Semantics without semantic content
Daniel W. Harris
Hunter College, CUNY
Correspondence
Daniel W. Harris, Department of Philosophy
Hunter College, CUNY. New York City, NY, 10065.
danielwharris@gmail.com
I argue that semantics is the study of the proprietary database of a
centrally inaccessible and informationally encapsulated input–output
system. This system’s role is to encode and decode partial and defea-
sible evidence of what speakers are saying. Since information about
nonlinguistic context is therefore outside the purview of semantic pro-
cessing, a sentence’s semantic value is not its content but a partial
and defeasible constraint on what it can be used to say. I show how
to translate this thesis into a detailed compositional-semantic theory
based on the influential framework of Heim and Kratzer. This ap-
proach situates semantics within an independently motivated account
of human cognitive architecture and reveals the semantics–pragmatics
interface to be grounded in the underlying interface between modular
and central systems.
Key words:
compositional semantics, constraint semantics, semantic values,
cognitive architecture, modularity
My aim is to answer two questions about compositional semantics and to
explore the relationship between them. First, a methodological question:
What kinds of semantic values should a semantic theory assign to expres-
sions? Second, a foundational question: What is the subject matter of
compositional semantics? My answer to the first question is that the se-
mantic value of an expression is a constraint on what speakers can say with
the expression, and not the content of what they say. My answer to the
second question is that semantics is the study of a modular component of
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the mind. I will defend each of these claims, in part by defending the latter
view and showing that it entails the former (Section 2), and then by showing
how to modify a standard compositional-semantic framework to make it fit
with both ideas (Section 3).
1 TWO CONCEPTIONS OF SEMANTIC VAL-
UES
My first order of business is to distinguish between two theories of the na-
ture of semantic values, which I will call content semantics and constraint
semantics.
1.1 Semantic values as contents
Content semantics is the view that an expression’s semantic value is its con-
tent and that this content may vary in a way that depends on extralinguistic
context. This idea is implemented in different ways by different theoretical
frameworks, in part because of disagreement about what contents are. The
most influential framework identifies the semantic value of an expression φ,
indexed to a world w, assignment g, and context c, with an extension JφK
w,g,c
(or, by λ-abstracting over the world parameter, with an intension JφK
g,c
).
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Idealizing away from tense, aspect, clause-type, and some other complica-
tions, the semantic value of “Ann smokes” can be specified in either of the
following ways, for example:
(1) JAnn smokesK
w,g,c
= 1 iff Ann smokes at w
(2) JAnn smokesK
g,c
= λw . Ann smokes at w
The sentence’s semantic content—the proposition that is true at all and only
worlds where Ann smokes—is given by (2). Sentential semantic values like
these can be derived by positing contents for lexical items—for example, a
referent for “Ann” as in (3) and the property of being a smoker to “smokes”
as in (4)—and formulating principles of content composition, such as (5).
(3) JAnnK
w,g,c
= Ann
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I will treat the framework of Heim and Kratzer (1998) and von Fintel and Heim (2011)
as my foil, refer to it as “the standard framework”, and use its claims and notation as a
starting point. There are interesting questions about how the morals of this essay apply
to various alternative frameworks, but I lack space to pursue them here.
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(4) JsmokesK
w,g,c
= λx
e
. x smokes at w
(5) functional application
If α is a branching node and tβ, γu the set of its daughters, then, for
any assignment g, α is in the domain of J¨K
w,g,c
if both β and γ are,
and JβK
w,g,c
is a function whose domain contains JγK
w,g,c
. In this case,
JαK
w,g,c
= JβK
w,g,c
(JγK
w,g,c
).
The overarching idea of clauses like (1)–(5) is that the semantic value of
a declarative sentence is a propositional content that can be computed by
positing contents for subsentential expressions and principles of content com-
position.
The assignment parameter g and context parameter c come into play
because many natural-language expressions are semantically underspecified.
Each of the following sentences cannot have any single proposition as its
semantic value, for example, because it expresses (or is used to express)
different propositions on different occasions.
(6) I smoke.
(7) The man smokes.
(8) He smokes.
The standard solution is to assume that the assignment and context param-
eters do some of the work in determining these sentences’ contents. For any
context c, there will be a speaker
c
who is the semantic value of “I” relative
to c, for example (Kaplan, 1989b). This yields the following value for (6).
(9) JI smokeK
g,c
= λw . speaker
c
smokes at w
This strategy has been extended in various ways to handle other expressions.
It is common to posit a hidden, context-sensitive domain restrictor in the LF
of every DP, so that (7) is understood to have an LF of the following form,
for example (Stanley, 2000; Stanley & Szab´o, 2000; Westerst˚ahl, 1984).
(10) [
DP
The man dom] smokes.
On this simplified version of the proposal, dom functions as an unpronounced
restrictive relative clause that somehow gets its value from context. Just how
contexts supply semantic values is usually left unclear, though it is widely
agreed that most context-dependent expressions depend in some way on
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facts about the mental states of whoever is involved in the conversation.
One popular view is that context-sensitive expressions’ semantic values are
fixed by speakers’ intentions.
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Finally, deictic pronouns, such as the occurrence of “he” in (8), are stan-
dardly taken to be sensitive to the assignment parameter. It is assumed that
each pronoun is subscripted with a numerical index, and that assignments
are mappings from indices to semantic values. The semantic value of a pro-
noun x
i
, relative to an assignment g, is gpiq, subject to presuppositional con-
straints imposed by x’s φ-features. This gives rise to assignment-dependent
sentential semantic values, such as (12).
(11) JHe
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smokesK
g,c
= λw . gp1q smokes at w if gp1q is male; else
undefined
The assignment relative to which an expression’s content is fixed is itself,
according to the standard framework, given by context. So although context
and assignment are often treated as distinct parameters, we can follow Heim
and Kratzer in assuming that each context, c, determines an assignment, g
c
,
thereby collapsing the two parameters:
(12) JHe
1
smokesK
c
= λw . g
c
p1q smokes at w if g
c
p1q is male; else
undefined.
What about a context fixes the operative assignment? Heim and Kratzer
(1998) say only that “the physical and psychological circumstances that
prevail when an LF is processed will (if the utterance is felicitous) determine
an assignment to all the free variables occurring in this LF” (p. 243). Most
attempts to be more specific point either to the speaker’s intentions (Heim,
2008; King, 2013) or to facts about the shared propositional attitudes of the
conversation’s participants (Clark & Marshall, 1981; Heim, 1982; Roberts,
2005; Stalnaker, 1978).
Why divide off a category of expressions that are indirectly sensitive to
context by being sensitive to assignments? The reason is that pronouns can
also have bound occurrences. For example, (8) can occur embedded in (13).
(13) [Every doctor]
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denies that he
1
smokes.
2
For example, Heim (2008); Kaplan (1989a); King (2013). This view should be distin-
guished from the view that although the semantic value of a semantically underspecified
expression φ is not itself a content, the content of what speakers say by uttering φ is a
matter of their intentions. The latter view, which is compatible with the nonexistence of
semantic content, and which I think is roughly correct, has been defended by Bach (1987,
1992); Neale (2004, 2016); Schiffer (2003).
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In the standard framework, binding is understood in terms of compositional
operations that abstract over the assignment-sensitive components of an ex-
pression, turning them into argument places in a complex predicate that
can compose with the binding expression. As Heim and Kratzer (1998) put
it, “roughly, what is meant by ‘variable binding’ is any semantic operation
which removes (or reduces) assignment dependency” (p. 116). A treatment
on which pronouns depend on contexts by depending on assignments is thus
necessary for a unified treatment of their bound and deictic (i.e., free) oc-
currences. Assignment-dependent expressions are therefore variables, unlike
directly context-dependent expressions. Just where to draw the line be-
tween variables and directly context-dependent expressions is not always
clear, though one crucial issue is whether they can be bound (Stanley &
Szab´o, 2000). I stress this distinction because it will become important
again later: One quirk of the semantic framework I will build in Section 3 is
that it classifies more expressions as variables than is sometimes assumed.
1.2 Semantic values as constraints
Constraint semantics, as I understand it, is the view that an expression’s
semantic value is not its context-relative content but something context-
neutral and therefore less informative. Roughly, the semantic value of an
expression φ is just what a competent speaker can know about what someone
would be saying in uttering φ, assuming they were speaking literally, but
without any knowledge about the context or the speaker’s intentions. For
an expression to be semantically underspecified is for there to be slack in
the constraint that its semantic value places on what it can be used to say.
For example, the semantic value of “he” tells a hearer that the speaker is
referring to a male (if they are speaking literally), but not which male. If a
view like this is correct, there may be no need for compositional semantics
to traffic in a theoretical notion of context at all.
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I am not the first to advocate constraint semantics. Sperber and Wilson
(1995) say that a sentence’s “semantic representation is a schema, which
must be completed and integrated into an assumption about the speaker’s
informative intention” (p.175; see also Carston 2006, p. 633). According to
Pietroski (2006), the meanings of declarative sentences “constrain without
determining truth/reference/satisfaction conditions” (p. 34). Bach (1987)
argues that “the semantics of an expression gives the information that a com-
petent speaker can glean from it independently of any context of utterance”
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Note that constraint semantics, as I conceive it, does not give up the idea that propo-
sitions are the things we assert, say, or mean.
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