Explanation: This document is an attempt to make an arcane and
not very well understood area of inquiry intelligible to someone who
knows no logic or linguistics. It was originally written for an
encyclopedia that wanted something accessible even to a pre-high-school
audience. But it doesn't appear in any encyclopedia, because I wasn't
willing to write something to the editors' specifications, and they
weren't willing to change their specifications. This episode is yet
another example of how bad a job semanticists have done of making even
well-informed laymen aware of what the issues are in the field.
Semantics is the study of the meaning of linguistic expressions.
The language can be a natural language, such as English or Navajo, or
an artificial language, like a computer programming language. Meaning
in natural languages is mainly studied by linguists. In fact,
semantics is one of the main branches of contemporary linguistics.
Theoretical computer scientists and logicians think about artificial
languages. In some areas of computer science, these divisions are
crossed. In machine translation, for instance, computer scientists may
want to relate natural language texts to abstract representations of
their meanings; to do this, they have to design artificial languages
for representing meanings.
There are strong connections to philosophy. Earlier in this
century, much work in semantics was done by philosophers, and some
important work is still done by philosophers.
Anyone who speaks a language has a truly amazing capacity to
reason about the meanings of texts. Take, for instance, the sentence
(S) I can't untie that knot with one hand.
Even though you have probably never seen this sentence, you can
easily see things like the following:
- The sentence is about the abilities of whoever spoke or
wrote it. (Call this person the speaker.)
- It's also about a knot, maybe one that the speaker
is pointing at.
- The sentence denies that the speaker has a certain
ability. (This is the contribution of the word
- Untying is a way of making something not tied.
- The sentence doesn't mean that the knot has one hand;
it has to do with how many hands are used to
do the untying.
The meaning of a sentence is not just an unordered heap of the
meanings of its words. If that were true, then ‘Cowboys ride
horses’ and ‘Horses ride cowboys’ would mean the
same thing. So we need to think about arrangements of meanings.
Here is an arrangement that seems to bring out the
relationships of the meanings in sentence (S).
[ [ [Make [Not [Tied]]]
[That knot ] ]
[With One Hand] ]
The unit [Make [Not [Tied]] here corresponds to the act of untying;
it contains a subunit corresponding to the state of being untied.
Larger units correspond to the act of untying-that-knot and to
the act to-untie-that-knot-with-one-hand. Then this act combines
with Able to make a larger unit, corresponding to the state of
being-able-to-untie-that-knot-with-one-hand. This unit combines
with I to make the thought that I have this state -- that is, the
thought that I-am-able-to-untie-that-knot-with-one-hand. Finally,
this combines with Not and we get the denial of that thought.
This idea that meaningful units combine systematically to
form larger meaningful units, and understanding sentences
is a way of working out these combinations, has probably been the most
important theme in contemporary semantics.
Linguists who study semantics look for general rules that
bring out the relationship between form, which is the observed
arrangement of words in sentences, and meaning. This is interesting
and challenging, because these relationships are so complex.
A semantic rule for English might say that a simple sentence
involving the word ‘can't’ always corresponds to a meaning
Not [ Able ... ],
but never to one like
Able [ Not ... ].
For instance, ‘I can't dance’ means that I'm unable to dance; it
doesn't mean that I'm able not to dance.
To assign meanings to the sentences of a language, you need
to know what they are. It is the job of another area of linguistics,
called syntax, to answer this question, by providing rules that
show how sentences and other expressions are built up out of smaller
parts, and eventually out of words. The meaning of a sentence
depends not only on the words it contains, but on its syntactic
makeup: the sentence
(S) That can hurt you,
for instance, is ambiguous -- it has two distinct meanings.
These correspond to two distinct syntactic structures. In one
structure ‘That’ is the subject and ‘can’ is an
auxiliary verb (meaning “able”), and in the other
‘That can’ is the subject and ‘can’ is a noun
(indicating a sort of container).
Because the meaning of a sentence depends so closely on its
syntactic structure, linguists have given a lot of thought to the
relations between syntactic structure and meaning; in fact, evidence
about ambiguity is one way of testing ideas about syntactic
You would expect an expert in semantics to know a lot about
what meanings are. But linguists haven't directly answered this
question very successfully. This may seem like bad news for
semantics, but it is actually not that uncommon for the basic
concepts of a successful science to remain problematic: a physicist
will probably have trouble telling you what time is. The nature of
meaning, and the nature of time, are foundational questions that are
debated by philosophers.
We can simplify the problem a little by saying that, whatever
meanings are, we are interested in literal meaning. Often,
much more than the meaning of a sentence is conveyed when someone uses
it. Suppose that Carol says ‘I have to study’ in answer
to ‘Can you go to the movies tonight?’. She means that
she has to study that night, and that this is a reason why she can't
go to the movies. But the
sentence she used literally means only that she has to study.
Nonliteral meanings are studied in pragmatics, an area of
linguistics that deals with discourse and contextual effects.
But what is a literal meaning? There are four sorts of
answers: (1) you can dodge the question, or (2) appeal to usage, or
(3) appeal to psychology, or (4) treat meanings as real objects.
(1) The first idea would involve trying to reconstruct
semantics so that it can be done without actually referring to
meanings. It turns out to be hard to do this -- at least, if you want
a theory that does what linguistic semanticists would like a theory to
do. But the idea was popular earlier in the twentieth century,
especially in the 1940s and 1950s, and has been revived several times
since then, because many philosophers would prefer to do without
meanings if at all possible. But these attempts tend to ignore the
linguistic requirements, and for various technical reasons have not
been very successful.
(2) When an English speaker says ‘It's raining’
and a French speaker says ‘Il pleut’ you can say that
there is a common pattern of usage here. But no one really knows how
to characterize what the two utterances have in common without somehow
invoking a common meaning. (In this case, the meaning that it's
raining.) So this idea doesn't seem to really explain what meanings
(3) Here, you would try to explain meanings as ideas. This is
an old idea, and is still popular; nowadays, it takes the form of
developing an artificial language that is supposed to capture the
"inner cognitive representations" of an ideal thinking and speaking
agent. The problem with this approach is that the methods of
contemporary psychology don't provide much help in telling us in
general what these inner representations are like. This idea doesn't
seem yet to lead to a methodology that can produce a workable
(4) If you say that the meaning of ‘Mars’ is a
certain planet, at least you have a meaning relation that you can come
to grips with. There is the word ‘Mars’ on the one hand,
and on the other hand there is this big ball of matter circling around
the sun. This clarity is good, but it is hard to see how you could
cover all of language this way. It doesn't help us very much in
saying what sentences mean, for instance. And what about the other
meaning of ‘Mars’? Do we have to believe in the Roman god
to say that ‘Mars’ is meaningful? And what about
‘the largest number’?
The approach that most semanticists endorse is a combination
of (1) and (4). Using techniques similar to those used by
mathematicians, you can build up a complex universe of abstract
objects that can serve as meanings (or denotations) of various sorts
of linguistic expressions. Since sentences can be either true or
false, the meanings of sentences usually involve the two
truth values true and false. You can make up
artificial languages for talking about these objects; some
semanticists claim that these languages can be used to capture inner
cognitive representations. If so, this would also incorporate
elements of (3), the psychological approach to meanings. Finally, by
restricting your attention to selected parts of natural language, you
can often avoid hard questions about what meanings in general are.
This is why this approach to some extent dodges the general question
of what meanings are. The hope would be, however, that as more
linguistic constructions are covered, better and more adequate
representations of meaning would emerge.
Though "truth values" may seem artificial as components of
meaning, they are very handy in talking about the meaning of things
like negation; the semantic rule for negative sentences says that
their meanings are like that of the corresponding positive sentences,
except that the truth value is switched, false for true and
true for false. ‘It isn't raining’ is true
if ‘It is raining’ is false, and false if ‘It is
raining’ is true.
Truth values also provide a connection to validity and to
valid reasoning. (It is valid to infer a sentence S2 from S1 in
case S1 couldn't possibly be true when S2 is false.) This interest
in valid reasoning provides a strong connection to work in the
semantics of artificial languages, since these languages are usually
designed with some reasoning task in mind. Logical languages are
designed to model theoretical reasoning such as mathematical proofs,
while computer languages are intended to model a variety of general
and special purpose reasoning tasks. Validity is useful in working
with proofs because it gives us a criterion for correctness. It is
useful in much the same way with computer programs, where it can
sometimes be used to either prove a program correct, or (if the proof
fails) to discover flaws in programs.
These ideas (which really come from logic) have proved to be
very powerful in providing a theory of how the meanings of
natural-language sentences depend on the meanings of the words they
contain and their syntactic structure. Over the last forty years or
so, there has been a lot of progress in working this out, not only for
English, but for a wide variety of languages. This is made much
easier by the fact that human languages are very similar in the kinds
of rules that are needed for projecting meanings from words to
sentences; they mainly differ in their words, and in the details of
their syntactic rules.
Recently, there has been more interest in lexical semantics --
that is, in the semantics of words. Lexical semantics is not so much
a matter of trying to write an "ideal dictionary". (Dictionaries
contain a lot of useful information, but don't really provide a theory
of meaning or good representations of meanings.) Rather, lexical
semantics is concerned with systematic relations in the meanings of
words, and in recurring patterns among different meanings of the same
word. It is no accident, for instance, that you can say ‘Sam
ate a grape’ and ‘Sam ate’, the former saying what
Sam ate and the latter merely saying that Sam ate something. This
same pattern occurs with many verbs.
Logic is a help in lexical semantics, but lexical semantics is
full of cases in which meanings depend subtly on context, and there
are exceptions to many generalizations. (To undermine something is to
mine under it; but to understand something is not to stand under it.)
So logic doesn't carry us as far here as it seems to carry us in the
semantics of sentences.
Natural-language semantics is important in trying to make
computers better able to deal directly with human languages. In one
typical application, there is a program people need to use.
Running the program requires using an artificial language (usually, a
special-purpose command language or query-language) that tells
the computer how to do some useful reasoning or question-answering
task. But it is frustrating and time-consuming to teach this
language to everyone who may want to interact with the program. So
it is often worthwhile to write a second program, a natural
language interface, that mediates between simple commands in a
human language and the artificial language that the computer
understands. Here, there is certainly no confusion about what a
meaning is; the meanings you want to attach to natural language
commands are the corresponding expressions of the programming
language that the machine understands.
Many computer scientists believe that natural language
semantics is useful in designing programs of this sort. But it is
only part of the picture. It turns out that most English sentences
are ambiguous to a depressing extent. (If a sentence has just five
words, and each of these words has four meanings, this alone gives
potentially 1,024 possible combined meanings.) Generally, only a few
of these potential meanings will be at all plausible. People are
very good at focusing on these plausible meanings, without being
swamped by the unintended meanings. But this takes common sense, and
at present we do not have a very good idea of how to get computers to
imitate this sort of common sense. Researchers in the area of
computer science known as Artificial Intelligence are working on
Meanwhile, in building natural-language interfaces, you can
exploit the fact that a specific application (like retrieving answers
from a database) constrains the things that a user is likely to say.
Using this, and other clever techniques, it is possible to build
special purpose natural-language interfaces that perform remarkably
well, even though we are still a long way from figuring out how to
get computers to do general-purpose natural-language understanding.
Semantics probably won't help you find out the meaning of a
word you don't understand, though it does have a lot to say about the
patterns of meaningfulness that you find in words. It certainly
can't help you understand the meaning of one of Shakespeare's
sonnets, since poetic meaning is so different from literal meaning.
But as we learn more about semantics, we are finding out a lot about
how the world's languages match forms to meanings. And in doing that,
we are learning a lot about ourselves and how we think, as well as
acquiring knowledge that is useful in many different fields and