
As it is closed on the lower end (and open on the upper end), maximizers are
↑
incompatible with the “big” term (The room became totally *loud/quiet) and
the midpoint cannot be calculated.
-
an upper closed scale has a maximal but no minimal element.
_
As it is open on the lower end (and closed on the upper end), maximizers are
↑
incompatible with the “small”term:
Ø
We are fully certain/*uncertain about the results and the midpoint cannot be
calculated.
-
A totally closed scale has a maximal and a minimal element. Therefore it is
compatible with maximizers, minimizers and half:
The figure was completely/least/half visible/invisible.
This shows that the open/closed distinction of measurement scales is useful in
determining the class of degree expressions a predicate is compatible with.
2.2.
Scale or gradient?
From A. Culioli’s theoretical framework the concept of gradient may be useful as well, when
working on degrees when the notion at stake is gradable.
2.2.1. The concept of gradient
The Interior (I) of a notional domain 14 contains all the points (or occurrences) qualitatively
identifiable to it. For instance if /be heavy/ is the notional domain, all occurrences designed as
/being heavy/ to a certain extent is identifiable to the type, which represents the organizing
centre of the notion. The exterior (E) is its complement:
really heavy
/
really not heavy
x
(I)
/
(E)
o.c.
However when the notion is gradable, there are quantitative differences in the properties of
these occurrences (altered forms) and they enable the construction of:
o a Boundary (B), comprising the altered forms:
really heavy
(I)
X
o.c.
14
not really heavy
(B)
[
]
altered forms
really not heavy
(E)
A notional domain is constructed around an organizing center, represented by a prototypical occurrence.
6
o and also the construction of a gradient. Its anchoring point is the organizing
center (which may serve as attractor):
x
o.c.
It is the varying distance with the center (and with the Boundary) that creates differences of
degree. And what is important is the orientation towards the centre, or away from the centre:
really heavy
(I)
x
not really heavy
(B)
[
]
really not heavy
(E)
o.c.
not in the least
Culioli explains: “This means that when we construct the gradient, one direction is headed
toward a less and less strong (or a weaker and weaker) degree, up to a posited last, imaginary,
point: not in the least or again not at all”15.
‘Degree’ here is defined as the quantity of a quality. Thus if we say: “less and less heavy”,
insofar as the quality /be heavy/ or /heaviness/ is concerned, it means a smaller quantity of this
quality. And if we I say “something is heavier than something else”, there is a greater quantity
of it.
The property-class /interest/ falls easily within the scope of quantifying a property through a
set of degrees. We may say:
a certain amount of interest; more interest; very interesting; of little interest…
2.2.2. Two compatible concepts
The concept of gradient shares features with the concept of scale.
-
like a totally-open scale, the gradient has no minima and no maxima.
o The center as attractor is not an attainable last point: there is no maximal point.
It only represents the highest value of the property involved. It may be expressed
by a superlative form (the heaviest) referring to the high degree16 when moving
towards the center.
o In the same way there is no minima. Thus the use of a superlative form when
moving away from the center (the least heavy). Nevertheless we find the
representation of an imaginary last point in metaphoric expressions like:
he didn’t even lift a finger; not a leaf stirred; he did not say a word; he did not drink a drop;
there wasn’t a soul.
- it is oriented.
It moves towards or away from the center, as a scale looks upward or downward. Yet in both
cases it should be considered that the move is “one way-oriented” since progression always
goes ahead in the chosen direction17.
15
A. Culioli (1995: 60).
16
R. Mery (1999 : 35).
7
For instance in fast you go ahead on the scale of /speed/; in slow you do the same on the scale
of /slowness/.
As Culioli18 states, in the case of “typed antonyms” (fast/slow; long/short; big/small), the
Exterior of the domain is provided with a centre, from which is anchored a gradient:
x
o.c.
x
o.c
This is why in each case, whichever direction is chosen, progression goes ahead.
2.3.
Scalar orientation
2.3.1. inverse polarity: the case of antonyms and bipolar comparison.
o inverse order in antonymic pairs.
Antonymic adjectives oppose a positive term and a negative term (like high/low, big/small,
tall/short, full/empty, fast/slow, expensive/inexpensive, accurate/inaccurate, pure/impure…)
They order along the same dimension (height, bigness, size, fullness, speed, cost, accuracy,
purity…) but they express inverse ordering relations19. The orderings are the inverse of each
other.
e.g.: fast and slow both denote scales concerned with /speed/. So they order along the same
dimension (degrees of speed), but they have opposite orientations due to their meaning: in
fact, the faster something goes, the further it is from speed zero; and the slower it is, the closer
it is to that zero point.20
Kennedy (2005) provides the feature of (/parameter for) polarity in totally closed scales as
follows:
“if the positive member of an antonym pair has a maximal degree, then this corresponds to
the minimal degree for the negative adjective, and vice versa. This is most clearly
illustrated by a pair like full/empty: if a cup is maximally full, then it is minimally empty
(not empty at all); likewise, if it is maximally empty, then it is minimally full (not full at
all).” So the orderings are the inverse of each other.
o In the case of bipolar comparison, the structure is acceptable as long as the
17
R. Rivara (1995 : 29) “Les propriétés graduables, donc comparables, doivent être conçues comme des
échelles orientées « vers le haut » (vers le plus haut degré de la propriété). Les opérations possibles sur ces
échelles, marquées par les adverbes de degré, ne peuvent consister qu’à aller jusqu’à un certain niveau dans la
direction inhérente à l’échelle. »
18
A. Culioli (1995: 54).
19
C. Kennedy (1995: 54)
20
R. Huddleston & G.K. Pullum (2002: 1099).
8
polarities (negative/positive) are not opposed (This table is as long as it is wide). If the
polarities are opposed21, there is a contradiction.
For instance * A Volvo is safer than a Fiat is dangerous is not acceptable since one term
(safe) is positively oriented, the other (dangerous) negatively oriented, which is different in:
This table is as long as it is wide.
The space telescope is longer than it is wide.
The ficus is shorter than the doorway is low, so it should fit in the room.
We have shown that inverse polarity is inherent in antonymic adjectives whereas
polarity has to be similar in bipolar comparison. This entails that polarity (scalar
orientation) is a matter of lexical meaning.
2.3.2. Orientation inverter: the case of diminishers.
In an exclamatory context, and if such property is unexpected, This book is interesting! means
that the book is ‘really’ interesting.
In terms of scale, it reaches a high degree on the scale of /interest/ since it means that it is
more interesting than expected, which ranks it high.
In terms of gradient on a notional domain, the gradient is oriented towards the attracting
centre, towards the high degree.
If you use a diminisher like slightly in This book is (only) slightly interesting, it inverts the
orientation of the gradient, and it turns you away from the attracting centre by pointing
towards the Boundary.
When polarity is inverted, the meaning of the structure changes. It is, once again, a
question of lexical meaning.
3. The effect of negation
Negation has an effect on scales and gradients. It may involve:
3.1.
Change in grading
In the case of unidimensional antonymic adjectives (e.g. easy) and in verbal pairs
(behave/misbehave) the affixal negation (or lexicalization of negation) in -less; in-; -un; mis-;
over, raises the problem of its effect on the gradable term:
- In such adjectives as easy/uneasy lexically negated uneasy is gradable (like easy),
whereas in useful/useless lexically negated useless (opposed to gradable useful) is nongradable.
- In such verbal pairs as:
calculate (NG)/miscalculate(G), estimate(NG)/overestimate(G), behave(NG)/misbehave(G),
21
Cross-polar adjectives in C. Kennedy (1997).
9
the second term differs from the first in having a gradable sense that permits degree
modification:
*He utterly calculated her response is not acceptable whereas He utterly miscalculated her
response is.
*I completely estimated his strength is not acceptable whereas I completely overestimated his
strength is.
3.2.
Change in location and/or orientation
3.2.1. Affixal and clausal negations: un- / not unBoth clausal (not) and affixal (un-) negatives negate the property, but they do differently.
- When they affect a non-gradable property they are equivalent:
This book is unavailable (NG) means there is no availability = it’s not available.
They denote that a negative term is constructed by evacuating the positive occurrences 22.
- With a gradable property they differ 23:
This book is uninteresting (G) does not mean it has no interest (≠ it’s not interesting). It
means it has not much interest. The same goes with unattractive, uncomfortable, uncommon,
uncomplicated...
→ The affixal negative un- means that the upper bound on the scale of /beauty/, /comfort /,
/frequency/, /complexity/ is (very) low. The scale is negatively oriented, the item is located on
its lower part but it does not reach zero degree24 :
__ uninteresting/unattractive/uncommun
(-)
When referring to the notional domain, affix un- negates the type, entailing something like
« not very25 », something like “it is not very interesting” ; “she is not very attractive…”. The
gradient is oriented away from the centre and the element is located on the Boundary, close to
the Exterior zone, as it shares more altered properties than properties of the type:
(I)
o.c.
(B)
[
(E)
x]
not very interesting/attractive/common
22
A. Culioli (1995: 75).
23
Ibid. (1995: 74).
24
The « not zero » implicature in R. Huddleston & G.K. Pullum (2002: 816).
25
The NOT VERY type in D. Bolinger (1972: 116).
10
- when a negatively affixed adjective (such as uninteresting) is under the scope of a
clausal negation (+ not), the affixal and the clausal negatives are not equivalent:
This book is not uninteresting
This girl is not unattractive
Such mistakes are not common, but they are not uncommon either 26
It means that the book has some interest, not so much, but still, it doesn’t lack interest.
This double negative entails that the upper bound on the scale of /interest/, /attractiveness/ and
/frequency/ is not very high.
It ranks somewhere on the average part on the scale: it’s rather/fairly
interesting/attractive/common.
The scale is positively oriented. It looks upward:
(+)
- not uninteresting/unattractive/uncommun
The gradient, on its part, is directed away from the external Boundary since the negative (-un)
is negated (not):
(B)
[
x
(E)
]
If you add an intensifier such as very or so, then it ranks the value in a higher position:
It is not very/so uninteresting/unattractive/uncommon [after all].
3.2.2. Negative polarity items.
An expression other than a superlative, referring to one of the poles on the scale (a drop, a
wink) may acquire negative polarity when under negative scope:
He didn’t drink a drop / a cup / a pint / at all
A drop denotes a minimal quantity as it is located on the negative pole (/minus (-) end) of the
scale representing the quantity of /drink/. The scale is positively oriented. Under the scope of
negation, a drop + neg. denotes the absence of a minimal quantity, therefore it means ‘no
quantity at all’, it indicates a zero degree.
As polarity is negative, we may consider that the orientation is inverted towards the negative
pole:
↑
X
A drop
26
↓
Ø
not a drop
R. Huddleston & G.K. Pullum (2002: 821).
11
This may be applied to the notional domain of /drink something/ in the way that drop, cup,
pint metaphorically represent the final imaginary point on the gradient (= “the least quantity
possible”). If that minimal degree is denied, then the Interior itself is denied. Therefore we
construct the complement, which is the Exterior of the domain. This leads to assert
negatively: he didn’t drink [anything] at all, in which any is the trace of an operation
scanning the possible occurrences (thing) within the entirety of the Interior (at all).
The movement goes from the extreme right part of the Boundary onto the Exterior zone:
drop
(I)
X
o.c.
(B)
[
really nothing at all
(E)
]
3.2.3. Entailing inferiority : comparison of equality.
When comparison of equality is the focus of negation, the negative entails inferiority:
e.g.: this chair is as heavy as the table / Kate is as cute as Jane
(a) it means that the chair is “at least” equal (not “exactly equal”), it may be even heavier and
Kate is at least as cute as Jane. It excludes only the relation of inferiority: it gives a lower
bound. ↑
(b) The negative in this chair isn’t as heavy as the table / Kate isn’t as cute as Jane denies
this exclusion. This is why it entails inferiority, meaning that this chair is less heavy than the
table and that Kate is less cute than Jane. It gives an upper bound.
(c) It may be considered that the orientation of the scale of /heaviness/ or /cuteness/ is
inverted as it implicates that the chair is lighter and Kate rather unattractive. The term moves
downwards along the negatively-oriented scale.
(+)
(+)
CHAIR
TABLE/CHAIR_________//////// upper bound__//////____
Lower bound//////
CHAIR
(-)
as heavy as
not as heavy as
(a)
(b)
(c)
In terms of notional domain the elements chair and table in the positive comparison of
equality (a) are at the same distance from the centre in the Interior. The same goes for Kate
12
and Jane. In the negative comparison of equality (b) and (c) chair and Kate are more distant
elements from their respective centre.
3.2.4. Lower degree than expected/necessary.
In several cases, negation indicates that the degree is lower than expected by the adjunct:
- The endpoint on the scale cannot be reached when the maximizer is negated:
I haven’t completely finished; I don’t fully understand you; I don’t quite27 understand you.
The negatives not completely; not fully; not quite indicate “less than fully”, and implicate that
the degree, although still high (“almost”, “not the case, but not far from it”), is lower than
expected. It refers to the Boundary, or the average part of the scale.
- The referring degree cannot be reached when the relative adjunct enough is negated:
In He hadn’t slept [enough to be fit in the morning], the negative indicates that the degree
(enough) necessary to validate the second term (the predication in the embedded clause in the
infinitive form) is not reached. It is lower than required. Here it entails that he was not fit in
the morning.
- The referring degree is not overpassed when relative adjunct too is negated:
He hadn’t worked [too late to be overtired in the morning] means that the validation of the
second term is not blocked. Here it entails that he was not overtired in the morning.
3.2.5. Upper degree than what the adjunct expresses.
When diminishers are the focus of negation, the effect is to push the scaling towards the top:
They didn’t praise him slightly implicates that they praised him a lot.
He didn’t just shout, he yelled implicates that the level of sound he emitted was higher than
what is meant by just.
3.2.6. Constructing high degree.
In an exclamatory context, negating the expression of possibility creates high degree:
He’s so stupid, it’s unbelievable!28
He’s so rich, it’s not just possible!
because it constructs a degree that is unattainable, i.e. too high to be reached or conceived.
A possible gloss is: “it’s impossible to conceive”.
This expression is relevant because the totally open scales of /stupidity/ and /richness/ have no
representation of their positive poles (no maxima, no minima). Therefore it is impossible to
reach a final degree.
27
R. Huddleston & G.K. Pullum (2002: 724) ‘’Note that quite has the maximal interpretation in negation, not the
moderate one (I don’t quite (maximal) follow you)”.
28
A. Culioli (1995: 83).
13
In terms of gradient, it points towards the attractor which is “the representation of the
imaginary absolute value of the property” 29.
Concluding remark
As a concluding remark in this study we may assess that gradability corresponds to some
semantic measurement, which is made available with semantic scales and the gradient in the
notional domain. Thus both scale structure and gradient are useful measuring tools for grades.
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29
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