Semantics: a coursebook, second edition

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From reference . . .
80
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(1) (b) (2) (c) (3) (a) (4) square, expensive, under, love (5) (b)
If you have scored at least 4 out of 5 correct, continue to the introduction.
Otherwise, review the relevant unit.
Introduction We have outlined the basic distinction between sense and reference (Unit 3)
and explored details of the use of reference (Units 4–7). In subsequent units
(9–11) we will develop the idea of sense in similar detail. The present unit
will act as a bridge between the preceding units on reference and the
following units on sense, introducing several notions, including extension
and prototype, which in certain ways bridge the conceptual and theoretical
gap between sense and reference. In other words, we are going to try to pin
down more speci
fically how the notions of sense and reference are related to
each other in determining the meaning of a linguistic expression.
To show what we mean when we talk of a ‘gap’ between reference and sense,
we look 
first at the question of how much a knowledge of the reference of
referring expressions actually helps a speaker in producing and understanding
utterances which describe the world he lives in.
Practice (1) In the case of expressions with constant reference, such as 
the Sun or the Moon, could a speaker be said to know 
what they refer to simply by having memorized a 
permanent connection in his mind between each 
expression and its referent?
Yes / No
(2) In the case of expressions with variable reference, such as
the man or the middle of the road, could a speaker be said
to know what they refer to by having memorized a
permanent connection in his mind between each expression
and its referent?
Yes / No
(3) How, in a given situation, would you know that in saying ‘the cat’ I was
not referring to a man sitting in an armchair, or to a book in his hand, or
to the clock on the mantelpiece? (Remember, from your answer to
question (2), that it cannot be because you have memorized a connection
between the expression the cat and some particular object, a cat, in the
world.)
..........................................................................................................................
(4) Might it seem reasonable to say, in the case of a referring 
expression with variable reference, such as the cat, that a 
speaker has memorized a connection between the expression 
and a set, or type, of the expression’s potential referents?
Yes / No
(5) How many potential referents are there for the expression the cat?
..........................................................................................................................

U N I T   8
Words and things: extensions and prototypes
81
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(1) Yes (2) No, because for such expressions there is no single referent with
which the speaker could establish a permanent connection in his mind.
(3) Because you know that the expression the cat can only refer to a cat,
and not to anything which is not a cat, and you know that men, books,
and clocks are not cats. (4) Yes (5) As many as there are (or have been, or
will be) cats in the world – certainly a very large number.
Comment The point that we are spelling out here is that someone who knows how to
use the word cat has an idea of the potential set of objects that can be
referred to as cats, i.e. he has some concept of the set of all cats. (This idea or
concept may only be a vague, or fuzzy, one, but we will come back to that
point later.) This leads us to the notion of the extension of a predicate.
Definition  The EXTENSION of a one-place predicate is the set of all individuals to 
(partial) which that predicate can truthfully be applied. It is the set of things which
can POTENTIALLY be referred to by using an expression whose main
element is that predicate.
Example The extension of window is the set of all windows in the universe.
The extension of dog is the set of all dogs in the universe.
The extension of house is the set of all houses.
The extension of red is the set of all red things.
Comment In the case of most frequent common nouns, at least, an extension is a set of
physical objects. Thus, extension contrasts with sense, since a sense is not a set
of anything. And extension contrasts with referent, since a referent is normally
an individual thing, not a set of things. Beside these contrasts, the notion of
extension has similarities to that of sense, on the one hand, and to that of
reference, on the other. Extension is like sense, and unlike reference, in that it is
independent of any particular occasion of utterance. Speakers refer to referents
on particular occasions, but words which have sense and extension have them
‘timelessly’. On the other hand, extension is like reference and unlike sense, in
that it connects a linguistic unit, such as a word or expression, to something
non-linguistic (i.e. outside language) be it a set of physical objects or an
individual physical object, or a set of abstract entities (e.g. songs, distances) or
an individual abstract object (e.g. a particular song, a speci
fic distance).
Practice (1) In the light of the above comment,
fill in the chart with ‘
’ and ‘’ signs
to indicate the di
fferences and similarities between these three concepts.
Sense
Extension
Reference
Involves a set
Independent of particular 
occasions or utterance
Connects language to 
the world

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