Naturalism and semantics∗

Luke Jerzykiewicz (ljerzyki@uwo.ca)

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).

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Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Mise-en-scene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 ade-

quate 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-scene

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 vari-

ous 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 in-

troduced only sparingly. Obviously, one wants to recognize that non-basic

‘things’ exist: there are hydronium ions, ecosystems, GDPs, maximal pro-

jections, 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 exam-

ple, 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 de-

scription 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 explana-

tions 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 them-

selves 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: Elimina-

tivists doubt that there is such a phenomenon as meaning to explain (here

we can recall the behaviourists). They tend therefore not to develop theo-

ries of meaning, and are not discussed here. Emergentists propose that we

should take meaning—or perhaps the terms in which meaning is to be expli-

cated—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 revolu-

tion (Wierzbicka (1996)). The decline of behaviourism and the advent of the

new science of mind was a tremendous opportunity to rehabilitate mentalis-

tic 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 cog-

nitive 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 infor-

mation 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. Cog-

nitive 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 understand-

ing 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

1This distinction, as we shall see, plays an important role in the other two theories

discussed below.2I 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

3Even 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).4In 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 defini-

tion 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 endeav-

our. 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 in-

tellectual 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 morpho-

logical 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 szczesliwa.

Its NSM semantic analysis runs as follows: The proper name ‘Janina’ denotes

a person.5 The verb ‘jest’ serves to link the adjective ‘szczesliwa’ 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 ‘szczesliwa.’ 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 substi-

tuting “Janina” for the variable P in (2). Notice that analysis nicely brings

out the difference between ‘szczesliwosc’ and apparent English translations

like ‘happiness.’ While the English term ‘happy’ is used frequently in every-

day contexts to refer to states of mild, temporary satisfaction, ‘szczesliwosc’

designates a profound sense of fulfilment (perhaps not unlike the French ‘bon-

heur’). 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.

5I 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 ‘szczesliwa.’ Impor-

tantly, 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 ‘szczesliwa’ 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 ‘szczesliwa’ or of one

of the following synonyms (English approximations in parentheses):

• zasycona (sated)

• zadowolona6 (contented)

6This 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 ‘szczesliwa.’

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 con-

cepts 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 dif-

ference 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.

7Actually, 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 hu-

man 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 phe-

nomenon 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 seman-

tic 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 se-

mantic 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 in-

dispensable—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 nat-

ural languages ought to be constructed.8 The principal ideas guiding the

formal approach can be traced via the work of Montague (1974), and David-

son (1967), through Tarski (1944) and ultimately to Frege (1953). At its core,

formal semantics develops the (intuitively very plausible) idea that to under-

stand a sentence of the vernacular is, at a minimum, to know its truth con-

ditions. If, without prior context, I inform you—a non-Polish speaker—that

it is the case that Janina jest szczesliwa, I am not being informative. But

if you manage to learn that that sentence is true if and only if Janina is

8Interestingly, 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 origi-

nally from work on the semantics of formal languages. I’d like briefly there-

fore 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 brack-

ets. The variables (A1, A2, . . . , An) range over propositions. Primitive

operators should constitute a logically complete set, as with ¬ (nega-

tion) 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:

9A 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 ele-

ments. 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 first-

order 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:

10The 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 ′ where M ′ 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 ′.

And, of course, we need also to say something about the semantics of pred-

icates. 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.

11For 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 truth-

conditions on the right. For example:

(T) “Snieg jest bia ly” is true if, and only if, snow is white.

A complete such list, as well as a complete set of rules for combining sen-

tences, 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, disquo-

tational) 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,

12For a charitable, if critical discussion, cf. Hartry Field (1972).13I’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 interpre-

tee 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

14The 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 Paryz”:

(4) Janina kocha Paryz.

JJaninaK = Janina. Type: < e >.

JParyzK = 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 ‘Jan-

ina’, and maps to a member of the domain (1 or 0). Similarly:

JkochaK(Paryz)(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 am-

biguity. 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 natu-

ral 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 right-

hand 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

15This 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````

NPHHH���

DP

D′

D0

The

N′

N0

millionaire

I′PPPP����

I0

+ past

VP

V′PPPP����

V0

call

NPPPPP����

DPJJ

the

N′aaaa!!!!

N0

governor

PPaaa!!!

from Texas

And here is the one which involves the millionaire telephoning from the state

of Texas to some governor or other:

(5b) IPhhhhhhh(((((((

NPHHH

���

DP

D′

D0

The

N′

N0

millionaire

I′`````

I0

+ past

VP

V′XXXXX�����

V′HHH���

V0

call

NPaaaa!!!!

the governor

PPaaa!!!

from Texas

22

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 right-

hand 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:

(5a′) Past [The x: GOVERNOR(x), BENEFACTIVE(x, Texas)]

∃e(CALL(e) & AGENT(millionaire, e) & PATIENT(x, e))

Whereas (5b) would be parsed as:

(5b′) 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 unam-

biguous 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 ‘szczesliwa’ and the

rough English translation ‘happy.’ Our FS analysis glossed over the point.16

16Unlike 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 in-

stance, 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 counter-

example to the theory. Now, notice that on a Davidson-inspired (so also FS)

17One 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)[(Fx ∧ (∀y)(Fy → 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 boot-

shaped. 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? Piet-

roski 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 lan-

guages 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 repub-

lic” 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 consid-

erably from both of the approaches considered so far. Unlike NSM, CS

acknowledges the fundamental importance of Chomskian work on the syn-

18This 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 straightfor-

ward 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 pro-

gramme. 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. Acquir-

ing 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 dis-

confirmation 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 utter-

ances. 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 peculiari-

ties, 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, com-

munity 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 syn-

tax 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 under-

standing 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 syntac-

tician 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 non-

trivial semantics is possible after all. Suppose, he argues, that we accept the

important contribution to the understanding of human languages made my

19Davidson 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 mental-

ism 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 sim-

pler 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 (un-

conscious) ‘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 fac-

ulty, as currently envisaged by CS. It also shows how semantics is thought

to link to related mental faculties—perception and motor faculties in partic-

ular—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 misun-

derstanding. 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 ob-

server is concerned. Jackendoff carefully avoids appealing to this notion;

the data-structures which inhabit the cognitive system, as he envisages it,

20We 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 rep-

resented (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 lit-

erature for dispensing with inner representations. More importantly, there is

an existence proof: Rodney Brooks’ (1991) robots are capable of complex in-

teractions 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 architec-

ture 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 mod-

ules 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 accord-

ing 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 en-

code salient observable aspects. In addition, they display inferential features

which tie them to other syntactic structures. (Syntactic structures repre-

21While 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 conscious-

ness (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 in-

terpretive 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 per-

ceptual 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 high-

level 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 pro-

posed. 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 phonol-

ogy, 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

22Cognitive 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 cor-

responding semantic representations is a matter of decomposing the sentence

into its semantic constituents. According to CS, the human cognitive sys-

tem—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 situa-

tion involving a Texan public official being contacted by a well-to-do caller:

(5α′)

23My handle on phonology is too tenuous to attempt an analysis. Asking someone else

to do it for me would be cheating. Sorry.

33

CALL(

[MILLIONAIRE

Thing

]),(

SENATOR(

ORIGIN([

TEXAS

Place

])

State

)Thing

)Event

The sentence is, as one might expect, fundamentally about an event, as in-

dicated by the category label in the main, outer square bracket. The event

type, the call, takes two parameters: the caller and the callee. Both indi-

viduals 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:

(5β′)

CALL

FROM([

TEXAS

Place

])

Path

([

MILLIONAIRE

Thing

]),(

[SENATOR

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 (5a′ and 5b′). 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 pro-

duced 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 ref-

erence 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 objec-

tions 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 modali-

ties 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, obli-

gations, and numbers) which manifestly lack perceptual features, the the-

ory makes only slightly different provisions: the data-structures that encode

them possess inferential rather than perceptual features. Interfaces to syntax

24For 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).25For 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 en-

tities. It is odd therefore that Jackendoff does not discuss such entities ex-

plicitly. 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 psycholo-

gism, 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 math-

ematical 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 stan-

dards. Those norms are no less real for their conventional nature (traf-

37

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 rec-

ognize 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, Jack-

endoff’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 pos-

sible) 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 in-

ferences 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 math-

ematical 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 ac-

tually 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 impres-

sions of the rest of his community. “Objective” fact and the appearance of

universality is established by communityconsensus. Unfortunately, this ac-

count 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 com-

munity. 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 mathemat-

ics. 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 sac-

rifices. 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 ap-

pealing 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 ar-

guments 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

26Let 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 analy-

ses—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 judge-

ments achieve objectivity, universality, fallibility as well as a host of other

interesting features not discussed here. Suppose for a second that that’s pos-

sible. 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 seman-

tic theory ultimately furnishing cognitive science with a proper account of

understanding for natural languages.

41

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