The Principle of Semantic
Compositionality
Francis Jeffry Pelletier
ABSTRACT. The Principle of Semantic Compositionality (some-
times called 'Frege's Principle') is the principle that the meaning of
a (syntactically complex) whole is a function only of the meanings
of its (syntactic) parts together with the manner in which these parts
were combined. This principle has been extremely influential
throughout the history of formal semantics; it has had a tremendous
impact upon modern linguistics ever since Montague Grammars
became known; and it has more recently shown up as a guiding
principle for a certain direction in cognitive science.
Despite the fact that The Principle is vague or underspecified at
a number of points - such as what meaning is, what counts as a part,
what counts as a syntactic complex, what counts as combination -
this has not stopped some people from viewing The Principle as
obviously true, true almost by definition. And it has not stopped other
people from viewing The Principle as false, almost pernicious in its
effect. And some of these latter theorists think that it is an empiri-
cally false principle while others think of it as a methodologically
wrong-headed way to proceed.
In fact, there are approximately 318 arguments against The
Principle which can be found in the literature, whereas there are only
three (or maybe four) arguments proposed in favor of The Principle.
This paper will adjudicate among these arguments. And at the end
it will suggest some other way to look at what proponents of
compositionality really want.
1. Introduction: What is semantic
compositionality?
The Principle of Semantic Compositionality
is the
principle that the meaning of an expression is a function
of, and only of, the meanings of its parts together with
the method by which those parts are combined, 1 As
stated, The Principle is vague or underspecified at a
number of points such as 'what counts as a part', 'what
is a meaning', 'what kind of function is allowed' and
the like. But this hasn't stopped some people from
treating it as an obviously true principle, true almost
by definition, nor has it stopped some others from
attacking it both on 'empirical grounds' and on theo-
retico-methodological grounds. It seems to me that
many of these discussions fail because of a lack of
precision on the abovementioned points and that other
discussions are best described as 'how compositionality
can/cannot be accommodated within theory X' rather
than whether The Principle is or is not true. In its most
general form, for instance as stated above, The Principle
makes no assumptions about what meaning is, nor does
it say how one can tell whether two expressions have
the same or different meanings. It makes no assump-
tions about what the parts of a complex expression are,
nor does it put any restrictions on what is the function
on the parts and the mode of combination. 2
In general, The Principle has received a good press.
It is rather difficult to find anyone who has other than
warm feelings towards The Principle, at least in the
philosophical literature. However, many writers in the
linguistic literature have pointed to certain types of
sentences for which they think it is difficult to give a
compositional account. Some of these sentences will
be considered below. My own feeling is that although
many of these sentences
can
be handled composition-
ally (indeed perhaps all of the ones I'll mention), still,
and nonetheless, the overall conclusion was right: com-
positionality is false. I shall not attempt to prove this
here. Instead I will merely sketch what I take to be an
alternative conception of semantics, one that relies on
'groundedness' rather than on 'functionality'. To this
end I will survey some of the arguments both for and
against The Principle of Compositionality and will argue
that none of them achieve what they have set out to
achieve; that is, none of them show that composition-
ality either is or isn't false, and thus all we are left with
is either the 'warm fuzzy feeling' that arises when a
theory claims to be compositional, or the 'challenge for
the establishment' feeling that arises when we claim our
theory is non-compositional.
Topoi
13:11-24, 1994.
© 1994
KluwerAcademic Publishers. Printed in the Netherlands.
12 FRANCIS JEFFRY PELLETIER
2. Some senses of 'eompositionality'
There have always been other notions of 'composition-
ality' that are appealed to in scholarly work concerning
whether The Principle is or isn't true. I mention here
a few of them and try to give a feel for what is
understood within the community by the notion of
compositionality.
1. The only way to combine meanings is by function
application.
The sentiment in (1) is attributed to Richard Montague
(see Thomason, 1974) by Brian Smith (1988), and has
been called 'the intuitive version of The Principle' by
Theo Janssen (1983).
2. Meanings of complex symbols are systematically
determined by their composition.
(2) is the understanding of 'compositionality' given in
Haugeland (1985).
3. By 'compositionality' we mean that the meaning
of the whole is a systematic function of the
meaning of its parts.
(3) is taken from Graeme Hirst (1987). Together, (2) and
(3) is what many people would understand by the notion
of compositionality.
4. 'Compositionatity' is taken to mean that with any
piece you can associate something such that, given
a whole made of parts, there is a way of system-
atically deriving the 'meaning' of the whole from
the 'meanings' of the parts.
This is taken from Brian Smith (1988), who is giving a
very general account of what the notion of composi-
tionality means in terms of algebras for syntax and
semantics. Together, these last three concepts of com-
positionality probably capture the popular notion that
the functions which are used to combine meanings of
parts into meanings of wholes have to in some sense
always 'work the same way'. If they combine to form
a given semantic category in one case where a noun
phrase is combining with a verb phrase in a certain way,
for example, then in all cases where a noun phrase is
combining in that way with a verb phrase, it has to form
an element of the same category. An extremely strong
version of that very notion of compositionality is
prevalent in the linguistics folklore. I have heard it on
numerous occasions, and instead of citing anyone in
particular, let my just attribute it to an anonymous
participant in a recent Linguistic Society of America
meeting.
5. 'Compositionality' means that the grammar obeys
the 'rule-to-rule hypothesis'.
We see here that we're getting more and more specific
understandings of what kinds of functions are going to
be permitted in order for it to be considered a com-
positional function. The general thrust is that a
compositional semantics has to be 'systematic', in some
or other sense of the term.
My own view is that one person's anarchy is another
person's favorite form of systematic organization. What
the above authors have just cited as being systematic
(and by implication, the kinds of things they think are
not systematic and hence not to be understood as falling
under The Principle) might very well be opposite to
sorts of things that I think are systematic. The Principle
itself makes no claims
at all
about what sorts of
functions there are. It would seem to me that it might
be quite easy to argue against the notion of com-
positionality, if you insist that the functions have to be
'systematic' in the sense that our authors have just given
us. 3 However, it would be much more difficult to argue
against the notion of semantic compositionality if you
allowed
any
conceivable function whatsoever. Yet this
is precisely what I intend to do later in the paper.
But before embarking on that task, I would like to
turn to the topic of the
extent
to which The Principle
applies. Our first quotation is taken from Allan (1986,
pp. 61-62). We'll see that Allan believes composition-
ality to be an extremely broad notion indeed.
The meaning of S's Utterance delivered to H in
context C is composed from:
i. The meaning of sentence I: that S uses.
ii. The meaning contributed by the prosody ~ with which E is
spoken.
iii. The meaningful input to the interpretation of E spoken with
in C and from background information .... Each of these
components of U's meaning is itself compositional ....
Sentence
meaning is compositional. It manifests a compositional hierarchy
such that the meaning of a sentence is composed from the
meanings of its constituent clauses (and their connectives), the
meaning of a clause is composed from the meanings of
its
constituent phrases, the meaning of a phrase is composed from
the meanings of its constituent words, and those in turn from
the meanings of their constituent lexemes and morphemes
(semantic primitives).
As we see from this quotation, Allan, a champion of
THE PRINCIPLE OF SEMANTIC COMPOSITIONALITY 13
The Principle, believes in compositionality "all the way
up and all the way down". But it is not just champions
of The Principle who have this view of the scope of
compositionality. Theorists who don't believe in the
notion of semantic compositionality also have the view
that the extent of The Principle is "compositionality all
the way up and down". They just deny that it occurs.
Here is a quotation taken from Kamp (i990).
The question here depends to a large extent at what we take the
data a semantic theory should account for• Thus, some people
would question whether anaphora resolution. •. is something that
a semantic theory should address . . . I think that a theory of
language should account for
all
linguistic data •, • What are the
facts that a comprehensive theory of language should explain?
• . .
My own answer is that linguistic meaning is to be under-
stood in terms of the potential to modify states of information
• , . The theory should include an analysis of the inference
mechanisms that create, modify and exploit the information states
in terms of which linguistic meaning is defined .... To sum up,
someone who takes seriously the idea that meaning is to be
extricated in terms of information change potential, will find the
change for a compositional theory as extraordinarily slim•
We see here that Kamp and Allan agree about what a
compositional theory would look like. It's a wide-
ranging theory, starting with the individual lexemes and
going all the way tt, the utterance in context. Allan
believes that all of that is compositional. Kamp thinks
that it is extrac, rdinarily unlikely to be compositional.
present in any of the parts, and so compositionality is
false.
It seems to me that this sort of argumentation is not
very good. One tactic to argue against it might be to say
that, when the mind infers these kinds of things that
'aren't there in the input', then in fact it is the action
of 'putting together' of these smaller parts which
introduces 'the things that the mind brings to bear'.
(Recall that The Principle did not only appeal to the
meanings of the parts but also it appealed to the method
by which the parts are composed; and one might say
that it is here that these other aspects of the meaning
of the whole are to be found.)
Another tactic, one that I am here in favour of, is to
argue that many things which might be thought to fall
under the rubric of 'being brought to bear by the mind
even though they aren't there in the parts' are not really
involved in the meanings of the composed whole. Let
me approach this by means of an analogy• Gestalt
psychologists have used examples such as the 'square'
shown in Figure 1.
r- 7
3. A psychological argument against The Principle
Certain arguments that have been raised against The
Principle of Semantic Compositionatity seem to be
less successful than others. A certain group of these
arguments point out that human minds bring to bear a
lot of in-built interpretations to things that they perceive.
For example, Gestalt psychologists have long ago
pointed but that people will tend to see many things
which 'aren't there' because their mind 'fills in the
gaps', or alternatively put, the mind makes certain
inferences about the whole that is expected when only
certain parts of the whole are seen. Since this can
happen in ordinary situations, such as vision for
example, some theorists conclude that the same thing
might be happening in linguistic contexts. The mind
might bring to bear many things that are not present in
the actual linguistic input. So, having brought these
things to bear, the meaning that is associated with the
combination of these linguistic inputs might not be
/..
Fig•
I. A Gestalt 'square'.
According to Gestalt psychologists, we see a square
in Figure 1, despite the fact that a carefut examination
reveals that the only things in the picture are empha-
sized corners. There is no square at all in Figure 1,
despite what we 'see'. From this some theorists claim
that the content of the entire picture in Figure 1 is
something over and above the contents of the parts of
the picture, since the contents of the parts are only the
four corners.
One style of objection to such a claim was raised in
the last paragraph: that the method of combining these
four parts into a whole includes putting them in a certain
relationship to one another, namely the specific rela-
tionship that would lead us to see a square. This is
14 FRANCIS JEFFRY PELLETIER
certainly a possible position for a compositionalist to
take on the Gestalt figures, and so far as I can see there
has never been an adequate rejoinder to this response-
to-Gestatt-objections-to-compositionality. But person-
ally, I would prefer to use the second tactic to argue
against the Gestaltist argument. I would like to say that
the square is
not
really there
at all.
In this regard I'm
reminded of a cartoon posted on the Psychology
Department bulletin board which had the comers of a
Gestalt square such as Figure 1, each being held by a
fireman outside of a burning building in which a woman
was trapped on the second floor. The firemen were
shouting 'Jump, Jump!' The title of the cartoon was
'Gestalt firemen play a joke'. The point is that even
though the trapped person might
perceive
a square of
safety netting being held by the Gestalt firemen, the fact
of the matter is that there was
no
square there. Similarly
one might say in Figure 1 that there simply is
no
square
there, regardless of what we seem to think. Figure 1
then represents no challenge to The Principle because
there is nothing in it other than the four corners. And
similarly, no Gestalt challenge to compositionatity can
work because we deny that the 'inferred meanings' are
there in the whole.
4. Some linguistic arguments against
The Principle
In the linguistic literature there have been numerous
attempts to show that compositionality is wrong, by
actually presenting cases where the parts of a sentence
have meanings that 'just can't' be combined to form the
correct meaning of the whole. 4
One type of challenge might be said to come about
because 'there are things that we know are in the
meaning of the whole that just are not in the parts'.
Consider the sentence:
6. A man is in this room
and its representation:
7. (3x) (Man(x) & In(x, this-room))
Note that in this representation there are variables which
are not in the original sentence. Furthermore note that
there is no 'and' in the original sentence yet (7) asserts
that there is an ampersand in the representation. Thus
there are things in the representation that are not in the
sentence. It is not clear to me whether this kind of an
argument should be taken seriously, although it has
been mounted by certain theorists who should remain
nameless. I will only point out that there is no reason
in the world that the composition function could not
insert variables or &s.
Here is another type of example.
8. Jane isn't liked by many men.
(8) is ambiguous. It could mean either of
8a. Most men do not like Jane.
8b. There is a specific group (of many men) who do
not like Jane.
So the original sentence is ambiguous and can be
understood in either one of those two ways. However,
if you were to embed (8) into a larger context the
ambiguity disappears. Consider
9. Jane isn't liked by many men and Sally isn't either.
10. Jane isn't liked by many men and Sally isn't liked
by them either.
Each of these last two sentences is unambiguous; in
each of those sentences the meaning of this first clause
is unique. But this first clause is just the ambiguous (8)!
In (9) the phrase 'Jane isn't liked by many men' only
has the meaning of (8a) whereas that very same phrase
in (10) has only the (8b) meaning. At least that's the
claim that some anti-compositional theorists make.
It seems to me that this is not a very successful
argument against compositionality. For one thing, the
meaning of the entire sentence in either of these latter
two cases is conditioned in part by the second conjunct,
and The Principle only predicts that the
entire
sentence
should mean whatever it is that (9) and (10) mean. It
does not say anything about the meaning of the
component parts of those sentences. It neither has
anything to say about
what
the meaning of the first
clause will be as parts of (9) and (10), nor does it say
what the meaning of these clauses will be in isolation,
nor does it have anything to say about the relationship
between the clause's meaning in isolation and its
meaning in some context. So, clearly the component
parts
could
be ambiguous in isolation, but in context
they are not ambiguous; or rather, the entire sentence
does not have an ambiguous first conjunct. So examples
like (8)-(10) in no way defeat The Principle.
A similar sort of example that might be seen as more
challenging is:
11. Dogs get fleas.
THE PRINCIPLE OF SEMANTIC COMPOSITIONALITY 15
This sentence is a 'generic' statement about the propen-
sities or the dispositions (etc.) of dogs - namely that
they are able to get fleas, or that they typically get fleas,
or that they get fleas under usual or normal circum-
stances. However, if you embed (11) into a larger
context, that portion of the sentence gets interpreted
differently. Consider:
12. When dogs get fleas it is best to keep them away
from children.
In this case the embedded sentence, 'dogs get fleas', is
interpreted as actual episodes or instances of dogs and
getting fleas, rather than about the propensities or the
dispositions of dogs. From this, some have concluded
(just as they have concluded from (8)-(10)) that there
has been a change of meaning of (11), brought about
by the embedding into a larger context; and thus it is
not solely the meaning of the component parts that goes
to making the meaning of the whole, as The Principle
predicts, but rather something in addition. Once again
however, this is a misunderstanding of what The
Principle is committed to. The Principle says only that
there is some meaning which can be attributed to the
entire sentence based solely on the meanings of its parts.
One relevant question, then, is: what are the parts of this
sentence? Well for sure, one of the parts is 'dogs get
fleas'. But equally for sure another part is that this
sentence is embedded inside of a 'when' clause. So it
is open for one to say that if a generic statement gets
embedded inside of such a clause, then the entire state-
ment has as its meaning that actual episodes of the
generic disposition are being manifested. This is all that
The Principle is committed to; and certainly this is
within the realm of compositional theories.
Another group of examples comes when the subject
term is a superlative construction (or other construc-
tion that picks out an endpoint on some scale). For
example, consider the following sentences:
13a. The first person landed on the moon in 1969.
b. The person with the biggest grant usually supports
the rest of the department.
c. The tallest person usually plays center for the
team.
d. The first case of AIDS was reported in 1975.
In these examples, whatever the meaning is of the
italicized subject terms - whether you take it to be
referential and hence it picks out the actual first person
or the actual person with the biggest grant or the actual
tallest person or the actual first case of AIDS, or
whether you're more indirect and think that a phrase
such as 'the first person' designates a function on
possible worlds which in each possible world picks out
the first person of that world - nonetheless, in none of
these sentences is it this that is being talked about. For,
in each of these sentences there is something about
the predicate which, in one way or another, gives an
idiosyncratic understanding as to how the subject should
be understood. It's not that the first person landed on
the moon in 1969 but rather that the first person who
landed on the moon did so in 1969. It's not that the
tallest person, whoever that might be, has the property
of usually playing center; but rather that, given a team,
the tallest person in that team usually plays center for
the team. Challenges such as these have formed the
basis for a number of attacks on The Principle.
Another attack has come from such sentences as:
14a. Every philosopher in the world can fit into this
room.
b. Every philosopher in New Zealand can fit into this
room.
It seems quite clear, so the argument against composi-
tionality goes, that in (14a) the meaning is 'distributive';
th~tt is, it says of each philosopher individually, that he
or she could fit into this room. However, (14b) could
have a collective meaning, in which case it would mean
that all of the philosophers in New Zealand taken
together could collectively fit into this room at the same
time. (14a) seems to talk about the fatness of individual
philosophers, (14b) seems to talk about the size or the
number of philosophers in New Zealand. Once again
this difference in the understanding of the sentence
(whether distributive or collective) seems to be not
traceable to either the verb phrase or the subject phrase,
but rather is somehow dependent upon our knowledge
of how many philosophers there are in the world and
how many philosophers there are in New Zealand - that
is to say, it relies on facts other than the meaning of
the component parts.
Non-restrictive relative clauses also have been seen
as forming challenges to The Principle of Semantic
Compositionality. Consider, for example:
15. Kim, whose paper was rejected from Linguistics
and Philosophy, began to rant and rave.
It seems clear that the meaning of the non-restrictive
relative clause construction is more than merely an and.
