Naturalism and semantics∗
Luke Jerzykiewicz ([email protected])
draft: October 2004
Abstract
Three attempts to furnish a scientific semantic theory are reviewed:
the natural semantic metalanguage (NSM); formal semantics (FS);
and conceptualist semantics (CS). It is argued that each can be made
compatible with naturalism, although the costs in each case are high.
NSM urges practitioners to recognize ‘meaning’ as a basic feature of
reality. FS requires that we countenance unlikely abstract entities as
basic explanatory posits. SC, while consonant with cognitive science’s
basic ontology, appears committed to the fallacy of psychologism. All
three approaches are rejected here as fully satisfactory approaches to
the study of meaning.
∗
Carleton University Cognitive Science Technical Report 2004-09 (www.carleton.ca/iis/TechReports).
1
Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Mise-en-scène . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Natural Semantic Metalanguage . . . . . . . . . . . . . . . . . . . .
4
Characterization . . . . . . . . . . . . . . . . . . . . . . . . .
4
Discussion and Criticism . . . . . . . . . . . . . . . . . . . . .
9
Formal Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 12
Discussion and Criticism . . . . . . . . . . . . . . . . . . . . . 23
Conceptualist Semantics . . . . . . . . . . . . . . . . . . . . . . . . 26
Characterization . . . . . . . . . . . . . . . . . . . . . . . . . 26
Discussion and Criticism . . . . . . . . . . . . . . . . . . . . . 35
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Introduction
Semantics is the study of ‘meaning,’ whatever that turns out to be. The
nature of meaning is of interest to cognitive scientists because mental states,
as well as linguistic utterances, are paradigm cases of the meaningful. To
date, the issue of precisely how semantics ought to be practised has not
satisfactorily been resolved. Part of the difficulty involves competing visions
of how (and whether) semantics is to be integrated into the broader scientific
enterprise. In what follows, I review three current approaches to the study of
meaning. My aim is partly descriptive and partly critical. I’d like to clarify
(for my own peace of mind, as much as anything else) the extent to which
each constitutes a naturalist theory of meaning. The three projects discussed
are these:
• the natural semantic metalanguage (NSM);
• formal semantics (FS); and
• conceptualist semantics (CS).
Let me say at the outset that the conclusion of the paper is largely negative:
In my view, none of these projects (in their current form, at least) are adequate to the task of characterizing meaning in a manner at once true to the
phenomena under scrutiny and compatible with naturalism. A way forward
that I find promising is briefly sketched toward the end of the paper.
Mise-en-scène
Outside of logic and mathematics, fully satisfactory definitions are hard to
come by. Still, we need a first-pass characterization of some key notions
before moving on to the particulars of the three semantic projects at issue.
2
Let me start with naturalism. I take naturalistic theories to be those
which do not posit basic entities, properties or events beyond those given
us by our best science. Furthermore, within science itself, broad ontological
continuity is recognized by the naturalist as a regulative ideal. The various branches of science, whatever their domain of enquiry, aim ultimately to
arrive at a single, continuous understanding of the workings of that which
exists. In keeping with this ideal, new entities, properties or events are introduced only sparingly. Obviously, one wants to recognize that non-basic
‘things’ exist: there are hydronium ions, ecosystems, GDPs, maximal projections, but also haircuts, kitsch, and Tuesdays. The non-basic posits are
understood by the naturalist to exist in virtue of being realized ultimately
by more basic entities and processes. Often, among a researchers’s goals is
to show precisely how higher level regularities—those regarding, for example, locative alternation or strong-acid titration—fall out as a consequence
of lower level facts about lexical and semantic representations or hydrogen
bonding. Science often comes short of that goal. The discovery and description tight causal links does not come easily. Still, the puzzle is more
complete than it was a hundred years ago. And a hundred years ago, it was
more complete than the century before that.
Naturalism, as I have characterized it, comes in three flavours: there is
an eliminativist, a reductive and an emergentist variety. The eliminativist
proposes that all explanations, if they are to count as really explanatory,
must in the long run be couched in the terms of the most basic physics (this
is Dennett’s (1995) ‘greedy reductionism’). Hardly anyone favours this sort
of line these days. And with good reason: we all frequently rely on explanations of all sorts that do not advert to photons or quarks. In contrast, the
emergentist holds that there are entities, processes or events which ought to
figure in our most basic descriptions of the world, yet which are not themselves posits of fundamental physics. This view finds many supporters. David
3
Chalmers (1996), has for instance argued that consciousness is probably just
such a basic phenomenon. Reductionists chart a middle course: they require
that all phenomena which are not themselves posits of fundamental physics
need to be reducible to some more basic phenomena or other. They do not
however require that all legitimate explanations be stated in physics’ terms.
With regard to semantics, the issue plays itself out as follows: Eliminativists doubt that there is such a phenomenon as meaning to explain (here
we can recall the behaviourists). They tend therefore not to develop theories of meaning, and are not discussed here. Emergentists propose that we
should take meaning—or perhaps the terms in which meaning is to be explicated—to be ontologically basic. I will argue that, for better or for worse,
both NSM and (perhaps surprisingly) FS come under this rubric. Finally,
the reductivist holds that both meaning and the posits in terms of which
meaning is cashed out are themselves explicable in more basic terms (and so
on). CS, the final semantic theory considered here, is a reductive naturalist
theory. Part of what needs to be settled with regard to semantics is the
variety of naturalism that we—and cognitive science as a whole—ought to
opt for.
Natural Semantic Metalanguage
Characterization
The NSM approach has been developed by Anna Wierzbicka, Cliff Goddard
and their associates. Its immediate intellectual motivations, according to
the proponents themselves, reach to the early days of the cognitive revolution (Wierzbicka (1996)). The decline of behaviourism and the advent of the
new science of mind was a tremendous opportunity to rehabilitate mentalistic concepts—including meaning itself—and to once again place them at the
forefront of one’s research agenda. Unfortunately, according to Wierzbicka,
4
the opportunity is now on the verge of being squandered; linguistics and cognitive science have been victims of their own success—the formal machinery
in computer science and in Chomsky-inspired syntax-studies have led to the
replacement of a science of meaning with a science of computation and information processing. For their part, NSM proponents question the utility of a
rigid syntax-semantics distinction.1 To study syntax at a remove from work
on meaning is simply to miss the point of the linguistic enterprise. Cognitive science, by their lights, succeeded in moving beyond the theoretical
commitments of the behaviourists precisely by taking the question meaning
seriously. NSM starts with a very reasonable observation: Hardly anyone,
with the exception perhaps of a few skeptical philosophers, can deny that
normal humans seem to possess a commonsensical, pretheoretic understanding of meaning. We ‘just know’ that our words and signs have significance.
Admittedly, we can’t always define them precisely and we are apt to misuse
terms on occasion. But normative issues such as these are really not to the
point. Our words are not mere noises or inert marks; they are imbued with
significance. The study of meaning, according to NSM proponents, starts
with that fact.
Not all meanings are on a par. A long philosophical tradition, stretching
via German Idealism at least to Arnaud, Leibniz and Descartes, teaches that
the content of some concepts is constitutive of the content of others. How
might this work? Consider the concept2 [triangle] (though this is not,
in fact, an example that Wierzbicka uses). It seems impossible to grasp
the content of this notion without a prior understanding of [side] and of
[angle]. In this sense then, [side] and [angle] are more basic concepts
1
This distinction, as we shall see, plays an important role in the other two theories
discussed below.
2
I follow standard practise by referring to concepts (as opposed to things or to words)
by using small-caps within square brackets.
5
than [triangle]. Indeed, the story goes, they are building blocks of which
[triangle] is made up. It seems reasonable to suppose then that some
concepts, at least, have constituent parts.3
A natural question to ask next is whether perhaps all concepts might
have further conceptual constituents. In other words, is it possible that all
concepts might be explicated fully in terms of other concepts? Here, NSM
answers in the negative. Two reasons are adduced. To see the first, consider
the meaning of the word ‘after.’ We can explicate by using synonymous
terms and phrases such as ‘subsequently’, ‘at a later time’, or even ‘afterward’
(OED). But it is fairly transparent that the defining terms are themselves just
as semantically involved, and perhaps more so, as the word being defined.
In fact, the definitions themselves presuppose a tacit understanding of the
very notion being explicated. This serves as evidence, Wierzbicka (1996)
and Goddard (1998) argue, for supposing that some lexical items, including
‘after’, do not decompose further. There is another reason also—this time one
with a more aprioristic flavour. Following Arnauld and Nicole (1996), NSM
proponents ask us to consider carefully what it would entail for all concepts
to be definable without remainder in terms of other concepts. Would this not
result in messy tangle of circular definitions, none of which would point to
anything beyond the web of concepts themselves? The concept-user would,
it would appear, be trapped in a sort of conceptual solipsism, unable to make
sense of any one notion except in terms of all others. But since, happily, we
are not stuck in that lamentable predicament, at least some concepts must
act as a sort of ground. We are invited to conclude that some concepts must
not be definable in terms of other concepts at all. Let us call such basic
concepts the primes.4
3
Even Jerry Fodor (1987), in an apparent moment of weakness, makes this sort of claim
with regard to [triangle]. For widely accepted counter-arguments, cf. Fodor and Lepore
(1992).
4
In fact, it is far from obvious whether either of the two arguments really work. I return
6
Let us, for the sake of argument, grant that the picture just presented
is, broadly speaking, correct. What, on the NSM account, does research in
semantics consist in? The task is two-fold. On the one hand, semanticists
work to identify those linguistic items which truly do not admit of definition in other terms—they dig up the bedrock of meaning, as it were. In
one sense, this sort of digging about the foundations is a familiar endeavour. Philosophers once spent a great deal of time trying to discern precisely
which concepts were foundational and which were derivative. In Hegel’s
(1812) work especially, this enterprise reached a high art-form. Of course,
Wierzbicka is not interested in a priori speculation of this sort, even if the intellectual motivation seems superficially similar. Rather, NSM linguists rely
on extensive empirical investigation to arrive at a hypothetical list of primes.
They reason that if primes are the primitive carriers of content, they ought
to be lexicalized—or, at the very least, they ought to appear as a morphological unit—in every language. (Though it does not follow, of course that
any universally lexicalized item is necessarily a prime.) As one can imagine,
to discover whether some particular concept—such as [after]—is in fact a
prime requires a tremendous amount of painstaking research in comparative
linguistics and anthropology (work for which, NSM practitioners are owed
a debt of gratitude by everyone interested in semantics, regardless of the
ultimate fate of their theory.)
The benefits for cognitive science of arriving at a complete list of semantic
primes would be significant. The terms on the list would constitute a sort of
semantic analogue of Mendelejev’s (1869) Table of Elements. It would be a
universal code in terms of which all derivative concepts could be explicated.
Indeed, this explicative task is precisely the second line of research for the
NSM theorist. Just how it can work can be made vivid on the basis of a
simple example. Consider the following sentence of Polish:
to this point below.
7
(1)
Janina jest szczȩśliwa.
Its NSM semantic analysis runs as follows: The proper name ‘Janina’ denotes
a person.5 The verb ‘jest’ serves to link the adjective ‘szczȩśliwa’ and the
person being designated: The person is presently in some state, the nature of
which is about to be specified. The key part of the semantic analysis concerns
the adjective ‘szczȩśliwa.’ In fact, this is a rather peculiar term in Polish;
one quite different from the English ‘happy’ (as Wierzbicka correctly notes).
Here is how its content can be spelled out in terms of semantic primes:
(2)
Person P feels something
sometimes a person thinks something like this:
something good happened to me
I wanted this
I do not want anything more now
because of this, this person feels something good
Person P feels like this.
[Wierzbicka (1996), p. 215; also Goddard (1998)]
We arrive at an NSM analysis of the sentence (1) itself simply by substituting “Janina” for the variable P in (2). Notice that analysis nicely brings
out the difference between ‘szczȩśliwość’ and apparent English translations
like ‘happiness.’ While the English term ‘happy’ is used frequently in everyday contexts to refer to states of mild, temporary satisfaction, ‘szczȩśliwość’
designates a profound sense of fulfilment (perhaps not unlike the French ‘bonheur’). At a minimum then, we can see that NSM analyses are extremely
useful to the comparative linguist as a tool for specifying subtle shades of
meaning.
5
I am not certain whether NSM endorses a direct reference theory for proper names or
considers names covert definite descriptions. But it’s not really a crucial point for us.
8
In fact, there is more going on. Each of the words which comprise the
definition (except the variable P, obviously) is the English lexicalization of
a semantic prime. If NSM is correct, and if the analysis is truly complete,
any competent speaker whose native language is the metalanguage used here
(so English) should be able to deduce the meaning of ‘szczȩśliwa.’ Importantly, the explication should translate with no loss of content into any other
human language by systematically replacing the English lexicalizations of
the primes with their correspondents. Of course, that this can work is, in
part, an empirical claim. But if it were indeed right, NSM would have found
the foundations on which meaning rests. This would be a very remarkable
achievement indeed.
Discussion and Criticism
A number of criticisms to the NSM framework and its effectiveness can be
raised. One immediate worry concerns the empirical adequacy of (2). To
count as a satisfactory semantic analysis of (1), the analysis would need to
be complete. If we accept that the terms of (2) are primes and that primes
are the primitive constituents of meaning, then a reasonable test for the
completeness of (2) suggests itself. Presented with (2) a native speaker of
Polish ought to be able to unambiguously identify the word it explicates. By
the theory’s own lights, the meaning of ‘szczȩśliwa’ just is what is given in
(2). Yet, in point of fact, (2) fails this test. A native speaker of Polish is at
chance when trying to determine whether (2) analyzes ‘szczȩśliwa’ or of one
of the following synonyms (English approximations in parentheses):
• zasycona (sated)
• zadowolona6 (contented)
6
This was, in fact, the favourite guess in a mini-run of the semantic reverse-engineering
experiment I conducted.
9
• zaspokojona (made to be at peace)
At best, it would appear, the analysis given in (2) is importantly incomplete;
more work is needed to identify further prime constituents of ‘szczȩśliwa.’
Admittedly, this need not trouble Wierzbicka overly. She has always very
reasonably maintained that NSM analyses are working empirical hypotheses.
But if the problem generalizes, it could spell trouble for NSM.
There are more fundamental worries too. The very idea of conceptual
‘primes’ is open to challenge. Assume, for the sake of argument, that some
lexical concepts truly are, in some important sense, composite.7 We were led
to posit semantic primes because, according to Arnaud, a network of concepts defined exclusively in terms of other concepts yields vicious circularity.
The trouble is that Arnaud was wrong: there now exists a considerable body
of literature, inspired by de Saussure (1966), which supposes that concepts
precisely are constituted negatively. That is, they are constituted via the difference relations between themselves and all other available concepts. Worse,
there exist successful computer implementations of the Saussurian idea using
semantic networks (see discussion by Goldstone and Rogosky (2002)). Even
if such semantic networks turn out in the end not to be the correct way of
cashing out human conceptual capacities, their sheer possibility scuttles any
a priori arguments for the necessity of semantic primes.
Suppose, for the sake of argument however (and contra Saussure), that
at least some lexical concepts really can’t be fully explicated in other terms.
7
Actually, even this is open to dispute. Fodor’s (1975, 1987) conceptual atomism pre-
cisely denies that any carriers of content (concepts) possess constituent structure. I omit
Fodor’s views and objections from my discussion here however because I have come to
believe that some crucial premises which the conceptual atomist relies upon are, in fact,
false. For an excellent empirical refutation of Fodor, see Goldstone and Rogosky (2002).
I hope to have a chance to address Fodor and Lepore (1992) versus Goldstone & Rogosky
(2002) in another paper.
10
It’s important to notice that even on such a scenario, NSM runs into choppy
waters. It certainly does not follow on this supposition that any concepts
are ontologically irreducible. All that follows (trivially, in fact) is that lexical
concepts are irreducible to other lexical concepts. Nothing prevents us from
supposing that lexical concepts can be explicated in some other way, perhaps
even in terms of elements which are themselves non-semantic. A plausible
candidate here might be unconscious information-bearing states of the human cognitive apparatus. In order to validly reach their desired conclusion,
Wierzbicka and Goddard must establish that the constituents of meaningful
terms need themselves to be meaningful (to us). They certainly think that
this is the case:
The NSM approach starts with the premise that semantic analysis
must be conducted in natural language, rather than in terms of
technical formalisms (abstract features, logical symbols, etc.), if
only because technical formalisms are not clear until and unless
they are explained in ordinary language.
[Goddard (1998), my emphasis]
But must we also follow them in thinking this? I don’t think we do. It
is hard to ask for a clearer avowal of what in the previous section I called
emergentism then the quote just cited. Now, emergentism with regard to
life (vitalism), consciousness (dualism), meaning or indeed any other phenomenon is a respectable and substantive philosophical doctrine. But, as
such, it doesn’t come for free. Semantic emergentism must be supported by
argument or empirical evidence. Instead, Goddard takes it as a premise. By
doing so, he abandons any hope he may have had of persuading those who are
inclined to accept semantic reductionism. Nor does Goddard thereby shield
himself from criticism. By adopting a substantive philosophical thesis as an
11
unargued premise, NSM places itself in substantial jeopardy. Should semantic emergentism be shown in future to be false or profoundly implausible (as
has indeed happened to vitalism and dualism), the entire enterprise collapses.
As things stand, in the absence of compelling arguments to suppose that semantic properties are ontologically basic, we are not compelled to buy what
NSM is selling. In fact, we would probably be unwise to do so. (That said, I
want to reiterate that NSM semantic analysis has a useful—and perhaps indispensable—role to play in cross-linguistic research. The NSM field-linguist
does valuable work by furnishing NSM-style decompositions. One day we
may need to cash out the so-called primes she employs in more ontologically
basic, non-intentional terms. But these are distinct issues.)
Formal Semantics
Characterization
The formal approach is very much the dominant, received view—at least
among philosophers and logicians—regarding how semantic theories for natural languages ought to be constructed.8 The principal ideas guiding the
formal approach can be traced via the work of Montague (1974), and Davidson (1967), through Tarski (1944) and ultimately to Frege (1953). At its core,
formal semantics develops the (intuitively very plausible) idea that to understand a sentence of the vernacular is, at a minimum, to know its truth conditions. If, without prior context, I inform you—a non-Polish speaker—that
it is the case that Janina jest szczȩśliwa, I am not being informative. But
if you manage to learn that that sentence is true if and only if Janina is
8
Interestingly, there are disputes within philosophy itself—notably about the nature of
mathematics, following Benacerraf (1973)—which tacitly presuppose that by ‘semantics’
one just means formal semantics. The assumption can have implications for the sorts of
solutions one is prone to seek to the existing puzzles. These ideas are developed in my
prospectus.
12
happy, then, the argument goes, you have learned the meaning of what I
said. Formal semantics aims to work out precisely how the truth conditions
of arbitrarily complex sentences are a function of the contribution made by
their parts. A further and related goal is to trace the logical relations between
sentences. (More on that below.)
A number of the basic tools employed by formal semantics derive originally from work on the semantics of formal languages. I’d like briefly therefore to review how interpretations are developed for formal languages (and
why they are needed). I start with simple sentential logic and move on to
first-order predicate logic after that, before once again returning to natural
languages. The section concludes with a critical discussion of the formal
approach.
It is possible to construct a simple system of sentential logic out of the
following elements:
• Primitive Symbols. These include variables, operators and brackets. The variables (A1 , A2 , . . . , An ) range over propositions. Primitive
operators should constitute a logically complete set, as with ¬ (negation) and ∨ (disjunction). Brackets are just syntax sugar to keep things
organized.
• Rules of Formation. There are three: If A is a variable, then A is
a well-formed formula (wff). If A and B are variables, then ¬A and
A ∨ B are wffs. Nothing else is well-formed.
• Definitions. There are three defined operators, in addition to the
primitive ones:
A → B =Def ¬A ∨ B
A ∧ B =Def ¬(¬A ∨ ¬B)
A ↔ B =Def (A → B) ∧ (B → A)
13
• Axioms. Russell and Whitehead’s logic includes the following axioms:
1. (p ∨ p) → p
2. q → (p ∨ q)
3. (p ∨ q) → (q ∨ p)
4. [p ∨ (q ∨ r)] → [q ∨ (p ∨ r)]
5. (q → r) → [(p ∨ q) → (p ∨ r)]
• Rules of Inference. There are three rules of inference:
Uniform substitution of wffs for variables.
Detachment. If A and A → B are theorems, so is B.
Replacement by definition. If A is defined as B, replace A for B or
B for A.
Each axiom is evidently a well-formed formula (wff). The rules of inference
and the definitions preseve syntactic well-formedness. Only wffs can therefore
be derived from the axioms via the rules of inference or definitions. Wffs so
derived are theorems. (This is a purely syntactic definition of theoremhood.)
A natural question to ask with regard to the set of theorems is whether they
are consistent—i.e. whether it is possible at any stage to derive φ and ¬φ
from the axioms via the rules of inference.9
Negation consistency cannot be demonstrated in syntactic terms alone.
One way to do so is to model the axiomatic system in another system, which
itself is known to be consistent (like arithmetic). Another way is to construct
a proof which shows that a contradiction cannot arise. This latter method
calls for the following additional elements:
9
A good reason to try to avoid negation inconsistency is that from A ∧ ¬A and the
Duns Scotus’ rule, p → (¬p → q), one can derive any wff at all. This has the catastrophic
effect of effacing the distinction between theorems and non-theorems.
14
• Domain. This is a set consisting of (at least) two non-linguistic elements. Some possible domains include D={hat, pipe}, D={>, ⊥} or
D={True, False}. Here, we can assume that the domain consists of two
elements D={1, 0}.
• Assignment Function. This function assigns one member of the
domain to each of the primitive variables in the language. If there
are n primitive variables in a given formula, there can be 2n distinct
assignment functions mapping variables to the domain.
• Model. The model is just an ordered pair consisting of the domain and
some particular assignment function: M =< D, v1 >. Its significance
will emerge in a moment.
To show the consistency of our axiomatic system, we needs to show that
nowhere in the infinite set of derivable theorems is there a formula as well as
its negation. Obviously this cannot be done by exhaustive search. Instead,
we proceed inductively. Let us call the degree of a wff the number of logical
operators it contains. Atomic formulae are of degree zero, since they do not
contain any logical operators. The negations of atomic formulae as well as
their conjunctins, disjunctions, conditionals and biconditionals are of degree
one. And so on. We can now define a valuation function which assigns each
wff, regardless of degree, to one of the elements in the domain.
• Valuation function. Given a model M, the valuation function (Vm )
extends the assignment function from wffs of degree zero to the set of all
wffs. It proceeds recursively. We assume that for degree zero wffs, the
assignment function specifies the domain assignments. It remains for
us to specify the domain assignment for wffs of the next higher degree.
In other words, we need to specify the effect of the logical operators on
domain assignment. Here’s how that’s done:
15
* Negation. Vm (¬A) = 1 ⇐⇒ Vm (A) = 0. In other words, a
degree one formula ¬A is mapped to 1 just in the case that the
degree zero formula A is mapped to 0; it is mapped to 0 otherwise.
* Conjunction. Vm (A ∧ B) = 1 ⇐⇒ Vm (A) = 1 and Vm (B) = 1.
* Disjunction. Vm (A ∨ B) = 1 ⇐⇒ Vm (A) = 1 or Vm (B) = 1 (or
both).
* Conditional. Vm (A → B) = 1 ⇐⇒ Vm (A) = 0 or Vm (B) = 1.
* Biconditional. Vm (A ↔ B) = 1 ⇐⇒ Vm (A) = Vm (B).
Let us say that a formula A is true in a model M iff Vm (A) = 1, i.e. if
that formula maps to the domain element 1 in the model. Let us also say
that a formula is valid if it is true in all models—so regardless of how its
constituent elements are themselves mapped to members of the domain. (The
semantically valid formulae are those which are tautologous.) Using the
valuations of the logical operators just given, we can verify that each of the
axioms of our sentential logic is a tautology. Moreover, the rules of inference
preseve validity. We can be sure therefore that all theorems derived in our
system will be tautologies (i.e. will map to 1). But, in the general case, if
φ is a tautology, ¬φ is a contradiction and therefore not a theorem. We see
therefore that the initial system is indeed consistent.
Sentential logic of the kind just discussed is vastly less powerful than firstorder predicate logic (with or without identity10 ). To extend the approach
just outlined to the construction of interpretations for first-order predicate
logic, one must furnish an interpretation for the universal and existential
quantifiers. Here they are:
10
The identity operator is needed inter alia for definite descriptions, as in “The woman
who walked on the Moon was Greek”, and for for sentences involving numerosity, such as
“There are at least seven cities in Europe” or “There are precisely three moons orbiting
Earth”.
16
* Universal Quantifier. Vm ((∀x)A) = 1
⇐⇒
Vm (A) = 1 for all
models M 0 where M 0 is defined exactly as the model M except possibly
with respect to its assignment of domain member to x.
* Existential Quantifier. Vm ((∃x)A) = 1 ⇐⇒ Vm (A) = 1 for some
model M 0 .
And, of course, we need also to say something about the semantics of predicates. Unlike sentential logic, where variables range over full propositions,
predicate logic variables range over entities. Predicates work as functions
which take the entities as parameters and map to members of the domain
(so to truth values). Predicates can be monadic, dyadic, or n-adic, according
to their number of parameters. Here’s how that works in the abstract:
Ga is a saturated monadic function which has taken the variable a as its
parameter. Its interpretation maps it to a member of the domain: 1 if
a in fact does have the property G and 0 otherwise.
(∃x)Gx is a unsaturated monadic function. It tell us that there is there is
at least one entity in the domain which satisfies the function such that
it maps to 1. We arrive at Ga by using a as the function’s parameter.
(∀y)(∃x)Gxy is an unsaturated dyadic function. It tells us that for any
entity in the domain, there exists some entity which stands in relation
G to it.
With these resources in place, we can now halt our discussion of the semantics
of formal languages. The topic is much richer than what I have had a chance
to outline here.11 Still, I have hopefully summarized enough to explain how
the formal approach to semantics can be extended to the natural languages.
11
For instance, I’ve not said anything about semantics for modal logics, an interesting
area of study. (Pre-Kripke these were dismissively known as muddle-logics as no clear and
consistent interpretation seemed possible.)
17
Much is owed in this regard to the work of Alfred Tarski. In a several
important papers published in Polish, French and German in the early 1930s,
Tarski offered a disquotational characterization of truth (for a language L).
This work helped to demystify the notion of truth and to rehabilitate it as
a philosophical topic of study.12 In brief, Tarski presupposed that we know
the meaning of our own sentences and proceeded to construct a recursive
characterization of truth on that basis. As with formal languages, one begins
by specifying, for a language L, the entities which names and singular terms
denote, as well as which entities L’s predicates are satisfied by (cf. assignment
function, above). One then constructs a list of the simple sentences of L, such
that the name of each sentence appears on the left-hand side, and its truthconditions on the right. For example:
(T) “S̀nieg jest bialy” is true if, and only if, snow is white.
A complete such list, as well as a complete set of rules for combining sentences, yields a recursive characterization of truth for L.
Donald Davidson (1967) inverses Tarski’s schema (T). Contrary to Tarski,
Davidson supposes that we understand the notion of (garden-variety, disquotational) truth and constructs a recursive characterization of meaning on that
basis. In essence, a Davidsonian theory of meaning for a language L begins
by pairing all of the simple sentences of L with their truth conditions; it
builds up compound sentences recursively. In general, to know the meaning
of a sentence of a language L is to know its truth conditions.13 Of course,
12
13
For a charitable, if critical discussion, cf. Hartry Field (1972).
I’m simplifying. In fact, Davidson is a holist about interpretation. To have a theory
of meaning for a language L is to have a theory which holistically pairs each sentence of
L with truth conditions such that words exercise a constant and systematic effect on the
meanings of sentence and such that radical disagreement betwen interpreter and interpretee is minimized (the famous ‘principle of charity’). Also, one needs to fill in contextually
determined terms like ‘today’ and ‘I.’
18
we need not know whether a given sentence is true to understand it; we need
only to know what would make it true (or false).
We just saw that the semantics for predicate logic involved two sorts
of mappings: Saturated formulae (ones with no variables) are mapped to
one of the members of the nonlinguistic domain—1 or 0. Let’s call these of
semantic type < t >. Unsaturated formulae (ones which contain variables)
denote functions. That idea can be readily adapted to cope with natural
language. Noun phrases can be taken to denote individuals. We’ll say that
these are of semantic type < e >, Verb phrases, on the other hand, can be
treated like formal predicates—i.e., they can be treated as denoting n-adic
functions which, when fully satisfied, map to truth values. We’ll say that
they are of semantic type < e, t >. Let me illustrate. Take as our example
the simple sentence, “Janina czyta.” Here is how its semantic interpretation
might work:14
(3)
Janina czyta.
JJaninaK = Janina (the person out in the world). Type: < e >.
JczytaK = a function mapping to 1 (in the domain) if the semantic value
of its parameter engages in the activity of reading and mapping to 0
otherwise. Hence, of type: < e, t >.
Here is the same idea expressed in a different notation:
"
f: D→ {0, 1}
For all x ∈ D, f(x) = 1 iff x reads
#
(Janina)
Things get only slightly more complicated in the case of dyadic predicates,
such as ‘loves,’ which require two parameters—one naming the lover and
14
The double brackets indicate the semantic value of what they contain. This analysis,
and what follows, is based on Heim and Kratzer (1998).
19
the other naming the thing loved. Hence, noun phrases continue to denote
individuals. The dyadic predicate is, once again, a function. This time
however, it is a function which takes an individual (the loved) as its parameter
and outputs another function. That second function takes a second individual
(the lover) as a parameter and maps to a truth value. Here’s how that works
for the sentence “Janina kocha P ary ż”:
(4)
Janina kocha Paryż.
JJaninaK = Janina. Type: < e >.
JParyżK = Paris (the city itself). Type: < e >.
JkochaK = f: D → {g: g is a function from D to {0, 1}}
For all x, y ∈ D, f(x)(y) = 1 iff y loves x. Type: < e, < e, t >>.
Alternatively, we can define a new symbol (λ) which means essentially the
same as ‘is a function.’ This lets us rewrite our two interpretations more
succinctly as follows:
JczytaK(Janina) = [λx : x ∈ D . x reads](Janina) = 1 if Janina reads
= 0 otherwise.
The function denoted by ‘czyta’ takes one parameter, the denotation of ‘Janina’, and maps to a member of the domain (1 or 0). Similarly:
JkochaK(Paryż)(Janina) = [λx ∈ D . [λy ∈ D . y loves x]](Paris)(Janina)
= 1 if Janina loves Paris
= 0 otherwise.
So much then for the bare basics of the semantics for simple declarative
natural language sentences.
20
An important difference between formal languages of the sort that
Tarski’s semantic characterization of truth applies to unproblematically and
natural languages which children acquire at their mother’s knee concerns ambiguity. The formulae of formalized languages are precisely constructed so
as to avoid the need to map two distinct interpretations to a single syntactic
formula. This is in general, of course, not the case for sentences of natural languages where ambiguous utterances abound. Consider the following
example15 :
(5)
The millionaire called the governor from Texas.
The sentence can mean one of two things: Either the millionaire telephoned
a governor of some undisclosed institution while she (the millionaire) was in
the Lone-Star State. Or, the millionaire placed a call to the Governor of
the State of Texas from parts unknown. As before, we can make a little bit
of headway spelling out an interpretation of (5) by means of the following
schema:
(5T) “The millionaire called the governor from Texas.” if, and only if, the
millionaire called the governor from Texas.
The problem is that this schema alone does not help us make sense of the
ambiguity. To get a handle on that, both the left-hand side and the righthand side of the schema need to be made considerably more sophisticated.
What is needed on the left-hand side of the formula is an unambiguous
restatement of (5) which makes salient the relationships between the various
parts. Here, work in syntax can be very helpful. The Chomskian revolution
has made it possible to at least imagine how a complete formalization of the
syntax of natural language might be possible in the very long run. Let us
15
This example is discussed, though not analyzed in detail, by Pietroski (2003b).
21
suppose for our purposes (falsely, it would appear) that X-bar rules of the sort
developed by Chomsky in his GB phase permit a correct characterization of
NL syntax. This will let us pry apart two syntacticly distinct sentence types,
a token of which one might utter by producing (5). Here is the first, involving
a Texas State Governor (or maybe a Texas-born governor) receiving a call:
(5a)
IP
`
```
``
I0
NP
HH
H
PP
P
P
DP
N0
I0
D0
N0
+ past
D0
VP
V0
PP
P
P
V0
millionaire
The
call
NP
PPP
P
DP
N0
J
!!aa
!
!
N0
the
a
a
PP
!aa
a
!!
governor from Texas
And here is the one which involves the millionaire telephoning from the state
of Texas to some governor or other:
(5b)
IP
(((hhhhh
hh
((((
0
I`
NP
H
H
H
DP
N0
I0
D0
N0
+ past
D0
```
``
VP
V0
XXXX
X
V0
PP
HH
H
!aa
!!
a
millionaire
V0
The
call
22
NP
!aa
!!
a
!
a
the governor
from Texas
Each of the two possibilities requires a distinct semantic interpretation—i.e.,
it requires that a different set of truth-conditions be inserted into the righthand side of schema (5T). Here, we can make use thematic relations and of
Davidson’s (and Charles Parsons’) work on the event-operator (e). (5a) can
be interpreted as:
(5a0 ) Past [The x: GOVERNOR(x), BENEFACTIVE(x, Texas)]
∃e(CALL(e) & AGENT(millionaire, e) & PATIENT(x, e))
Whereas (5b) would be parsed as:
(5b0 ) Past ∃e(CALL(e) & AGENT(millionaire, e) & PATIENT(governor, e)
& SOURCE(e, Texas))
By inserting a Chomskian syntactic tree into the left-hand side of (5T) and
a Davidsonian event-analysis into its right-hand side, we arrive at an unambiguous semantic interpretation for (5). In the general case, by matching
simple sentences with their semantic interpretations, and by specifying the
rules via which both the syntactic and the semantic (left- and right-hand
side) analyses are to be extended, one arrives at a recursive characterization
of meaning for some natural language L. The devil, as ever, is in the details.
Discussion and Criticism
How plausible is it that FS is capable (in its current form) of providing us
with a materially adequate explanation of the nature of meaning? There have
already been hints of trouble. We saw NSM offer an explanation (albeit a
flawed one) of the difference between the Polish adjective ‘szczȩśliwa’ and the
rough English translation ‘happy.’ Our FS analysis glossed over the point.16
16
Unlike NSM, FS would spell out the difference between the two notions extensionally:
the set of entities which satisfies the one predicate is distinct from the set of entities which
satisfies the other. They are therefore semantically distinct. Of course, one can sensibly
wonder whether this is an explanation or just a redescription of the facts in set theory.
23
Moreover, NSM was able to recognize that while we certainly do use words to
make truth-evaluable claims, we also cajole, request, apologize, give orders,
and, in general, put language to a variety of other uses (cf. Wittgenstein
(1953)). FS does not seem readily equipped to accommodate this.17 Having
noted these apparent shortcomings, I will leave them aside here. Instead,
I want to focus on one recent criticism of FS due to Prof. Paul Pietroski
(2003a,b).
Natural languages are, fairly obviously, human capacities. A theory of
meaning for a natural language pairs up linguistic signals with interpretations
(whatever those may turn out to be in the end). Competent speakers of
natural languages are able to effect such a pairing relatively effortlessly in real
time, even if neither they nor we know quite how the underlying mechanisms
work. It seems reasonable to think that a theory of meaning for a natural
language ought therefore to be a theory of understanding—i.e., a theory
which explains how it is that people come to pair signals with interpretations.
Pietroski (2003b) argues that, contrary to appearances, FS fares poorly as a
theory of understanding, in this sense. Consider the following example:
(6)
France is a hexagonal republic.
In the right context, this sentence can express a true idea: Suppose, for instance, that someone jokingly suggests that countries’ political constitutions
can be read off their geographic shapes. Suppose also that, on their story,
hexagons are monarchies. One can imagine tokening (6) so as offer a counterexample to the theory. Now, notice that on a Davidson-inspired (so also FS)
17
One could perhaps replace truth-conditions in the meaning schemas with felicity-
conditions in the style of Austin (1962). Thus, in the case of declarative sentences, the
felicity-conditions would just reduce to truth-conditions, whereas in the case of speech-acts
with a different illocutionary force, we might need a significantly complex analysis than
that offered by the Davidsonian event-analysis alone.
24
account, ignoring the complexities of the left-hand side, the meaning schema
for (6) is essentially this:
(6T) “France is a hexagonal republic” if and only if
(∃x)[(F x ∧ (∀y)(F y → y = x)) ∧ Hx ∧ Rx]
It would seem then that the theory requires that there be a real, robust
entity in the world which simultaneously satisfies two predicates—viz. being a
republic, as well as being hexagonal. Now, undoubtedly, France is a republic.
Likewise, there is a sense in which France is hexagonal, much as Italy is bootshaped. But it is doubtful whether there exists a single entity in the world
with both of these properties. Rather, it seems more plausible that we are
able simultaneously to think of France under two descriptions. Consider what
happens when we add even more complexity into the mix:
(7)
France scored two goals in the quarter-final.
To suggest that there exists an entity which is hexagonal, a republic and
scored two goals is to adopt desperate measures. What sort of entity might
that be? Geographical? Socio-economic? Socio-geographico-sportive? Pietroski asks whether perhaps it would not be more sensible to question whether
theories of meaning (which explain how we come to understand sentences
like (6) and (7)) ought really be theories of truth. Sure, we can express true
thoughts using our words. But, in general, the truth of our utterances is
a massive interaction effect involving our intentions, contexts, listeners and
(importantly) the world. To ask a theory of understanding for human languages to be a theory of truth is to ask it to be a theory of everything (a
point Chomsky (2000) also makes). Instead, Pietroski argues, we can hang
on to the idea that theories of meaning should have the general form of a
Tarski-style recursive definition without requiring that the right-hand side
of the schema specify anything as full-blooded as a set of truth conditions.
25
Instead, one might think of lexical items, such as ‘France’ as certain kinds of
‘recipes’ for constructing representations.18 . “France is hexagonal.” leads to
the construction of one kind of mental representation. “France is a republic” leads to another. The notion [France] constructed in each instance is
different. But the two are such as to be able to be combined in (6), even if
“France is hexagonal, scored two goals, and a republic” begins to stretch our
mental resources.
Let me close with yet another problem for FS. If one rejects Pietroski’s
criticisms and hangs on to the idea that a theory of understanding (not only
has the formal character of, but) really is a theory of truth, one still needs to
explain the fundamental posits FS averts to. We saw above how meanings can
be characterized in terms of sets (or, equivalently of functions and satisfiers).
However, the ontological status of sets, and of abstract entities generally, was
left undetermined. We know that they are abstract entities. But just what
those might be, whether they truly exist, and whether they can be reduced
to better-understood natural entities is unclear. This is not the place to get
into the philosophy of mathematics. But the worries are worth keeping in
mind, if only to remind us that the explenanda in terms of which FS explains
meaning are not themselves well understood. The approach is, in this sense
at least, tacitly committed to a sort of emergentism regarding meaning.
Conceptualist Semantics
Characterization
Jackendoff’s (1983, 1987, 2002) conceptualist semantics (CS) differs considerably from both of the approaches considered so far. Unlike NSM, CS
acknowledges the fundamental importance of Chomskian work on the syn18
This idea is not unlike certain proposals alive in current cognitive psychology; cp.
Barsalou (1999)
26
tax of natural language. In this respect at least, CS is not unlike some of
the sophisticated work being done in formal semantics (Larson and Segal
(1995)). CS differs from FS however in not attempting to hook linguistic
items up with referents ‘out in the world’—at least not in any straightforward way (see below). CS is at once a radical extension of the Chomskian
programme and an attempt to integrate work in linguistics with the rest of
cognitive science. In this section I outline how this is supposed to work.
In the next, I present some objections which—by Jackendoff’s (2003) own
admission—remain a source of worry for CS.
CS begins by taking on board the key insights of the Chomskian programme. Let me take quick moment to lay those out: The normal human
child is born with a ‘language acquisition device’, or a dedicated cognitive
apparatus for acquiring the language to which the child is exposed. Acquiring a language is not a matter of hypothesis formation and disconfirmation,
as empiricist theories suppose. An unbounded set of possible grammars is
compatible with the finite data available to the learner; empiricist theories
have a hard time explaining why most candidate theories are never so much
as entertained. Repeated studies have shown that, in fact, children are highly
resistant to negative evidence, including explicit correction. Hypothesis disconfirmation does not seem to play a role. As a matter of fact however,
children’s syntactic performance does come into line with that of others in
their linguistic community. And, of course, children are able to generalize:
they are able to construct an unbounded number of novel, grammatical utterances. The sole plausible explanation is that language constitutes an innate
cognitive mechanism, and that the child’s apparent ‘learning’ of her native
tongue is really the setting a finite number of innately-specified parameters.
(For a more careful exposition of this rather familiar story along with its
analogues in semantics, see Pinker (1989).)
The proper object of study for linguistics (or, at least so far as syntax is
27
concerned) is the linguistic competence of an idealized mature speaker. In
essence, one asks: what must the algorithm which the mind/brain’s dedicated
syntactic-module implements be like for the performance of the competent
speaker to be what it is (abstracting from inessential, individual peculiarities, memory constraints and the like). Language understood as this sort of
dedicated, mental algorithm is sometimes called i-language: it is individual,
internal and intensional. Admittedly, this picture contrasts rather sharply
with the perhaps more commonsenseical notion of language as a publically
observable set of marks. Rather, what we typically think of as ‘languages’
(so Hungarian, Tagalog, Putonghua) are rough-and-ready abstractions. In
fact, there exist a number of more-or-less similar, mutually intelligible, community practices. These linguistic community practices arise as the effects
of the interaction between speakers’ i-languages. (Chomsky (2000).)
Chomskian mentalism has been a very rich source of insight into the syntax of natural languages. Yet Chomsky himself has remained sceptical about
the possibility of developing a semantic theory (hence the mutual hostility
between NSM and Chomskian linguistics). The worry, it seems, has been
that it is next to impossible to draw a principled line between our understanding of language and our understanding of the world.19 And if this sort
of distinction cannot reliably be drawn then semantics threatens to become a
sort of grab-bag ‘theory of everything.’ One can see why a hard-nosed syntactician might view that outcome as ultimately threatening the entire linguistic
enterprise. (This, I take it, was the motivation for Chomsky’s attacks on the
‘generative semantics’ work in the 1970s.)
Jackendoff maintains, contra Chomsky, that a bounded, rigorous and nontrivial semantics is possible after all. Suppose, he argues, that we accept the
important contribution to the understanding of human languages made my
19
Davidson too argued against there being a distinction between one’s conceptual scheme
and one’s knowledge of language.
28
Chomskian syntax (whether GB or Minimalist). Suppose we accept mentalism and nativism, as well as the focus on i-language. One of the key founding
assumptions of the Chomskian program has been the combinatorial structure
of syntax: complex syntactic structures are built up recursively out of simpler constituents.20 An unargued assumption at the core of the program has
been that syntax, and syntax alone, displays this sort of structure. But, as
things stand, that assumption flies in the face of current linguistic practise.
As a matter of fact, phonologists have pursued generative theories of their
own, quite independently of syntax, for several decades. The phonological
structure of language is understood today to obey proprietary combinatorial
principles, ones quite independent of the compositional principles at work in
syntax. Jackendoff (2002, 2003) urges that linguistic theory should catch up
to linguistic practise. We should explicitly recognize that syntax, phonology
and semantics each constitute distinct combinatorial modules of the language
faculty, and that each executes its own computations over proprietary (unconscious) ‘representations’. On such a view, the study of semantics (much
like the study of syntax) involves theorizing about the sorts of computational
data-structures and processes which take place in the relevant portion of the
mind/brain.
Figure 1 (below) illustrates the overall architecture of the semantic faculty, as currently envisaged by CS. It also shows how semantics is thought
to link to related mental faculties—perception and motor faculties in particular—as well as to the world at large. Before discussing the inner workings
of the semantic faculty as pictured there, let me ward off a possible misunderstanding. The term ‘representation’ is often used to convey that some
entity stands in for some other entity for some purpose in so far as an observer is concerned. Jackendoff carefully avoids appealing to this notion;
the data-structures which inhabit the cognitive system, as he envisages it,
20
We saw an emphasis on combinatorial structure in our discussion of FS, above.
29
typically do not stand in any interesting one-to-one relation to the external
world. Nor is there a little homunculus in the brain to whom things are represented (Dennett (1991)). Rejecting representations may seem like a radical
move. Philosophers have taken CS to task in part for being solipsistic for
this reason. In fact, there is a well-established precedent in the cognitive literature for dispensing with inner representations. More importantly, there is
an existence proof: Rodney Brooks’ (1991) robots are capable of complex interactions with their environment (including collecting pop-cans left around
the MIT lab) without the benefit of inner representations. The activation
vectors at the higher levels of the robots’ hierarchical subsumption architecture do not correspond to any features in the world at large. They do not
represent anything out there at all. I read Jackendoff to be suggesting that
the computational states within the higher perceptual and semantic modules are very much in the same boat. They are fine-grained enough to allow
complex responses to emerging situations, and that’s what really matters.21
Caveats in place, let us return to Figure 1. CS semantic representations
are data structures in the unconscious mind/brain. They are formed according to their own rules of formation, constituting a largely autonomous level
of processing. This level acts as an interface between syntactic structures,
on the one hand, and the perceptual and motor modules on the other. The
syntactic structures for concrete entities display perceptual features which encode salient observable aspects. In addition, they display inferential features
which tie them to other syntactic structures. (Syntactic structures repre21
While on this topic, let me mention also that Goddard (1998) suggests that Jack-
endoff’s semantic elements are ‘abstract’ and therefore not to be identified with ordinary
word meanings. Goddard is right to say that the data structures manipulated by the CS
semantic faculty are not ordinary word meanings if the latter are accessible to consciousness (as they often are). He is wrong however to suggest that they are abstract entities,
if by that one understands what philosophers typically do: acausal, atemporal, platonic
objects (cf. Burgess and Rosen (1997)).
30
Figure 1: The semantic faculty’s place in the cognitive mind (Jackendoff
2002, p.272).
31
senting abstract entities obviously lack the perceptual features, but possess
inferential features nonetheless.) The semantic module acts as a sort of interpretive interface between syntax and the outputs of the perceptual and
motor faculties. Jackendoff argues that our experienced reality (though not,
of course, the world as such!) results from the output of the brain’s perceptual modalities. In some sense, CS pushes the world of experience “into
the brain” (Jackendoff 2002; p.303). The job of semantics, as CS sees it, is
to connect the world as experienced by us with the structures which inhabit
the language faculty. One way to understand that is to view the semantic
faculty as mediating between the sorts of data-structures furnished by highlevel vision (see Biederman’s 1995 geon theory for instance) and the rest of
the language faculty. Semantic structures thus do not represent elements of
the external situation in any direct way. The structures which inhabit the
semantic module do not have a meaning; rather, they do all of the things that
meanings are supposed to do. They are meanings (Jackendoff 2002; p.306).22
One may wonder what happens to the lexicon on the picture just proposed. Rather than positing a dedicated lexicon in which individual lexical
items are stored as tough in a box, CS posits only interfaces between each
of the three generative modules. In some sense, the lexicon just consists in
these interfaces. The smooth functioning of the overall system gives rise to
the appearance that there exist coherent data-units (words) with a phonology, syntactic role and a semantics. Under the hood however, there are only
regularities in the way that the three modules come to interact. This permits
Jackendoff to explain situations where the coordination comes apart slightly
or fully. (On this account, ‘pushing up daisies’ and other idioms have a
22
Cognitive semantics has sometimes been accused of vacuously translating from one
language (say, English) into another language, ‘semantic-markerese’ (cf. Lewis (1972), for
example). By tying the semantic structures to perception and to action, as he has done,
Jackendoff (2003) blunts the force of this criticism. Ironically, FS has no parallel way out.
32
normal syntax and phonology but interface as a unit with a single semantic
item: [DIE]. Likewise, nonsense phrases like “twas brillig and the slithy toves
did gyre and gimble in the wabe” have a phonology and perhaps even some
syntax but fail to interface with any semantic structures.)
It might be helpful to close by contrasting a CS analysis of a natural
language sentence with those given in previous sections. Recall example (5):
(5)
The millionaire called the governor from Texas.
Analyzing a sentence of the vernacular is a matter of lining up its phono-
logical, syntactic and semantic representations. We discussed the syntactic
representations corresponding to this sentence (above).23 Giving the two corresponding semantic representations is a matter of decomposing the sentence
into its semantic constituents. According to CS, the human cognitive system—both within the semantic module, as well as outside—has available to
it a small repertoire of conceptual types. We employ these to make sense of
our physical surroundings, plan, imagine, and so on. The conceptual types
also play an important role in constructing semantic interpretations on the
basis of information available from the syntax module. Among the primitive
types used by CS are at least the following: [thing] [place] [direction]
[action] [event] [manner] [amount]. A fist step toward analyzing (5) is
furnishing it with a gloss in terms of these semantic types.
Recall that (5) is ambiguous between two possible readings; we will need
two distinct semantic analyses. Let us begin with the CS gloss on the situation involving a Texan public official being contacted by a well-to-do caller:
(5α0 )
23
My handle on phonology is too tenuous to attempt an analysis. Asking someone else
to do it for me would be cheating. Sorry.
33



"
#

 SEN AT OR( ORIGIN (

M
ILLION
AIRE

 CALL(
),(

Thing
State



Thing
"
T EXAS
Place
#   
) ) 
)



Event
The sentence is, as one might expect, fundamentally about an event, as indicated by the category label in the main, outer square bracket. The event
type, the call, takes two parameters: the caller and the callee. Both individuals are represented in the CS analysis. How the mind/brain manages to
‘refer’ to these two worldly entities—in other words how it manages to pick
out and track those entities in the world—is left, appropriately enough, to
the cognitive psychology of perception and of attention. One further fact
matters for semantics: In this case, the callee is further modified by having
their place of origin specified.
Here is the contrasting case, where the calling is being done from Texas:
(5β0 )


"
T EXAS
# 

) 


 F ROM (
 CALL

Place




Path






#
"
# 
 "
 M ILLION AIRE
SEN AT OR 
(
),(
) 

 Thing
Thing
Event
Again, the overall content concerns an event. In this case however, the call
is coming from Texas, as indicated by the [path] information. One might
envisage filling in the path details along the lines suggested by the work of
Talmy (2001) or Regier (1996). In other words, what is being labelled [path]
here, might stand in for some particular set of activations of a structured
connectionist network, trained to be sensitive to location. (The details do
34







not matter much for us. It is important though that there are ways of cashing
the labels out in computational terms.)
Note that sentence (5) can’t mean that the millionaire is from Texas
because the semantic construct which expresses this possibility cannot be
built up on the basis of the two possible syntactic analyses (5a0 and 5b0 ). That
is, the mind/brain of the hearer cannot construct this (otherwise perfectly
sensible) idea from the resources provided.
Discussion and Criticism
CS has its share of critics. Some dismiss it as hopelessly vague. And they
have a point. Lined up next to the rigorous-looking formalizations which FS
theorists produce, current versions of CS look rather flimsy by comparison.
Proponents of NSM have been critical of Jackendoff too. Wierzbicka (2003,
conference presentation) repeatedly emphasized that CS has not succeeded in
producing a single full semantic description of any natural language sentence
or sentence fragment. From this, she concluded that her own project was the
best—indeed, the only—well-worked out alternative to formalist approaches.
In my view, criticisms from both sources are somewhat disingenuous. I have
already argued that until formal semantics can constitute a theory of human
understanding, it cannot count as an explanation of meaning. For its part,
NSM fails to explain semantic notions in non-semantic terms and therefore
it too can be accused of not yet having provided a single full explanation
of a semantic phenomenon. Wierzbicka may be right that CS has not produced a single semantic decomposition which takes us right from the level of
the syntax-semantics interface, via semantic structures, through molecular
semantic primitives, down to the cognitive psychology of perception. But
isn’t that a bit much to hope for so early in the game?
Instead of focusing on criticisms which FS and NSM level at conceptualist
semantics, let me here reiterate those raised by Jerzykiewicz and Scott (2003).
35
Essentially, they amount to the charge that, as it stands, the theory of reference on which CS relies entails the fallacy of psychologism. Psychologism,
recall, is the attempt to account for the necessary truths of mathematics in
terms of contingent psychological facts. Frege (1953) raised seminal objections to that sort of project.24 Most philosophers since then have regarded
psychologistic theories as patent non-starters.25 This does not necessarily
mean that Jackendoff is wrong (in fact, I don’t think that he is). It does
mean though that for CS to be fully defensible, it must provide an explicit
discussion and defence of psychologism, showing either that the doctrine is
not a fallacy or that the charge does not apply.
What then is the problem? In essence, Jackendoff’s (2002) account of
abstract objects (Section 10.9.3) looks like it’s on shaky ground. As we just
saw, on the CS account, conceptual structures within the generative semantic
module are not themselves interpreted—they do not have a semantics. They
just are the semantics of natural language. The fine-grained data-structures
that inhabit the semanticmodule interface richly with perceptual modalities and with motor outputs, while individually not necessarily representing
anything in the world as such. The familiar appearance that words refer
to entities and events can be explained—for concrete referents, at least—in
terms of the relationship between semantic constructs and the outputs of
perceptual faculties. It is these outputs that we consciously experience as
our ‘world’. In the case of abstract objects (like beliefs, mortgages, obligations, and numbers) which manifestly lack perceptual features, the theory makes only slightly different provisions: the data-structures that encode
them possess inferential rather than perceptual features. Interfaces to syntax
24
For a very good historical and sociological account of the psychologism controversy,
yet one sensitive to philosophical detail, see Kusch (1995). For a Frege-inspired attack on
Chomsky, see Dartnall (2000).
25
For a recent example of this, see Burgess and Rosen (1997)
36
and phonology treat all conceptual structures similarly, regardless of whether
their constitutive features are exclusively inferential or, inpart, perceptual.
So, in effect, Jackendoff’s reductive, naturalistic theory of concepts rejects
platonism and identifies abstract objects with the cognitive structures that
express them.
The paradigm cases of abstract objects are mathematical and logical entities. It is odd therefore that Jackendoff does not discuss such entities explicitly. If the CS account of abstract objects is to work at all, it must
work for them. The trouble is that CS entails psychologism, the view that
the necessary truths of mathematics and logic are to be accounted for in
terms of contingent facts about human cognition. According to psychologism, 2 + 2 = 4 is a fact of human psychology, not a fact that is independent
of human beings. Frege (1953) raised seminal objections to this doctrine and
today psychologism is typically viewed as a patent fallacy. There have been
several notable attempts to defend psychology-inspired theories of the nature
of mathematical objects (Kitcher (1983), Maddy (1990) among them). But
these have not, it seems, met with much success. The good news is that there
is room for discussion. Haack (1978) points out that it is far from obvious
whether Frege’s objections continue to apply to modern, cognitive theories.
Frege’s target was the introspectionist psychology of the day, and (Jackendoff
1987, 2002) carefully avoids this approach. It may, therefore, be possible to
articulate a theory of abstract objects consonant with CS, yet responsible to
the philosophical literature.
To get off the ground, a CS-inspired account of abstract entities must
cope with a number of challenges. Mathematics is an odd domain and mathematical judgements are unique in a number of respects. A good theory has
to explain at least the following three features of mathematical judgements:
• Universality. Some norms derive their authority from community standards. Those norms are no less real for their conventional nature (traf37
fic rules come to mind), but they are only true by agreement. By
way of contrast, norms governing the behavior of abstract logical and
mathematical entities are universal (a point stressed by Nagel (1997)).
Community standards derive their authority from the norms, and not
vice-versa. Even people with untutored intuitions can come to recognize the truth of a law of logic or mathematics, though they may
require quite a bit of reflection to do so. CS needs an explanation of
how some abstract objects (which are supposed to be mental entities)
come to possess these inferential features. Are they innate? If so, Jackendoff’s appears to be committed to a version of Fodor’s language of
thought hypothesis, in spite of having explicitly rejected Fodor. Are
they learned? If so, the poverty of stimulus problem rears its ugly head.
• Objectivity. Logic, geometry and mathematics are not uninterpreted
formal systemsthat people happen to universally assent to regardless
of which community they inhabit. Formal interpretations of physical
phenomena permit predictions concerning the behaviour of objective
reality even in contexts vastly beyond the scope of actual (or possible) human experience. Many researchers have commented on the
‘unreasonable’ effectiveness of applied mathematics, even in contexts
where the original mathematical tools were developed for purely formal
reasons. How does mathematical reasoning manage to preserve truth
about distant contexts if mathematical objects are merely psychological
data structures with local inferential features? In other words, quite
apart from its universality, how, on the psychologistic account, does
mathematics come by its objectivity?
• Error. It is tempting to account for the validity of logical inference
in terms of the way that (normal, healthy) cognitive systems actually
reason. But we can make mistakes regarding the properties of abstract
38
objects. Even professional mathematicians occasionally draw false inferences about mathematical objects. And a real feeling of surprise
and discovery can accompany mathematical innovation—that moment
when humanity discovers that we have all been conceiving of some
mathematical construct incorrectly all along. The intuition that mathematical objects can have properties quite different from those imputed
to them, even by professionals, fuels platonist intuitions (Godel 1947).
Validity cannot merely consist in a conformity with the way people actually reason—it is a property of arguments that conform to the way
we ought to reason.
How psychologism can account for this remains uncertain. Jackendoff (pp.
330-332) suggests several mechanisms of social “tuning” that can serve to
establish (universal) norms within a community—norms against which error
may be judged and the appearance of objectivity can arise. So when Joe
mistakes a platypus fora duck (p. 329), his error is relative to the impressions of the rest of his community. “Objective” fact and the appearance of
universality is established by communityconsensus. Unfortunately, this account does quite poorly with logic and mathematics. A mathematical or
logical discovery happens when one member of the community realizes that
something is wrong with the way the community conceptualizes some aspect
of the field, and demonstrates that error to the other members of the community. The issue here is how a whole community can be shown to be in
error when the objective reality against which the error is judged is mere
community consensus. Platonism has an obvious solution to this issue, one
involving acausal abstract objects, but since CS does not countenance those,
it will have to work hard for one.
None of this demonstrates that CS is incoherent. Rather, it is intended as
a signpost toward research which could usefully be done to bolster CS, as well
as to undermine some of what is currently done in several key branches of
39
anti-naturalistic philosophy, including much of the philosophy of mathematics. But, in any case, until CS offers a compelling solution to the problems
just identified, it cannot be accepted as an adequate account of the nature of
semantics. CS, much like the other two approaches discussed above, is not
(in its current form) an acceptable theory of meaning for cognitive science.26
Conclusions
Each of the three projects outlined here is compatible with naturalism (as
defined at the outset), provided we are willing to make some important sacrifices. In the case of NSM, we need to acknowledge that semantic posits are
ontologically irreducible; they are emergent phenomena, brute facts about
the universe. Few linguists or philosophers are willing to pay this price at
the moment, though I suspect that this option would become increasingly appealing if no reductive explanation of semantics proved capable of delivering
an adequate theory. For its part, FS wheels out the mathematical machinery
of sets and functions to lay siege to meaning. The posits of mathematics are
themselves taken as ontologically basic and hence (yet again) as not standing
in need of any further explanation. Most philosophers today seem to find this
plausible (Shapiro (2004), Burgess and Rosen (1997)). A minority, whose arguments I find compelling resist (Field (1989), Maddy (1990)). And, in any
case, there are other problems. (Pietroski 2003a) has argued, convincingly I
think, that a theory of understanding for natural languages must come apart
from a theory of truth. To the extent that FS supposes that a theory of
understanding just is a theory of truth, it runs into trouble. Finally, as we
saw, Jackendoff (2002) offers a seemingly plausible theory of understanding
for natural languages. CS is a reductive account that makes a serious effort
26
Let me reiterate that the ideas expressed in the above section were developed jointly
with Sam Scott.
40
to integrate insights from phonology, syntax, semantics, psycholinguistics,
neuroscience as well as philosophy. To buy into CS however, we seem to
need to give up our best account of the nature of logic and mathematics.
Most philosophers would find this price prohibitive. It seems then that there
are good reasons for rejecting all three of the views discussed here.
Let me close by placing my own chips on the board. If I were a betting
man, I’d lay odds on CS. I think that CS will, in the long run, subsume
NSM by showing how what is best in that approach—the semantic analyses—are to be cashed out in generative terms. I suspect moreover that CS
will eventually arrive at an adequate theory of the nature of logical and
mathematical posits, one which is broadly psychologistic yet not vulnerable
to Frege’s and Nagel’s arguments. The key there, I think, is to accept the
anti-psychologism arguments as defining criteria on any adequate theory of
logical and mathematical understanding. With enough attention to detail,
there are probably explanations to be found for how our mathematical judgements achieve objectivity, universality, fallibility as well as a host of other
interesting features not discussed here. Suppose for a second that that’s possible. Prof. Pietroski has suggested that a theory of human understanding
ought to take the form of a Tarskian truth theory (even if it need not, in
fact, be a theory of truth). That proposal could, it would seem, be combined
with Jackendoff’s CS to yield a hybrid semantic theory. In other words, if a
compromise-solution to the question of the nature of mathematical objects
can be found, there need not exist any deep incompatibility between formal
semantics and conceptualist semantics. My bet is on that sort of semantic theory ultimately furnishing cognitive science with a proper account of
understanding for natural languages.
41
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