MARTIN DAVIES
MEANING,
STRUCTURE
AND
UNDERSTANDING*
0. Let us say that a language L is an ordered pair (50, ~ ) where 50 is a
set of sentences and Jd is a set of meaning specifications of the form
s means that p,
one for each sentence in 50. If such a meaning specification occurs in
2L then s means in L that p. Then L = L' just in case L and L' contain
precisely the same sentences with precisely the same meanings.
Further, let us say that a formal theory which has for each sentence
s in 50 at least one theorem of the form
s is T r ~ p ,
together with a canonical proof procedure which yields for each such
s precisely one such theorem (the canonical theorem for s), is
interpretational for L iff L = (50, ~ ) where ~ is the set of meaning
specifications which result by replacing 'is Tr ~ ' by 'means that' in
the canonical theorems. If a theory 0 is interpretational for L then
'Tr" can be read as 'true in L'. 1
1. Given a language L (= (50, ~ ) ) a semantic theorist may notice that
there is a systematic similarity of meaning specifications amongst
sentences which are syntactically similar. He will then set out to
reveal how the meanings of the sentences of L are systematically
related to the syntactic forms of those sentences. That is, he will set
out to construct a theory of meaning for L; a theory which assigns
semantic properties to syntactic constituents of sentences of 9° and
derives therefrom the meaning specifications in o4L The (or a) best
theory of meaning for L is the (or a) theory which reveals most fully
how the meanings of sentences depend upon the semantic properties
of recurrent syntactic constituents.
Exactly similarly, a semantic theorist may notice, within the set of
canonical theorems of a truth theory 0 which is interpretational for L,
a systematic similarity of truth condition specifications amongst senSynthese 48 (1981) 135-161, 0039-7857/81/0481-0135 $02.70.
Copyright © 1981 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.
136
MARTIN
DAVIES
tences which are syntactically similar. He will then set out to construct a truth theory which reveals most fully how the truth conditions of sentences depend upon the semantic properties of recurrent
syntactic constituents. The resultant theory might, but might not, be 0.
2. All this is not to insist that everyone who claims to be a meaning
theorist must be interested in the internal workings of theories of
meaning, or interpretational theories of truth, for particular languages.
Indeed, the expression 'theory of meaning' is notoriously ambiguous as
between (1): theory which yields meaning specifications for all sentences of some particular language, and (2): philosophical theory
about the notion of meaning. My semantic theorist is concerned, inter
alia, with theories of meaning in the first sense. But considerable
progress towards a theory of meaning in the second sense can be
made by asking under what conditions a language is an actual
language of a given population. 2
There are three brief points to be made here. First, answering this
question about the actual language relation cannot fail to contribute
towards a theory of meaning in the second sense since surely the
notions of meaning in a language and truth in a language must be
explicated in terms of what it would be to use that language. 3 Second,
whatever the details of the answer given, it is bound to speak of the
propositional attitudes of members of the population. According to
Lewis, for example, L is an actual language of G just in case there is
in G a convention of truthfulness and trust in L. 4 This involves in part
that members of G have, at least potentially, some knowledge about
each sentence s of L along the lines (supposing s to mean in L that p)
that ordinarily members of G utter s only if they believe that p, and
that ordinarily members of G who hear an utterance of s come to
believe that p. Third, if L is an actual language of G then members of
G are related in a certain way to the output of all theories of
meaning for L (that is, to the meaning specifications for sentences of
L) and to the output of all interpretational theories of truth for L.
But, as I am using the expression 'actual language', it does not follow
from the fact that L is an actual language of G that members of G are
related in any interesting way to what the semantic theorist regards as
the (or a) best theory of meaning for L, or to the (or a) best
interpretational theory of truth for L. This is particularly clear if the
set of sentences of L is finite.
MEANING,
STRUCTURE
AND UNDERSTANDING
137
To provide an illustration of this third point, let us consider a
language L0 with just ten proper names, ten one-place atomic predicates, and ten two-place atomic predicates. L0 has 1,100 sentences.
The semantic theorist will set himself the not very difficult task of
revealing how the truth conditions of these t,100 sentences depend
upon the denotation and satisfaction conditions of the 30 simple
syntactic constituents. But suppose that the speakers of this language
are taught the meanings of the 1,100 sentences one by one and are ted
to believe that these are just 1,I00 scattered sentences from a much
larger language. Imagine that they are so much in the grip of this false
belief that they are blind to the interrelations which so impress the
semantic theorist, and thus, for example, can be brought to revise
their opinion as to the meanings of any set of sentences of L0 without
revising their opinion as to the meaning of any sentence outside that
set. Then they are not interestingly related to the best interpretational
theory of truth for L0, even though they have L0 as an actual
language.
Someone might set himself the task of producing, for each population G of which L0 is an actual language, an interpretational truth
theory to whose internal workings the members of G do stand in
some interesting relation. If, in particular, he set himself the task of
producing a theory whose internal workings had a structure isomorphic to the structure of the competence of members of G then he
could, in the case described, offer the theory with 1,100 axioms
comprising its canonical output. Clearly this man's task is different
from that of the semantic theorist. Equally clearly, since there is no
reason why members of G might not have a competence with a
structure quite unrelated to what we perceive as the syntactic and
semantic features of sentences of Lo, this man's task may lead him to
construct truth theories of a hitherto unfamiliar kind. 5 The constraint
which guides this man (let us call it the mirror constraint) may lead
him to the best theoretical description of the competence of speakers,
but it will not, in general, lead to the best theory of meaning for the
language of those speakers.
3. What impresses the semantic theorist is not the structure in which
a certain kind of blindness issues, but rather the structure to which
those people are blind. The semantic theorist judges that there are
systematic interrelations between the syntactic composition of sen-
138
MARTIN
DAVIES
tences of a certain language L (for example, the language L0) and the
meanings of those sentences, such that explicit mastery of those
interrelations would (a) allow one to project to the meanings of
hitherto unmet sentences of L, and (b) oblige one to revise one's
opinions as to the meanings of certain sentences if one revised one's
opinions as to the meanings of certain others. In short, the semantic
theorist judges that the sentences of L are semantically structured.
Semantic structure is not structure which must be explicitly mastered if
one is to use the language (that is, if one is to have the language as an
actual language), and it is not structure which must be implicitly
mastered either. Rather, it is structure which could be explicitly
mastered.
Thus I suggest that the semantic theorist should seek to construct
interpretational truth theories which meet the following structural
constraint (SC). 6
If, but only if, there could be speakers of L who, having
been taught to use and know the meanings of sentences (of
L) s~. . . . . sn (and so, inter alia, to know the truth conditions of s~. . . . . sn), could by rational inductive means go
on to use and know the meaning of the sentence s (and so,
inter alia, to know the truth condition of s), then a theory
of truth for L should employ in the canonical derivations
of truth condition specifying biconditionals for sl . . . . . sn
resources already sufficient for the canonical derivation of
a biconditional for s.
The SC speaks of the possibility of reflective, explicit projection of
meanings by 'rational inductive means'. In this respect it differs, at
least superficially, from a constraint (call it S*) which speaks rather
of the possibility of unreflective projection of meanings by speakers
relevantly like us. For might it not have been (1)" that the possibilities
of unreflective projection outran the possibilities of explicit projection, or (2): that the possibilities of explicit projection outran the
possibilities of unreflective projection? One short response might be
that although both these things are theoretical possibilities they do not
in fact obtain; it is a contingent fact, but a fact nevertheless, that the
SC and (S*) deliver the same answers in all actual cases. But even if
this response is correct, the motivation for the SC may become
clearer if we briefly pursue the suggested possibilities.
Concerning (1) it may plausibly be said that once the notion of
MEANING,
STRUCTURE
AND UNDERSTANDING
139
unretlective projection is clarified sut~ciently to exclude mere causation of one belief by another (clarification which might be suggested
by §12 below), and once it is properly appreciated that unreflective
projection must enable one to proceed from knowledge to knowledge
and not merely to true belief, then we shall be able to argue that
unreflective projection cannot outrun the possibilities of explicit
projection. I do not know whether such an argument can be made out,
but it is surely reasonable to expect that a proponent of the constraint
(S*) will, if he takes himself to be doing semantics, accept that either
such an argument can be made out or else (S*) must be revised to
exclude possibility (1). 7 So let us suppose that by argument or by fiat
(S*) excludes possibility (1). Concerning (2) it should be noted that
we are not concerned with memory limitations which may prevent
unreflective projection to the meanings of very long sentences, but
rather with the imagined possibility that speakers are so constituted
that there is a certain construction which they cannot unreflectively
master although its significance can be worked out explicitly. My
position regarding this bare theoretical possibility is that we should
describe such a situation as one in which there is semantic structure
which speakers cannot unreflectively master, rather than as one
in which there is no semantic structure. Thus I prefer the SC
to (S*).
There are, however, two related concessions which should be made
to the proponent of (S*). One is that in such a case of possibility (2)
the semantic structure discerned in the construction by the semantic
theorist would have no r61e to play in the explanation of the use of
the construction by unreflective speakers of the language. Thus if
one's ultimate motivation for doing theoretical semantics is that it
contributes to our explanations of speakers' behaviour then one's
operation in accordance with the SC rests upon the fact noted above
that explicit and implicit projection do agree. The second concession
is that it might be argued that the possibility of unreflective projection
provides the conceptual location of the concept of semantic structure.
In that case the notion of semantic structure governed by the SC
would best be regarded as a theoretical or idealized extension of a
philosophically more basic notion.
4. The SC can be divided into two parts. The 'if' part says that if it is
possible to work out what s means given only tha~ s~ means that
p ~ , . . . , s , means that Pn, then a semantic theory for L should show
140
MARTIN
DAVIES
how the meaning of s is a product of the semantic properties of
constituents of sl . . . . . s,. If s l , . . . , s, are sentences of L and L is a
syntactically straightforward language then s will itself be a sentence
of L. A theory may infringe the 'if' part by failing to discern sufficient
structure in s l , . . •, s,.
The 'only if' part says that if a theory for L reveals the meaning of
s as a product of the semantic properties of constituents of si . . . . . s,,
then we must attribute a computational lack to those who know the
meanings of s~. . . . . s, but do not know the meaning of s. If L is a
syntactically straightforward language then we can reformulate the
'only if' part so that it requires of a theory that only if s is a sentence
of L should the theory be such that the resources used in deriving
theorems for s ~ , . . . , s, suffice for derivation of a theorem for s. But,
as we shall see in §7, the complications of syntax do not always allow
this reformulation. A theory may infringe the 'only if' part by discerning too much structure in si . . . . . s,, typically by "preprocessing"
those sentences into an unnecessarily complicated form.
I shall briefly rehearse three of the attractive features of the SC.
(A) The SC constrains theories of truth for familiar languages in the
way in which most semantic theorists wish them to be constrained.
(B) But while most semantic theorists employ a finite axiomatization
constraint the SC goes to the heart of the semantic theorist's project
in a way in which the finite axiomatization constraint does not. (C)
Nevertheless, if a language L is explicitly learnable then a theory of
truth for L meeting the SC will have only finitely many proper
axioms, s
The remainder of this paper falls into two parts. In the first part I
shall defend the SC against a range of objections. In the second part I
shall introduce a notion of full understanding such that speakers of L
who are full understanders of L do stand in an interesting relation to
a theory of meaning, or an interpretational truth theory, for L which
meets the SC.
5. The first objection is that the SC obliges a semantic theorist to
uncover semantic structure where there is none, for it confuses
semantics with etymology. Words like 'hydrophone' will best be
treated as semantically simple, for although in languages of which
MEANING,
STRUCTURE
AND UNDERSTANDING
141
ours is a descendant expressions corresponding to 'hydro' and 'phone'
were genuinely semantic primitives, such structure as there is in
'hydrophone' in English is "dead structure". The SC nevertheless
obliges us to uncover that structure since it is possible for speakers
who know the meanings of sentences containing for example,
'hydroelectricity', 'hydrography' and 'hydrokinefic', and sentences
containing 'mania' and 'phobia', to go on by rational inductive means
to know the meanings of sentences containing 'hydromania" and
'hydrophobia'.
To this objection I reply that the phrase 'rational inductive means"
is not to be understood so broadly as to include bringing to bear
general non-semantic knowledge. Certainly knowledge of the meanings of sentences containing words with the 'hydro-' prefix would
allow one to conclude that the word 'hydrophobia' applies to a phobia
having something to do with water. But to know that is not yet to
know the meaning of 'hydrophobia', for not just any phobia having
something to do with water is hydrophobia. (For example, a phobia
produced by harnessing the energy of falling water might not be
hydrophobia.) It is only by invoking general non-semantic knowledge
(including knowledge about etymology) that one reaches the conclusion that the word 'hydrophobia' applies to a phobia which is
related to water in a quite specific w a y , and in particular that it
applies to a phobia of water. And even general non-semantic knowledge may not allow one to reach the correct conclusion about the
meaning of 'hydrometer' or indeed of 'hydrophone'.
6. The second objection is that the SC seems to involve an unwanted
relativity to the psychological state of semantic theorists. The semantic theorist's task is different from that of the man who sets himself to
produce a theory whose internal workings have a structure which
mirrors the structure of the competence of members of some population. Confusion of these two tasks would involve importing into a
criterion for the best theory of meaning for a language an unwanted
relativity to the psychological states of members of certain populations. 9 But, the objection runs, although that confusion is avoided
by the SC, which theory is judged best according to the SC still
depends upon the semantic theorist's perception of syntactic and
semantic similarities amongst sentences.
One might reply that of course the theorist's judgement as to which
142
MARTIN
DAVIES
is the best theory depends upon his perception of similarities, and that
this is only because which theory is best in fact depends upon facts
about similarities. But the objector has more to say. For is it not
possible that someone might simply project from the meanings of
sentences containing 'pig', 'big', and 'cat' to the meaning of a sentence
containing 'fat'? Such a person might be amazed that we could not
see the functional dependence which was so obvious to him. Suppose
then that such a person set out to construct a theory of meaning for
English. How is one to judge between the theory which he thinks best
and the theory which we think best?
It is a substantive question whether we really do share a language
with this person. The question arises not merely because our competence has a different structure from his, but because of a doubt as
to whether he employs the same concepts of pigs, cats, bigness and
fatness that we do. That is, we may allow that our languages share the
same set of grammatical sentences having extensionally equivalent
truth conditions, but question whether the same truth theory could be
interpretational for both languages. And it is a substantive question
whether this person really has knowledge about the meanings of
sentences. But if an example can be made out for which these
questions do not arise then I think we must admit that here as
elsewhere justification of our judgements may come to an end. It is
possible, if not imaginable, that a rational being whose "form of life"
was different from ours might judge semantic structure differently
from us. But since the only point of view from which we can judge
semantic structure- or anything e l s e - is that internal to our form of
life, there is nothing to do but to make this admission and proceed.
7, The third objection begins from the rather irregular behaviour of
feminine suffixes. '° The SC obliges the semantic theorist to uncover
structure in the words 'actress' and 'conductress' (and in 'typiste' and
'artiste'). But while there are, doubtless, etymological explanations of
the meanings of 'actress' and 'typiste', are not these words best
treated as semantic primitives in English? Indeed, since 'artistress' is
not a word of English and neither is 'runneress', it seems that
uncovering structure in 'actress', for example, is incompatible with
the aim of providing a semantic theory for the language which people
actually speak and not just for a language which people might have
spoken but do not (and incompatible, too, with the spirit of the 'only
if' part of the SC itself; see §4).
MEANING,
STRUCTURE
AND UNDERSTANDING
143
This objection points to two features of natural language which we
may call surface syntactic (ss-) irregularity and ss-impoverishment.
Clearly '-ess' makes a systematic contribution to the words 'actress',
'conductress', and so on, a contribution recognition of which would
enable one to project to the meaning of "directress" given the
meaning of 'director'. The semantic theorist will wish to reveal this
functional dependence of meanings of wholes upon meanings of
parts, and the SC obliges him to do so. But, because of ss-irregularity
in English, the person who is projecting meanings will go wrong, for
he will predict that 'executress' means female executor. What he
needs in order to correct his prediction is a piece of purely syntactic
information that in this case one says not '-ess' but '-ix'. Ss-irregularity in a language makes the language difficult to learn explicitly
(and difficult to learn simpliciter) but it need not constitute a problem
for the semantic theorist. For the semantic theorist will in general
distinguish between sentences at the level of surface syntax and
sentences to which a systematic semantic theory can be directly
applied (sentences at the level of input to such a theory). At the level
of input he will uncover a single syntactic element 'FEM'; at the
surface the rtle of this suffix is filled variously by '-ess', '-ix', '-e' and
SO o n .
There is a general strategy here. If the SC obliges the semantic
theorist to uncover structure, and the resultant theory yields truth
condition specifications for unwanted sentences but only because of
ss-irregularity, then the semantic theorist will have done his job if he
provides a theory meeting the SC for a language without ss-irregularity which is nevertheless related to the original language by
syntactic rules which meet whatever constraints are reasonably imposed upon syntactic theory.
Imagine that we found a language in which (to describe the situation controversially) 'FEM' had as many different surface realizations
as there were items to which it could be applied. Imagine, in particular, that the surface realizations involved fairly radical alterations
of the stems to which the suffix was applied. Then the SC does not
oblige the semantic theorist to uncover structure. He could meet the
SC just by distinguishing pairs of semantic primitives. But alternatively he could provide a theory for a language with a single
feminine suffix, leaving it to syntactic theory to generate the totally
irregular surface forms. Which of the two approaches is to be
preferred depends upon the details of the syntactic theory required
144
MARTIN
DAVIES
and of course the methodological constraints under which construction of syntactic theories proceeds.
I turn to ss-impoverishment. A very simple example is this. We find
a population who use just a proper subset 5Po of the set of sentences
.900 of L0, although all 30 semantic primitives of L0 occur in 5e~. Let
d/o be the subset of d/0 corresponding to ~¢o and let Lo = (5¢~, d~).
Clearly the semantic theorist cannot construct a theory which both
meets the SC and delivers truth condition specifications for precisely
the sentences of Lff; any theory for Lo which meets the SC will
deliver truth condition specifications for all the sentences of L0. But
equally clearly the fact that there are such sets of sentences as 5e~does not constitute an objection either to the letter or to the spirit of
the SC. Intuitively, Lo is hardly a language; it is an artificially
impoverished fragment of a language. The semantic theorist has done
his job when he has provided a theory for L0. The syntactic theorist
must mark out the grammatical sentences of Lo.
Natural languages typically suffer from ss-impoverishment. H The
absence of any feminine form of 'runner' in English might be an
indication of such impoverishment. Another symptom is found in the
many eminently comprehensible but ungrammatical sentences of
English.
The plea of ss-impoverishment excuses the semantic theorist for
providing a truth theory which generates truth condition
specifications for sentences (at its level of input) which have no
surface realization in the language under consideration. But it is a
plea which must be entered with caution. Consider a modal language,
say the result of adding '[3' to L0. Call this language L~. Suppose that
a semantic theorist distinguishes between surface syntax in which one
finds, for example, 'E]Fa' and the level of input to a semantic theory,
at which one finds instead '(Vw)(World(w)~ F'(a, w))', and suppose
that the theorist provides a truth theory along familiar Tarskian lines
for this first-order language. Such a theory wilt yield truth condition
specifications for sentences such as 'World(a)', and '(Vw)F'(w, w)',
which have no surface realization in L~. Can the semantic theorist
excuse this feature by claiming that L~ suffers from ss-impoverishment? He cannot. The possibility of projecting to the meanings of
hitherto unmet sentences of L~ obliges the semantic theorist to reveal
how the meaning of ' [ ] F a ' is a product of the semantic properties of
'[~', 'F' and 'a'. If the only way to reveal this were to award the
MEANING,
STRUCTURE
AND UNDERSTANDING
145
surface sentence ' D F a ' the complicated possible worlds structure at
the level of input to a theory, then the claim of ss-impoverishment
might have some plausibility. But, as the construction of homophonic
truth theories for modal languages shows, 12 the semantic theorists
need uncover no more structure than is obviously present in the L~
sentence. In the case of L~ he can discharge his obligation as a
semantic theorist without delivering truth conditions for sentences
outside LI. He cannot do this for L8.
8. The fourth objection is really an objection schema. It is possible to
imagine circumstances in which two groups of people use two sets of
sentences 9, and 90+ where 9° is a proper subset of 9,+, and the
sentences of 9, are used by the members of both groups in exactly the
same kinds of circumstances. Thus there is nothing in their use of the
sentences of 9, to suggest that they mean different things by the same
sentences. But members of the 3°+ group are able to project from the
meanings of 9, sentences to the meanings of 9,+ sentences and have
the property that revision of their beliefs about the meanings of
certain 5e sentences is accompanied by revision of their beliefs about
the meanings of certain 9,+ sentences. Thus, since it is possible to
project from the meanings of 9' sentences to the meanings of 9,+
sentences, the semantic theorist is obliged to hold that the language
L = (9,,Jg) is merely an artificially impoverished fragment of L +=
(9,+,~+). But, the objection continues, this is not always the right
thing to say. And, since the SC both has this unfortunate consequence and is the only constraint which could keep the semantic
theorist apart from the man who sets out to mirror the structure of a
competence in the structure of a theory, it would be better for the
semantic theorist to give up theoretical semantics and retire to this
other, safer, project governed by the mirror constraint.
The schema of a reply is this. In the cases in which one wants to
deny that L is merely an artificially impoverished fragment of L + the
fact that members of the 9° group have no use for sentences in the
extension provides us with a reason for denying that members of the
two groups mean the same things by the same sentences, that is, for
denying t h a t / d C_Vd+. Given what members of the 9, group mean by
the shared sentences it is not possible to project to the meanings of
sentences in the extension.
The structure of the competence of members of a population is not
146
MARTIN
DAVIES
a structure which has to be mirrored in the structure of a semantic
theory come what may. For there are cases in which members of a
population really do use an artificially impoverished fragment of a
language; cases in which, for example, speakers of one language have
phrase book knowledge of the meanings of just a proper subset of the
sentences of a second language. But in general, and particularly in
cases where speakers use only one language, the structure of the
competence is a crucial source of evidence as to the conceptual
resources of the speakers. Consequently it helps us to judge what
they mean by their sentences. We should not credit speakers with
inexplicably restricted employment of sophisticated conceptual
resources if we can explain their behaviour (and, in particular, explain
the structure of their linguistic competence) in terms of fuller
employment of simpler conceptual resources.
To provide more than this reply schema we need to consider an
example. Suppose that 5e+ contains three classes of sentences: (1)
'Rabbit', 'Not Rabbit', 'Rabbit Moving', 'Not (Rabbit Moving)', 'Rabbit (Not Moving)'; (2) 'Bug', 'Not Bug', 'Bug Moving', 'Not (Bug
Moving)', 'Bug (Not Moving); (3) 'Rain', 'Not Rain'. Suppose that Se
contains the sentences from classes (1) and (3), but only the sentences
'Bug' and 'Not Bug' from class (2). Two groups of speakers use the
shared sentences in just the same situations. They assent to 'Rabbit' if
there is at least one rabbit present, and 'Not Rabbit' if there is not.
They assent to 'Rabbit Moving' if there is a rabbit present which is
moving, and 'Rabbit (Not Moving)' if there is a rabbit present which
is not moving. They assent to 'Rain' if it is raining, and 'Not Rain' if it
is not. They assent to 'Bug' if there is at least one bug present, and
'Not Bug' if there is not. The objection to the S C in this case is that
we may not wish to say that the ~e group are speaking a mere
fragment of the language of the 5e+ group, even though members of
the ~e+ group can project from the meanings of 'Bug' and 'Rabbit (Not
Moving)' to the meaning of 'Bug (Not Moving)', whereas the last
sentence is entirely lost upon members of the 5e group. 13
The reply is that in the case described, the members of the two
groups mean different things by 'Bug'. The 5e+ group mean that there
is a bug here, just as by 'Rabbit' they mean that there is a rabbit here.
They have and employ the concepts of a bug and of a rabbit. They do
not, and neither do members of the ~e group, have or employ the
concept of a raindrop. Members of the 5e group either do not have, or
MEANING, STRUCTURE AND UNDERSTANDING
147
else have but do not employ here, the concept of a bug; they do not
mean by 'Bug' that there is a bug here. If they did mean that then it
would have to be an intellectual lack which prevented them from
working out the meaning of 'Bug (Not Moving)'. But the hypothesis
that they use 'Bug' simply as a feature placing expression, on a par
with 'Rain', affords us an alternative explanation (and, in this case, a
better explanation) of that inability, and allows us to say that the 3°
group speak (the whole of) a language although not strictly a sublanguage of the language L + of the 5e+ group. 14 Over a period of time
members of the 5e group may simultaneously enrich their conceptual
resources, revise what they mean by 'Bug', and come to use 'Bug
(Not Moving)'. They may become speakers of L +. But doing that is not
for them to extend their language.
The reply schema also gives us something to say about a difficulty
which arises with mass terms. 15 It would be unsatisfactory to
represent the surface expression 'gold' by two semantically primitive
predicates at the level of input to a semantic theory: 'GI' true of
things which are made of gold (such as rings), and 'Gz" true of
quantities or parcels of the stuff. For it would then be utterly
mysterious how someone who had mastered both uses of 'gold' and
one use of 'iron' could work out the meanings of sentences containing
'iron' in its other use. So it might be suggested that one of the
predicates 'G~' and 'G2' is really a semantic constituent of the other,
or that they share a semantic constituent. We might retain the
predicate 'G2' of quantities and replace 'GI' by '~(G2)' such that
x satisfies '~(G2)' if[ X is constituted of a quantity which
satisfies 'G2'.
The difficulty then arises that many speakers can deal with 'This ring
is gold' and yet cannot make anything of 'This is a quantity of gold' or
of 'This constitutes that'. We do not want to attribute a mere
computational lack to these speakers, yet they use 'This ring is gold'
in just the circumstances in which it would be appropriate to say 'This
ring is ~(G2)'.
Here again the solution to the difficulty is to deny that the speakers
who can only use 'This ring is gold' mean by it that this ring is ~(G2).
They lack, or at least do not employ, the concept expressed by 'G2'.
Their 'gold' is not '3~(G2)'. Later their language may change. Still later
they may have the conceptual resources to employ a predicate
148
MARTIN
DAVIES
'~(G*)' instead of 'G2', where 'G*' is a name of a particular kind of
matter or stuff, chemically specified.
The availability of these replies should not, of course, be allowed to
obscure the theoretical possibility of explicably restricted employment of sophisticated conceptual resources.
9. Thus, in sum, I would claim that the SC is the correct guiding
principle for the semantic theorist provided that he recognizes
(1) that there is a difference between projecting meanings and
bringing to bear general non-semantic knowledge;
(2) that the only point of view from which he can judge is his own;
(3) that the features of ss-irregularity and impoverishment may
complicate the picture by requiring the introduction of syntactic
rules; and
(4) that he must be prepared to view linguistic performance holistically in order to determine what speakers mean by their sentences.
II
10. The semantic theorist can follow his guiding principle without any
involvement with the question whether speakers whose actual language is L know explicitly or implicitly all that is stated by the (or a)
best theory of meaning, or of truth conditions, for L. Indeed, it is
clear from the fact that speakers whose actual language is L0, for
example, may be totally blind to the interrelations which impress the
semantic theorist that any claim of explicit or implicit knowledge of
the (or a) best theory of meaning or of truth conditions is mistaken
unless the speakers' implicit knowledge of a theory comes to no more
than this: that the speakers know propositions which are expressed
by the (canonical) theorems of the theory. And surely it can be agreed
on all sides that if this is what implicit knowledge comes to then the
notion of such knowledge is utterly uninteresting and, in fact, fantastically misleading. For if that is what implicit knowledge comes to
then we can with equal justification attribute implicit knowledge of
any or all of an infinite collection of theories. If this is psychological
realism then psychological realism is indeed disreputable.
11. But speakers whose actual language is Lo, for example, need not
be totally insensitive to the interrelations which impress the semantic
MEANING,
STRUCTURE
AND UNDERSTANDING
149
theorist. L e t us say that speakers who are so blind are not full
understanders of L0. In general a speaker A is a full understander of a
language L just in case A has L as an actual language and A is
sensitive (in ways to be specified) to the semantic structure of L (as
discerned b y the semantic theorist guided b y the SC).
Suppose that s is a sentence of a certain language L (for example,
the language L0) and that s' is a sentence of L which is built from the
semantic elements discerned in s by the semantic theorist. Then if A
has L as an actual language, A knows what s means and A knows
what s' means. But if A is a full understander of L then A meets the
further condition that, h o w e v e r those states of knowledge were
originally produced, they are now so causally related that if A were to
change his belief about the meaning of s' then he would revise his
belief about s in a corresponding way. If A is a full understander of L
then his semantic beliefs about sentences of L are differentially
interrelated.
The phrase 'in a corresponding way' can be spelled out as follows.
If A were to revise his belief about the meaning of s' in that respect
of the meaning which the semantic theorist discerns as a deductive
consequence of the presence in s' of the syntactic item ~r assigned the
semantic property II, and if what A believed about the meaning of s'
as a result of this revision were to be the deductive consequence of
the revision of 17I to II', then A would revise his belief about the
meaning of s (and the meanings of any other sentences containing (r)
in such a way as would be the deductive consequence of the assignment to o- of II' rather than II.
If A is a full understander of L then he is, inter alia, in a state in
which he has semantic beliefs about s and other sentences containing
or, and these semantic beliefs have a c o m m o n feature associated with
~r. L e t us call such a state a cr semantic state. Since A's semantic
beliefs about sentences containing or are in line with the meaning
specifications in ~t (where L = ( S e , ~ ) ) , A is in the particular ~r
semantic state which we may call the (cr, L) state. In fact, e v e r y o n e
who has L as an actual language is in the (o-, L ) state. But, as we have
just seen, A is also in a state in which his semantic beliefs about
sentences containing o- are differentially interrelated. H e is in the cr
differential state.
These two states are logically independent. This is particularly clear
in the case of a finite language such as L0. It is a theoretical possibility
150
MARTIN
DAVIES
that someone might have L0 as an actual language while believing
(falsely) that the sentences of L0 are just 1,100 scattered sentences
from a much larger language. (See §2.) If o- is an expression of L0
then such a person could be in the (or, L0) state without being in the cr
differential state. Similarly, it is a (bare) theoretical possibility that
someone might have phrase book knowledge of the meanings of just
some of the sentences containing 'Rabbit', 'Bug' and 'Rain' as used in
the 5¢÷ group. (See §8.) In particular, someone might have such
knowledge of the meanings (as used in the 5¢÷ group) of just those
sentences which are also used (but with different meanings) in the 5e
group. For a certain language L which is strictly a sub-language of the
language L ÷ of the 5e÷ group, such a speaker could be in the ('Bug', L)
state without being in the 'Bug' differential state. (Such a case of
phrase book knowledge constitutes an example of explicably restricted employment of sophisticated conceptual resources.) Conversely,
for any expression tr, being in the tr differential state is compatible
with being in any of a host of tr semantic states.
A Martian who was a full understander of L would be in these two
states although their realization in the Martian could be different from
their realization in A. Since as philosophers we are not in the business
of a priori physiology we need have nothing to say about the
physiological realization of A's, or a Martian's, or anyone else's,
semantic and differential states. 16 But we can use the notions of such
states in a philosophical elucidation of full understanding. What
suggests itself is that A is a full understander of L just in case for
each semantic primitive cr discerned by the (or a) best theory of
meaning, or of truth conditions, for L, A is in the (tr, L) state and the
tr differential state. It follows, of course, that a full understander of L
is in corresponding states with respect to semantically complex
expressions as well. 17
12. We have so far only a counterfactual characterization of the odifferential state: A is in the o- differential state just in case A is in
some or semantic state and if A were to change his belief about the
meaning of some sentence containing o- then A would change in
corresponding ways his beliefs about the meanings of other sentences
containing or. But this counterfactual condition's obtaining with respect to every semantic primitive cr is neither necessary nor sufficient
for full understanding of the language. It is not necessary because
MEANING,
STRUCTURE
AND UNDERSTANDING
151
intuitively a person might be a full understander even though if he
were to change any of his semantic beliefs then a kind of semantic
blindness would be triggered so that he would not make corresponding revisions elsewhere. And it is not sufficient because intuitively a
person might not be a full understander even though if he were to
change any of his semantic beliefs then a kind of semantic perception
would be triggered so that he would make corresponding revisions
elsewhere. Altering the definition by replacing 'if A were to' by 'A is
such that if he were to' or 'A is so causally organized that if he were
to' does not overcome these inadequacies.
We can move towards a more satisfactory definition if we say that
A is in the o- differential state just in case A is in some o" semantic
state and A is in a state E such that:
(i) E is causally operative in the production of A's semantic beliefs at
the time t;
(ii) for any sentences s and s' containing o-, A's being in £ at time t
and E's being causally operative at t and A's revising at t his
semantic belief about s together provide an explanation of A's
revising at t his semantic belief about s' in a corresponding way.
If, for example, A is a full understander of L0 and s ~ . . . , s. and s
are sentences of L0 such that s is built from semantic primitives
discerned (in accordance with the SC) in s~. . . . . s., then there are
causally operative states of A such that for any revision of A's
semantic belief about s there is a corresponding revision of A's
semantic beliefs about at least some of s~. . . . . s. such that A's being
in those causally operative states and A's thus revising his belief
about s together provide an explanation of A's thus revising his
beliefs about s~. . . . . s.. For any such sentences, if A is in such states
let us say that A's belief about the meaning of s is differentially
determined by his beliefs about the meanings of sl . . . . . s.. (In an
unsatisfactory counterfactual formulation: If A were to revise his
semantic belief about s then he would revise his semantic beliefs
about s~. . . . . s. in corresponding ways.)
Thus, as promised at the end of §4, there is an interesting relation
between full understanders of a language and the best theory of truth
conditions for that language according to the SC. There is, for
example, an isomorphism of structure between an interpretational
theory of truth for L0 meeting the SC and the psychological state of a
full understander of L0. A full understander's semantic belief about s
152
MARTIN
DAVIES
is differentially determined by his semantic beliefs about s~. . . . . s. if[
in the canonical derivations of truth condition specifications for
s~. . . . . s. resources are used which are already sufficient for the
canonical derivation of a truth condition specification for s. What
corresponds under this isomorphism to the assignment by the theory
of a particular semantic property to an expression o- (simple or complex)
is the full understander's particular ~ semantic state. What corresponds
to the canonical derivations for sentences containing e employing
c o m m o n resources (in the case of a semantic primitive to their
employing a c o m m o n axiom) is the full understander's being in the ~r
differential s t a t e ) s
13. So far we have concentrated on the finite language Lo, but it
should be clear in what respects the story needs to be complicated in
the case of full understanding of an infinite language. A full understander of an infinite language does not straightforwardly have a
semantic belief about each sentence of the language. About some
sentences he has a potential belief. For each sentence s, a full
understander is in a state adequate to yield, on confrontation with s, a
semantic belief about s, and the full understander's beliefs and
potential beliefs are differentially interrelated. Suppose that a full
understander has actual beliefs about s~ and s2 and a potential belief
about s3, where s~, s2 and s~ share a semantic element 0-. Suppose that
he revises his belief about sl in that respect of the meaning which is
associated in a semantic theory with 0-. Then intuitively this will not
only result in a corresponding revision in his belief about s2; it will
also result in a change in the belief about s3 which he would come to
have on confrontation with s3.
If A is a full understander of an infinite language L then, for each
semantic primitive cr of L, A's actual and potential semantic beliefs
about sentences of L containing cr have a c o m m o n feature associated
with cr and are in this respect in line with the meaning specifications
in A~ where L = (Se, Ad): A is in the (or, L) state. And A's actual and
potential semantic beliefs about sentences of L containing cr are
differentially interrelated: A is in the o- differential state. Although it is
not quite as obvious as in the case of the finite language Lo, these two
states are still logically independent. 19
I have argued that we can introduce a notion of full understanding
in such a way that there is an interesting relation between full
understanders of a language, whether the language be finite or infinite,
MEANING, STRUCTURE AND UNDERSTANDING
153
and the (or a) best theory of truth conditions for that language
according to the SC. Specification of this relatiori does not so far
involve talk of psychological mechanisms, or of implicit or tacit
knowledge. To these two matters I now turn.
14. The first question then is whether it is proper to suppose that
there are in a full understander;s head mechanisms corresponding one
by one with the proper axioms of the (or a) best theory of meaning, or
of truth conditions, for the understood language.
Given what we know about the possibility of explicit projection of
meanings on the basis of explicit recognition of syntactic similarities,
it seems that one explanation of the very complicated network of
semantic beliefs (actual and potential) which we find in a full understander of an infinite language is that a full understander contains, at
least partly as a product of his linguistic training, mechanisms of two
kinds. First, there would be mechanisms which discern the syntactic
structure of perceived sentences and isolate semantic primitives,
including modes of containment. Then there would be, for each
semantic primitive or, a mechanism which contributes in a characteristic way to the production of semantic beliefs. These mechanisms
would need to be sensitive to feedback produced by revision of
semantic beliefs.
If, as seems plausible, a psycholinguistic theory along these very
general lines affords the best explanation of the observed facts about
a full understander then scientific realism permits us to attribute such
mechanisms to the heads of full understanders. A slightly different
but obviously related kind of explanation will plausibly be appropriate
for full understanders of finite languages.
15. The second question, whether we should attribute implicit beliefs
or knowledge about semantic primitives to ordinary, unreflective,
untheoreticat full understanders, is more difficult. The importance of
this question has been reduced by our already allowing realistic talk
of mechanisms. It is doubtful whether there is anything left for a
linguist to argue about. But still there may be some philosophical
interest in asking whether facts about differentially interrelated
semantic beliefs about sentences warrant the attribution to full
understanders of (implicit) semantic beliefs about semantic primitives.
154
MARTIN
DAVIES
One argument against the attribution of such beliefs points to the
difficulty of finding a satisfactory propositional content for the beliefs
about, for example, the natural language equivalent of the existential
quantifier. Nobody would wish to attribute to a ten year old child a
belief, explicit or implicit, about infinite sequences differing from
other infinite sequences in at most the ith place. But this difficulty is a
product of our choice of formal language for use at the level of input
to a theory of truth conditions. There are alternative formal languages
for which no corresponding difficulty arises, z°
Should we attribute to understanders the belief that the word
composed of the sixth letter of the English alphabet followed by the
ninth letter followed by the fourth letter followed by the fifteenth
letter denotes Fido? Perhaps; if there is empirical evidence that it is
on the basis of the positions of letters in the English alphabet that full
understanders recognize occurrences of 'Fido'. It is more likely that,
in the case of written language, this recognition is based on perceived
shape. So we might attribute to full understanders of a language
containing 'Fido' a belief whose content involves the concept of
looking like this, or looking F where ' F ' is a shape predicate which
one learns ostensively.
So there looks to be no good argument from the complexity of the
semantic properties assigned to semantic primitives, nor from the
complexity of the syntactic descriptions of semantic primitives, to the
conclusion that we cannot reasonably attribute (implicit) beliefs about
semantic primitives.
16. Another argument against the attribution of such beliefs might
seem to be contained in Nagel's 'The boundaries of inner space'. 21
Nagel considers the fact that a certain movement of the thumb is the
product of activation in 300 motor units which can individually be
brought under intentional control. He offers two reasons against
saying that we know implicity that to move our thumbs we have to
activate the 300 motor units at once, or saying that we move our
thumbs by (unconsciously) activating the 300 motor units. One reason
is that 'if I [attempt to activate them all at once] nothing may happen,
or I may produce a dreadful cramp in my thumb', and the other is that
it is 'pointless to apply [the term "knowledge"] to the integrative
capacity that permits the production of a complicated sequence of
movements, each of which could be produced separately but which
MEANING,
STRUCTURE
AND UNDERSTANDING
155
are in fact produced in a different way when they occur as part of the
sequence'.
It is difficult to see how the second reason could have any application in the semantic case if science reveals that our semantic
beliefs are the product of mechanisms which discern syntactic structure and mechanisms associated with semantic primitives, any more
than it could have application in the case of perception if science
reveals that our phenomenal states are the product of devices which
analyze stimuli into line, angle, motion, and so on. 22
The first reason looks more promising because in the semantic case
the more one concentrates upon discerning the syntactic structure of
a sentence the more difficult it is to understand it. (Normally we just
see what it means.) Similarly, the more one concentrates upon discerning line, angle, motion and so on the more difficult it is to tell
what shape one is looking at. (Normally we just see what shape it is.)
But there is a reply available to the attributer of beliefs about
semantic primitives, namely that in many cases of action which we do
want to view as the product of beliefs, habituation can result in
bungling if one tries to be selfconscious about acting. So we still have
no good reason not to attribute such beliefs.
17. Yet another argument is offered by Mark Platts. 23 He suggests
that the motivation for attributing implicit beliefs must be that such
attribution is thought to be explanatory of the beliefs which understanders unquestionably have about whole sentences, or at least
about utterances of whole sentences. And he points out that our only
route onto the supposedly e x p l a i n i n g facts is via the facts to be
explained. This would be an explanation of a 'somewhat dubious
kind'.
But it would be a mistake to think that the only reason to attribute
semantic beliefs could be in order to provide a scientific explanation.
The man interested in explanations of that k i n d - the linguist- will, I
suspect, be happy to talk about mechanisms. He might go on to speak
of these mechanisms as realizing cognitive structures and, believing
that what philosophers single out as conscious beliefs probably form
an 'uninteresting subpart of the full cognitive structure', he may see
no reason not to speak of implicit belief. 24 We could disagree with this
man at most over whether his use of the phrase 'implicit belief' is
misleading.
156
MARTIN DAVIES
A better reason to attribute semantic beliefs about semantic primitives would be that it forms part of an attribution of a total network
of propositional attitudes in terms of which we make sense of
behaviour, including linguistic behaviour. This making sense of
behaviour had better not be open to Platts' style of objection since
presumably he will agree that the only route onto the total network of
propositional attitudes is via the totality of behaviour which it enables
us to make sense of.
18. I want to suggest however that we do have a reason for not
attributing to understanders (implicit) semantic beliefs about semantic
primitives.Z5
First, consider the case of a device, such as a "smart bomb", which
produces suitably interconnected pieces of behaviour which we can
explain in terms of the device's internal mechanisms. We might be
tempted to attribute to the device a range of beliefs in terms of which
we would be able to make sense of the behaviour. But notoriously a
range of beliefs is not enough; we would need to attribute at least one
desire as well. And the attribution of a desire, for example the
attribution to a smart bomb of a desire to drop explosives on an area
looking thus and so, seems quite empty in this case. One indication of
this emptiness is that it is pointless to ask why the bomb desires that.
What is more, as a consequence of the emptiness of the desire
attribution, the attributed beliefs are correlated with pieces of
behaviour far more closely than in standard cases of propositional
attitude attribution; in standard cases it is very impressive that no
particular pattern of behaviour is guaranteed by the presence of any
particular belief. So in the case of a device like a smart bomb it is natural
to say that the explanation of its behaviour in terms of propositional
attitudes simply reiterates the prior explanation in terms of internal
mechanisms.
Then second, consider the case of a full understander A to whom
we are inclined to attribute (implicit) beliefs about semantic primitives; for example, the belief that tr has semantic property II. The
putative beliefs about semantic primitives do not interact at all with
other beliefs which we uncontroversially attribute to A. For example,
if we produce in A the explicit belief that tr has a different semantic
property II' then there is no felt incompatibility of beliefs in A . 26 What
is more, the pieces of A's behaviour to whose explanation the
MEANING,
STRUCTURE
AND UNDERSTANDING
157
attribution of (implicit) semantic beliefs could contribute are just A's
unreflective judgements about the meanings of sentences as uttered.
But then, although we can award to A the desire to believe concerning sentences as uttered the deductive consequences of his beliefs
about semantic primitives, the very close correlation between attributed beliefs and pieces of behaviour in the relevant class renders A's
case sufficiently analogous to that of a smart bomb to suggest that
here also we would simply be reiterating the prior explanation in
terms of mechanisms. If this is correct then, if we value the difference
between propositional attitude explanations and mechanistic
explanations, we should decline to attribute to A (implicit) semantic
beliefs about semantic primitives. 27
I argued, in §§ t2 and 13, that there is an interesting relation between
a full understander of a language and the (or a) best theory of
meaning, or of truth conditions for that language. It is not, as we have
just seen, in any important sense an epistemological relation. Rather,
it is a relation of isomorphism between two structures: the structure
of the full understander's network of differentially interrelated
semantic beliefs about sentences and the structure of the set of
canonical derivations in the (or a) best theory of truth conditions
according to the SC.
19. This sketch of an account of full understanding of a language
mediates, I now suggest, between two other accounts which are
often opposed to each other. On one account, the low-profile account, understanding L is just being able to know the meanings of all
the sentences of L. On the other account, the high-profile account,
understanding L is knowing (implicitly) a theory of meaning for L.
The low-profile account may well be an account of having L as an
actual language but it is not a genuine alternative account of full
understanding, for it ignores some of the observable facts about
linguistic competence. It would be too easy to ridicule the claims of
implicit knowledge and psychological realism if one were to ignore
the facts upon which those claims are based.
The high-profile account may, or may not, go beyond my preferred
account, according as 'implicit knowledge' or 'implicit belief' is intended in an epistemologically interesting or an epistemologically
uninteresting sense. If it is meant uninterestingly, then the high-profile
account need not go beyond the preferred account together with an
158
MARTIN DAVIES
acceptable dose of psychological realism. If it is meant interestingly
then, I have just suggested, it goes beyond the preferred account in a
way which is unjustified given our grasp upon the notion of propositional attitude explanation.
POSTSCRIPT
20. The issues of this paper parallel issues concerning syntactic
theory. In particular, the opposition between the low-profile and
high-profile accounts of understanding parallels the opposition between the low-profile account of syntactic competence, upon which it
consists only in knowledge for each string whether or not it is a
grammatical sentence, and the high-profile account, upon which it
consists in (implicit) knowledge of all that is stated by a syntactic
theory.
We can mediate between these two accounts. We can agree with
the low-profile account that the high-profile account's use of the
epistemological terms 'knowledge' and 'belief' is inappropriate, and
that if one pays attention only to the fact that a man knows which
strings are grammatical then one has no reason to attribute to that
man cognitive states or mechanisms corresponding to the rules of a
particular syntactic theory. And we can agree with the high-profile
account that the low-profile account ignores some of the available
data, and that if one pays attention to the data concerning differential
interrelations amongst beliefs as to the grammaticality of sentences
then one does have reason to attribute to speakers cognitive states or
mechanisms corresponding to the rules of a syntactic theory; which
theory depends upon the details of the data.
If one combines the two low-profile accounts then linguistic competence consists merely in the ability to recognize grammatical sentences and to know what they mean. If one combines the two
high-profile accounts (as linguists typically do) then linguistic competence consists in the ability to interpret sentences as uttered by
bringing to bear one's (implicit) knowledge of what is stated by the
relevant clauses of a syntactic and a semantic theory.
A proponent of the low-profile accounts will urge that the linguist's
claim that speakers recognize a certain sentence as being the result of
a certain transformation, for example, can amount to nothing more
than the claim that speakers recognize the sentence as grammatical
MEANING,
STRUCTURE
AND UNDERSTANDING
159
and know what it means, and he will urge that the linguist's way of
putting this claim is grotesquely misleading. 2s But however unfortunate the linguist's use of epistemological vocabulary may be, the
low-profile accounts do not constitute an adequate alternative. For
those accounts fail to explain observable facts about the ways in
which a speaker's judgements about the grammaticality and meaning
of one sentence will change if he comes to change his beliefs about
certain other superficially quite dissimilar sentences.
Magdalen College, Oxford
NOTES
* An early version of this paper was written while 1 was visiting Monash University in
the first half of 1979. I am grateful to Jan Crosthwaite, Lloyd Humberstone, Denis
Robinson and Barry Taylor for valuable discussions. Subsequent revisions were made
as a result of comments by Simon Blackburn, John McDoweU, Christopher Peacocke
and Mark Sainsbury.
t See McDowell, 'Truth Conditions, Bivalence and Verificationism ~, fn Evans and
McDowell (eds.), Truth and Meaning (Oxford, 1976), esp. §1. This definition of an
interpretational truth theory is, of course, closely related to Tarski's Convention T.
2 It should be noted that my use of the expression 'actual language' in this paper is not
entirely in line with that of Peacocke, 'Truth Definitions and Actual Languages', in
Evans and McDowell (eds.) op. cit.
See Strawson, 'Meaning and Truth', in Logieo-Linguistie Papers (London: Methuen,
1971).
4 Lewis, 'Languages and Language', in Gunderson (ed.), Language, Mind and Knowledge: Minnesota Studies in the Philosophy of Science, Volume 7.
Here I am indebted to Jan Crosthwaite.
6 This constraint differs from that of my 'Meaning and Structure', Philosophia (forthcoming), only in that the word 'understand' has been replaced by 'know the meaning of'
for reasons which are made clear by the second part of the present paper. A similar
constraint can be imposed upon theories of meaning.
v See Sainsbury, 'Understanding and Theories of Meaning', Proceedings of the Aristotelian Society 80 (1979-80), §2.
8 For these three points, see 'Meaning and Structure'.
9 See Peacocke, 'Necessity and Truth Theories', Journal of Philosophical Logic 7
(1978), §IV.
Jo Remarks by John McDowell and Gareth Evans suggested this objection.
~ Cases of ss-irregularity can be redescribed as cases of (perhaps very radical)
ss-impoverishment. Sometimes it is unclear which description is more natural; consider
'fox' and 'vixen'.
12 As, for example, in Peacocke, 'Necessity and Truth Theories' and my 'Weak
Necessity and Truth Theories', Journal o[ Philosophical Logic 7 (1978).
160
MARTIN
DAVIES
~3 The objection schema was put to me by Barry Taylor. The example of predicational
and feature-placing languages is suggested by Evans, 'Identity and Predication', Journal
of Philosophy 72 (1975). A. C. Jackson pointed out that it would be realistic to allow
that both groups of speakers use 'Bug Moving', 'Not (Bug Moving)' and indeed 'Rain
Moving', 'Not (Rain Moving)'. This would highlight the fact that the 5~ group have no
use for the internally negated 'Bug (Not Moving)' except on a reading upon which it is
equivalent to 'Bug & Not (Bug Moving)',
~4 Given that we should not hasten to attribute intellectual lacks to speakers, this yields
a general methodological principle. See Evans, op. cit.
15 Here I am indebted to Denis Robinson.
16 Cf. Dummett, 'What is a Theory of Meaning? (II)', in Evans and McDowell (eds.),
op. cit., p. 70.
~7 We can also introduce the notion of full understanding of an individual sentence. It
is not sufficient for A to be a full understander of a sentence s that A should know the
meanings of s and of all the sentences which can be constructed using the semantic
elements which the semantic theorist discerns in s. It is also required that those pieces of
knowledge should be differentially interrelated. Consequently, A is a full understander of
L just in case A is a full understander of every sentence of L.
C[. Peacocke's example ('Truth Definitions and Actual Languages', p. 170) of one who
knows what Brezhnev says in the first sentence of his speech yet does not understand
Brezhnev's utterance of that sentence.
~8 Throughout this section I am indebted to Christopher Peacocke. He has suggested
that the a differential state can be defined using the notion of differential explanation as
employed in his Holistic Explanation: Action, Space, Interpretation (Oxford, 1979),
The cr differential state would be a state E such that, for every sentence s containing ~,
A's being in E differentially explains A's belief about the meaning of s in that respect
of the meaning which the semantic theorist discerns as a deductive consequence of the
presence in s of cr. Thus, for example, a speaker's being in the 'is mortal' differential
state would inter alia differentially explain the speaker's believing 'Socrates is mortal'
to mean that Socrates is mortal. A's semantic beliefs about sl . . . . . s, would be said to
differentially determine his semantic belief about s just in case the states which
differentially explain A's semantic beliefs about sl . . . . . s, differentially explain his
semantic belief about s. The isomorphism of structure could then be specified as in the
text.
19 One way for A to be in the (~r, L) state but not in the cr differential state, where
occurs in infinitely many sentences of L, is for there to be finitely many sentences
containing cr to whose semantic structure A is insensitive. Whether the requirement
that A should have knowledge, and not merely true beliefs, about the meanings of
sentences can be used to rule out other ways is unclear.
2o For example, the language of Grandy's anadic logic; see 'Anadic Logic and English',
Synthese 32 (1976) and Advanced Logic for Applications (Reidel, 1977).
21 Journal of Philosophy 66 (1969). Cf. Platts, Ways of Meaning (Routledge & Kegan
Paul, 1979), at p. 232.
z2 Cf. Chomsky and Katz, 'What the Linguist is Talking About', Journal of Philosophy
71 (1974), at p. 359.
23 Platts, op. cit., at p. 234.
MEANING,
STRUCTURE
AND UNDERSTANDING
161
24 Chomsky, Reflections on Language (Fontana]Collins, 1975), p. 163.
25 In this section I am indebted to Denis Robinson.
26 This is analogous to the point made at p. 489 of Stich, 'What Every Speaker Knows',
Philosophical Review 80 (1971).
27 And if we value this difference then we must disagree with Chomsky's view cited in
footnote 24, and hold that his use of the expression 'implicit belief' is indeed
misleading.
28 See, for example, Cooper, 'The Deletion Argument' in Midwest Studies in Philosophy, Volume H: Studies in the Philosophy of Language (University of Minnesota,
1977).