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Revealing Criterial Vagueness in Inconsistencies

Steven Verheyen

1,2

2
, Anne White

3
, and Paul Égré

1Laboratoire de Sciences Cognitives et Psycholinguistique, Département d’études cognitives, ENS, EHESS,
PSL University, CNRS

2Laboratory for Experimental Psychology, Faculty of Psychology and Educational Sciences, KU Leuven

3Institut Jean Nicod, Département d’études cognitives, ENS, EHESS, PSL University, CNRS

un accès ouvert

journal

Mots clés: categorization, vagueness, individual differences, semantic memory, ad hoc categories

ABSTRAIT

Sixty undergraduate students made category membership decisions for each of 132
candidate exemplar-category name pairs (par exemple., chess – Sports) in each of two separate
sessions. They were frequently inconsistent from one session to the next, both for nominal
categories such as Sports and Fish, and ad hoc categories such as Things You Rescue from
a Burning House. A mixture model analysis revealed that several of these inconsistencies
could be attributed to criterial vagueness: participants adopting different criteria for
membership in the two sessions. This ﬁnding indicates that categorization is a probabilistic
processus, whereby the conditions for applying a category label are not invariant. Individuals
have various functional meanings of nominal categories at their disposal and entertain
competing goals for ad hoc categories.

INTRODUCTION

Dans 2006 the number of planets in our solar system suddenly dropped from nine to eight. Ce
dramatic change was not due to some astronomical catastrophe, but to a change in the criteria
for Planets adopted by the International Astronomical Union (IAU). Seeing that Pluto has not
cleared the neighborhood around its orbit as the new criteria prescribed, the IAU decided that
Pluto should no longer be considered a Planet, but belongs in the category of Dwarf Planets.
Dans 2015 the High Court of Tarbes (France) overruled the earlier decision by the supreme court
of appeal (Cour de Cassation) that involuntary homicide cannot be committed on a fetus,
effectively changing what it means to be a Person. Both examples serve to show that even in
scientiﬁc and legal contexts, where precision is arguably of the utmost importance, concepts
are vague and the criteria for determining whether an instance belongs in a category or not are
subject to change (Egré, 2018). Most of the concepts we use in our daily lives can be argued
to be vague.

In psychology, the vague rather than well-deﬁned nature of categories was convincingly
demonstrated by McCloskey and Glucksberg (1978), who showed that participants not only
differed in opinion as to whether items should be considered category members or not, mais aussi
changed their answer when asked the same question one month later. Participants presented
with a list of candidate instances for nominal categories such as Fish and Sports, responded
with a nonmodal answer (a response that is different from the majority response) sur 17%
of the membership questions and provided inconsistent answers (a change in response after a

Citation: Verheyen, S., Blanc, UN., &
Égré, P.. (2019). Revealing Criterial
Vagueness in Inconsistencies. Open
Esprit: Discoveries in Cognitive
Science, 3, 41–51. https://est ce que je.org/
10.1162/opmi_a_00025

EST CE QUE JE:
https://doi.org/10.1162/opmi_a_00025

Supplemental Materials:
https://doi.org/10.1162/opmi_a_00025;
osf.io/pnm9a/

Reçu: 16 Juin 2018
Accepté: 22 Mars 2019

Intérêts concurrents: Les auteurs ont
a déclaré qu'aucun intérêt concurrent
exister.

Auteur correspondant:
Steven Verheyen
steven.verheyen@kuleuven.be

droits d'auteur: © 2019
Massachusetts Institute of Technology
Publié sous Creative Commons
Attribution 4.0 International
(CC PAR 4.0) Licence

La presse du MIT

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Criterial Vagueness Verheyen et al.

one-month interval) sur 12%. These results have been replicated by Hampton, Dubois, and Yeh
(2006), who reported values for these inter- and intraindividual variability measures of 19% et
10%, respectivement. Since the abandonment of the classic view of concepts as involving singly
necessary and jointly sufﬁcient membership conditions (Rosch, 1973; Rosch & Mervis, 1975;
Ryle, 1949; Wittgenstein, 1953), these differences are not recognized as mistakes, but as a
manifestation of faultless disagreement (Kölbel, 2004; Wright, 1995), or permissible variation
(Raffman, 2014), indicating that there are multiple, equally competent ways of applying a
vague concept.

Although the idea that nonmodal responses characterize vague categories was not new
at the time (see Borel, 1907, and Black, 1937, for predecessors of the idea), McCloskey and
Glucksberg’s (1978) work contributed to interindividual variability becoming a hallmark of
vague categories. Nowadays, the existence of borderline items for which individuals can fault-
lessly disagree regarding category membership is considered to be central to what it means for
a category to be vague (Kennedy, 2013; Forgeron, 2008; Wright, 1995).

The interindividual variability observed in categorization tasks is generally thought to
result from both indeterminacy with respect to the conditions for application, and indeter-
minacy with respect to the extent of application given ﬁxed conditions (Verheyen & Storms,
2013, 2018). Three people may disagree as to whether chess and hiking are Sports, because
one believes Sports should have competitive and gamelike properties, while the other two only
label activities that require physical effort Sports. On the basis of whether they consider hiking
sufﬁciently effortful or not, the latter two could still disagree as to whether to call it a Sport.
The former indeterminacy is commonly referred to as criterial vagueness, while the latter is
known as degree vagueness (Devos, 1995, 2003; for a similar distinction, see Alston, 1964;
Burks, 1946; Kennedy, 2013; Machina, 1976).

In contrast to interindividual variability, intraindividual variability has not caught on as
a hallmark of vague categories. Although it has been acknowledged that vague categories
have borderline cases for which an individual might feel equally inclined to apply and to
deny the category label (Schiffer, 2003)—evidenced by increased categorization reaction times
and lower conﬁdence ratings (Koriat & Sorka, 2015), as well as competing responses to the
same stimulus at a given time (Malt, 1990)—within-subject inconsistencies in categorization
rarely constitute the topic of investigation themselves (see Hampton, Aina, Andersson, Mirza,
& Parmar, 2012, for a notable exception). Intraindividual categorization differences tend to be
accounted for in terms of shifting thresholds. What is believed to change from one occasion
to the other, is the extent of the evidence the individual requires to apply the category label,
not the conditions for application (Hampton, 1995; McCloskey & Glucksberg, 1978). Incon-
sistent answers are thus thought to reﬂect degree rather than criterial vagueness. The implicit
assumption here seems to be that qualitatively different conceptions of a category might be
entertained by different people, but not by an individual. It is this hypothesis that we put to
the test in this article.

OUTLINE

The observation by McCloskey and Glucksberg (1978) that people provide inconsistent an-
swers when asked to repeat a categorization task indicates that the information that is retrieved
from semantic memory is not invariant. The probabilistic nature of the semantic retrieval
process is corroborated by the modest reliability of repeated exemplar generation (Bellezza,
1984un; Blanc, Voorspoels, Storms, & Verheyen, 2014), category deﬁnitions (Barsalou, 1989;
Bellezza, 1984b), feature importance ratings (Hampton & Passanisi, 2016), and typicality

OPEN MIND: Discoveries in Cognitive Science

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Criterial Vagueness Verheyen et al.

judgments (Barsalou, 1987, 1989; Hampton & Passanisi, 2016). While these studies allow
one to establish how much change to expect from one occasion to the next, they do not indi-
cate what it is that changes over time. The purpose of this article is to elucidate whether the
criteria that are used to establish category membership may change.

Criterial vagueness has not yet been demonstrated within individuals. Different individ-
uals have been shown to use distinct criteria for categorization, cependant (Verheyen & Storms,
2013; Verheyen, Voorspoels, & Storms, 2015; Blanc, Storms, Malt, & Verheyen, 2018). Ce
has been achieved using a mixture model that identiﬁes subgroups of categorizers depending
on the latent conditions they adhere to for categorization (criterial vagueness). Within each of
the identiﬁed subgroups, the participants were also found to differ on the extent to which they
required instances to demonstrate these conditions to be eligible for categorization (degree
vagueness). The rationale behind the mixture model is that the use of distinct criteria will show
in the relative frequency with which items are endorsed in subgroups. The items chess and
darts will be more often categorized as Sports in a group emphasizing competitive and game-
like properties than in a group looking to physical exertion to establish category membership.
The use of distinct thresholds will show in the proportion of categorized items. Participants
who require little evidence for category membership will also include items that have rela-
tively lower categorization frequencies in the subgroup, whereas very demanding participants
will only include items that are frequently endorsed, as this indicates that these items score
high on the subgroup’s categorization criterion.

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Our design involves having participants complete a categorization task twice. We will
apply the mixture model described above to the repeated data to determine whether any of
the participants are assigned to different subgroups on the two occasions. This would indicate
that their inconsistent answering reﬂects criterial vagueness. We will investigate both nominal
categories like Fish and Sports, and ad hoc categories like Things You Rescue from a Burning
Maison. Because unlike nominal categories, ad hoc categories violate the correlational struc-
ture of the environment and are not well established in memory (Barsalou, 1983), we expect
more intraindividual categorization differences and more criterial accounts of inconsistent
answers in ad hoc categories.

DESIGN AND PROCEDURE

All materials, data, and analysis scripts are available on the Open Science Framework
(Verheyen, Blanc, & Égré, 2019un).

Ethics Statement

This study was conducted with the approval of the Social and Societal Ethics Committee of
KU Leuven. Written informed consent was obtained from all participants both at the start
of the ﬁrst and second categorization session.

Participants

We invited 65 ﬁrst-year psychology students at KU Leuven to take a categorization task
twice, in exchange for course credit. Sixty of them completed both sessions (92%). Of these
60 participants, 5 were male (8.33%). The participants’ age ranged between 17 et 20 années
(M = 18.08, SD = 0.65).

Materials

Verheyen and Storms (2013) and Verheyen et al. (2015) investigated whether degree and cri-
terial vagueness could account for interindividual categorization differences in nominal and

OPEN MIND: Discoveries in Cognitive Science

Criterial Vagueness Verheyen et al.

ad hoc categories, respectivement. We selected three nominal categories and three ad hoc cate-
gories from among the categories in these articles that showed evidence of criterial vagueness
in the form of two subgroups of participants identiﬁed by the mixture analysis. Among the
ﬁve qualifying ad hoc categories, we did not include the two categories with a very uneven
distribution of participants over subgroups since we expected hardly any participants in our
sample to subscribe to the categorization criteria of the smaller subgroup (comprising less than
10% of the participants in the original paper). In order to have an equal number of nominal
catégories, we randomly selected three among the four qualifying nominal categories.

The nominal categories Fish, Sports, and Tools had 24 items each. The ad hoc categories
Things You Rescue from a Burning House, Means of Transport Between Brussels and London,
and Weapons Used for Hunting had 20 items each. These items comprised the full range of
category membership, including several clear members and clear nonmembers, but mainly
borderline cases. All the materials were presented in Dutch.

Procedure

Participants were administered a computerized categorization task in which the materials were
presented in two blocks (nominal vs. ad hoc) of three categories each. The presentation order
of blocks, categories within a block, and items within a category was randomized for every
participant. Separate screens for each category would display the categorization instructions
on top, indicating that participants could answer yes or no to the question of whether the
items that followed belong to the category or not. A third response option, labeled unknown,
was meant to be used when participants did not know a particular item or felt an item was
ambiguous and did not know which meaning was intended.

Approximately one month after completing the categorization task, participants were
presented the same task again. Following McCloskey and Glucksberg (1978), they were
informed that some instances of the ﬁrst session could appear again.

RÉSULTATS

We report the results in two separate sections. In the ﬁrst, we use linear mixed-effects models
to investigate whether the prevalence of inconsistencies across categorization sessions differs
between nominal and ad hoc categories. In the second section, we apply the mixture model
from the studies that informed the stimulus selection to the repeated categorization data in
order to determine to what extent differences between sessions represent criterial vagueness.

Prevalence of Inconsistencies

Seventy-three percent of the participants provided at least one inconsistent response (c'est à dire., un
change in response across sessions: yes/no, yes/unknown, or no/unknown) for each of the six
catégories. Sixteen participants (27%) answered consistently on one category, but not on the
other ﬁve (Fish: n = 7; Rescue: n = 6; Sports, Transport, and Weapons: n = 1). No one
answered consistently for the nominal category Tools. A parallel pattern was observed for the
items. Inconsistent answers were observed for all items (n = 132) except for eight (94%). Le
items that yielded perfectly consistent answers were all clear members of the target categories
(Fish: goldﬁsh, trout; Sports: skiing, swimming, tennis; Tools: axe, hammer; Rescue: people).
None of the items for the other two ad hoc categories yielded perfectly consistent answers.

Chiffre 1 depicts the proportion of inconsistent responses for each of the participants (gauche
panel) and each of the target items (right panel). En moyenne, the participants provided an

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Criterial Vagueness Verheyen et al.

Chiffre 1. Boxplots of the proportion of inconsistencies across sessions for each participant (gauche
panel) and each target item (right panel). Boxplots for nominal categories are depicted in white;
boxplots for ad hoc categories are depicted in gray. The bands in the boxes represent the median
valeurs.

inconsistent answer on 16.06% of the membership questions for the nominal categories and
sur 19.00% of the membership questions for the ad hoc categories.

To establish whether ad hoc and nominal categories differed with respect to intraindivid-
ual differences, we determined whether participants’ repeated responses were inconsistent or
not and ﬁtted a binomial mixed effects model to the resulting variable, using the lme4 package
(Bates, Maechler, Bolker, & Walker, 2015) in R version 3.4.3 (R Core Team, 2017). The ﬁxed
part of the model contained the main effect of the binary variable block, indicating whether
the answers pertained to a nominal (1) or ad hoc (0) catégorie. The random part of the model
included random category, item, and participant intercepts, and an interaction between the
block and participant variables. The main effect of block (β = −.35, SE = .19, z = −1.88,
p = .06) was not signiﬁcant at α = .05. This result was supported by comparing the BIC of the
above model to that of an alternative model from which the main effect of block was removed
= 6, 900.80).1 Autrement dit, we did not reject the null hy-
(BICsimple
pothesis that the prevalence of intraindividual differences differs between nominal and ad hoc
catégories.

= 6, 894.60 vs. BICfull

Prevalence of Criterial Vagueness

Chiffre 2 holds a graphical depiction of the mixture model (Lee & Wagenmakers, 2014). Il
considers each categorization decision xip the outcome of a Bernoulli trial (1 for yes, 0 pour
Non) with the probability of a membership response to item i by participant p expressed by rip.
It assumes the data result from a mixture of participants who adhere to different criteria for
categorization. Depending on a participant’s latent group membership zp, different estimates

1 The smaller BIC value for the simple model indicates that it provides the more parsimonious account of the
data in terms of ﬁt and complexity (Schwarz, 1978). The increase in ﬁt that is obtained by discerning between
nominal and ad hoc categories in the full model does not warrant its added complexity/ﬂexibility compared to
the simpler model.

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Criterial Vagueness Verheyen et al.

Chiffre 2. Graphical model representation of the mixture model.

are obtained for the item parameters β
je, which express the extent to which the items dis-
play the group’s categorization criterion. The β
i are compared against the participant’s internal
threshold θp to establish the items’ category membership. Whereas differences in β
i signal
vagueness in criteria, differences in θp capture degree vagueness or the amount of evidence
participants require for category membership. The parameter α determines for each group the
shape of the function that relates the extent to which an item surpasses/falls short of the thresh-
old to the probability of categorization. The function is S-shaped: it starts off at a zero when the
− θp difference is large and negative, demonstrates an increase for small differences between
β
je
β
i and θp, and asymptotes to one when the difference grows large and positive. The value of
α reﬂects the steepness of the function at the point of subjective equality (the point for which
the categorization probability equals .50, when β

= θp).

Latent group membership zp is parameterized in the model as a categorically distributed
random variable with πg reﬂecting the probability of belonging to group g. The threshold
parameters θp are drawn from normal hyper-distributions, parameterized by group-speciﬁc
means and precision 1. We employed a uniform Dirichlet prior for the membership probabili-
ties πg, a half-normal distribution centered at 0 with precision 1 for each α, and normal priors
centered at 0 with the precision set to 1 for the remaining model parameters.

The repeated categorization data from the current study were merged with the catego-
rization data that were available for the same materials from earlier work (Verheyen et al., 2015;
Verheyen & Storms, 2013). The merging ensures that we have enough data to obtain reliable
parameter estimates for the different subgroups. The two sets of categorization responses by
the participants who took the categorization task twice were included as independent entries.
Unknown responses were treated as missing values. For each of the nominal categories, le
merged data thus comprised 370 categorization responses to each of 24 items (2 × 60 new

OPEN MIND: Discoveries in Cognitive Science

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Criterial Vagueness Verheyen et al.

réponses + 250 responses from Verheyen & Storms, 2013). For the ad hoc categories, le
merged data comprised 374 × 20 categorization responses (2 × 60 new + 254 from Verheyen
et coll., 2015). The mixture model was applied to these merged data sets.

Separate model estimates were obtained for each of the categories using WinBUGS
(Lunn, Thomas, Best, & Spiegelhalter, 2000) by running three chains of 10,000 samples each,
with a burn-in of 4,000 samples. The chains were checked for convergence and label switch-
ing. For every category a two-group solution was obtained since for all six selected categories
two subgroups of participants were identiﬁed by the original mixture analyses (Verheyen &
Storms, 2013; Verheyen et al., 2015). The original groups were recovered in the analysis of
the merged categorization data, as evidenced by the correlations between the posterior means
i estimates (all r > .95). (For a substantive interpretation
of the old and new group-speciﬁc β
of the categorization criteria, see section 1 of the Supplemental Materials [Verheyen, Blanc,
& Égré, 2019b].)

The focus here will be whether the 60 participants who completed the categorization
task twice are assigned to a different group upon repetition. This would indicate that they
relied on distinct criteria for categorization in the two sessions. Group membership was de-
termined based on the posterior mode of zp. We observed numerous group changes from
Session 1 to Session 2.2 For only 27% of the participants no change in group membership was
observed. These participants were placed in the same group on both occurrences of the cate-
gorization task for all six categories. Seventy-three percent of participants thus demonstrated a
group change for at least one category. Thirty-two percent of participants changed group for two
catégories. Three percent changed group for three categories. There were no participants
for which a group change was established for more than three categories. These percentages
indicate that criterial vagueness is present within individuals.3

For the nominal category Fish, 9 out of 53 participants (17%) who demonstrated at least
one inconsistency were placed in different groups on the two occasions. For Sports and Tools
these percentages equaled 24% (14/59) et 28% (17/60), respectivement. Fewer group changes
were observed for the ad hoc categories: 11/54 (20%) for Rescue, 7/59 (12%) for Transport,
et 9/59 (15%) for Weapons. We constructed a new variable indicating whether the mixture
analysis placed participants in different groups on the two repetitions or not, and ﬁtted a bi-
nomial mixed-effects model to it. The ﬁxed part of the model contained the main effect of the
binary variable block, indicating whether the answers pertained to a nominal (1) or ad hoc (0)
catégorie. The random part of the model included random category and participant intercepts,
and an interaction between the block and participant variables. The effect of block (β = .48,
SE = .28, z = 1.75, p = .08) was not signiﬁcant at α = .05. This result was supported by

2 Participants changing groups tended to have a high probability of being assigned to a subgroup in one
session and a low probability of being assigned to the same group in the other session, rather than having
similar assignment probabilities in both sessions. See section 2 of the Supplemental Materials (Verheyen et al.,
2019b) for details.

3 The percentages demonstrate that intraindividual variability can be due to criterial vagueness, but pre-
sumably overestimate the overall prevalence of criterial vagueness. We observed slightly more intraindividual
categorization differences than earlier studies did (16% compared to 12% in McCloskey and Glucksberg, 1978,
et 10% in Hampton et al., 2006). This discrepancy might be due to our selection of categories with known crite-
rial vagueness (established between rather than within individuals). The earlier studies included a broader range
of nominal categories than we did, which need not all display criterial vagueness. According to Verheyen and
Storms (2013), 5 out of 8 categories in Hampton et al. (2006) demonstrated criterial vagueness; 6 out of 10 ad hoc
(2015) displayed criterial vagueness. The fact that we also counted an unknown
categories in Verheyen et al.
response on one occasion and a yes or no response on the other occasion as inconsistencies might contribute
to the discrepancy as well.

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comparing the BIC of the above model to that of an alternative model from which the main
= 372.30). While group changes
effect of block was removed (BICsimple
thus appeared less frequent for the ad hoc categories than for the nominal categories, ce
difference was not signiﬁcant.

= 369.35 vs. BICfull

GENERAL DISCUSSION

For three nominal and three ad hoc categories, participants decided on the category member-
ship of various target items. They completed the task twice, separated by a one-month interval.
Inconsistent answers were ubiquitous. Participants rarely provided identical responses on both
occasions. We established that this intraindividual variability was not exclusively the result of
degree vagueness (participants changing the amount of evidence required for membership,
given constant conditions across sessions), as was assumed up until now. Several of these
inconsistencies could be attributed to criterial vagueness: participants adopting different con-
ditions for application in the two sessions. Each of these participants was placed in distinct
groups on the two sessions by a mixture model that identiﬁes latent groups of participants who
employ different categorization criteria.

For nominal categories the existence of criteria differences within individuals indicates
that people have various “meanings” at their disposal, which are probabilistically retrieved
from semantic memory. McCloskey and Glucksberg (1978) refer to these meanings as func-
tional categories, suggesting that they can be relied upon to serve different purposes (par exemple.,
FISH in the zoological vs. the seafood sense; see also Hampton et al., 2006, and Verheyen &
Storms, 2013). The possibility to recruit different subsets of category knowledge allows for
efﬁcient processing in that information that is most relevant to accomplish particular tasks can
be focused on (Yeh & Barsalou, 2006). It might make memories and truth judgments less re-
liable, cependant, as information recall and property veriﬁcation might differ depending on the
functional meaning that is accessed (Hampton et al., 2012). The challenge for future work is to
determine how particular meanings are likely to become activated on a given occasion and to
establish whether it is tenable to argue for context- and task-independent category representa-
tions if people are highlighting a particular conceptual content whenever they use a category
label (Braisby, 1993).

The observation that inconsistent categorization responses can result from criterial vague-
ness holds for both nominal and ad hoc categories. We found no signiﬁcant difference regard-
ing the prevalence of inconsistencies or of criterial changes in nominal vs. ad hoc categories.
This might strike some as surprising given that ad hoc categories are thought to be less rooted
in the environment and in semantic memory than nominal categories are (Barsalou, 1983) et
therefore might be expected to show less stability. The lack of a stability difference might be
an indication that the ad hoc categories we selected should be considered goal-derived cate-
gories: ad hoc categories that have become well-established in memory, Par exemple, through
frequent use (Barsalou, 1985). The observation that one and the same individual may use differ-
ent criteria for recruiting items that fulﬁll the category’s goal, would then be an indication that
people sometimes entertain competing goals—such as traveling comfortably or fast between
Brussels and London—the prominence of which might change from one occasion to the next
(see also Voorspoels, Storms, & Vanpaemel, 2013, who showed that individuals can provide
multiple ideal characteristics of goal-derived categories).

There is no reason to assume that the occurrence of criterial vagueness is speciﬁcally
related to particular word classes (Verheyen & Storms, 2018). Our ﬁndings pertain to nominal
and ad hoc categories, but are likely to generalize to other paradigmatic examples of vague

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catégories, such as gradable adjectives like Intelligent and Healthy. The individual-level symp-
toms of vagueness that were discussed in the introduction for nouns have also been shown to
exist for gradable adjectives. They too show competing responses to borderline items (border-
line contradictions; see Alxatib & Pelletier, 2011; Egré & Zehr, 2018; Hersh & Caramazza,
1976; Ripley, 2011), increased reaction times and decreased conﬁdence ratings for borderline
items (Brownell & Caramazza, 1978; Hersh & Caramazza, 1976), and inconsistent responding
across categorization sessions (Egré, de Gardelle, & Ripley, 2013; Hersh & Caramazza, 1976).
Solt (2018) offers a treatment of how degree and criterial vagueness can account for inter- et
intraindividual differences in the application of gradable adjectives. Much like Verheyen and
Storms (2013) argued for nouns, she suggests that the judge- and context-dependent weight-
ing of the multiple dimensions that underlie many gradable adjectives, is responsible for the
observed variability in their use.

Our examples of vague concepts pertain to higher level categories, which tend to be
comprised of heterogeneous instances that share similar functions rather than appearances.
For perceptual categories it remains to be seen whether inconsistent answers can be attributed
to criterial vagueness. Whether it can might depend on the frequency with which individuals
categorize instances differently. We know that children as young as 14 months old can ﬂexibly
shift the criteria they use for categorizing objects in response to tasks requirements or instruc-
tion (par exemple, from using shape to relying on material; Élise & Oakes, 2006). We believe
that the more this occurs, the more likely it becomes that individuals will develop multiple
representations that remain accessible for later (functional) utiliser (Schyns & Rodet, 1997).

Enfin, this article advocates the study of intraindividual differences in vagueness re-
recherche. Although interindividual variability is generally considered a hallmark of vague cate-
gories, its manifestation is not necessarily due to vagueness, but can be an indication of stable
differences between subgroups of categorizers. Par exemple, the same light stimulus may
be categorized as one color by a color-normal perceiver, but stably (without uncertainty or
unclarity being experienced) as another color by a person with protanopia (a form of color
blindness characterized by a tendency to confuse reds and greens and by a loss of sensitivity
to red light; Paramei, Bimler, & Cavonius, 1998). En outre, interindividual application differ-
ences can often be systematically related to properties of the individuals (tall people imposing
higher height requirements than short people to name others tall; Verheyen, Dewil, & Egré,
2018; higher educated people applying nominal categories more conservatively; Verheyen
& Storms, 2018; older people looking at traditional rather than modern materials to apply
container labels; White et al., 2018). Intraindividual differences cannot be attributed to par-
ticipants’ background differences and therefore provide a more direct window into the prob-
abilistic nature of categories.

REMERCIEMENTS

We thank the audience at ESSLLI 2017 for suggesting this study, and Tom Heyman for helpful
comments on an earlier version of this article.

INFORMATIONS SUR LE FINANCEMENT

SV was funded by the European Research Council under the European Union’s Seventh Frame-
/ ERC Grant Agreement 313610, and by KU Leuven
work Programme (FP/2007-2013)
Research Council grant C14/16032. AW is a Research Assistant at the Research Foundation–
Flanders (FWO) and acknowledges KU Leuven Internal Research Fund PDM 18/084. PE was
funded by ANR project TriLogMean (ANR-14-CE30-0010). SV and PE also acknowledge grants

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ANR-10-LABX-0087 IEC and ANR-10-IDEX-0001-02 PSL* for research conducted at the
Department of Cognitive Studies of ENS in Paris.

CONTRIBUTIONS DES AUTEURS

SV (Conceptualisation: Equal; Conservation des données: Equal; Analyse formelle: Lead; Méthodologie: Lead;
Gestion de projet: Equal; Logiciel: Lead; Visualisation: Lead; Rédaction – ébauche originale: Lead;
Rédaction – révision & édition: Equal); AW (Conservation des données: Equal; Gestion de projet: Equal;
Ressources: Lead; Rédaction – révision & édition: Equal); PE (Conceptualisation: Equal; Funding
acquisition: Lead; Rédaction – révision & édition: Equal).

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