FORMAL SEMANTICS - Yilmaz Kilicaslan

Handout 2
Some Basic Assumptions
Yılmaz Kılıçaslan
October 01, 2009
What Semantics Deals With
Semantics misses an advantage enjoyed by many other sciences. It cannot like them has a
clear-cut answer to the question of what it deals with. In rough terms, semantics is concerned
with the meaning of signs. No one would dispute this definition. However, this concise
definition leaves us with two new questions:
1. What is the meaning of meaning?
2. What is a sign?
The Meaning of Meaning
The first question sounds somehow paradoxical. From one point of view, one may argue that
there is no reason for asking such a question: as we are all homo significans - meaningmakers, we are all supposed to know what meaning is. However, even great philosophers are
not in agreement with respect to the characterization of meaning. For John Locke, meaning’s
natural home is the mind. For Hilary Putnam, "meanings just ain't in the head!" but it is the
external world that accommodates them. A third-approach is to postulate a third realm, a
realm of senses, which coordinates the elements in the equation of meaning. It was Gottlob
Frege who adapted this Platonic approach to modern philosophy. Besides, some philosophers
do not want to be entirely engaged in any of these approaches. Jon Barwise and John Perry
think themselves “as pursuing the second strategy while exploiting insights of the third, in a
way that explains the motivations behind the first.” (pp. 4-5)
Obviously, a study on semantics cannot start by taking the meaning of meaning for granted.
This, of course, does not mean that we are totally ignorant with regard to this issue. If we
knew nothing of what meaning is, we would not be able to ask or make sense out of the
question above: the question would have been constructed by predicating something unknown
of itself.
Fortunately, things are rarely discrete: apparently, we are neither totally ignorant of what
meaning is nor are we clearly aware of its precise characterization. As we are meaningmakers, we certainly have a prescientific concept of meaning. But, the problem is that this
prescientific concept seems to be too slippery to serve as a basis for semantics. Among many
others, Putnam (1975) holds the view that “the reason that so-called semantics is in so much
worse shape than syntactic theory is that the prescientific concept on which semantics is based
– the prescientific concept of meaning – is in much worse shape than the prescientific concept
of syntax.” (p. )
That slipperiness of meaning has led some linguists, particularly those working within the
tradition of transformational generative grammar, “to regard semantics as an intractable,
perhaps ultimately unfathomable, part of language.” (Dowty et al. p. 1) We surely do not
share this pessimism. Our prescientific concept of meaning is an intuitive one. We are of the
opinion that this intuition derives from our daily practice of making meaning. Hence, we can
sharpen our intuition by scrutinizing concrete meaningful cases and thereby find our way. Let
us start with a specific example.
Smoke means fire.
Transitive verbs encode relations between at least two items, namely the referents of their
subject and object. As mean is used as a transitive verb in (1), it is not unreasonable to take
meaning to be a relation. Meaning as a relation is a cornerstone idea of Barwise and Perry’s
situation semantics. In their theory, meaning in general, and linguistic meaning in particular,
is characterized as a relation between situations, where situations are parts of reality with
individuals having properties and standing in relations at various spatiotemporal locations.
They maintain that an organism’s felicitous survival depends on its attunement to those
relations between situations that are significant to its well-being. The explanation they offer
for the example above derives from this view of meaning:
There is a lawlike relation between smoke and fire. Situations where there is
smoke are, by and large, close to situations where there is fire. And it is
attunement to this relation that enables us to learn about fires from smoke. Being
attuned to this relation does not presuppose language, only the ability to detect
smoke, to respond in some way appropriate to fire, and to do the latter on the
occasion of the former. (Barwise and Perry 1999: 12)
For situation theoreticians, attunement to a meaning relation amounts to picking up
information about one situation from another. In the given example, it is the smoky situation
that yields information about another situation, namely the fire situation. In fact, situation
semantics offers an information-theoretic account of meaning where the property of being
meaningful is equated with the property of being informative.
Several further remarks are in order about the meaning relation. Probably the most
straightforward one is that this is not a symmetrical relation. Sentence (1) says that smoke
carries information about fire; but not the other way around. In more technical terms, smoke is
the signifier and fire is the signified. Furthermore, we know that it is out of the causal relation
between fire and smoke that the meaning relation in (1) arises. However, the latter (i.e. the
meaning relation) should not be identified with the former (i.e. the causal relation). That is,
sentence (1) is not synonymous with sentence (2).
Fire causes smoke.
Causation is a relation that resides in the material world, whereas meaning is a mental
relation. More precisely, no meaning relation exists in the absence of cognitive organisms.
Barwise and Perry (1999) make this point clear particularly for expressions:
If expressions were not systematically linked with kinds of events, on the one
hand, and states of mind, on the other, their utterance would convey no
information; they would be just noises or scribbles, without any meaning at all.
These systematic links are essential to meaning, and for this reason essential to
any theory of meaning as well. (Barwise and Perry 1999: 3)
Judge (1985) states the necessary involvement of a third element in a meaning relation in
stronger and more general words (and makes this statement a major theme of his book entitled
‘Thinking About Things’):
… no signifier yields information by itself; it must be referred to by some agent to
some feature or features of the real world. (Judge, 1985: 4)
The rather implicit cognitive element is sometimes explicitly encoded by a to-phrase:
Smoke means fire to us.
It is worth noting that the same adjunction is not possible for the sentence expressing a causal
*Fire causes smoke to us.
In contrast to the meaning relation, the causal relation holds in the material world in a way
independent of any cognitive activity.
We have now the constituting elements of a sign: a signifier, a signified and a cognitive state.
As Chandler points out, we, as homo significans, make meanings through our creation and
interpretation of signs. Some philosophers (such as Peirce) even argue that we think only in
signs. We are certainly good users of signs. But, this certainly does not mean that we know
very well what signs are.1 We know what they are for, i.e. its function. However, we need to
have a closer look at its structure.
There are two dominant views as to the structure of a sign: that of the linguist Ferdinand de
Saussure and that of the philosopher Charles Sanders Peirce.
Saussurean Sign
Below is a Saussurean diagram of the sign.
For Saussure, a sign has a dyadic or two-part structure: a sign is a union of a signifier
(signifiant) and a signified (signifié). The signifier is the form which the sign takes and the
signified is the concept it represents. A sign is always a combination of these two. It is not
possible to have a totally meaningless signifier or a completely formless signified. This
This is like knowing how to walk but being not able to tell how to do it.
relationship between a signifier and the signified is referred to as signification. The horizontal
bar in the diagram of the sign suggests that the signifier and the signified can be distinguished
only for analytical purposes. According to Saussure, these two parts are as inseparable as the
two sides of a piece of paper (Saussure 1983; Saussure 1974). They are 'intimately linked' in
the mind 'by an associative link' - 'each triggers the other' (Saussure 1983, 66; Saussure 1974,
66). Saussure presented these elements as wholly interdependent, neither pre-existing the
other (Silverman 1983, 103). This interdependence and interaction between the two elements
is represented in the Saussurean diagram by the arrows.
The Saussurean account of the sign up to this point might seem to be in conflict with our
claim that cognition is a necessary component of every sign. In fact, Saussure does not
exclude the cognitive element form his account but argues for just the opposite. For Saussure
the linguistic sign is wholly immaterial. Both the signifier and the signified are purely
'psychological' (Saussure 1983, 12, 14-15, 66; Saussure 1974, 12, 15, 65-66). Saussure was
focusing on the linguistic sign (such as word), privileging the spoken word. Below is an
explanation of his view of linguistic sign in Chandler’s words:
A linguistic sign is not a link between a thing and a name, but between a concept
and a sound pattern. The sound pattern is not actually a sound; for a sound is
something physical. A sound pattern is the hearer's psychological impression of a
sound, as given to him by the evidence of his senses. This sound pattern may be
called a 'material' element only in that it is the representation of our sensory
impressions. The sound pattern may thus be distinguished from the other element
associated with it in a linguistic sign. This other element is generally of a more
abstract kind: the concept.
As for the signified, most commentators who adopt Saussure's model still treat
this as a mental construct, although they often note that it may nevertheless refer
indirectly to things in the world. Saussure's original model of the sign 'brackets
the referent': excluding reference to objects existing in the world. His signified is
not to be identified directly with a referent but is a concept in the mind - not a
thing but the notion of a thing. (Chandler 1984)
A more pictorial elaboration of the Saussurean sign can be given as follows:
To sum up, Saussurean conception of meaning is purely relational rather than referential:
relationships have primacy over things in the process of making meaning. Meaning is
produced by signs through their systematic relation to each other rather than deriving from
any inherent features of signifiers or any reference to material things. Thus, in the Saussurean
system of signs, 'everything depends on relations' (Saussure 1983, 121; Saussure 1974, 122).
Peircean Sign
If philosophers like Charles Sanders Peirce are right when they say we think only in signs,
then it is obvious that Sausure’s dyadic matrix of sign system encloses the mind within its
boundaries. Fortunately, Peirce offered a triadic model for the sign which permits an escape to
non-mental reality. While Saussure envisages the sign as a combination of sound image and
idea, a dyad, Peirce considers the sign as a constituent part of an indivisible triad, along with
the object and the interpretant:
'A sign, or representamen, is something which stands to somebody for something
in some respect or capacity. It addresses somebody, that is, creates in the mind of
that person an equivalent sign, or perhaps a more developed sign. That sign which
it creates I call the interpretant of the first sign. The sign stands for something, its
object. It stands for that object, not in all respects, but in reference to a sort of
idea, which I have sometimes called the ground of the representamen' (Peirce
1931-58, 2.228).
Peirce's model of the sign includes an object. This correlate of the sign does not feature
directly in Saussure's model. Peirce made a distinction between two kinds of objects, the
immediate and the mediate or dynamical object (cf. Eco 1976, Deledalle 2000). The
immediate object is a mental one. It is the object “as the Sign itself represents it, and whose
Being is thus dependent upon the Representation of it in the Sign” (Peirce 1931-58, 4.536).
The mediate or dynamical object is the object outside of the sign. It is “the Reality which by
some means contrives to determine the Sign to its Representation” (Peirce 1931-58, 4.536).
As Nöth(1990) points out, this definition of the dynamical object should commit one to an
ontological realism. But, it is noteworthy that hesitating to use the term real object, Peirce
added “perhaps the Object is altogether fictive” (Peirce 1931-58, 8.134).
The representamen comes close to Saussure’s signifier (Silverman 1983, 15). However, it can
be material. It is non-material when it is a thought-sign. For Peirce, any thought whatsoever is
a representamen, representing something to someone. It is interesting to note that according to
Peirce, a representamen that is a thought-sign is a non-mental, external sign, too. By
“external” Peirce means that which does not depend on how anyone in particular thinks, feels
or believes.
The interpretant is similar in meaning to Saussure’s signified (Silverman 1983, 15). However,
as Chandler points out, “the interpretant has a quality unlike that of the signified: it is itself a
sign in the mind of the interpreter”. Peirce noted that “a sign... addresses somebody, that is,
creates in the mind of that person an equivalent sign, or perhaps a more developed sign. The
sign which it creates I call the interpretant of the first sign” (Peirce 1931-58, 2.228).2
Peirce was aware that since every sign creates an interpretant which in turn is the
representamen of a second sign, semiosis results in a “series of successive interpretants” ad
infinitum (Peirce 1931-58, 2.303, 2.92). Umberto Eco uses the phrase 'unlimited semiosis' to
refer to this potentially infinite series of successive interpretants.
Peirce conceived the interaction between the representamen, the object and the interpretant as
a process and coined the term 'semiosis' to refer to this triadic process (Peirce 1931-58,
5.484).3 According to Peirce, signs are not a class of objects. A sign comes into existence only
through semiosis, which necessarily has a cognitive effect on the interpreter: “Nothing is a
sign unless it is interpreted as a sign” (Peirce 1931-58, 2.308). Deledalle’s (2000) following
statement gives a good insight of what kind of process semiosis is:
Properly speaking, semiosis starts because a representamen is opaque, but, when
the representamen is transparent semiosis becomes a blind process. (p. 40)
Typology of Signs
We saw above that Peirce’s sign is a trichotomy consisting of a representamen, an object and
an interpretant. In fact, Peirce was fascinated by tripartite structures. He postulated ten
trichotomies to develop an elaborate typology of signs (Peirce 1931-58, 2.233-71).4 One of
trichotomies, which Peirce referred to “as the most fundamental division of signs” (Peirce
1931-58, 2.275), classifies signs with respect to the relation between the representamen and
object. The three members of this trichotomy are icon, index and symbol. An icon is a sign
which signifies by its own quality. An index depends on its object and a symbol depends on
conventions between its interpreters in order to signify successfully. Employing the
Saussurean terms signifier and signified instead of the Peircean terms representamen and
object respectively, Chandler offers the following definitions of the three types of signs with
some illustrative examples:
Icon/iconic: a mode in which the signifier is perceived as resembling or
imitating the signified (recognizably looking, sounding, feeling, tasting or
smelling like it) - being similar in possessing some of its qualities: e.g. a
portrait, a cartoon, a scale-model, onomatopoeia, metaphors, 'realistic'
sounds in 'programme music', sound effects in radio drama, a dubbed film
soundtrack, imitative gestures.
Index/indexical: a mode in which the signifier is not arbitrary but is directly
connected in some way (physically or causally) to the signified - this link can
be observed or inferred: e.g. 'natural signs' (smoke, thunder, footprints,
echoes, non-synthetic odours and flavours), medical symptoms (pain, a rash,
pulse-rate), measuring instruments (weathercock, thermometer, clock, spiritlevel), 'signals' (a knock on a door, a phone ringing), pointers (a pointing
'index' finger, a directional signpost), recordings (a photograph, a film, video
or television shot, an audio-recorded voice), personal 'trademarks'
(handwriting, catchphrase) and indexical words ('that', 'this', 'here', 'there').
In fact, Peirce borrowed the term semiosis from the Epicuran philosopher Philodemus (cf. ).
Nöth (1995) notes that Peirce postulated “sixty-six and even 310 = 59,049 classes of signs.”
Symbol/symbolic: a mode in which the signifier does not resemble the
signified but which is fundamentally arbitrary or purely conventional - so
that the relationship must be learnt: e.g. language in general (plus specific
languages, alphabetical letters, punctuation marks, words, phrases and
sentences), numbers, morse code, traffic lights, national flags.
The following quote from Tyson (1999) gives parallel descriptions of the three classes of
An index is a sign in which the signifier has a concrete, causal relationship to the
signified. For example, smoke signifies fire; a knock on the door signifies that
someone is there. An icon is a sign in which the signifier physically resembles the
signified. For example, a painting is an icon to the extent that the picture
resembles the subject it represents. A realistic painting of President Kennedy is an
icon. A symbol is a sign in which the relationship between signifier and signified
is neither natural nor necessary but arbitrary, that is, decided on by the
conventions of a community or by the agreement of some group. (Tyson, 1999, p.
Semiology and Semiotics
The theory or study of the sign is usually referred to as semiology by those working in the
Saussurean linguistic paradigm and as semiotics by those adopting the Peircean philosophical
tradition. But, it is also true that nowadays the term semiotics is more likely to be used as an
umbrella term to cover the whole field, or as a synonym of semiology (cf. Nöth 1990).
Henceforth, we will use the term semiotics from a rather Peircean perspective as referring to
the study of the sign in action (i.e. semiosis).
As should be understood what has been said up to this point, the range of what can be a sign is
very wide: an object, a gesture, a sound, a words, a thought – in short, anything that can be
perceived or cognized – can be a sign. However, as Tyson points out, “of the three
recognized classes of signs – index, icon, and symbol – semiotics limits its study to signs that
function as symbols” (p. 218).
Semiotic Triangle
Charles William Morris (1901-1979), whose influence on the development of semiotics was
decisive in the 1930s and 1940s, derived three dyadic relations, which he considered to be the
basis of three dimensions of semiosis and semiotics. The three branches are the following:
1. syntactics (syntax)—how signs relate to other signs (example: how the word “dog”
relates to the other words in the sentence “The dog ate my homework.”)
2. semantics—study of how signs relate to things (example: how the word “dog” relates
to an actual dog)
3. pragmatics—actual use of codes in everyday life; effects of signs on human behavior
and how people mold signs and meanings in their actual interaction (example: How
would the sentence “The dog ate my homework” be used in everyday life? How would
my teacher react to it?)
Only symbolic systems, systems where signs are symbols, fully embody these three dyadic
relations. In such systems, whereas syntax is concerned with symbol-symbol relations, and
semantics with symbol-referent relations, pragmatics is primarily concerned the relationships
between symbols and the thoughts and reference phenomena which their usage bring about. It
is a common practice to schematize this division of labor by a so-called semiotic triangle.
Below is a fairly well-known semiotic triangle depicted by Ogden and Richards:
The lower edge of the triangle corresponds to our main concern, semantics. What this edge
says is the following: Semantics is concerned with the relationship of symbols to what they
stand for, their referents. This relationship is not causal, but imputed. The imputation is said
to be a true one when the symbol really stands for the referent.
If we narrow down the range of signs to linguistic ones, we come to the field of linguistics.
Semiotics recognizes language as the most fundamental and important sign system (cf. Tyson
1999). The following quote from Chandler (??) includes the views of leading
semioticians/semiologists underlying this importance:
Saussure argued that 'nothing is more appropriate than the study of languages to
bring out the nature of the semiological problem' (Saussure 1983, 16; Saussure
1974, 16). Semiotics draws heavily on linguistic concepts, partly because of the
influence of Saussure and because linguistics is a more established discipline than
the study of other sign systems. Structuralists adopted language as their model in
exploring a much wider range of social phenomena: Lévi-Strauss for myth,
kinship rules and totemism; Lacan for the unconscious; Barthes and Greimas for
the 'grammar' of narrative. Julia Kristeva declared that 'what semiotics has
discovered... is that the law governing or, if one prefers, the major constraint
affecting any social practice lies in the fact that it signifies; i.e. that it is articulated
like a language' (cited in Hawkes 1977, 125). Saussure referred to language (his
model being speech) as 'the most important' of all of the systems of signs
(Saussure 1983, 15; Saussure 1974, 16). Language is almost invariably regarded
as the most powerful communication system by far. For instance, Marvin Harris
observes that 'human languages are unique among communication systems in
possessing semantic universality... A communication system that has semantic
universality can convey information about all aspects, domains, properties, places,
or events in the past, present or future, whether actual or possible, real or
imaginary' (cited in Wilden 1987, 138). Perhaps language is indeed fundamental:
Emile Benveniste observed that 'language is the interpreting system of all other
systems, linguistic and non-linguistic' (in Innis 1986, 239), whilst Claude LéviStrauss noted that 'language is the semiotic system par excellence; it cannot but
signify, and exists only through signification' (Lévi-Strauss 1972, 48).
Language exists only through signification because it is an example of a symbolic sign
system. Tyson (1999) explains the symbolic nature of language as follows:
The sound-image “tree” refers to the idea of a tree only because speakers of
English have agreed to use it that way. While smoke is an index of fire, and a
realistic painting of fire is an icon of fire, the word fire is a symbol of fire. There
is no quality of fire inherent in the word fire. (Tyson 1999, p. 218)
However, we should issue a word of warning about the conventionality of linguistic meaning.
Word meanings and relations among word meanings constitute the field of lexical semantics,
which falls outside the scope of this course. What we will be concerned with is structural
semantics. This latter is not conventional but driven by syntactic, and maybe also pragmatic,
principles. Having a look at the study of semantics in its relation to the corresponding
enterprises in the other two domains of linguistics will be useful from both empirical and
methodological points of view.
Linguistic Triangle
As Dowty et al (1981) point out, when constructing the syntactic component of a grammar,
the aim is to give an account of (native) speakers’ judgments of grammaticality, grammatical
relations, etc. Some facts are easy to account for. For instance, the grammaticality of John ate
the apple vs. the ungrammaticality of apple john the ate should not be a big problem for
anyone’s theory of grammar. Some facts, on the other hand, are more puzzling. For example,
why is French more flexible than English in terms of verb movement: Catherine mange
toujours du pain vs. *Catherine eats always bread? This question was still to be fully
answered in the beginning of the nineties.
Dowty et al add that in constructing the semantic component of a grammar, we are attempting
to account for speakers’ judgments of synonymy, entailment, presupposition, contradiction,
truth, and so on. Just as in syntax, some semantic facts are harder to account for than others. It
is relatively easy to account for the fact that John stayed and Mary left entails John stayed
(i.e. if the former is true then the latter must be true). It is more difficult, on the other hand, to
account for some other facts. Dowty et al mention the following cases as among those which
pose problems for any semantic theory:
Case 1: “Every teacher is better than any student. John is better than every teacher. Therefore,
John is better than any student.” This argument seems valid, in that the conclusion follows
logically from the premises. Why then is the following argument, which is apparently parallel,
not valid: “Nothing is better than a long and prosperous life. A ham sandwich is better than
nothing. Therefore, a ham sandwich is better than a long and prosperous life.”?
Case 2: The sentence John believes that my neighbor keeps a pet alligator might be true
while John believes that the mayor keeps a pet alligator is false in a situation where my
neighbor is the mayor.
The first case hints that semantic interpretation is not under the rigid control of surface
syntactic structure. The second case suggests that semantic interpretation may involve flexible
pragmatic evaluations such as reference to mental states.
A distinction is commonly made between
what sentences linguistically encode versus
what utterances communicate explicitly in particular contexts.
The idea is simply that apart form some scientific expressions, a linguistic expression does not
encode every aspect of its interpretation, but an important component of this interpretation is
obtained from the context of use. In Case 2 above, the sentences are entirely silent with
respect to the question of whether John knows that the neighbor is the mayor. This is a
question to be resolved with respect to the utterance of the sentences in a particular context of
use. As briefly mentioned when introducing the three dimensions of semiotics, it is
pragmatics that is primarily concerned with the question of how a linguistically encoded
meaning is enriched to an actual interpretation in a particular context of use.
In fact, pragmatics is the branch of linguistics that is most difficult to define. The
characterization above rests on the dichotomy between what is linguistically structured versus
what is given by the context of usage. As Levinson (1983) puts is, the heart of the definitional
problem for pragmatics is that this term “covers both context-dependent aspects of language
structure and principles of language usage and understanding that have nothing or little to do
with linguistic structure” (p. 9). In some approaches, pragmatics is defined as the field of
linguistics that deals with the context-dependent aspects of interpretation, irrespective of
whether the meaning is linguistically encoded or not.
Formal Semantics
It is important for a linguistic theory (and for, arguably, any other scientific theory) to be
characterized with a formal rigor and mathematical preciseness for, at least, the reasons stated
by Chomsky (1957):
Precisely constructed models for linguistic structure can play an important role, both
negative and positive, in the process of discovery itself. By pushing a precise but
inadequate formulation to an unacceptable conclusion, we can often expose the exact
source of inadequacy and, consequently, gain a deeper understanding of the linguistic
data. More positively, a formalized theory may automatically provide solutions for
many problems other than those for which it was explicitly designed. Obscure and
intuition-bound notions can neither lead to absurd conclusions nor provide new and
correct ones, and hence they fail to be useful in two important respects. I think that
some of those linguists who have questioned the value of precise and technical
development of linguistic theory have failed to recognize the productive potential in
the method of rigorously stating a proposed theory and applying it strictly to
linguistic material with no attempt to avoid unacceptable conclusions by ad hoc
adjustments or loose formulation. (p. 5)
Transformational and several other generative approaches have brought considerable formal
rigor and explicitness to syntax. One of the questions which this course will address, albeit
indirectly, is whether semantics can be characterized with a similar degree of mathematical
preciseness. Many linguists working within a generative paradigm have a negative answer to
this question; as mentioned above, they regard semantics as an intractable, perhaps ultimately
unfathomable part of language.
Philosophers and logicians, on the other hand, find semantics perfectly tractable but are made
uncomfortable by the idea that approaches to semantics which work very well for formal
languages could be usefully applied in the domain of natural languages. These two types of
languages contrast radically in terms of how easy they lend themselves to semantic analysis.
Formal languages are man-made. Hence, they are tidy and well-behaved languages. Natural
languages, on the other hand, seem hopelessly messy for a semantic analysis: they are full of
ambiguities and unruly exceptions.
Richard Montague challenged the assumption that there exists an important theoretical
difference between formal and natural languages (cf. Montague 1974). He built up a
framework which has paved the way for the development of an explicit, substantive theory of
semantics for natural language. That framework will be the major subject of this course.
Truth-Conditional Semantics
In many semantic systems, including Montague semantics, semantic study is considered to be
basically concerned with those aspects of meaning or interpretation that are truth-conditional.
Such systems adhere to the following dictum: To know the meaning of a (declarative)
sentence is to know what the world would have to be like for the sentence to be true. In other
words, to give the meaning of a sentence is to specify its truth conditions.
For example, we will have produced the meaning of the sentence The Washington Monument
is west of the Capitol Building, once we have specified the state-of-affairs making this
sentence true. This sentence would be true just in case a certain entity named by the words
“the Washington Monument” and another entity named by the words “the Capitol Building”
stand in a certain spatial and temporal relation named by the words “is west of.”
But, one might think at this point that what we have done is circular. More precisely, what has
been put forth as the meaning of a particular sentence of English (which is the language under
study) looks like just a longer and more complex, but perhaps synonymous, sentence of
English (whose connection to the world is yet to be specified). To vanish this feeling of
circularity, we should firstly note that sentences and states-of affairs are altogether different
sorts of things. The former are linguistic entities whereas the latter are configurations of
objects in the world. The feeling of circularity arises from the fact that we used a sentence of
English to describe the state-of-affairs corresponding to the sentence of English whose truthconditional meaning was to be accounted for. That is, English served as both our metalanguage and object-language. A part of the air of circularity would be dissipated if we had
chosen an example from a language other than English. Our object language could be French,
for instance: Le Monument de Washington est á l’ouest du bâtiment de Capitol. Or, as a more
effective remedy, we could change our meta-language to a sufficiently large set of pictures or
an elaborate system of gestures.
It is also worth noting that it is not logically necessary to approach to the explication of the
notion of meaning from a truth-conditionally oriented perspective. We have already seen that
there are various philosophical views of meaning. For example, some consider meaning to
reside in mind. One holding this view should, of course, not be expected to adhere to a
version of truth-conditionalism. In order to be self-consistent, such a semanticist could take
the meaning of a sentence to be a mental image or idea formed by someone who understands.
Principle of Compositionality
Since there are infinitely many non-synonymous well-formed sentences of any language (and
of any interesting logical language), any theory of truth-conditional semantics must be
prepared to specify an infinite number of truth conditions. Just as in syntax, we need some
recursive devices to achieve this purpose. However, even if we manage to construct a system
for recursively specifying an infinite class of states-of-affairs, there is also the problem of
ensuring that the truth-conditions – however generated – are matched up in the right way with
the well-formed sentences of the object language.
A particular strategy for attacking both these problems at once is to let the rules for specifying
truth conditions to work in tandem with the syntactic rules. The idea is that syntactic
generation of each sentence will be mirrored semantically, and in this way we will generate an
infinite class of truth conditions while putting them in correspondence with object-language
sentences. Adherence to this strategy has in fact become one of the cornerstones of truthconditional semantic, and it is known as Frege’s Principle or the Principle of
Compositionality: The meaning of the whole is a function of the meaning of the parts and
their mode of combination.
When analyzed to its smallest parts, the meaning of a complex expression is composed of the
meaning of the individual words, which is called lexical meaning, and the meaning of the way
the words are combined, which is called structural meaning.
Structural meaning comprises the meaning derived from the syntactic structure of an
expression. Consider the following set of sentences (from Kearns 2000):
a. The rat that bit the dog chased the cat
b. The cat that chased the dog bit the rat
c. The rat that chased the cat bit the dog
d. The dog that chased the rat bit the cat
e. The dog that bit the rat chased the cat
f. The dog that chased the cat bit the rat
g. The dog that bit the cat chased the rat
h. The dog that chased the cat chased the rat
i. The dog that chased the rat chased the cat . . . and so on . . .
We see that a large number of different sentences with different meanings from a vocabulary
of seven words are based on a single syntactic structure.
Model-Theoretic Semantics
In any mathematical theory about an empirical domain, the phenomena of interest are
modeled by mathematical structures. The theory itself does not talk directly about the
empirical phenomena: it talks about the modelling structures. The predictive power of the
theory arises from the conventional correspondence between the model and the empirical
Similarly, the frameworks within which we will carry out our semantic analyses will involve
the construction of abstract mathematical models of those things in the world making up the
semantic values of expressions in the object language.
The leading idea of model theory is that one can learn about the meaning of expressions and
the correlations between expressions and meanings by investigating in detail how the meaning
of complex expressions is related to the meaning of the simpler expressions they are
constructed from. Given that the meanings in question are objects or configurations in the
world, a sensible strategy is to study the relationships among those objects and configurations
in order to gain insight into the relationships between meanings that get associated with
expressions by the compositional process. In practice, this often means using the apparatus of
set theory to represent semantically relevant aspects of the relationships between objects and
configurations, and employing appropriate set-theoretic constructs as the objects in a model
that are assigned as semantic values of expressions.
In studying the connection between expressions and their meanings it is common practice to
take advantage also of the fact that many expressions might have meant something different
than what they actually do, without the language therefore having been significantly different
than it is. It happens, for example, that in English we use the proper name “Noam Chomsky”
to denote a particular individual in the world; but any other name, logically speaking, would
have served as well, and by the same token we might well have used the name “Noam
Chomsky” to denote any other individual. This fact allows us to systematically vary the
meaning assigned to such expressions, and observe the effect on the meaning of related
expressions. By such means we may learn various things about the appropriate assignment of
meaning to make to expressions of language.
Taking into account all the possible correspondences between expressions and semantic
values, we might say that each pairing represents a possible interpretation of the language in
question. A model begins by specifying what sorts of thing there are in the world, and then,
with respect to this assumed ontology, specifies an interpretation of the object language.
Given this notion of a model, we can investigate certain interesting things which remain
invariant under changes in interpretation.
Possible Worlds Semantics
We have already observed that in giving the truth conditions for a sentence we make reference
to “how the world would have to be” in order for the sentence to be true. Thus, the meaning of
a sentence depends not just on the world as it in fact is, but on the world as it might be, or
might have been, etc. – i.e. other possible worlds. One quite naturally understands “I wish that
I were richer”, for example, as expressing a certain relation between a speaker of the sentence
and possible worlds differing from the actual one by an increase in the speaker’s wealth.
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