How can we dene the meaning of a word?

October 22, 2014

1 Introduction

Despite the fact that the mental lexicon appears to be organized by meaning (at

least partially) [Marslen-Wilson, 1994, Meyer and Schvaneveldt, 1971], there is

no consensus on what word meaning... means [Braun and Sider, 2007]. Many

dierent, pairwise incompatible theories of meaning were proposed as solutions

during the last century.

To provide a basis for comparing these dierent theories, I will begin with

an overview of the explanatory work a theory of meaning is expected to do.

After establishing the comparison criteria, I will present three competing

theories (the classical, prototype and exemplar theories) by summarizing their

claims and evaluating their explanatory performance.

In the conclusion, I will single out exemplar theory as the most promising

candidate, and attempt to identify possible future directions.

2 Comparison criteria

The quality of a scientic theory is a function of its explanatory power. This

section provides a short review of several inuential linguistics studies. In the

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sequel, I will compare the competing theories by their ability to account for the

phenomena revealed by these experimental results.

For detailed explanations of the experiments, the reader is referred to the

respective original papers.

2.1 Typicality

In 1973, Rips et al.[Rips and Smith, 1973] demonstrated the existence of a typ-

icality gradient: people classied some species of birds as more typical than

others, and this typicality was shown to correlate with the verication time of

sentences involving these species. The usual example: robins are rated more

typical than eagles, and verifying the truth of Aneagleisabird takes more time

than that of A robin is a bird .

The results have been replicated for various categories including clothing,

vegetables and furniture, as well as dierent sentence processing tasks [Rosch.E., 1975].

Somewhat surprisingly, even abstract number-theoretic categories (e.g. prime

numbers) display typicality eects

[Armstrong and Gleitman, 1983].

2.2 Fuzzy Boundaries

Some categories have fuzzy boundaries. On the level of a single individual,

one thinks of where a cup ends or a bowl begins (which may depend on its

contents!) [Labov, 1973], on the interpersonal level, more pressing issues, e.g.

the controversial boundary between fetus and human being in the abortion

debates.

Cognitive anthropoligsts were not the rst to notice the issue of fuzzy degree

of membership (despite what some sources claim! [CogLinWiki, 2014]). Indeed,

while Aristotle armed the existence of essential properties, he regarded mean-

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ing as inherently fuzzy and ambigous, at least on the interpersonal level; so have

most philosophers since then [Tierney, 2002, Peirce, 1902].

The most important study is due to Labov [Labov, 1973]: no set of attributes

(in their case, opposing sentences) is sucient to unambigously separate bowls

from cups. However, a careful analysis of the data led to the creation of an

accurate linear classier

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.

2.3 Knowledge Eect

Background knowledge also aects categorization, as well as determination of

meaning. Best exemplied by the recenty study of Lin et al. [Lin and Murphy, 1997]:

the same items in the synthetic category tut get wildly dierent typicality scores

depending on whether tuts are introduced as agricultural or venatic tools.

2.4 Mental Lexicon

An important goal for a theory of meaning (at least w.r.t. linguistics) is ex-

plaining the organization of the mental lexicon. Several studies indicate that

the mental lexicon is organized semantically. The most important experimental

idea of this eld is priming: the observation that detecting or recalling a stim-

ulus biases the processing speed of subsequent stimuli [Marslen-Wilson, 1994,

Meyer and Schvaneveldt, 1971]. An example, certainly semantic: dog is a prime

for wolf [Matsukawa, 2005]. The verication time eects in typicality are also

instances of priming.

Another phenomenon that requires explanation is that humans can acquire

new vocabularly, and that newly learned words take their place among the

others. Related to that, one should also mention compositionality: the common

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attributes are assigned weights, the sum of all weights (hence linearity) is proportional to

predicted degree of membership

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sense observation that the meaning of a compound depends on the meaning of

its constitutents[Kamp and Partee, 1995].

3 Theories of Meaning

3.1 The Classical (Aristotelian) Theory

3.1.1 Description

A misnomer, since the theory is neither classical nor related to Aristotle. In its

clearest formulation, given by Labov

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[Labov, 1973], the classical theory holds

that meaning is

discrete: concepts are clearly separated from each other by formal or functional

properties,

invariant: all occurrences of a concept are the same,

conjunctively-dened: all essential properties must be present together for a

concept to be recognized,

composed-of-atomic-primitives: categories cannot be subdivided indenitely;

i.e. every concept satises a unique checklist of criteria.

A typical example would be bachelor, supposedly satisfying the unique checklist

{unmarried,male}. Which is, of course, nonsense: what about a four yearold boy, or the Pope? Wittgenstein once remarked that no-one ever produced

a working example of a denitional analysis, and not for the lack of trying

[Wittgenstein, 1953]!

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amusingly in the form of a classical checklist!

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3.1.2 Evaluation

The classical theory has little to say about typicality. By the way, this is not

very surprising, since refuting this theory was an overarching goal of Rosch's

typicality studies [Rosch.E., 1975]. Indeed, if verifying X is a bird involves a

unique checklist, then it should take the same time for any bird X, but this

is not what happens [Rips and Smith, 1973]. This also shows that the mental

lexicon is not organized according to classical meaning. Needless to say, unique

checklists also oppose fuzzy membership.

What about compositionality? One observes that adjectives don't commute

with hyponyms: hamsters are animals, but large hamsters are usually not

large animals. This is at odds with a unique checklist for the word large3.

3.2 Prototype Theory

3.2.1 Description

In the face of the numerous unexplained experimental phenomena, classical

theory becomes untenable. Rosch's study provides the foundation for the most

popular family of alternatives, the so-called prototype theories.

The dening

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feature is the presence of prototypes, i.e. summary representa-

tions of concepts. The common variant (identied by Hampton [Hampton, 1979],

and clearly inspired byWittgenstein's idea of family resemblances [Kamp and Partee, 1995])

holds that a prototype is akin to a list of related features, weighted by impor-

tance. Unlike the classical checklists, these feature lists don't care about dis-

creteness, conjunctiveness or even consistency - e.g. a prototype for the word

dog will include the attributes short hair and long hair, as well as beige

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Some advocates of the classical theory react by claiming that large is polysemous. Sincepositing enough polysemy can account for any empirical observation, one would prefer a

classical explanation for why this systematic polysemy occurs in the rst place.

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Another essentialist notion! Should I say prototypical?

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and black, presumably with dierent weights!

3.2.2 Evaluation

Prototype theory is consistent with typicality

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eects: an instance is more typ-

ical than another if it has a higher weight of prototypical features. It is still

unclear why X isabird is easier to verify for typical birds than for atypical ones,

but at least one does not see an outright contradiction.

The situation is even better with fuzzy boundaries. The weighted lists pro-

vide a very natural framework for that. Armstrong observes that words with def-

initional meanings (e.g. odd) still display typicality eects [Armstrong and Gleitman, 1983].

However, this causes no actual problems, as long as one distinguishes typicality

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from fuzzyness

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. After all, an eagle, while atypical, is still unambigously a bird!

On the other hand, it seems that prototype theory cannot account for the

semantic structure of the mental lexicon. Compositionality is the usual culprit.

Armstrong observes that if you combine, say foolish and bird into the phrase

foolish bird, it is no longer a xed matter... which foolish elements and which

bird elements are intended to be combined ([Armstrong and Gleitman, 1983]

p. 272), and there are too many phrasal categories to be mentally represented in

terms of prototypes [Armstrong and Gleitman, 1983, Kamp and Partee, 1995].

Barsalou's experiment is denitive: people can make up categories on-the-y

(e.g. clothing to take on a vacation), and even these ad-hoc categories, not

described by a single word, produce typicality eects [Barsalou, 1983]. Such

categories could not have been stable mental representations.

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its raison d'tre

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goodness of exemplar

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degree of membership

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3.3 Exemplar Theory

3.3.1 Description

Another reaction to the failures of the classical theory, this one due to Medin

[Medin and Schaer, 1978]. The exemplar theory rejects summary representa-

tions, opting instead for memories, e.g. the concept of dog being represented

by the set of all remembered dogs. These memories are supposed to provide a

basis for classication whenever a new object is encountered.

Exemplar theory is a radical departure from the previous theories. On one

hand, exemplars avoid the drawbacks of the classical and prototype theories, on

the other hand, exemplar theory faces its own new, unique challanges.

3.3.2 Evaluation

Exemplar theory is the natural setting for typicality phenomena. Typical items

are the ones that are the most similar to the remembered category members.

This explains why e.g. a robin is a more representative bird than an eagle or

an ostrich. Typical items are easier to categorize because they are similar to

more category members [Medin and Schaer, 1978].

Exemplars convincingly account for fuzzy boundaries: a newly encountered

object can easily be similar to two or more remembered categories (e.g. both

tocups and to bowls).

Mental lexicon eects work so-so: priming is relegated to the realm of general

memory, and one gets an eective

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explanation for compositionality.

The main diculty is with explaining knowledge eects: the study on tuts

comes to mind [Lin and Murphy, 1997]. How can the typicality score of certain

items be decided before any exemplars are encountered? Here, one reaches the

explanatory limits of the theory [Nosofsky, 2011].

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if not unproblematic; can there really be a set of remembered foolish things?

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Theory Typicality Fuzzy Boundaries Knowledge Eect Mental Lexicon eects

Classical + Prototype + + + Exemplar + + +

Table 1: Comparison of the theories of meaning

4 Conclusion

As Table 1 shows, there is no denitive end to the meaning debate. At least

the failure of the classical model should be clear. Its successors, the prototype

and exemplar theories, are much more powerful, but they still have signicant

explanatory blind spots.

The question of the mental lexicon is fundamental, yet Barsalou's work shows

that prototype theory will not be able to account for that [Barsalou, 1983].

The strongest candidate is therefore exemplar theory, which at least doesn't

contradict the experimental evidence [Nosofsky, 2011]. One could hope for a

further generalized exemplar theory, which solves the remaining issues. But are

there new paradigms emerging?

There's a lot of future directions to explore. Exemplar theory presumably

needs to be integrated with theories of memory formation, which should provide

evidence for the soundness of the concept. The case for prototypes is strong as

well: while pure prototype theory cannot work, a pluralist approach could still

maintain the word meaning has both prototype and exemplar features.

Either way, we're far from done: while we have come a long way since the

days of the classical, a truly satisfactory theory should correctly predict the

results of these experiments, but it should also speak about several phenomena

that we couldn't take into account

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in this comparison: basic level categories,

superordinates, induction, continuous valuations etc. Until we get there, the

nature of meaning remains a mystery.

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mostly because the present theories are agnostic or silent on these issues

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