Extremely costly intensifiers are stronger than quite costly ones
Erin Bennett (erindb@stanford.edu), Noah D. Goodman (ngoodman@stanford.edu)
Department of Psychology, Stanford University.
Abstract
We show how the wide range in strengths of intensifying degree adverbs (e.g. very and extremely) could be explained bypragmatic inference based on differing cost, rather than differing semantics. This predicts a linear relationship between themeaning of intensifiers and their length and log-frequency. We
test this prediction in two studies, using two different dependent measures, finding that higher cost does predict stronger
meanings. We discuss the implications for adverbial meaning
and the more general question of how extensive non-arbitrary
form-meaning association may be in language.
Keywords: intensifiers; degree adverbs; scalar adjectives;pragmatics; m-implicature

Introduction
How do different words get their meanings? For instance,
why is an “extremely good paper” better than a “quite good
paper”? The traditional answer (de Saussure, 1916) is thatdifferent meanings have been arbitrarily and conventionallyassigned to the different word forms. This view has beenchallenged by a number of examples in which word meaning appears to be non-arbitrarily related to properties of theword. In some cases, the phonetic form of a word is systematically related to its meaning, for example rounded vowels and voiced consonants tend to refer to round objects(Köhler, 1947; Ramachandran & Hubbard, 2001; Holland &Wertheimer, 1964; Davis, 1961). In other cases, orthographic
form is diagnostic of meaning, for example, speakers of Hebrew who have never seen Chinese characters are nonethelessabove chance at matching them to their corresponding Hebrew words (Koriat & Levy, 1979). Similarly, the length ofwords predicts aspects of their meanings: across languages
longer words refer to more complex meanings (Lewis, Sugarman, & Frank, 2014). In this paper, we explore adjectival
intensifiers1 , like extremely and quite, as a case study in whichto empirically explore the relationship of meaning to factors
like word form and distribution of usage. Intensifiers forma good case study both because they are amenable to simple
quantitative measures of meaning (such as the numeric extent
to which they shift the interpretation of a scalar adjective) and1 Intensifiers are adverbs that modify scalar adjectives to increase
the degree. The word “intensifier” is often used to denote thefull range of degree adverbs, be they “amplifiers”, or “downtoners” (Quirk, Greenbaum, Leech, & Svartvik, 1985). The “intensifiers” we are looking at in this paper are, according to this typology, “amplifiers” because they increase (rather than decrease) the
threshold associated with a gradable predicate. This typology also
distinguishes between two different kinds of amplifiers: those that
increase an adjective maximally (e.g. completely and utterly) andthose that merely increase (e.g. greatly and terribly). We do notmake this distinction. The word “intensifier” is sometimes used
for a completely different linguistic phenomenon, where a reflexive
is used for emphasis, e.g. “The king himself gave the command,”
which we do not analyze in this paper.

because theoretical considerations, which we lay out shortly,
suggest a relationship between their meaning and their usage
cost (e.g., due to frequency and length).
In the next section we start from the model presented
by Lassiter and Goodman (2013) to explain the meaning of
scalar adjectives, like tall and expensive. This probabilistic
Rational Speech Acts (Frank & Goodman, 2012; Goodman& Stuhlmüller, 2013) model describes how a threshold on
meaning (e.g. the minimum price that counts as an expensive watch) can be established by pragmatic inference thattakes into account statistical background knowledge (such as
the distribution of prices for watches). We explore the effect of having multiple versions of the adjective that have thesame meaning but different costs, and find a M(arkedness)implicature (Levinson, 2000): more marked (costly to utter)versions will be interpreted as implicating higher values. This
motivates the hypothesis that a major portion of the meaning of intensifiers comes from this process rather than fromconventionally associated meanings. Concretely, this predicts
that the meanings of intensifiers are influenced by their form(in length) and their distribution (frequency) of usage. The
impact of word length is reminiscent of the results of Lewis
et al. (2014), who studied noun categories. While word frequency is known to have major effects on sentence processing(Levy, 2008, e.g.), the prediction that frequency should affectmeaning is more novel.
We confirm, in two experiments, that English intensifiers inadjective phrases are indeed interpreted as much higher degrees (e.g. in the case of expensive, higher prices) for bothlonger and less frequent intensifiers. This holds in quantitative judgments of meaning and in forced comparisons, andacross a number of adjectival dimensions. We conclude witha discussion of different interpretations of these phenomena
and future directions.

The semantics of intensifying degree adverbs
Our paper focuses on intensifying degree adverbs applied toscalar adjectives2 . Scalar adjectives have been described ashaving a threshold semantics (Kennedy, 2007), where, for example, expensive means “having a price greater than θ” andθ is a semantic variable inferred from context (e.g., $100).
Above the threshold degree θ, the adjective is true of an object, and below, the adjective is false. Lassiter and Goodman(2013) give a formal model of how this threshold might beinferred for a particular context, which we extend to intensifiers.
2 Some of these intensifiers can also apply to verbal and nominal

predicates, and different restrictions apply for different intensifiers,
e.g. I truly like carrots is an acceptable utterance, whereas I very likecarrots is not. See Bolinger (1972) for a discussion.

BackgroundPrevious researchers have proposed that adjective phrases
modified by intensifiers have the same semantics as unmodified adjective phrases, except with new, higher thresholds(Kennedy & McNally, 2005; Klein, 1980; Wheeler, 1972).
That is, some threshold, inferred from context, exists above
which objects are expensive and below which they are not,and the intensifier very determines a new, higher thresholdfor very expensive. They suggest that the intensified thresholds are determined by first collecting the set of objects in thecomparison class for which the bare adjective is true, and thenusing that as the comparison class to infer a new threshold, i.e.
very expensive laptop means “expensive for an expensive laptop”. This analysis results in the expected intensification of
adjectives (“expensive for an expensive laptop” has a higher
threshold for being true than simply “expensive for a laptop”)
and is appropriately sensitive to different domains (e.g. theabsolute difference in price between thresholds for expensive
and very expensive is much higher in the context of “Thatspace station is very expensive,” than in the context of “Thatcoffee is very expensive.”). However, this account does not,in and of itself, distinguish between the graded strengths ofdifferent intensifiers, for example, very expensive and phenomenally expensive.
Intuition suggests that different intensifiers do have different strengths (e.g. outrageously seems stronger than quite),and we provide further evidence of this in our experiments,
where participants interperet and compare different intensifiers. It could be that the degree of strength of different intensifiers is conventionally specified by the lexicon. But thesemantics must then specify how these entries affect the very
flexible threshold of the relevant adjective. In addition, themultitude of intensifiers (Bolinger, 1972) and their apparent
productivity3 suggest a more parsimonious solution would be
welcome. That is, having a lexically determined meaning foreach different intensifier might overlook the similarity amongwords of this class.
We propose instead that each time a scalar adjective isused, in each phrase, it introduces a free threshold variable(that is, a new token threshold is inferred for every time thelexical entry of the adjective is accessed). Further we propose that intensifiers contribute nothing to the literal, compositional semantics4 . This implies that different adjectival
phrases (e.g. “very expensive watch” and “extremely expensive watch”) have equivalent meanings, though with thresholds that will be separately assigned based on context. However, the intensifiers do affect the production cost of the corresponding sentences, and it is this cost difference that results
in meaning differences.
We next outline and extend Lassiter and Goodman’s modelof scalar adjectives to include several copies of the relevant
3 For example, altitidinously expensive is not in common usage,
but one can easily interpret altitidinously as a novel intensifier.
4 We take this strong view for rhetorical purposes. It is highly
likely that some intensifiers have other aspects of meaning.

adjectival phrase, each with its own threshold variable. We
show that simply having different thresholds for different adjective phrases—and being aware of alternative utterances
and their relative communicative costs—is sufficient to communicate the wide range of degrees designated by intensifying degree adverbs.

Model
Lassiter and Goodman (2013)’s model belongs to the family of Rational Speech Act (RSA) models in which speakerand listener communicate by recursively reasoning about
each other’s goals and inferences. These models have beenshown to account for many phenomena in pragmatics (Frank& Goodman, 2012; Goodman & Stuhlmüller, 2013). The
adjective model accounts for uncertainty about the adjectival threshold by including a lifted semantic variable, which
the pragmatic listener infers at the same time that she infers
the speaker’s intended meaning. We assume every adjective
phrase has its own such variable θi 5 , together notated ~θ, but tootherwise mean the same thing, so that, for example, expensive, very expensive and phenomenally expensive all denote:
λx.price(x) > θi .
Given an utterance ui (e.g. an expensive laptop or a very
expensive laptop) and a set of thresholds, a literal listener L0
will use Bayesian inference to update his prior beliefs P(d)about the degree d (e.g. the laptop’s price) given that thedegree is greater than the threshold for that utterance.
PL0 (d|ui , θi ) ∝ P(d) · δd>θi
A speaker with the goal of communicating some actual degree d assigns a utility U(ui |d) to each utterance such that heprefers utterances which will inform the literal listener, but
avoids utterance cost, C(ui ):U(ui |d,~θ) = ln (PL0 (d|ui , θi )) −C(ui )Given a set of alternative utterances (e.g. the speaker might
be choosing between saying very expensive as opposed to expensive or extremely expensive, or saying nothing at all), thespeaker S1 will choose utterances according to a softmax decision rule (Sutton & Barto, 1998) with optimality parameter
λ, so that:~

PS1 (ui |d,~θ) ∝ eλU(ui |d,θ)A pragmatic listener L1 uses the prior probability, P(d), ofdifferent degrees, along with knowledge of the cost of each
5 Other versions of this model could easily be imagined in which

the threshold for an adjective phrase is determined by the basic
threshold for the adjective and some transformation on that threshold(e.g. multiplication, addition, etc.) caused by the intensifier. If thetransformation is mostly regular, with a single parameter needing to
be inferred for each intensifier, and if the values of these parameters
are inferred for each adjective phrase, then such a model would befunctionally equivalent to the one we describe here.

PL1 (d,~θ|ui ) ∝ P(d) · PS1 (ui |d,~θ)L1(price | utterance)

As an initial exploration, we simulated such a model withthree alternative adjective phrases (i.e. three intensifiers) withcosts of 1, 5, and 10. We also included a null utterance, withtrivial meaning (always true) and cost of 0. The prior distribution of degrees along this adjective’s scale (which we will
discuss as “prices” for concreteness and consistency with ourExperiment 1) was a gaussian peaked at 0. We used an optimality parameter of λ = 5 in our simulation.
Though the literal semantics are identical (except that they
have different threshold parameters), the different phrases received different interpretations: the more costly intensifiers
corresponded to less probable, more extreme prices (Figure1). This can be seen as an M-implicature: more costly intensifiers are assigned strong, less probable, meanings. The
model therefore predicts an association between intensifier
meaning and utterance cost.
0.6
cost
prior
1
5
10

0.4
0.2

ances are more costly) 8 and frequency (rarer intensifiers are
harder to access and therefore more costly). In a number ofdifferent tasks, lexical frequency affects difficulty in an approximately logarithmic way. For instance word recognition
time (McCusker, 1977) and reading time in context (Smith &Levy, 2013) are both logarithmic in frequency. We thus use
the log-frequency (whose negative is also called surprisal) as
the quantitative contribution to cost.
We thus predict a linear contribution of longer and higher
surprisal intensifiers to the meaning. This leaves open the therelative importance of length and surprisal, and potential interactions (as well as other factors that might enter into cost),
which can be explored via regression models.
expected standardized "price"utterance, in order to guess both the thresholds for each utterance and which degree the speaker intended to communicate6 :

−1

0

1

Figure 1: Modeling intensifiers as M-implicature: morecostly intensifiers correspond to more extreme meanings.

Factors affecting utterance cost
We have identified the intensifier’s cost, C(ui ), as a potentially critical factor of its interpreted meaning. The quantitative form predicted by the model of the relationship between
cost and meaning is a approximately linear (Figure 2).7 .
To connect this linear prediction to empirical facts, we stillmust specify (at least a subset of) the factors we expect toimpact cost. The most natural notion of cost is the effort a
speaker incurs to produce an utterance. This could include
cognitive effort to access lexical items from memory, articulatory effort to produce the sound forms, and other such direct costs. Speakers might also seek to minimize comprehension cost for their listeners, resulting in other contributions tocost. For the purposes of this paper, we restrict to the moststraightforward contributors to production cost and use proxies that are straightforward to quantify: length (longer utter6 We assume a uniform prior on thresholds θ .
i
7 This second simulation was identical as the first, except run ona more discretized scale for 6 different utterance costs (or “intensifiers”).

●
1.00

●
0.75

●
●
2

4

6

Figure 2: Model prediction of expected price as cost of intensifier increases, based on intensifiers evenly spaced in cost.
The relationship is approximately linear.

Experiment 1

2

standardized "prices"●
1.25

utterance cost

0.0
−2

●
1.50

The proposal detailed above predicts an association between
measures of cost and strength of interpretations. In Experiment 1, we test this qualitative prediction by eliciting free response price estimates from people and determining whether
these prices are correlated with our independent measures ofutterance cost.

Method930 participants with US IP addresses were recruited throughAmazon’s Mechanical Turk and paid $0.40 for their participation, of whom 1 was excluded for saying they did not follow
the directions in a post-experiment survey.
We asked participants to estimate the prices of different
objects based on descriptions of those objects. The descriptions included intensifiers paired with the adjective expensive(Figure 3). There were three categories of objects (laptop,
watch, and coffee maker) and 40 intensifiers (see Table 1). We
chose intensifiers that have a wide range of frequencies andexcluded intensifiers that are either more commonly used tosignal affect than to signal degree (e.g. “depressingly expensive” might indicate a degree, but it mainly indicates affect)
8 We measure length in number of syllables, although length incharacters (which might be a relevant source of utterance cost in a
written format, as our experiments were in) has similar predictive
power to syllable length in all of our analyses.
9 The full experiment can be found at http://cocolab.stanford.edu/cogsci2015/intensifiers/Experiment1

Table 1: Intensifiers from Experiment 1, number of occurences in Google Web 1T 5grams corpus, and number of syllables.
ngram
surpassingly
frightfully
uncommonly
mightilystrikingly
decidedly
exceedingly
amazingly
remarkably
desperately
incredibly
significantly
particularly
veryfrequency
11156
65389
1357472521354804178178069774351384225
1902493
21399684416030
19939125
41066217
292897993

syllables
4
3
4
3
3
4
4
4
4
3
4
5
5
2

ngram
colossally
astoundingly
outrageously
supremely
acutely
excessively
intensely
radically
terriblyutterly
seriously
totallyquite

frequency
11167
73041
24001029613449393187728010847651414254
19060592507480
12570333
20950052
55269390or are ambiguous between other parts of speech (e.g. “super”
can be used as an intensifier, as in “super expensive”, but it
can also be used as an adjective, as in “super hero”). Eachparticpant gave price judgments for every intensifier-category
pairing in a randomized order (different for different participants).We chose the domain of price and used only the adjective expensive because price constitutes a quantitative scalewith standard units (dollars for our US participants) on which
to measure the different intensifers.

Figure 3: Screenshot from Experiment 1 target question.
Corpus Methods Table 1 shows word frequency and lengthin syllables for the intensifiers used in the experiment. The
frequencies were collected from the Google Web 1T 5-grams
database (Brants & Franz, 2006)10 In the analysis below we
use word length and word surprisal (negative log-frequency)
as proxies for a word’s cost, as motivated above. The syllable lengths of our intensifiers and the surprisals were clearlycorrelated, but not strongly so (r = 0.27, t = 16, p < 5e − 16).

Results and Discussion
If the meaning of an intensifier is stronger for higher cost intensifiers, we would expect to find that as surprisal increases
and length in syllables increases, the prices participants give
will also increase. We find that this is the case.
We ran a linear mixed effects regression with centered fixed
effects of syllables, surprisal, and their interaction, and random intercepts and slopes for syllables and surprisal for bothparticipant and object. We used the logarithm of participants’
10 We also ran the same analyses on frequency information collected from the Google Books American Ngrams Corpus (Michel etal., 2011) and found similar results.

syllables
4
4
4
3
3
4
3
3
3
3
4
3
1

ngram
terrifically
phenomenallyfantasticallyinsanelyawfully
extraordinarily
markedlyunusually
exceptionallynotably
truly
extremely
especiallyfrequency
62292
1207692509893596446515199004561213704
158393920542313141835
19778608
21862963
55397873

syllables
4
5
4
3
3
6
3
4
5
3
2
3
4

price estimates as the dependent variable, because of evidence
that people’s representation of numbers, including prices, islogarithmic (Dehaene, 2003, e.g.)11 .
Our results are shown in Figure 4. Both measuresof cost play a role in predicting participants’ price estimates. We found a significant main effect of surprisal (β =0.0536, SE = 0.00902,t(3) = 5.94, p < 0.05) such that lessfrequent words tend to be associated with higher price estimates. We also found a significant main effect of syllable length (β = 0.0900, SE = 0.0189,t(4) = 4.76, p < 0.05),
above and beyond surprisal, such that longer words predict
stronger meanings. We also found a significant interaction(β = 0.0196, SE = 0.00520,t(3.5) = 3.77, p < 0.0005) between surprisal and syllable length, wich may indicate thatthe relationship between the two predictors of cost is not simply additive, and that having multiple sources of communicative cost (i.e. length and surprisal) might increase the implicature even more. Although these effects are significant,the marginal and conditional R2 values (Barton, 2015) were0.015 and 0.72 respectively, indicating that much of the variance in estimated prices is captured by the random effects
rather than the fixed effects of surprisal and syllable length.
Overall, intensifiers that are less frequent and longer (andtherefore are more costly to utter) also tend to be interpreted
as having stronger meanings, at least when used to modify
expensive. Furthermore, the relationship appears to be linear in surprisal and length (though with an interaction), as
predicted. This is consistent with the M-implicature model
introduced above.

Experiment 2
The M-implicature account described above implies that
there is no semantic interaction between the intensifier andthe adjective it is applied to. Instead an intensifier should contribute similar cost, and therefore meaning, to the different
adjectival phrases in which it occurs12 . To explore this issue,
11 I.e. the perceptual distance between two prices the same dollar
amount apart is more for small numbers (e.g. $3 and $6) and less forlarge numbers (e.g. $1,543 and $1,546).
12 If the bigram frequency of the modified adjective (“very expensive”) deviated from that expected based on independent word fre-

Experiment 1
coffee maker

laptopwatch

log(price)

7.5
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6.0
5.5
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5.0

● ● ●●● ● ●●● ●●●●●●● ● ●● ●●●●●● ● ●● ●
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syllables

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10.0 12.5 15.0 17.5

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10.0 12.5 15.0 17.5

surprisal

Figure 4: Results of Experiment 1. As surprisal and length in syllables increase, participants’ free response prices increased.
we would like to extend our results to additional adjectival
scales. However, most scales are not so easily quantifiable
as price; we require a different dependent measure in orderto probe them. For Experiment 2 we used a forced-ranking
dependent measure, which allows us to consider additional
adjectival scales. This dependent measure has the added benefit of providing a more sensitive measure of the differencesin degrees between similar adjectival phrases.

Method1330 participants with US IP addresses were recruited throughAmazon’s Mechanical Turk and paid $0.40 for participation.
3 said they did not follow the directions in a post-experiment
survey and were excluded from the analysis.
We asked participants to order (by clicking and dragging)
various adjective phrases with the same adjective but different intensifiers according to strength of meaning. Because
arranging these phrases required participants to be aware of
the full set of adjective phrases and access all of them on thesame computer screen, not all of our 40 intensifiers could effectively be presented at once. We divided the 40 intensifiers
from Experiment 1 into four lists of 10 intensifiers. Each list
was randomly paired with one of four adjectives (old, expensive, beautiful, and tall). For each adjective-list pairing, participants were shown every combination of the 10 intensifierswith one adjective. Participants were asked to move the adjective phrases across the screen, reordering the phrases fromthe “lowest” to the “highest” degree (Figure 5). Each participant completed four trials, seeing all four lists and all four
adjectives. The list-adjective pairings were randomized between participants.The division of the intensifiers into lists of
10 was constant, so that the same 10 intensifiers were always
shown together.

Results and Discussion
Our results for Experiment 2 are shown in Figure 6. We
ran an ordinal mixed effects regression with centered surquencies our frequency-based cost account would predict an interactive effect on meaning. This would be a relatively small effect, andthe relevant bigrams were too sparse in our corpora to pursue.
13 The full experiment can be found at http://cocolab.stanford.edu/cogsci2015/intensifiers/Experiment2

Figure 5: Screenshot from Experiment 2 target question.

prisal and syllable lengths and their interaction as fixed effects, and random intercepts and slopes for syllables andsurprisal for both participant and adjective. As in Experiment 1, we found strong main effects of surprisal (β =0.432, SE = 0.0934,t = 4.63, p < 0.05) and syllable length(β = 0.671, SE = 0.122,t = 5.50, p < 0.005), and a significant interaction (β = 0.0725, t = 2.01, p < 0.05). In thisexperiment, a much higher proportion of our explained variance was due to our fixed effects (marginal R2 = 0.18, andconditional R2 = 0.22). In other words, we again found thatparticipants assign stronger interpretations to intensifiers withhigher surprisals and/or higher syllable lengths, extending
now across four different adjectival scales.

General Discussion
Motivated by a recent probabilistic model of scalar adjectives(Lassiter & Goodman, 2013), we showed how adjectival intensifiers could potentially get their meaning through a pragmatic M-implicature, despite having vacuous literal meaning
to add to an adjective. Our model predicted a linear relationship between the intensity of an intensifier and its cost,measured here in terms of length and log-frequency. In two
experiments we provided evidence that intensifier meanings
do depend systematically on the length and frequency of distribution of those word forms. While it is unlikely that this ac-

Experiment 2
beautifulexpensiveold●ranking

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Figure 6: Results of Experiment 2. As surprisal and length in syllables increase, participants’ rankings increased.
counts for all intensifier meaning, it does suggest that a major
portion of meaning comes not from arbitrary, conventional
association of signal to sign (de Saussure, 1916), but fromfeatures of the word’s form and distribution.
It should be noted that, since this is a correlational study,
such a relationship does not confirm that an intensifier’s costcauses it to have a given meaning. This correlation is predicted by the model sketched above, but it might be predictedby other analyses of intensifiers and their meanings. Rarity
in particular might be correlated with strength of meaning
merely because more extreme meanings refer to less probable things in the world, are therefore talked about less, andtherefore the words with those meanings will necessarily berarer. Although it seems reasonable to suspect that word frequencies reflect the probabilities of the real-world concepts
they describe, it might also be the case that improbable things
are more likely to be commented on, and so the frequencies
of words that describe rare concepts might be inflated. In addition, this confound on causal direction exists only for word
frequency (and its effect on syllable length) and not for syllable length directly. Although the length of a word certainly
depends on frequency of use, it seems unlikely that it also depends directly on the real-word prevalence of the concept it
refers to.
A number of issues remain to future work, including thecausality of the relationship we have described and the otheraspects of intensifier meaning (such as polarity or affective
color). However we believe that the preliminary results presented in this paper already have interesting implications. For
the semantics of adverbial modifiers, we have shown how
pragmatic mechanisms could be central in establishing flexible contributions to sentence meaning. For the broader question of form-meaning mapping, we have suggested a sourceof non-arbitrary association based on both properties of theword form and of its distribution.

Acknowledgments
This work was supported by a James S. McDonnell Foundation Scholar Award to NDG and ONR grant N00014-13-10788.

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