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Hampton
Concepts as Prototypes
THE
PSYCHOLOGY
OF
LEARNING
AND
MOTIVATION
VOL.
46,
79
113
CONCEPTS AS PROTOTYPES
James A. Hampton
City University, London
“.. whatever vagueness is to be found in my words must be attributed to our ancestorsfor not having been predominantly interested in logic.”
Bertrand Russell,
I.
Introduction
The Prototype Theory of conceptual representation in large part owes its beginningsto Rosch and Mervis (1975), who, in the space of a couple of years, published a stringof major papers laying out the empirical basis for the theory.
The motivation for the
theory came from a perceived crisis in philosophy and linguistics to do with definingthe meaning of words.
To the lay person, who has never worried too much about
such things, the meaning of words is just given in the dictionary.
The trouble is that
most dictionary definitions are really only approximate or partial. The word “red” forexample is not defined by a fixed interval of the color spectrum, but is the name for aimprecisely defined region with vague edges.
The word “chair” could perhaps be
defined as a movable object made for sitting on that stands on the floor, and has aback.
However once again the actual use of the word tends in practice to allow for
vagueness – designers continually create new objects for sitting on and new contextsin which to sit, so that it is often unclear whether they should be counted as chairs or
not.
The central insight of prototype theory is that word meanings, and the
conceptual classes that the words name, are distinguished one from another not interms of an explicit definition, but in terms of similarity to a generic or best example.The concept red is the class of colors that are centered around a particular point on thespectrum that everyone tends to agree is the
prototype
red.
Indeed Berlin & Kay
(1969) reported that there was better agreement about the
best
examples of color
terms, than there was about the boundary between one color and another (for examplebetween red and orange).
The category of red things is therefore the category of
things whose color is sufficiently similar to a prototypical red (and dissimilar fromother prototypes).
Similarly there are concept representations for “chair” and “stool”
and “bench” and “sofa”, each of which is associated with a prototype example of theclass.
Objects are then classified on the basis of which prototype they are most
similar to.
Rosch, Simpson and Miller (1976) showed that people could readily learn novel categories based around prototypes (a point already demonstrated by Posner & Keele,1968), and Rosch and Mervis (1975) analysed a number of semantic categories suchas fruit, sport or vehicle to show that what members of the category had in commonwas not some set of defining features, but a sufficient degree of resemblance to eachother.
In some of their writings it is implied that the
best example
of the category,
whatever that might be, would be the prototype. However it quickly became clear thatthe prototype should better be considered as a more abstract, generic concept, that wasconstituted from the different ways in which the category members resembled eachother, and differed from non-members.
Unlike a best example, an abstract prototype
allows for the representation of different possible values of relevant features – such asthat apples can be red, green, brown, or yellow, or that furniture can be sat on, slepton, used for storing things, or provide a surface for supporting things.
An apple that
had
all
these colors, or a piece of furniture that served
all
these functions would not
necessarily be prototypical.
Prototypes then are the centers of clusters of similar objects, and prototype concepts form similarity-based categories.
The center of the cluster is well established and
agreed upon, but the boundary between one category and another may be subject tovagueness and disagreement. Talk of clusters with centers implies a spatial metaphor,and
prototypes
have
often
been
discussed
as
points
in
similarity
space
.^
A
mathematical exploration of the implications of this approach can be found inGärdenfors (2000), and Osherson and Smith (1981) included a similarity space as partof their formalization of prototype theory. Spaces however have additional structuralproperties which impose unnecessarily strict constraints on prototypes. Verbeemen etal. (2004) have explored the degree to which natural categories can be represented in
Hampton
Concepts as Prototypes
spaces (through multidimensional scaling), and concluded that at least for somesemantic domains, a non-spatial similarity model provides a better fit.
Following its introduction into cognitive psychology, prototype theory was also taken up enthusiastically by cognitive linguists such as Ross (1973) and Lakoff(1987), and anthropologists such as Kempton (1978) and Randall (1976).
Ross
(1973) for example proposed that the syntactic class NOUN in English is basedaround a prototype. He suggested a scale of “nouniness” associated with a hierarchyof syntactic acceptability in different contexts.
The more nouny a word or phrase
was, then the more contexts in which it would behave like a noun.
A useful recent
source of different views on the value of prototypes in linguistic theory can be foundin Aarts et al. (2004).
While Rosch & Mervis provided overwhelming evidence for widespread prototype effects in semantic concepts and in category learning, the development of the theoryin psychology subsequently remained relatively underspecified.
In one of the last
papers in the series, Eleanor Rosch (1978) discussed the theoretical underpinning ofthe data, and warned that a distinction should be made between the empiricalphenomena of prototype effects, and any theoretical model that concepts are actuallyrepresented by prototypes. In fact, she doubted that the latter was the case.
The purpose of this paper will be to re-examine Prototype Theory and the evidence with which it is associated. One of the major difficulties with the theory may be that,with the early withdrawal of Rosch from the field, it has lacked a champion todevelop and refine a working model of prototype representations, as new empiricalresults have been discovered. Thus, at various times, the theory has been criticised inmany ways. For example, it is claimed that the theory lacks any way to represent thevariability allowed on different dimensions within a category (for example the rangeof possible sizes of apples, rather than just their average size). The theory is said notto be able to account for some categories having wider or more flexible boundariesthan others (and hence is unable to explain why a sphere half-way in size between abasketball and a watermelon is more likely to be a watermelon than a basketball,Rips, 1989).
The theory is said to rely too heavily on statistical cue validity to
determine feature weights (i.e. on the relative frequency of the feature for membersand non-members of the category), and so to ignore causal dependencies amongfeatures such as that birds need their wings in order to fly.
The theory is said to be
circular in that no account is offered of why our attention is drawn to particular setsof features or particular sets of objects in the first place.
In every case, the criticisms may be well-founded, but what has been lacking is a coordinated attempt to modernise the theory to incorporate mechanisms to deal withthe failures. It is of course easy to find data that a model has no way of explaining, if
the model was not created with those data in mind. However one is then faced with achoice of discarding the model altogether, or of adapting the model to fit the data.
A notable exception to the lack of development of prototype theory has been the work on category learning of Don Homa and colleagues (e.g. Homa, 1984; Homa etal. 1981) and of J. David Smith and Paul Minda (e.g. Smith & Minda, 2000). Both ofthese groups of researchers have generated valuable evidence that in classificationlearning paradigms, there are conditions under which abstraction of prototypes doesindeed
occur.
They
have
also
developed
precise
quantitative
models
of
how
prototypes develop and are used in such learning situations.
The question remains
however whether the original aim of prototype theory – to provide an account of thenatural concepts that we use to understand our everyday world and that serve tosupport
the
meanings
of
common
nouns
in
natural
language
can
be
met
satisfactorily.
The chapter therefore will focus on the original evidence on which Prototype Theory was based, and will discuss which aspects of that evidence should be retained ascentral to the theory, and which aspects may be less crucial.
I will also use this
opportunity to present new results relating to prototype effects, and to reflect on someof the theoretical debates that surround the model.
There is a nice irony here, in that
the theory as applied to itself would suggest quite plausibly that “Prototype Theory”as a concept is itself a family of related concepts in which different importance mightbe attached to different assumptions of the theory.
A prototype of Prototype Theory
might be that presented by Rosch and Mervis, or that described in Hampton (1995),but other characterizations have been offered (e.g. Osherson & Smith, 1981). Leavingthis irony aside, it is important first to try to capture the more essential characteristicsof a prototype model, in order to consider how the central insights of the approach canbe made consistent with recent evidence on the nature of conceptual representation.
II.
The Origins of Prototype Theory
Prototype theory enjoyed rapid and considerable success in the years following Rosch and Mervis. Researchers were quick to apply the general notion of a prototypeto a wide range of domains, such as clinical diagnosis and social stereotypes. Thetheory and its applications have been described in detail elsewhere (Hampton, 1997c;Murphy, 2002), so what follows will be a brief sketch.
In general the way in which
prototype structure was demonstrated for a domain was to establish one or more offour key phenomena about categories in that domain.
Hampton
Concepts as Prototypes
showed that while a small number of McCloskey & Glucksberg’s borderline itemswere indeed unfamiliar (is euglena an animal?), others were highly familiar (is awoman an animal?).
With some few notable exceptions, Hampton (1998) found that
for the majority of borderline cases, the probability of being placed in the categorywas directly predictable from judgments of how typical or representative the itemswere of the category prototype.
It seems then that, at least in terms of empirical
evidence, prototype theory is best placed to account for vagueness. Providing there issome randomness in the prototype representation or in the way that it is used, then wecan expect probabilistic responding at the borderline, leading to disagreement andinconsistency in categorization.
Other psychological models can also explain vagueness.
Exemplar models (Medin
& Shaffer, 1978; Nosofsky, 1988) propose that concepts are similarity clusters verymuch
like
prototypes,
with
the
exception
that
there
is
no
central
abstracted
representation of the prototype.
Instead there is a memory store containing a
selection
of
actually
encountered
exemplars
(items
that
have
previously
been
categorized as falling under the concept).
An item is categorized into the class to
which it has maximum average similarity, the average being calculated across allstored exemplars.
However categorization is explicitly probabilistic, with relative
similarity to different categories determining the likelihood of being placed in onecategory rather than another.
It is only once categories have been very well learned
(or where the categories are very distinct from each other) that responding becomesall-or-none, and disagreement or inconsistency disappear.
The other class of models, theory-based or knowledge-based models, have in fact little to say about vagueness, but being Descriptivist, the same story can be given asfor prototype and exemplar models.
These models (Murphy & Medin, 1985; Rips,
1989; 2001) propose that concepts are individuated in terms of the role that they playin naïve theories that we use to explain our world. When this idea is cashed out intoactual proposals for what is represented mentally, then concepts actually look verymuch like prototypes again, but with an important difference.
Like a prototype
representation
there
are
different
features
or
attributes
involved;
degree
of
membership depends on the features that a potential item may have; and typicalitywill depend on how closely an item resembles the paradigmatic case of a categorymember. The crucial difference is that similarity to prototype is not a simple functionof matching attributes, but involves deeper causal information.
One way to think of
this is to suppose that in addition to having a set of features, a theory-based prototypehas a set of information about the
relations
between those features. If an item has the
features, but does not have them in the right relations to each other (which willinclude causal dependencies), then its similarity to the prototype will be poor.
Authors of these theories of concepts may well resent the appropriation of their ideasinto a form of prototype account, yet if they are to explain probabilistic responding,and residual effects of surface similarity in their data, (to say nothing of typicalityeffects) they are left with little alternative.
Taken more broadly, borderline cases are in fact an instance of a much more general problem – the problem of vagueness in natural language.
Interest in vagueness goes
back at least as far as the Ancient Greek philosopher Eubulides of Megara, whodevised the Sorites Paradox to illustrate the problem. Sorites means a heap in Greek,and the paradox involves asking how many grains of sand are needed to constitute aheap of sand.
It appears for example that removing a single grain from a heap could
not of itself turn a heap into a non-heap.
Yet repeating the action will eventually
leave no sand left at all, so that at some point the heap must cease to be a heap. In factthis must presumably happen before the number of grains reaches some (againunspecified) small number. The paradox can be run in the opposite direction as well,by starting with a single grain (not a heap) and then asking if addition of one graincould turn the collection of grains into a heap.B.
P
HILOSOPHICAL
A
CCOUNTS OF
V
AGUENESS
Resolution of the problem of vagueness remains a current goal in philosophy, logicand indeed psychology (Hampton, 2005; Kamp & Partee, 1995; Keefe & Smith, 1997;Osherson & Smith, 1997).
A notable attempt to resolve the issue is to relate
vagueness to epistemological uncertainty.
Williamson (1994) has developed an
epistemological account of vagueness, in which it is claimed that the meaning of termsis actually precise, but that we all have different partial understanding of what thatmeaning may be.
Because the true meaning may be highly complex, and does not
correspond to any simple definitional rule, the average language user learns toapproximate to that meaning.
This approach is an example of the Externalist view of
concepts/meaning, described above.
A concept is something external to the thinker,
that we come to represent in our minds more or less accurately as the case may be.Concepts and the meaning of terms that name them are constituted by the existence ofa particular class in the external world. Our representation of that class may thereforeshow signs of inaccuracy and vagueness.
Hence disagreement and inconsistency are
to be expected, just as if one asked people to rank order a set of rivers in terms of theirlength, or historical events in terms of their chronological order. Different people willknow the answer with different degrees of accuracy and reliability. It is of course alsopossible that the true meaning is not a class in the external world but a type oflanguage use sanctioned by the social structure of the language group.
In both cases
Hampton
Concepts as Prototypes
5
however, the definition of a term is external to the individual, and so vagueness couldreflect a partial grasp of that definition.
This is clearly a defensible position if one takes an Externalist view of what a concept is – namely an entity that exists in external reality rather than in our heads.The position is also (perhaps paradoxically) quite consistent with the existence ofprototypes in our minds – as Fodor (1998) has made quite clear.
It may be the case
that the concept of an X is clearly defined and delineated in the real world, but thatmy understanding of it is sufficiently partial that I am unable to decide clearlywhether a particular sample is actually an X. My understanding of the concept couldin fact be a descriptivist prototype, acquired from experience with typical cases of X,that has led me to form an internal representation of beliefs about Xs.
There is a sensible view, expressed by Bertrand Russell (1923) that says that vagueness is inherent in the relation between a representation and the world. There isno vagueness in the world itself. As he wrote: “things are what they are, and there isan end of it. Nothing is more or less what it is, or to a certain extent possessed of theproperties which it possesses.”
The challenge for the Externalist view of concepts is
then to find anything at all to say about the properties of concept classes, given thatthe very act of describing those properties introduces a symbolic representation whichmust on all accounts involve vagueness.
In fact one would have liked to ask Russell
what possible candidate “properties” he had in mind.
It would be a trick question of
course, since he could only answer in language in which by necessity the property inquestion would be vague, and so a thing might possess it to only a certain extent.Perhaps it is better to think of things being what they are, and not of “havingproperties” at all (see Quine, 1948, and Mellor & Oliver, 1997 for discussion of thispossibility). Perhaps the very notion of ascribing a property to a thing is to create thelogical problem of potential vagueness.C.
F
URTHER
S
TUDIES OF
V
AGUENESS
What do people say about the vagueness of their categories?
In a recent study
(Hampton, 2004) I presented people with 8 category lists that included borderlinecases and non-members, and first asked them to rate each word with one of threeresponses “definitely in the category” “intermediate” and “definitely not in thecategory”.
Once people had given their ratings they were then asked to go through
the booklet once more and indicate which of a number of possible reasons they mighthave for giving an “intermediate” response.
The most common reasons chosen were
variability of criterion (“because it depends on whether you take the category in abroad or in a narrow sense”), 31%, and epistemological uncertainty about the item
(“because I don’t know enough about the item to say”), 25%. Two other reasons thatreached double figure percentages were category polysemy (“because it depends onhow you define the category “), 15%, and item polysemy (“because it depends on howyou define the item”), 11%.
So it seems that people’s intuitions about vagueness do
include the possibility that they did not know enough about an item, but at the sametime they see the category terms as being vague in the sense of having broader andnarrower senses, and having different ways of being defined.
Both of the latter
reasons
are
consistent
with
prototype
representations
with
variable
dimensional
weights and variable criterion placement.
They are not however consistent with the
idea that all vagueness is caused by uncertainty.
A follow-up to this study considered the question of stability of category decisions over time.
One particular suggestion for handling vagueness in logic, supervaluation
theory (Kamp & Partee, 1995), proposes that there is a given region of vagueness atthe boundary of a category.
It should therefore be the case that if people were given
three response choices in categorization – “definitely yes”, “possibly”, and “definitelyno”, there should be less inconsistency in a test-retest measure.
The idea is that
people may not know how to categorize the “possible” items, and so may shift theirdecisions about this subset of vague borderline cases, responding in a probabilisticway depending on their current whim. Yet they may have a much clearer idea of whatis definitely in the category and what is definitely not in the category.
The
study,
conducted
with
my
student
Bayo
Aina,
involved
two
groups
of
participants.
One
group
categorized
the
same
lists
of
category
items
using
a
traditional “yes”/”no” decision, while the second group had three options as outlinedin the previous paragraph.
Both groups returned a week later to make the decision
again.
The proportion of responses remaining the same on the second occasion was
83% in the two-choice condition, and only 73% in the three choice condition.
So
there
was
clearly
no
well-defined
boundary
region
that
people
could
easily
discriminate.
Why though was there a
drop
in consistency given the 3 options?
One
possibility is that with 3 options there are more opportunities to change your mindthan with just 2.
We therefore reanalysed the data, collapsing the 3 options into 2 by
either comparing definitely yes with the other two, or comparing definitely no withthe other two.
Is it perhaps the case that we can consistently judge what is
“definitely” in a category, but find it harder to judge what is definitely not? When theboundary between “definitely yes” and the other options was examined, 84% ofresponses remained the same, and exactly the same degree of stability was observedbetween “definitely no” and the other two options.
The results therefore supported
the view that instability due to vagueness is the same across the category scale.
No
matter whether the criterion is set high (“definitely yes” versus “not definitely yes”),
Hampton
Concepts as Prototypes
The final issue arising from category vagueness concerns the mapping of sentences innatural language onto logic.
We commonly like to think that when we make
assertions then the things that we say may be true or false. Nothing could be plainer.However it turns out that within every statement there is a sometimes uneasy trade-offbetween the truth or falsity of the statement and the interpretation of the words withinit (Bill Clinton’s narrow legal definition of “sex” in the Monica Lewinksi scandal is agood case in point).
If there are borderline cases of category membership, then how
does one handle the truth of statements that involve such cases?
The problem lies in
the famous dictum of the Law of the Excluded Middle. As Frege (1903/1970) put it:
A concept that is not sharply defined is wrongly termed a concept. Such quasi-conceptual constructions cannot be recognized as concepts by logic; it is impossibleto lay down precise laws for them. The law of excluded middle is really just anotherform of the requirement that the concept should have a sharp boundary…….Has thequestion ‘Are we still Christians?’ really got a sense, if it is indeterminate whom thepredicate ‘Christian’ can truly be asserted of, and who must be refused it?
Early attempts to rescue the situation with Zadeh’s fuzzy set logic (Zadeh, 1965) came to grief as it was quickly noticed that while (probably) a consistent logic initself, with useful applications in control engineering, the logic made the wrongpredictions about behavioral data such as judgments of typicality, or categorization incomplex concepts (Osherson & Smith, 1981; 1982; Roth & Mervis, 1983). Hampton(1997b) reviewed a series of studies I conducted on this question from which it isclear that when people form conjunctions (Sports which are also Games), disjunctions(Fruits
or
Vegetables)
or
complement
conjunctions
(Dwellings
which
are
not
Buildings) they do not respect the constraints of set logic – fuzzy or otherwise. As abrief example, people say that chess is a sport which is a game, but that it is not asport, they say that a mushroom is not a fruit and that it is not a vegetable, but that it is
one or the other, and they say that a tent is not a dwelling, but that it
is
a dwelling
that is not a building.
These studies and others (e.g. Cohen & Murphy, 1984)
strongly suggest that people form quasi-logical combinations of nouns using thenatural language conjunctives “and” “or” and “not”, not by forming Boolean setintersections,
unions
or
complements,
but
by
combining
the
prototypes
of
the
concepts in question (see Hampton, 1987).
As a further example, Hampton (1996)
showed that judgments of membership in a conjunction showed
compensation
.^
The
more typical an item was as a member of class A, then the less similar it needed to beto B, to be counted as a member of the conjunction A^B.
For example if judging
whether faces are those of a “happy child”, the more typically childish an already
clearly childish face became, the less happy the child needed to look in order to stillcount in the category. Logical conjunction just doesn’t work this way.
The discovery of this non-logical system for combining concepts is one of the key factors supporting prototype representations, since it flies in the face of grounding themeaning of terms in extensionally delineated classes in the world, and of groundingcomplex concepts in set logic.
It is not then surprising to find the whole process of
conceptual combination becoming one of the major battlegrounds in the debatebetween externalist and descriptivist theories of concepts.
In a number of books and
papers, Fodor (e.g. Fodor & Lepore, 1994) has presented the case that conceptscannot be prototypes as follows (I paraphrase):
a.
It is a fundamental tenet of the representational theory of mind that thoughtis compositional – that is that the meaning of a complex thought is solelymade up from the meaning of its component parts, and the syntacticalfunction of the linguistic structure that links them together.
b.
Concepts are the component parts from which complex thoughts are created
c.
Therefore concepts must compose in the way stated
d.
Prototypes
do
not compose
in
this way,
therefore
concepts cannot be
prototypes.
Fodor doesn’t claim that concepts don’t
have
prototypes, just that they are not
themselves
prototypes.
So,
terminological
tussles
aside,
what
we
have
is
the
suggestion that the entities that psychologists study and like to call concepts, are not infact concepts, and might better be called conceptions or prototypes. A different levelof mental representation contains our concepts. These concepts are atomistic symbols(cannot be further analysed into simpler terms such as descriptions), and have therequisite properties of composing according to Boolean logic. It is possession of theseconcepts that explains the compositional properties of our thought.
It will be interesting to see if this proposal can be cashed out into empirical predictions about those circumstances in which concepts “proper” are involved inthinking, and those in which we rely instead on our prototypes.
One possible way
forward may be in differentiating rule-based and similarity-based systems of thinking(Smith & Sloman, 1994).
Ashby et al. (1998) have intriguing data that in category
learning there are two independent systems that learn through either hypothesis testingof rules or through accumulation of associative similarity-based links, and that theseare associated with different brain regions.
There is also assorted evidence emerging
that individuals differ systematically in whether they use similarity or rules in solvingconceptual problems (Hampton & Estes, 2000; Winman et al., 2005).
Hampton
Concepts as Prototypes
The issue of how to marry our ability to think in logical terms with the flexibility and adaptability of our conceptual system is a key issue for cognitive science. Clearlyif we went around thinking that something could be an A which is a B, but at thesame time not an A, we would be continually falling into reasoning errors.
In fact,
when faced with logical arguments dressed up in real world situations, it wouldappear that most people find it very hard to judge the logical validity of arguments(Henle & Michael, 1956).
My guess is that thinking in terms of set logic and
compositional concepts is a relatively late cultural acquisition that arose with thedevelopment
of
civilisations
involving
technology,
economic
accounting
and
mathematics in the last few thousand years.
To use language for logical thinking
requires that we
stipulate
and then hold constant the meaning of words in the given
context, so that Frege’s dictum of sharp boundaries can be respected.
For example,
we could answer Frege’s question, “Are we still Christians?” in one of two ways.Following Frege we could stipulate (for example) that a Christian is one who isbaptised into some closed set of recognized churches– hence everyone on the planetis either a Christian or not a Christian.
If we then stipulate who Frege is referring to
by“we” we can check whether the set defined by “we” is included within the setdefined by “Christian”.
QED.
Alternatively we can take the question in a non-
logical way, as asking (perhaps even rhetorically) whether the current trends in ourreligious beliefs and practices have taken us away from the original “true” notion ofChristianity. This way of answering the question requires a discussion about the truemeaning of Christianity – it becomes no longer a question about sets of entities andtheir set relations, but a question about concepts and how they should be defined.Having identified the fundamental core beliefs and values that we want the term“Christian” to imply, we can then come to some broad judgment about the degree towhich such values are prevalent within the group of people defined by “we” (whichin turn may not be well-defined as a group, but admit of clear and borderlinemembers).
This example illustrates the problem that we have. When we use language we may be either referring to sets in the world or alternatively asserting the meaning of ourwords.
I suspect that sentences such as “the cat is on the mat” with literal
interpretations
and straightforward truth evaluation, are quite rare in our daily
discourse. 4.
Conclusions about Vagueness
In sum, category vagueness provides support for prototype representations given anadditional assumption that the representation itself or the processes that utilize that
representation are subject to random or contextual noise. It is interesting that otherpsychological accounts of concepts, such as the theory-based view (Murphy & Medin,1985) have little to contribute to the discussion about vagueness.
It seems that
disagreement and inconsistency of categorization of familiar items, and the close linkbetween probability of categorization and similarity to the category are key pieces ofevidence in favour of the prototype view. Exemplar models however make much thesame predictions, since they share with prototypes the idea that categorization issimilarity-based and probabilistic.
Alternative philosophical accounts of the phenomenon of vagueness exist which do not require that concepts be prototypes.
In the case of epistemological uncertainty
however, it may be possible for peaceful coexistence between an externalist accountof concepts and a prototype-based account of our mental representations of thoseconcepts (see also Prinz, 2002). When it comes to the use of concepts as elements ofthoughts, to be combined compositionally through logical operations, then prototypesdo not have the right properties.
They have been shown to combine in non-logical
ways, and do not respect the clean rules of set logic.
To some, this is devastating
news for prototypes as a component of the future of cognitive science.
Our
conceptual thought is logical, so our thought cannot be based on prototypes.
To
others, this fact about prototypes goes some way to explaining the vast literature onhuman reasoning – we just are very bad at thinking logically most of the time,whereas we are pretty good at shifting the meaning of our terms mid-argument if itwill suit our purposes.
IV.
Typicality
Variation in the typicality of category members is often cited as one of the core tenetsof prototype theory. However it is questionable whether the simple fact of typicalityvariation itself is particularly discriminating between prototype theory and otheraccounts of concepts. The problem is that when instructed to judge typicality orgoodness-of-example it may be unclear just what aspect of the category memberspeople may be attending to. Barsalou (1985) found that there were several differentfactors involved in determining mean typicality scores for common taxonomiccategories like Bird or Fruit, including resemblance to other category members (aspredicted by prototype theory) but also frequency of instantiation (how often the itemis encountered) and fit to ideals (how well the item meets some goal or purpose – forexample for artifact concepts). Subsequently Medin and Atran (2004) have reportedthat in non-student populations the notion of “goodness of example” as originally
Hampton
Concepts as Prototypes
the item with some generic representation of the category. Increasing the difficulty ofdiscriminating the false items from the true items requires that a greater amount ofinformation needs to be retrieved, with the result that a greater difference is seen inresponse time for typical vs. atypical items, and atypical items are more likely to berejected from the category. Associative links between items and the category nameprovide
a
separate and
dissociable source
of variance
between
items affecting
categorization time. Hence typicality is not just associative strength.
Typicality continues to prove itself an important variable. A recent study by Kiran and Thompson (2003) will serve to illustrate this.
They set out to treat naming
deficits in four patients with fluent aphasia.
Over many weeks the patients were
trained in category sorting and naming of pictures, identifying semantic attributesapplicable to target pictures and answering yes/no questions about the features of thetarget. Patients were either trained with a set of 8 typical category items, or with a setof 8 atypical items, and generalisation was tested to 16 other category members.
The
results were striking.
Training on atypical items generalized to the rest of the
category, whereas training on typical items did not.
If one conceives of the category
concept as being represented by a prototype in a feature space then clearly activationof widely spaced atypical examples will generalize to the whole region of the space,whereas activation of a cluster of typical examples near the centre will generalize lesswidely.
(Similar conclusions were drawn from a quite different paradigm – the
release from Proactive Interference in short term recall – by Keller & Kellas, 1978).B.
S
TABILITY OF TYPICALITY JUDGMENTS
As with categorization decisions, there is also considerable variability in people’stypicality judgments. Barsalou (1987) conducted a series of studies of the instabilityof typicality ratings and rankings, and concluded that the high levels of shift in anindividual’s ratings from one occasion to another argued for prototypes beingconstructed in working memory anew each time a typicality rating task waspresented. In a recent study conducted with my student Lara Olufon we set outfurther to investigate the within-participant stability of typicality ratings. In particularwe tested a prediction of prototype theory that had not been tested before. Oneplausible source of variability in typicality judgments would be variation in therelative weight given to different aspects of the prototype. Perhaps on one occasion aperson feels that being sweet is the most important feature of a typical fruit, whereason other occasions they feel that being round is more important. The effect of thisvariation will be that the relative similarity of items to the prototype will change.
However this change will only be observed for items that have one but not the otherof the features. Items that have all of the features will still be the most typical,regardless of any shift in weight from one feature to another. In spatial terms, shifts indimensional weight that stretch or shrink different dimensions will leave the centre ofthe category unmoved, although distance of atypical items from the centre will beaffected. We therefore predicted that the items judged most typical would be leastlikely to shift their ranking on a retest a week later.
Note that it is also true that items with few or none of the prototype features should show less variability. However lacking enough features, these items would not fall inthe category, and so would not be included in a list of category members. Wehypothesized that all items in the category would have at least half of the full set ofweighted features. Hence variability should increase monotonically across thetypicality scale within the category.
A possible confound here is the extra stability of items at the two ends of a sequence. For example, the item judged most (or least) typical will still tend to bemost typical if its typicality increases, and will only risk a change in rank if itstypicality decreases. So the chances of a change are half as great for an end item asthey are for an item in the middle of the ranking order where a change either up ordown on the scale risks a change in the rank position. Items in the middle of a rankorder are also more likely to be jumped over by items on each side, than items at theend that have items on one side only. To control this confound, we compared thestability of items at the top end of the ranking (most typical), with those at the bottomend (least typical). Confounds due to position in the list relative to the end and themiddle should be equal for both ends, so the predicted extra stability of typical itemsshould show up as greater stability for the top end of the list compared with thebottom end of the list.
Nine category members were selected in each of 8 common taxonomic categories studied by Hampton & Gardiner (1983), such as birds, clothing and weapons. Carewas taken to space the items equally along the typicality scale. In addition, 9 categoryfeatures were selected for each category. Participants ranked the items for typicalityand the features for their importance. They did the same task on two occasions aweek apart, and correlations were calculated between the ranks given on eachoccasion. Median correlation between the first and second rankings was 0.77 for bothfeature importance and typicality rankings. Results also clearly showed greaterstability for the top four ranks in the list than the bottom four ranks. Mean probabilityof the top four most typically ranked items retaining the same typicality rank was0.33, and for the bottom four atypically ranked items was only 0.27. The difference
Hampton
Concepts as Prototypes
was significant on an ANOVA with end (top or bottom) and distance from the end (1– 4) as within-subjects factors.
Consistent with the hypothesis that instability in people’s concepts may reflect changes in the weights attributed to different prototype features, we therefore foundthat typical category members were more consistently ranked than were atypicalcategory members.
As a final demonstration that typicality is an effect of similarity, rather than availability or some other variable, I conducted a short study with Wenchi Yeh inwhich participants gave typicality judgments for items that (unknown to them) wereconstructed in quadruples. Within a quadruple were two pairs of similar items, whichwhen re-paired within the quadruple would constitute two pairs of dissimilar items.For example the pairs “goose and turkey” and “pelican and toucan” were similarpairs, which were then re-paired as “goose and pelican” or “turkey and toucan” tocreate dissimilar pairs. The measure taken was very simple – the degree ofcorrelation in the ratings or rankings given to each member of a pair, across thedifferent participants in the experiment. Thus for example, one group of studentsrated all the items for typicality, and then the correlation was calculated acrossindividuals of the ratings given to each member of a similar pair such as
goose:turkey
and to each member of a matched dissimilar pair such as
goose:pelican
. The idea
was that if individuals vary in the weight that they attach to different dimensions of aprototype, then there should be a stronger correlation for similar pairs than fordissimilar pairs. Having the same feature profile, similar pairs would move up ordown together as feature weights changed across individual raters, whereas dissimilarpairs would not. This was what was found. The stronger the similarity between apair of items, the larger the correlation between the ratings given to the items bydifferent people.C.
C
ONCLUSIONS ABOUT TYPICALITY
In sum, typicality effects can be identified that are not simply to do with thefamiliarity or availability of category members. Theories of concepts that do not basecategorization on similarity tend to be dismissive of typicality effects. Armstrong etal.’s (1983) results are often cited as discrediting the use of typicality to argue forprototype representations. However it is increasingly clear that a great many tasks areinfluenced by typicality effects, and these effects are rooted in differences ofsimilarity or degree of match between an item and a conceptual representation. Forprototype and exemplar theory, similarity-based typicality effects are a central plank
of the models. The wide range of such effects is therefore a key piece of evidence forthis type of theory.
V.
Genericity
Genericity in linguistics and the philosophy of language refers to sentences that either(a) refer to a kind rather than a particular, or (b) assert general properties
typically
true
of a class or individual. The following sentences illustrate these two phenomena:
The potato was first cultivated in South AmericaJohn smokes a cigar after dinner(examples and definition from Krifka et al. 1995, p2.)
In the first sentence “the potato” refers to the kind, not to an individual potato,whereas in the second the sentence implies that this is John’s usual habit, and not thatJohn never has dinner without smoking a cigar afterwards.
The two kinds of genericity coincide when people are asked to give general properties of a kind – which is the task that Rosch and Mervis (1975) used to developprototype theory. For our purposes then, genericity refers to the finding that peoplegenerate descriptions that are typically true of the concept, where “typically true”implies that typical category members will have the property, but atypical categorymembers may not.
A commonly observed phenomenon in all natural languages is the fact that many sentences may be neither universally true, nor simply false, but may instead be trueunder some notion of “generally true” or “typically true”. When asked to describebirds and say what is distinctive about them compared with other related categories,people will commonly start with “has wings” and “flies”, and then go on to describeother distinguishing features such as 2 legs, feathers, hatched from eggs andmigratory. There appears to be no intuitive difference to the respondent between therelevance of saying that birds fly and saying that they have feathers. This in spite ofthe fact that there are well-known examples of flightless birds, and many species ofinsect that fly, whereas all birds (at least before they are prepared for the oven) andonly birds have feathers. Given that there is a single defining feature – feathers – thatis both necessary and sufficient to discriminate birds from other types of creature, whydo people not recognize this fact and define the word’s meaning in this simple way?
In fact, birds turn out to be a rather special and potentially misleading case. Early theories of semantic memory such as the classic paper by Smith, Shoben & Rips
Hampton
Concepts as Prototypes
We thought it would be interesting to see how people responded when the sentences were universally quantified. Suppose now that you are asked to judge the likelihoodthat the following statements are true:
All ravens are black
All jungle ravens are black
All young jungle ravens are black
If people use their prototypes for constructing complex concepts in order to make these judgments, then they should continue to say that the sentences are less likely tobe true as the number of modifiers increases. However if the presence of a universalquantifier triggers Fodorian atomistic concepts and logical intersection, then it cannotbe the case that the first statement is more true than the others. Clearly in all worldsin which it is true that “all ravens are black”, it is also true that “all jungle ravens areblack” and similarly that “all young jungle ravens are black”. If a property holds trueof a whole class it must necessarily be true of any arbitrarily defined subset of thatclass.
Our results were overwhelmingly in favour of the prototype theory. Across both individuals and items the large majority had lower estimates of truth likelihood for themodified sentences than for the unmodified. We refer to this as the InverseConjunction Fallacy, since it takes the opposite form of Tversky and Kahneman’sConjunction Fallacy (Tversky & Kahneman, 1983), where likelihood estimates aregreater for a conjunction of facts than for a single component fact.
We followed this experiment with one in which we varied the mutability of the attributes in the predicate part of each sentence. Mutability has been established bySloman et al. (1998) as an important variable within conceptual representations. Asdiscussed in an earlier section, certain attributes in a conceptual representation areinvolved in many causal or other dependency relations with other attributes – forexample the motor of a car is involved in causal relations with the car’s function, itsneed of fuel, its contribution to pollution etc. Such attributes tend to be less mutable– it is harder to imagine an example of the concept that is like other examples in everyrespect except missing just this one feature.
We gave people a task in which they
had to choose the more likely of two generic sentences with modified subjects, onewith a mutable predicate (e.g. “Brazilian doves are white”) and one with a lessmutable predicate (e.g. “Brazilian doves have wings”). We discovered a strongpreference for the sentence expressing the less mutable feature. Thus not only isattribute information inherited by the complex concept (Brazilian dove) from thesimple noun concept prototype (dove), but the degree of confidence with which it is
inherited depends on the internal structure of the prototype, in keeping withHampton’s (1987) account of the formation of Composite Prototypes.B.
C
ONCLUSIONS ABOUT GENERICITY
Genericity is crucially important in the argument for prototypes. If it is true that werepresent a concept in terms of its typical features, then there is no requirement thatthose features will be true of all members of the category, and indeed people may noteven be aware, without conducting a memory search, of which features are universallytrue and which are not. Exemplar models would also not expect all features to be trueof all category members, but here an important failing of exemplar models comes tothe fore. Since they have been developed almost exclusively with respect to thecategorization of individual particulars, there is very little that the models have to sayabout categorization of whole classes or kinds, or the truth of generic statements abouta class. While they do a good job of predicting the learning dynamics andgeneralization performance for certain kinds of category structure, they have not beenset the task of deciding whether a class as a whole has a particular property, orwhether a class as a whole belongs in a superordinate class. In effect, thedevelopment of the models has been too restricted to tightly controlled artificialstimulus sets to offer much help with understanding many of the effects observed innatural language.
VI.
Opacity: The Failure of Category Definitions
The fourth phenomenon considered to support a prototype view of concepts is thedifficulty that has been encountered in generating good accurate definitions of themeanings of content words (particularly nouns and verbs) in any language. Thisproblem was famously expounded in Wittgenstein’s
Philosophical Investigations
(1953) in relation to the category of games. It appears that (in keeping with thediscussion of genericity above), people know lots of things about games – theyinvolve people, they take place over a period of time, they are done for their ownsake, they involve rules, they involve winning and losing, they are unpredictable – butno set of these different features can be found that discriminates games from non-games, except by using a prototype rule.
In work originally done for my PhD (Hampton, 1979), I interviewed people about their definitions of 8 different semantic categories. The questions included askingwhat was true of all category members, what was true of typical members, what would
Hampton
Concepts as Prototypes
make something a borderline case – what features it would have, and what it wouldlack, and even what the word might mean if applied metaphorically to a thing or aperson. Features were then listed, regardless of where in the interviews they weregenerated, and a separate group of people judged whether each of a list of potentialcategory members had those features. Finally a third group categorized the list ofitems and made judgments about how good a member they were, or how related anon-member they were.
The question was whether the set of category members
could be distinguished in terms of a set of common features. The results were thathalf of the categories could be defined in this way, but half could not. A similarproportion of definable categories was found by McNamara & Sternberg (1983) usinga procedure where each individual’s definitions was compared to their own categoryjudgments.
Of course the procedure is perhaps unnecessarily restrictive in its insistence on relying only on empirical evidence generated by respondents. Semanticists certainlytake a much more unconstrained view of how the task should be done. Thus:
... semanticists are not obliged to take informants’ judgments at face value.
(Wierzbicka, 1990),
or
... why should the “real meaning” of a word correspond to what people think of as themeaning of that word? Folk theories should no more be a criterion in semantics than they arein syntax or any other aspect of linguistics.
(Bouchard, 1995).
There is a serious issue here that arises frequently at the interface between psychology and other branches of cognitive science such as linguistics or philosophy.In a way reminiscent of the externalist theory of concepts propounded byphilosophers, it is common for semanticists to see the analysis of word meaning asbeing the analysis of an abstract cultural artifact, such that a word’s “true meaning inEnglish” need not correspond directly to its current usage. This is a knotty problemthat will take some unravelling. On the one hand, psychological methods can beaccused with some justification of being crude and open to unwanted demandcharacteristics. We know, for example, that when generating features of a word’smeaning people are driven by pragmatic considerations of trying to be as relevant aspossible. Thus they may neglect to mention many features of birds (such as “has aheart”) that they would nonetheless agree to be true, simply because they are lessrelevant to the perceived communicative goal of distinguishing birds from othercreatures. More recently psychologists have also taken to asking people for
metalinguistic reflections on concept meaning – for example rather than asking for thedefinition of a term, asking whether the term has a definition (Armstrong et al, 1983),or asking whether membership in a class is all-or-none or graded (Estes, 2004; Kalish,1995). This methodology, while instructive, is also subject to the same question – atwhat level should we take what people say about how their mind works as a constrainton our theory of the mind? We don’t study perception or attention this way (althoughresearchers may get some useful ideas via introspection), but somehow one feels thatconceptual contents just
are
what people claim they are. One is reminded of the wag
who claimed that Wagner’s music is not nearly as bad as it sounds.
There are some writers who still hold that given proper attention to the task and a degree of training, definitions of word meanings can be provided. Sutcliffe (1993)suggested that in following Wittgenstein psychologists have been looking in thewrong place for monothetic definitions of classes – it is not the many ways in whichgames resemble each other or differ that will tell you what constitutes a game, it is atthe more abstract level in which games are differentiated from other broad classes ofhuman activity. Wierzbicka (1972; 1985; 1987) has been the most tireless proponentof getting on with the task of actually giving definitions. For example her answer toWittgenstein is as follows (Wierzbicka, 1990, p. 469):
Games
Things that people do
When they do something for some time
For pleasure
Imagining that they are in a world
Where they want to cause some things to happen
Where they know what they can do and what they cannot do
And where no one knows all that will happen
This definition is proposed to apply to board games, card games, ball games etc. and to exclude non-games such as a child idly throwing a ball against a wall and catchingit again, which according to Wierzbicka would not be called a game in English. It is,in my view, a great pity that such definitions are not put to the test against a panel ofcompetent speakers of English, rather than being tested against the author’s (albeitexpert) intuitions. It is easy to suggest potential counterexamples – category membersthat the definition excludes such as games that are played for money rather thanpleasure (poker, professional golf), or games that are entirely predictable (simplecomputer games like space invaders), and non-members that are included such aswatching Reality-TV shows and voting for one’s least or most favourite participant in
Hampton
Concepts as Prototypes
about it. A descriptivist account of the contents of a concept will involve some set offeatures (i.e. broadly speaking a prototype). As a result if you and I differ in whetherwe think one of the features applies, then in effect we have
different concepts
. Given
the data on instability described earlier, it would then follow that like stepping in theproverbial river, we never access the same concept twice. An answer needs to begiven to this challenge, but (happily) space and time do not permit such a venture atthis point. Just to note that it is a challenge not just to prototype theory but to all ofcognitive science in as much as the latter aims to individuate concepts by representingconceptual contents (Fodor, 1998).
VII.
Conclusions
I have covered a considerable amount of ground in this discussion of current issuesconcerning prototype representations. I hope to have convinced the reader that inspite of the unpopularity in certain quarters of prototype theory as a serious contenderfor representing concepts, the phenomena of prototypes are still with us, and still inneed of explanation. Four major types of phenomenon have been reviewed, all ofwhich seem to fit best with the prototype theory:
a.
Membership in conceptual categories is vague, not only because peopledon’t know enough about the domain, but also because word meanings areflexible and cannot be pinned down.
b.
Degrees of typicality within a category influence a wide range of cognitiveprocesses – from category-based induction, through memory interferenceand sentence processing, to the treatment of aphasics, and variation intypicality is not just about familiarity or availability of concepts in memory,but about similarity to the rest of the class.
c.
The problem of how to treat the semantics of generic sentences is one ofmajor importance, and prototype theory is the only account of conceptrepresentation that explains why so much of our semantic knowledge takesthe form of statements that are “typically” true, rather than having auniversally quantified truth. It is also the only approach that explains thenon-logical combination of concepts under different forms of linguisticconnective.
d.
Finally the difficulty of defining word meanings remains a live issue.Prototype concepts cannot by their nature be simply defined. The problemcan be stipulated away by taking an atomistic view, or it can be pushed backa level by taking a deference view, but neither of these will ever be acomplete account of how the individual brain is able to use its internal
representation of concepts for understanding, thinking and talking about itsworld.
At various points, I have tried to bring into the discussion notions that are common currency in philosophy, such as the Externalist view of conceptual contents, and ideasof deference and conceptual atomism. The integration of philosophy, lexicalsemantics and psychology into a true cognitive science of concepts is still a ratherdistant goal. Not only are the methods of enquiry of the three fields very different, butthe value placed on different kinds of evidence varies widely as do the intuitiveassumptions that drive the development of theory. However the goal remains acrucially important one. It should be possible for example for philosophy to setinteresting research agendas for psychology, and for the data from psychology andlinguistics to pose theoretical challenges for philosophy. The final unifying theory ofconcepts will need to explain how people’s use of language is vague, variable, genericand opaque, as well as explaining how concepts can be reduced to atomic symbols forthe understanding of logical reasoning. After all, Gödel and Frege, Wittgenstein andRussell developed their notions of the logical forms of natural reasoning with just thesame biological apparatus as the rest of us. The mistake is to take our ability toappreciate the logical necessity of simple arguments such as A^B
A as the paradigm
case of thought that requires explaining. Our minds have evolved to find it much lesseffortful to run down the vaguely drawn channels characterized by the range ofphenomena reviewed here. The central notion of a prototype remains at the heart ofour understanding of this way of thinking.
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