报告 - 麻省理工学院人工智能研究专业

报告

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, 法国国家科学研究中心

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

3Institut Jean Nicod, Département d’études cognitives, ENS, EHESS, PSL University, 法国国家科学研究中心

开放访问

杂志

关键词: 分类, vagueness, individual differences, semantic memory, ad hoc categories

抽象的

Sixty undergraduate students made category membership decisions for each of 132
candidate exemplar-category name pairs (例如, 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
过程, 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.

介绍

在 2006 the number of planets in our solar system suddenly dropped from nine to eight. 这
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.
在 2015 the High Court of Tarbes (法国) 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, 概念
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, 但是也
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) 在 17%
of the membership questions and provided inconsistent answers (a change in response after a

引文: Verheyen, S。, 白色的, A。, &
Égré, 磷. (2019). Revealing Criterial
Vagueness in Inconsistencies. Open
头脑: 认知方面的发现
科学, 3, 41–51. https://doi.org/
10.1162/opmi_a_00025

DOI:
https://doi.org/10.1162/opmi_a_00025

补充材料:
https://doi.org/10.1162/opmi_a_00025;
osf.io/pnm9a/

已收到: 16 六月 2018
公认: 22 行进 2019

利益争夺: 作者有
声明不存在竞争利益
存在.

通讯作者:
Steven Verheyen
steven.verheyen@kuleuven.be

版权: © 2019
麻省理工学院
在知识共享下发布
归因 4.0 国际的
(抄送 4.0) 执照

麻省理工学院出版社

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

one-month interval) 在 12%. These results have been replicated by Hampton, Dubois, and Yeh
(2006), who reported values for these inter- and intraindividual variability measures of 19% 和
10%, 分别. 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; 维特根斯坦, 1953), these differences are not recognized as mistakes, but as a
manifestation of faultless disagreement (Kölbel, 2004; 赖特, 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
当时 (see Borel, 1907, 和黑色, 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 (肯尼迪, 2013; 史密斯, 2008; 赖特, 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, 因为
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; 肯尼迪, 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, 安德森, 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
给另一个, 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,
1984A; 白色的, Voorspoels, Storms, & Verheyen, 2014), category deﬁnitions (巴尔萨卢, 1989;
Bellezza, 1984乙), feature importance ratings (Hampton & Passanisi, 2016), and typicality

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

判断 (巴尔萨卢, 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, 然而 (Verheyen & Storms,
2013; Verheyen, Voorspoels, & Storms, 2015; 白色的, Storms, Malt, & Verheyen, 2018). 这
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 (程度
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. 参加者
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.

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Our design involves having participants complete a categorization task twice. 我们将
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
房子. Because unlike nominal categories, ad hoc categories violate the correlational struc-
ture of the environment and are not well established in memory (巴尔萨卢, 1983), we expect
more intraindividual categorization differences and more criterial accounts of inconsistent
answers in ad hoc categories.

DESIGN AND PROCEDURE

All materials, 数据, and analysis scripts are available on the Open Science Framework
(Verheyen, 白色的, & Égré, 2019A).

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.

参加者

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 参与者, 5 were male (8.33%). The participants’ age ranged between 17 和 20 年
(米= 18.08, 标准差= 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

开放的心态: 认知科学的发现

Criterial Vagueness Verheyen et al.

ad hoc categories, 分别. 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
类别, 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.

程序

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
参与者. 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), 他们是
informed that some instances of the ﬁrst session could appear again.

结果

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 (IE。, A
change in response across sessions: yes/no, yes/unknown, or no/unknown) for each of the six
类别. Sixteen participants (27%) answered consistently on one category, but not on the
other ﬁve (鱼: n = 7; Rescue: n = 6; Sports, Transport, and Weapons: n = 1). 没有人
answered consistently for the nominal category Tools. A parallel pattern was observed for the
项目. Inconsistent answers were observed for all items (n = 132) except for eight (94%). 这
items that yielded perfectly consistent answers were all clear members of the target categories
(鱼: goldﬁsh, trout; Sports: skiing, 游泳, tennis; Tools: axe, hammer; Rescue: 人们).
None of the items for the other two ad hoc categories yielded perfectly consistent answers.

数字 1 depicts the proportion of inconsistent responses for each of the participants (左边
panel) and each of the target items (right panel). 平均而言, the participants provided an

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

数字 1. Boxplots of the proportion of inconsistencies across sessions for each participant (左边
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
价值观.

inconsistent answer on 16.06% of the membership questions for the nominal categories and
在 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, & 沃克, 2015) in R version 3.4.3 (R核心团队, 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) 类别. 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 换句话说, we did not reject the null hy-
(BICsimple
pothesis that the prevalence of intraindividual differences differs between nominal and ad hoc
类别.

= 6, 894.60 与. BICfull

Prevalence of Criterial Vagueness

数字 2 holds a graphical depiction of the mixture model (李 & 货车制造商, 2014). 它
considers each categorization decision xip the outcome of a Bernoulli trial (1 for yes, 0 为了
不) 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
分类. 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 (施瓦茨, 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.

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

数字 2. Graphical model representation of the mixture model.

are obtained for the item parameters β
我, 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
我
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).

我

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
以 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, 这
merged data thus comprised 370 categorization responses to each of 24 项目 (2 × 60 新的

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

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

Separate model estimates were obtained for each of the categories using WinBUGS
(Lunn, 托马斯, 最好的, & Spiegelhalter, 2000) by running three chains of 10,000 samples each,
with a burn-in of 4,000 样品. The chains were checked for convergence and label switch-
英. 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, 参见部分 1 of the Supplemental Materials [Verheyen, 白色的,
& Égré, 2019乙].)

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
类别. 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 在......之外 53 参与者 (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) 和 28% (17/60), 分别. Fewer group changes
were observed for the ad hoc categories: 11/54 (20%) for Rescue, 7/59 (12%) for Transport,
和 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)
类别. 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.,
2019乙) 欲了解详情.

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% 相比 12% in McCloskey and Glucksberg, 1978,
和 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 在......之外 8 categories in Hampton et al. (2006) demonstrated criterial vagueness; 6 在......之外 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.

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

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, 这
difference was not signiﬁcant.

= 369.35 与. 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
场合. 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 (例如,
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 & 巴尔萨卢, 2006). It might make memories and truth judgments less re-
liable, 然而, 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
标签 (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 (巴尔萨卢, 1983) 和
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, 例如, 通过
frequent use (巴尔萨卢, 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

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

类别, 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 (边界-
line contradictions; see Alxatib & Pelletier, 2011; Egré & Zehr, 2018; Hersh & Caramazza,
1976; Ripley, 2011), increased reaction times and decreased conﬁdence ratings for borderline
项目 (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- 和
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-
系统蒸发散 (例如, from using shape to relying on material; Ellis & Oakes, 2006). 我们相信
that the more this occurs, the more likely it becomes that individuals will develop multiple
representations that remain accessible for later (functional) 使用 (Schyns & Rodet, 1997).

最后, this article advocates the study of intraindividual differences in vagueness re-
搜索. 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. 例如, 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). 此外, 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.

致谢

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

资金信息

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

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

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.

作者贡献

SV (概念化: 平等的; 数据管理: 平等的; 形式分析: 带领; 方法: 带领;
项目管理: 平等的; 软件: 带领; 可视化: 带领; Writing – original draft: 带领;
写作——复习 & 编辑: 平等的); AW (数据管理: 平等的; 项目管理: 平等的;
资源: 带领; 写作——复习 & 编辑: 平等的); 聚乙烯醇 (概念化: 平等的; 资金
acquisition: 带领; 写作——复习 & 编辑: 平等的).

参考

Alston, 瓦. 磷. (1964). Philosophy of language. 恩格尔伍德悬崖, 新泽西州:

Prentice Hall.

Alxatib, S。, & Pelletier, F. J. (2011). The psychology of vague-
内斯: Borderline cases and contradictions. 头脑 & 语言,
26, 287–326. 土井:10.1111/j.1468-0017.2011.01419.x

巴尔萨卢, L. 瓦. (1983). Ad hoc categories. 记忆 & 认识, 11,

211–227. 土井:10.3758/bf03196968

巴尔萨卢, L. 瓦. (1985). Ideals, central tendency, and frequency of
instantiation as determinants of graded structure in categories.
实验心理学杂志: 学习, 记忆, 和
认识, 11, 629–654. 土井:10.1037//0278-7393.11.1-4.629
巴尔萨卢, L. 瓦. (1987). The instability of graded structure: Implications
for the nature of concepts. 在U. Neisser (埃德。), Concepts and con-
ceptual development: Ecological and intellectual factors in cate-
gorization (PP. 101–140). 剑桥: 剑桥大学出版社.
巴尔萨卢, L. 瓦. (1989). Intraconcept similarity and its implications
for interconcept similarity. 在S. Vosniadou & A. Ortony (编辑。), 辛-
ilarity and analogical reasoning (PP. 76–121). 剑桥, 英国:
剑桥大学出版社. 土井:10.1017/cbo9780511529863.
006

Bates, D ., Maechler, M。, Bolker, B., & 沃克, S. (2015). Fitting lin-
ear mixed-effects models using lme4. Journal of Statistical Soft-
器皿, 67, 1–48. 土井:10.18637/jss.v067.i01

Bellezza, F. S. (1984A). Reliability of retrieval from semantic mem-
奥里: Common categories. Bulletin of the Psychonomic Society,
22, 324–326. 土井:10.3758/bf03333832

Bellezza, F. S. (1984乙). Reliability of retrieval from semantic mem-
奥里: Noun meanings. Bulletin of the Psychonomic Society, 22,
377–380. 土井:10.3758/bf03333850

黑色的, 中号. (1937). Vagueness: An exercise in logical analysis. Phi-

losophy of Science, 4, 427–455. 土井:10.1086/286476

Borel, 乙. (1907). Un paradoxe économique: Le sophisme du tas
de blé et les vérités statistiques. La Revue du Mois, 4, 688–699.
[English translation by Égré, P。, & Gray, 乙. (2014). An economic
悖论: The sophism of the heap of wheat and statistical truths.
Erkenntnis, 79, 1081–1088. 土井:10.1007/s10670-014-9615-z]
Braisby, 氮. 右. (1993). Stable concepts and context-sensitive classi-
ﬁcation. Irish Journal of Psychology, 14, 426–441. 土井:10.1080/
03033910.1993.10557948

Brownell, H. H。, & Caramazza, A. (1978). Categorizing with over-
lapping categories. 记忆 & 认识, 6, 481–490. 土井:10.
3758/bf03198235

Burks, A. 瓦. (1946). Empiricism and vagueness. Journal of Philos-

奥菲, 43, 477–486. 土井:10.2307/2018954

Devos, F. (1995). Still fuzzy after all these years. A linguistic evalua-
tion of the fuzzy set approach to semantic vagueness. Quaderni
di Semantica, 16, 47–82.

Devos, F. (2003). Semantic vagueness and lexical polyvalence.
Studia Linguistica, 57, 121–141. 土井:10.1111/j.0039-3193.2003.
00101.X

Egré, 磷. (2018). Qu’est-ce que le vague? [What is vagueness?]. 巴黎,

法国: Collection Chemins Philosophiques, 弗林.

Egré, P。, de Gardelle, 五、, & Ripley, D. (2013). Vagueness and order
Journal of Logic, 语言和

effects in color categorization.
信息, 22, 391–420. 土井:10.1007/s10849-013-9183-7
Egré, P。, & Zehr, J. (2018). Are gaps preferred to gluts? 仔细看看
In G. 瓦. Sassoon, L. McNally, &
at borderline contradictions.
乙. Castroviejo (编辑。), The semantics of gradability, scale structure,
and vagueness: Experimental perspectives (PP. 25–58). 柏林,
德国: 施普林格. 土井:10.1007/978-3-319-77791-7_2

Ellis, A. E., & Oakes, L. 中号. (2006). Infants ﬂexibly use different
dimensions to categorize objects. Developmental Psychology,
42, 1000–1011. 土井:10.1037/0012-1649.42.6.1000

Hampton, J. A. (1995). Testing the prototype theory of concepts.
记忆与语言杂志, 34, 686–708. 土井:10.1006/
jmla.1995.1031

Hampton, J. A。, Aina, B., 安德森, J. M。, Mirza, H. Z。, & Parmar, S.
(2012). The Rumsfeld effect: The unknown unknown. 杂志
of Experimental Psychology: Learning Memory & 认识, 38,
340–355. 土井:10.1037/a0025376

Hampton, J. A。, Dubois, D ., & Yeh, 瓦. (2006). The effects of prag-
matic context on classiﬁcation in natural categories. 记忆 &
认识, 34, 1431–1443. 土井:10.3758/bf03195908

Hampton, J. A。, & Passanisi, A. (2016). When intensions don’t map
onto extensions:
Individual differences in conceptualisation.
实验心理学杂志: 学习, 记忆, 和
认识, 42, 505–523. 土井:10.1037/xlm0000198

Hersh, H. M。, & Caramazza, A. (1976). A fuzzy set approach to mod-
iﬁers and vagueness in natural language. 实验杂志
心理学: General, 105, 254–276. 土井:10.1037//0096-3445.
105.3.254

肯尼迪, C. (2013). Two sources of subjectivity: Qualitative as-
sessment and dimensional uncertainty. Inquiry, 56, 258–277.
土井:10.1080/0020174x.2013.784483

Kölbel, 中号. (2004). Faultless disagreement. Proceedings of the Aris-
totelian Society, 104, 53–73. 土井:10.1111/j.0309-7013.2004.
00081.X

Koriat, A。, & Sorka, H. (2015). The construction of categorization
判断: Using subjective conﬁdence and response latency

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/

d
我
r
e
C
t
.

米

我
t
.

e
d
你
哦
p
米

我
/

我

A
r
t
我
C
e
–
p
d

F
/

d
哦

我
/

我

1
0
1
1
6
2
哦
p
米
_
A
_
0
0
0
2
5
1
8
6
8
3
6
3
哦
p
米
_
A
_
0
0
0
2
5
p
d

我

乙
y
G
你
e
s
t

哦
n
0
7
S
e
p
e
米
乙
e
r
2
0
2
3

Criterial Vagueness Verheyen et al.

to test a distributed model. 认识, 134, 21–38. 土井:10.1016/
j.cognition.2014.09.009

李, 中号. D ., & 货车制造商, E.-J. (2014). Bayesian cognitive mod-
eling: 实用课程. 剑桥, 英国: 剑桥大学
按. 土井:10.1017/CBO9781139087759

Lunn, D. J。, 托马斯, A。, 最好的, N。, & Spiegelhalter, D. (2000). WinBUGS:
A Bayesian modelling framework: Concepts, 结构, 和前-
tensibility. Statistics and Computing, 10, 325–337. 土井:10.1023/
A:1008929526011

Machina, K. F. (1976). Truth, belief and vagueness. Journal of Philo-

sophical Logic, 5, 47–78. 土井:10.1007/bf00263657

Malt, 乙. C. (1990). Features and beliefs in the mental representation
of categories. 记忆与语言杂志, 29, 289–315.
土井:10.1016/0749-596X(90)90002-H

McCloskey, 中号. E., & Glucksberg, S. (1978). Natural categories:
Well deﬁned or fuzzy sets? 记忆 & 认识, 6, 462–472.
土井:10.3758/bf03197480

Paramei, G. 五、, Bimler, D. L。, & Cavonius, C. 右. (1998). Effect of lumi-
nance on color perception of protanopes. 视觉研究, 38,
3397–3401. 土井:10.1016/s0042-6989(97)00454-9

R核心团队.

(2017). 右: A language and environment for statisti-
cal computing. R Foundation for Statistical Computing, 维也纳,
奥地利. Retrieved from https://www.R-project.org/.

Raffman, D. (2014). Unruly words. 牛津, 英国: 牛津大学

按. 土井:10.1093/acprof:oso/9780199915101.001.0001

Ripley, D. (2011). Contradictions at the borders. 在R中. Nouwen,
右. van Rooij, U. Sauerland, & H.-C. Schmitz (编辑。), Vagueness
in communication (PP. 169–188). 柏林, 德国: 施普林格.
土井:10.1007/978-3-642-18446-8_10

Rosch, 乙. (1973). On the internal structure of perceptual and seman-
tic categories. 在T. 乙. 摩尔 (埃德。), Cognitive development and
the acquisition of language (PP. 111–144). 纽约: Academic
按. 土井:10.1016/B978-0-12-505850-6.50010-4

Rosch, E., & Mervis, C. 乙. (1975). Family resemblances: 学习
in the internal structure of categories. 认知心理学, 7,
573–605. 土井:10.1016/0010-0285(75)90024-9

Ryle, G. (1949). The concept of mind. 伦敦, 英国: Hutchinson.

土井:10.4324/9780203875858

Schiffer, S. (2003). The things we mean. 牛津, 英国: Oxford Uni-

大学出版社. 土井:10.1093/0199257760.001.0001

施瓦茨, G. (1978). Estimating the dimension of a model. Annals of

统计数据, 6, 461–464. 土井:10.1214/aos/1176344136

Schyns, 磷. G。, & Rodet, L. (1997). Categorization creates func-
tional features. 实验心理学杂志: 学习,
记忆, 和认知, 23, 681–696. 土井:10.1037//0278-7393.
23.3.681

史密斯, 氮. J. J. (2008). Vagueness and degrees of truth. 牛津, 英国:
牛津大学出版社. 土井:10.1093/acprof:oso/9780199233007.
001.0001

Solt, S. (2018). Multidimensionality, subjectivity and scales: Experi-
mental evidence. 在E中. Castroviejo, L. McNally, & G. 瓦. Sassoon
(编辑。), The semantics of gradability, vagueness, and scale struc-
真实: Experimental perspectives (PP. 59–91). 柏林, 德国:
施普林格. 土井:10.1007/978-3-319-77791-7_3

Verheyen, S。, Dewil, S。, & Egré, 磷. (2018). Subjectivity in gradable
形容词: The case of tall and heavy. 头脑 & 语言, 33,
460–479. 土井:10.1111/mila.12184

Verheyen, S。, & Storms, G. (2013). A mixture approach to vagueness
and ambiguity. PLoS ONE, 8(5), e63507. 土井:10.1371/journal.
pone.0063507

Verheyen, S。, & Storms, G. (2018). Education as a source of vague-
ness in criteria and degree. 在E中. Castroviejo, L. McNally, &
G. 瓦. Sassoon (编辑。), The semantics of gradability, vagueness,
and scale structure: Experimental perspectives (PP. 149–167).
柏林, 德国: 施普林格. 土井:10.1007/978-3-319-77791-7_6
Verheyen, S。, Voorspoels, W., & Storms, G. (2015). Inferring choice
criteria with mixture IRT models: A demonstration using ad hoc
and goal-derived categories. Judgment and Decision Making,
10, 97–114.

Verheyen, S。, 白色的, A。, & Égré, 磷. (2019A, 行进 20). Revealing cri-
terial vagueness in inconsistencies. Retrieved from osf.io/pnm9a.
Verheyen, S。, 白色的, A。, & Égré, 磷. (2019乙). Supplemental material
for “Revealing criterial vagueness in inconsistencies.” Open
头脑: 认知科学的发现, 3. 土井:10.1162/opmi_
a_00025

Voorspoels, W., Storms, G。, & Vanpaemel, 瓦. (2013). 相似
and idealness in goal-derived categories. 记忆 & 认识,
41, 312–327. 土井:10.3758/s13421-012-0252-y

白色的, A。, Storms, G。, Malt, 乙. C。, & Verheyen, S. (2018). Mind the
generation gap: Differences between young and old in the repre-
sentation of everyday lexical categories. Journal of Memory and
语言, 98, 12–25. 土井:10.1016/j.jml.2017.09.001

白色的, A。, Voorspoels, W., Storms, G。, & Verheyen, S. (2014). 问题-
lems of reliability and validity with similarity derived from cate-
gory ﬂuency. Psychiatry Research, 220, 1125–1130. 土井:10.1016/
j.psychres.2014.10.001

维特根斯坦, L.

(1953). 哲学

investigations (2nd 版。).

牛津, 英国: 布莱克威尔.

赖特, C. (1995). The epistemic conception of vagueness. The Southern
Journal of Philosophy, 33, 133–159. 土井:10.1111/j.2041-6962.
1995.tb00767.x

Yeh, W., & 巴尔萨卢, L. 瓦. (2006). The situated nature of concepts.
The American Journal of Psychology, 119, 349–384. 土井:10.2307/
20445349

开放的心态: 认知科学的发现

我

D
哦
w
n
哦
A
d
e
d

F
r
哦
米
H

t
t

:
/
/