Manifestation and Compositionality
José Tomás Alvarado
Instituto de Filosofía, Pontificia Universidad Católica de Valparaíso
Av. El Bosque 1290, Viña del Mar, Chile
jose.alvarado.m@ucv.cl
The manifestation challenge against realism raises the question of how the realist can explain the
understanding of the truth-conditions of evidence-transcendent propositions, to which he seems to be
committed. Here it is contended that the manifestation requirement should be construed in tandem with the
principle of compositionality of meaning. When both the manifestation and the compositionality principles
are taken into account then much of the force of the argument against realist conceptions of meaning is lost.
The particular cases of propositions about the past, other minds, inaccessible regions of space-time and about
unsurveyable domains are considered. Finally, a line of argument on the part of the anti-realist is considered
and addressed to the effect that a distinction should be made in every case between the sub-sentential
components whose contribution is under the reach of our epistemic capabilities and the sub-sentential
components whose putative contribution is evidence-transcendent. The anti-realist claim will be rejected.
This work is concerned with one aspect of Dummett’s famous manifestation challenge for
realism. A realist position can be understood here as the doctrine that the truth conditions of
propositions or sentences1 obtain (or fail to obtain) quite independently of our awareness of
that fact, or even, quite independently of our cognitive capacities for coming to know that
they obtain or fail to obtain. A realist semantics for a certain domain of discourse, in some
way, discloses the entities, objects, properties, events and states of affairs about which such
discourse talks. If those states of affairs are ontologically robust, i.e. if those states of
affairs obtain objectively and independently of human opinion –or so we believe- then the
semantics of the sentences talking about those states of affairs should reflect that fact.
Within a realist semantics the propositions of the domain in question determinately and
objectively obtain or not. It is well-known how Dummett sees here the ground for some
classical logic laws like the law of excluded middle or the semantic principle of bivalence,
at least when the domain of propositions considered is not effectively decidable. Consider
the case of a proposition with a determinate truth-value although that truth value is, in fact,
unknowable for us. It seems that a realist semantics where truth conditions are independent
of our cognitive capabilities has to admit the possibility of such unknowable proposition
with a determinate truth value. The manifestation challenge questions the intelligibility of
this admission and, then, questions the intelligibility of a realist semantics in general.
The general idea is the following2. The meaning of a proposition is something that
surely each competent speaker of the language in question should grasp. The understanding
of the meaning of a proposition (or a sentence, if you prefer) has to be manifested in the
verbal explanations of that meaning displayed by the speaker, if questioned about it, or in
the correct uses that the speaker makes of the proposition in different circumstances. Verbal
explanations clarify the meaning of a proposition making reference to other propositions
whose meaning is taken as already understood. It is obvious that these verbal explanations
should stop somewhere. So finally speakers should manifest their linguistic competence in
their linguistic uses. Now, a linguistic usage can only be deemed “correct” if there are
recognizable circumstances where the proposition in question is known to obtain –or
known not to. Suppose again the hypothesis of an unverifiable proposition. If that
proposition really has a meaning constituted by certain truth conditions entertained by the
speakers who, in fact, do grasp its meaning, then how can those speakers manifest the
1
understanding they putatively have of the truth conditions constituting its meaning? There
are no recognizable circumstances where the uses of the proposition could be correct or
incorrect, so there is no possibility that they could manifest their understanding of its
meaning. How then, can one say that the speaker really understands the meaning of such a
proposition?
There are many things to say about this train of thought, not the least of which is
whether meaning should always be considered as supervenient on linguistic uses or whether
a determinate meaning can be gathered as supervenient on linguistic uses or even
dispositions of “correct use” for a proposition. The well-known paradoxes proposed by
Kripke (interpreting Wittgenstein) seem to suggest that they cannot3. However all these
questions will be left aside here. This paper is concerned with a more specific issue
considering the manifestation challenge, as has been usually construed by philosophers
with anti-realist inclinations, in relation with the principle of compositionality. It is
generally agreed that the capacity of a speaker of understanding potentially infinite
sentences that can be formed with the terms of a language and with its syntactic formation
rules, can only be explained in terms of a finite repertoire of items known by the speaker. It
is unfeasible to hypothesise an infinite capacity on the part of speakers to grasp expressions
for they are simply finite human beings. It is supposed that speakers are capable of
understanding the meaning of potentially infinite different sentences framed within a
language because they are in command of a finite –or recursive- set of “axioms”
constituting the truth theory for the language in question. These axioms deliver the truth
conditions of each of the infinite possible sentences as theorems. The crucial point in
question in this work is whether the same idea by which understanding of infinite sentences
on the part of finite creatures –like us- could also be used to explain how we can understand
the truth conditions of propositions that appear to transcend the evidence we may gather to
support them.
To make sufficiently clear the central argument of this work, it will be required a
certain amount of prior conceptual clarification of the crucial concepts involved here of
manifestation and compositionality, and of the corresponding principles by which meaning
is supervenient upon use and by which the meaning of a proposition is constituted by the
systematic contributions of its semantic parts. However, it may be convenient to explain
before why the defenders of the manifestation argument and, specifically, the defenders of
anti-realism motivated by the manifestation argument are inclined to think that
considerations arising out of the principle of compositionality are of no avail to the realist
who wishes to address the challenge. Here is the explanation given by Neil Tennant of how
the anti-realist may answer a criticism which appeals to the compositionality of meaning:
We shall be able to identify at least one constituent responsible for the undecidability of S. Let us
suppose it is universal quantification over numbers. The universal quantification even of a decidable
numerical predicate can be pro tempora undecidable; the classical meaning of the universal quantifier
accordingly contributes a possibly recognition-transcendent ingredient to the meaning of any arithmetical
sentence in which it occurs. Now such recognitional capacities as can be exercised in evidence of semantic
understanding are, in the arithmetical case, always concerned with the status of texts as proofs. But, given the
well-known incompleteness phenomena (which, it is worth noting, can be established intuitionistically), the
semantic understanding whose manifestation is thus limited cannot support attributions to arithmetical
statements of such meanings as can be relied upon in general to render them determinate in truth value
[Tennant (1987) p. 112]4.
2
The realist might suggest here that a certain statement S has determinate truth value
although it transcends what we can recognise in the circumstances. Our understanding of
the meaning of statement S comes, like in any other case, from our knowledge of the terms
occurring in S and their mode of connection. The fact that S is undecidable should be a
result –somehow- of the contribution made by their terms and their mode of connection.
Tennant contends that the capacities of recognition involved with the understanding of the
terms connected in S do not guarantee that there is a determinate truth value for S. For
example, if S were an arithmetical statement, the incompleteness results would prevent the
idea that there must be a proof either of S or of ¬S. In other words, the ability to recognise
the obtaining of the object (or property) to which a sub-sentential component makes
reference is not sufficient to guarantee determinate bivalence for the propositions where
those sub-sentential components occur. As far as the realist wants to defend the bivalence
of the propositions in the domain in question –whatever this domain may be- then, the
considerations coming from compositionality are insufficient to address the challenge
posed by the manifestation argument.
But, are they? It is obvious that there is some misunderstanding here. The realist is
just trying to contend that an undecidable proposition can be understood as possessing
determinate truth value and that this understanding comes from the sub-sentential
components connected in the proposition in question and their manner of connection. The
realist is not contending that there should appear a way of determining the truth value in
question from the meaning of the sub-sentential components appearing therein and their
mode of combination, i.e. the realist is not contending that the sub-sentential components of
the sentence can deliver a decision procedure by which we can come to a verdict about
whether the sentence in question is true or false. Of course, understanding should be
connected to the knowledge of how to verify or refute the sentence in question if, petendo
principio, one were to suppose that understanding of meaning only happens as the antirealist says that it happens, but this is surely something that cannot be taken for granted in
an argument designed to argue in favour of semantic anti-realism.
Maybe, then, there are other reasons whereby the considerations coming from the
principle of compositionality can be neutralised, but it seems clear that this sort of
argument put forth by Tennant cannot neutralise them. It will be better, now, to proceed to
clarify the key concepts and principles involved here, and then, consider in detail some
crucial cases where the hypothesis of this work can be put into test, i.e. statements about the
past, statements about other minds, statements about inaccessible regions of space-time and
statements about unsurveyable domains (like the transfinite in mathematics).
1. The principle of manifestation
As has been said, there are here two crucial principles at work, both independently
plausible. Consider first the principle of manifestation. In rough form, what is stated by the
principle is that one can only attribute to a speaker understanding of the meaning of a
proposition p if that speaker displays in the relevant circumstances the required linguistic
behaviour by which he could be deemed to have correct dispositions to use p.
Understanding of meaning should be supervenient on uses. Let, then, the principle of
manifestation be:
(1)
∀p∀S ((p is understood by S) ↔ (S manifests dispositions of correct use of p))
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Here, in (1), “p” is ranging over sentences, and “S” is ranging over speakers. The idea is
that a condition both sufficient and necessary for S to have understanding of a sentence p is
that S has manifested dispositions of correct use of p. In other words, that in which
understanding of the proposition p consists is having the said correct dispositions of use.
Some comments are in order here.
First, why does the notion of “understanding” appear in (1)? It is a common
contention that the meaning of a certain sentence s is that which is known by a speaker
about what makes such sentence true or false. And that which is known about the truth
conditions of sentence s is the understanding that S has of the meaning of s. It is supposed
that the very least that is required for a speaker of a language to make successful speech
acts in that language is to grasp the meaning of the expressions of the language he is using.
In principle, it should be taken for granted that any speaker knows the meaning of the
expressions he is using for communicating. Although normally a speaker cannot give
precise and explicit formulations of that which he understands when he utters a sentence, it
is supposed that a sufficiently conscious reflection on the part of such speaker would make
that content explicit. The meaning of a sentence s is, then, what a speaker understands
could be the case if s were true in the relevant circumstances. Of course a speaker may not
know whether a certain sentence s is true or not, but when one attributes to him grasp of the
meaning of sentence s the very least that one is attributing to him is understanding of the
truth conditions of s5.
Second. Principle (1) can be further explained by the working of another more
special principle, to the effect that having dispositions of correct use of p is a matter of
displaying those dispositions in correct uses of p. A speaker, then, “manifests”
understanding of the meaning of a proposition by using correctly that proposition in
different contexts. Then:
(2)
∀p∀S ((S has dispositions of correct use of p) ↔ ∃s (s a correct use of p by S))
Although here principle (2) appears as saying that one correct use of p is required to
postulate a disposition of correct use by S, the formulation should be taken as a first step
towards a more precise qualification of what it takes for some speech act s to manifest the
dispositions of which it is, in some way, a result6. The point is that that postulation of
dispositions is just a matter of existing correct uses of p by S. The manifestation challenge
works swiftly under these premises if the hypothesis of a certain unverifiable proposition q
is considered. As the realist separates truth from verification (or idealised verification, or
super-assertibility, if it is preferred), he should grant that there might be unverifiable
propositions. But a proposition can be correctly used just if there are circumstances where it
recognisably obtains, i.e. where it is verifiable. Then:
(3)
∀p ((p can be correctly used) → (p is verifiable))
Now, suppose that q is unverifiable. It follows from the quantified conditional (3) that q
cannot be correctly used, so there is no correct speech act s by speaker S of proposition q.
By the principle stated in (2) this means that S does not have dispositions of correct use of
q. By the principle stated in (1), moreover, this means that speaker S does not understand
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proposition q. If meaning is constituted by truth conditions that are possibly evidencetranscendent, as the realist wants, and, further, if the meaning of a proposition is that which
is understood by the speaker about those truth conditions, we have got a contradiction.
The principle of manifestation, in brief, connects meaning to dispositions of use,
and, then, connects dispositions of use to correct linguistic uses. That is, meaning comes to
be supervenient on linguistic uses. As is usual with questions about supervenience, whether
meaning just is a set of dispositions for linguistic uses or, more cautiously, whether
meaning is simply somewhat dependent on dispositions of use should be left here as
indeterminate. The usual justification for the principle of manifestation comes from some
considerations concerning how can one attribute to a speaker understanding of the meaning
of an expression, and this sort of justification inclines one to think in terms of a less strong
connection between meaning and dispositions of linguistic use. In general, facts of type A
are said to be supervenient on facts of type B if and only if any two possible worlds wi and
wii that are alike in exactly the same B facts should also be alike in exactly the same A
facts. Contrapositively, if any two possible worlds wi and wii have at least one difference in
respect of the A facts obtaining there, then there should be at least one difference in respect
of the B facts obtaining in those worlds. As has been remarked by several philosophers, the
relation of supervenience under this characterisation need not be asymmetric7, but this fact
should not bother us too much. The formulation can be supplemented sufficiently to render
the desired kind of connection between facts A and facts B. Let, then facts A be
supervenient on facts B and facts B not supervenient on facts A (if you like, we can call
this new relation supervenience*). When the case under consideration is related to
attributions of meaning-understanding to a speaker and the linguistic uses displayed by that
same speaker, the relation of supervenience can be further refined by taking it to work not
just in the case of the distribution of facts over complete worlds, but relating it to the
distribution of facts over some specific parts of them, namely, the distribution of facts about
understanding of meaning by speakers. Then, the desired supervenience could admit of a
formulation along the following lines: let a M-fact be a fact about whether a speaker S
understands the meaning of an expression p of the language. On the other hand, let a U-fact
be a fact about speaker S’s uses of p. Then, any two speakers concerning whom the U-facts
are alike are such that the M-facts about them are also the same. Contrapositively, any two
speakers concerning whom the U-facts differ should be such that the M-facts relating them
also differ.
There are many issues that arise concerning the supervenience relation described.
For example, it follows from the formulation that any two speakers who have at least one
different use of an expression p should understand it differently (if they are both really
entitled to have “understanding” of p). This seems on the face of it too strong. Where can
one find two speakers who have exactly the same uses of a certain expression of their
common language? It seems to follow from this that there are no two speakers of a
language, or almost, with the same understanding of –almost- any expression of their
language8. Important as these questions might be, it is not necessary to answer here them.
One can simply suppose here, at least for the sake of argument, that a single set of linguistic
uses of an expression p allows one to postulate the existence of a disposition of correct use
of p and that –further- this single disposition allows one to postulate on the part of the
speaker to which such linguistic uses and such disposition of use have been attributed the
understanding of the meaning of expression p.
5
A third comment in relation to the principle of manifestation, as has been explained
above, has to do with how it can be related to a principle of individuation for propositions.
In general, a principle of individuation is a theoretical thesis by which the conditions of
identity of certain type of entities are introduced by an equivalence relation obtaining
between entities of other sort, i.e.
(4)
∀α∀β ((#α = #β) ↔ (α ≈ β))
Here in proposition (4) “α” and “β” are ranging over entities of some or other sort. The
function # maps the entities in the domain to which both α and β both belong to entities of
the desired domain that is introduced by the principle. On the other hand, the relation ≈ is
an equivalence relation obtaining between the entities of the domain which the principle of
individuation is taking as a base9. The general idea behind a principle of individuation
following this general form is that, if there are some type of entities to which we can make
legitimate reference in our theorising about the world, with sufficiently sharp conditions of
identity, then a principle like (4) authorises to make legitimate reference to entities of other
domain which works as counter-domain for the function #. Entities in this latter domain
have sufficiently sharp conditions of identity in so far as the entities of the base domain
have themselves sharp conditions of identity and the equivalence relation ≈ defined over
them is sufficiently precise. A stock example in contemporary philosophy of one such
principle is the so-called “Hume principle” for the introduction of numbers: the number of
Fs is identical to the number of the Gs if and only if the objects falling under F can be put
in a one-to-one and onto relation with the objects falling under G.
In the present case related to propositions, the base domain is constituted by
linguistic uses and the entities introduced are going to be propositions. Then:
(5)
∀p∀q ((p = q) ↔ ∀s ((s is a use of p) ↔ (s is a use of q)))
Here “p” and “q” are ranging over propositions, of course, and “s” is ranging over linguistic
uses. The rough idea behind an abstraction principle could be that any two propositions that
have the same correct linguistic uses are just one and the same proposition. Hence the sets
of correct uses are conditions of identity for propositions. There are many problems ahead
to make this principle really workable, but, again, it is not necessary to go into those
problems here. For the purposes of this work, one need only take into account the fact that
the principle of manifestation can induce a principle of individuation to introduce abstract
entities into our preferred ontology. If our ontology admits as legitimate entities “correct”
linguistic uses of an expression and, further, accepts certain relations of equivalence
between these linguistic uses, i.e. that of being correct uses of the “same” content, then
there should not be any qualm in relation to the introduction of propositions into our
ontology as precisely those entities whose conditions of identity come by the classes of
correct uses of them10.
2. The principle of compositionality
The other great principle involved in the argument of this work is the principle of
compositionality. The usual justifications of the principle focus on two basic facts: (a)
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human beings, speakers of known languages, have finite cognitive capacities. When it is
said that a human being “knows” a certain language L, that in which knowledge of L
consists should not be something that could demand an infinite amount of memory or an
infinite amount of cognitive processing on the part of speakers said to know it; (b) the
second fact concerns the infinity, or potential infinity of propositions that can be
meaningfully constructed in a language. A speaker knowing a language, having a finite
repertoire of words, can in principle construct and understand an infinite number of
sentences uttered in that language11. This fact requires explanation, and the most plausible
explanation for it rests on the structure of composition by which sentences in a language are
composed. A common speaker should be in command of a certain “theory” by which the
“basic pieces” of language are given and by which the mode of correct combination of
those basic pieces is grasped. If the basic elements and the formation rules of sentences out
of the elements are mastered by a speaker, then there seems to be a strong reason for
thinking that the language as a whole is mastered by that speaker. A speaker understands a
language L if he understands the finite items constituting the “theory” by which any
expression of L can be constructed.
There may be further discussion about what is the exact form of the theory of
meaning for a certain language, and also there may be further discussion about in what
sense can a speaker be said to “know” the theory of meaning for a language L12, when
normally a speaker cannot explicitly state such “theory” as a precise set of postulates for L.
According to received lore a theory of meaning for a language L has the same structure as a
theory of truth for that language along the lines designed by Tarski13. In traditional truth
theories the notion of meaning is taken for granted and used as a way of illuminating the
nature of “truth” for that language (if the tarskian procedure counts as –really“illuminating” what does truth consist in for that language). The idea of Davidson, in
contrast, is that exactly the same theoretical structure can be exploited to elucidate the
meaning of the expressions of a language L, taking this time the notion of truth for granted
and using it to illuminate the meaning of the expressions said to be true. Meanings are,
then, explained as truth-conditions that will obtain (or will fail to) in different
circumstances according to how the expression is constructed out of its linguistic elements.
A competent speaker of language L is said to understand the expressions of L
precisely because he is capable of delivering the meaning-theorems for each one of those
expressions, given his previous grasp of the axioms and rules of the theory of truth for L.
But, as should be obvious by now, the “understanding” of the meaning of, say, p, is that
which is subjected to the conditions postulated by the principle of manifestation. The
principle of manifestation states that speaker S has understanding of the truth-conditions of
proposition p in so far as he has dispositions of correct use of p, which can be postulated in
accordance with the overt linguistic behaviour displayed by speaker S in his linguistic uses
of p. At the same time, the principle of compositionality states that speaker S comes to
understand proposition p in accordance with how such proposition is constructed out of its
basic linguistic elements. In other words, speaker S comes to understand proposition p from
his previous understanding of the axioms and rules for the theory of truth for language L
where p is framed. Now, it appears that there are two different stories about how
understanding of meaning is “possible” or “explainable” and one could ask further whether
those two different stories can cohere and, if so, how.
Now, the point is that a theory of truth for a language L in some sense “represents”
that which a competent speaker of L knows when that speaker knows the meaning of the
7
expressions of language L. If the question is whether, for example, a speaker understands
the proposition Fa, the answer to that question comes from the usual axioms and rules of
the theory of truth for L. If a speaker S knows to what entity the name “a” refers and to
what property the predicate “F(ξ)” refers, and –further- if he knows that the proposition Fa
is true if and only if that object to which the name refers and that property to which the
predicate refers are such that the object falls under the property, then he understands the
meaning of Fa. There is no indication here of dispositions of use of that proposition, nor of
overt linguistic behaviour on the part of speaker S by which one could be justified in
postulating the disposition of use of the proposition Fa. The suggestion given by the picture
of the theory of truth for a language L is that a speaker S understands a proposition like Fa
if and only if S understands basically what the name “a” and the predicate “F(ξ)” refer to,
i.e. what entities are about which one is talking here.
How can the principle of manifestation enter into this picture? There are, prima
facie, two ways by which the operation of the principle of manifestation can be conceived
of in the broad context of a view of meaning, in which it comes from the axioms and rules
of derivation of a theory of truth for the language in question. One way is conceiving
simply that each of the propositions of the language should have associated dispositions of
use and, moreover, overt linguistic behaviour by which these dispositions can be
sufficiently hypothesised. Now, under this form of construction of the manifestation
principle, it follows that attribution of understanding of the meaning of the propositions of a
language to a speaker S is only possible if S has dispositions of correct use for each one of
those propositions, and only if S has shown in linguistic uses of all those propositions that
he really has dispositions of correct use of them. That is, he should have correctly used all
of them in a manner sufficient to postulate an underlying “disposition” of correctly using
them. Normally a single correct use would not be sufficient for postulating a disposition in
S, so S should have to display multiple uses of each one. It might be obvious that this
construction of the manifestation requirement could be completely at odds with the basic
tenets of the principle of compositionality. In fact, no being with finite capacities –
cognitive or otherwise- could possibly “manifest” understanding of the meaning of the
infinite propositions of a language. Language, then, could result in being unlearnable for
finite beings like us.
There is another construction of the manifestation requirement, nevertheless, much
more feasible and that, very probably, is more into line with what has been envisaged by
their proponents14. The rough idea is that a speaker can be said to understand the meaning
of the expressions of the language he uses just in case he displays the disposition of correct
use of the expressions of that language. What expressions? Not complete propositions, or
sentences, as should be now obvious. He should display correct uses of the elements of the
language that enter into the axioms of the theory of truth for the language considered, i.e.
the names and predicates, and then, the connectives and operators. It is not necessary for
the speaker to show dispositions of use specific for each of the propositions of the
language. One could perfectly well maintain that a speaker S understands a language if he
has dispositions of correct use for each of the names and the predicates. In other words, his
dispositions of correct use of propositions have to be deemed somewhat dependent on his
dispositions of correct use for elementary expressions. For example, one might ask whether
a speaker S understands the proposition “Fa”. The proposition “Fa” is constructed by the
saturation of the predicate “F(ξ)” by the name “a” and its truth condition is the fact –if there
8
is one- of the object denoted by “a” falling under the property denoted by “F(ξ)”. How can
S “manifest” his understanding of Fa? Well, there is always the alternative that he might
have used the same proposition Fa on other occasions where his speech act of stating that
Fa has been found correct by all standards, epistemic and pragmatic. But, there is also the
possibility that he has not used Fa before. This is the normal situation with most speakers,
when one comes to ask whether he understands or not some expression. In this second case,
one may simply inquire if he has used the name “a” correctly before and if he has used the
predicate “F(ξ)”correctly before. If the answer is positive for both of these questions, then
one will have reason to suppose sufficiently justified that speaker S has dispositions of
correct use of “a” and “F(ξ)”, and, consequently, that he understands the meaning of “a”,
“F(ξ)” and that he understands the meaning of the proposition “Fa”.
The point can now be seen in the following way. There are two restrictions on how
a speaker can understand the meaning of a potentially infinite number of propositions of a
language. First, the capacity required on the part of the speaker must not be infinite, or –
otherwise- simply too large for rational beings like us. Second, one can only attribute
understanding of the meaning of an expression to a speaker if he can be supposed to be
endowed with dispositions of correct use of those expressions. By the principle of
compositionality a speaker understands a language if he understands its parts and their
mode of combination to form more complex expressions. In what does the understanding of
such speaker of the parts and modes of combination of them consist? The manifestation
requirement proposes that the understanding consists in the possession of dispositions of
correct use. So, there are no dispositions of use for complete propositions, at least, no
immediate dispositions, but dispositions that could be characterised somewhat as
“derivative” from the basic ones related directly to the elements occurring in the axioms of
the theory of truth and in the modes of combination incorporated in the clauses for the
logical connectives, other operators (modals, tenses, etc.) and the rules of formation of
meaningful expressions from meaningful expressions15.
This train of thought, by which the manifestation requirement is connected tightly
with the deliverances of a theory of meaning for a language, broadly construed as a theory
of truth for that language, has obvious consequences –or so it seems- for the manifestation
challenge. Consider again the situation. The anti-realist is challenging the realist to explain
how it is that a speaker could have understanding of the truth conditions of propositions
that are evidence-transcendent. An unverifiable proposition is a proposition that cannot be
correctly used, for there are no recognisable circumstances where speakers of a language
could assess whether the statement is true or false. But, now it appears that this question is
wrong from the beginning. The problem is not –in any case- the problem of how to explain
understanding of evidence-transcendent propositions or sentences. As in any other case, the
understanding of such proposition can be explained by the understanding of its semantic
elements and their mode of combination. If there are dispositions of correct use for the
semantic elements that are integrating the offending unverifiable proposition, and if –
further- the speaker displays also dispositions by which he shows how to master the form of
connection of those semantic elements to form a more complex meaningful expression,
then there should not be any further question of whether the speaker really understands its
meaning.
The challenge, if there is one, has to be posed in relation to specific semantic
components of the propositions of a language that have themselves such a nature, that no
9
speaker could possibly display overt linguistic behaviour by which he could be deemed to
possess dispositions of correct linguistic usage of them. That is, once again, semantic
components out of which propositions are constructed, not complete propositions as such. It
is perfectly possible, on the other hand, that unverifiable propositions result from a
construction out of some semantic components that are themselves perfectly legitimate and
well understood by speakers grasping them. This has to be taken as simply a matter of the
result of licit semantic combinations that deliver from some legitimate semantic
components, some other semantic complexes.
Of course, this train of thought could be of no avail against someone that is not
inclined to think that the meaning of a proposition –or sentence- is a function of only the
semantic components that appear in that proposition or sentence and the mode of their
combination there. If there is an irreducible contribution coming from the context where an
expression is used, not amenable to general treatment or theorising, then the existence of
dispositions of correct use connected to the clauses of a theory of meaning for a language
constructed in the vein of a Tarskian theory of truth for that language, will not be sufficient
to deliver the required dispositions of correct use for the complete propositions or sentences
that are considered. Some other dispositions of use will be irreducibly connected to
complete propositions, if speakers can be credited with understanding of those propositions
at all. In the case of indexical expressions we are used to the taming of those contextual
elements. Indexical expressions are usually understood as expressions where there is a
systematic reference to a variable contextual element. But here, although the context is
variable, the aspect of that context that should be taken into account is always the same and
is connected, as a matter of general semantic discipline, to the “character” of the
expression. This phenomenon, then, is no real threat to the principle of compositionality. A
speaker might be said to develop a certain disposition of correct usage connected to the
peculiar character of a certain expression, although this character may deliver multiple
propositional contents when used in different contexts. The real problem comes when it is
sustained that no amount of general semantic theory can handle all possible different
meanings that the same expressions can have when used in different contexts16. If the
deliverances of the compositional clauses of a theory of truth for a language are simply not
sufficient to render the meaning of any expression that can be formulated in that language,
then it is useless to think in dispositions of correct use connected to those compositional
clauses. Understanding of the meaning of an expression will require some other
dispositions somewhat connected to complete propositions and to classes –probably
vaguely defined- of contexts of utterance sufficiently similar between them. The solution
proposed here will not work if someone prefers this style of semantic theory17.
Naturally, here is not the place to discuss –not even roughly- the merits of this
different approach to semantic theory. This work is simply conducted under the supposition
that a semantic conception where the principle of compositionality is not sufficient to
deliver a complete understanding of the meaning for a language is false, because it will
make the language unlearnable for finite beings like us. It will be convenient to recall
nonetheless, that as a matter of fact, almost all convinced anti-realists have embraced the
principle of compositionality in its full strength18. It may happen that committed antirealists should prefer a more relaxed compositional principle if they pretend to maintain
their position with real impact against more traditional realist semantics. The point is that if
the principle of compositionality is respected when coming to understand how the
expressions of our languages have a definite meaning that can be grasped by speakers like
10
us with finite cognitive capabilities, then the manifestation challenge is much less
formidable than many of those committed anti-realists have so far envisaged.
3. Some cases
As has been shown, then, there is a case for maintaining that the manifestation challenge
should not bother a realist too much, at least not when it comes to the question of whether
there are reasons coming from the manifestation argument recommending, for example,
global anti-realism. But it may be now too early for this conclusion. The point is that,
although in general there seems to be a quite general strategy to which the realist may resort
for addressing the manifestation challenge in different areas, when one comes to consider
how the challenge can be addressed in specific cases, the difficulties might subsist for
reasons completely inherent to how propositions of the offending class are constructed out
of their semantic components. This section will try to explore how the considerations
coming from the principle of compositionality fare in different specific areas of debate for
which concerns have been raised about whether there could be truth-conditions in the
realist sense instead of anti-realist assertibility-conditions. The cases that will be considered
are: propositions about the past, propositions about other minds, propositions about
inaccessible areas of space-time and propositions about unsurveyable domains.
3.1. The reality of the past
In the case of propositions about the past, the debate between realist and anti-realist
conceptions has been focused on whether the understanding of truth-conditions of pasttense propositions could –or could not- be rendered intelligible by the procedure of “truth
value links”. Consider a sample past-tense proposition:
(6)
Caesar was stabbed by Brutus on the ides of March.
If one applies the manifestation requirement to the proposition (6), then a speaker S will be
said to understand it only in case he has dispositions of correct use of (6) in the appropriate
circumstances, under standards both epistemic and pragmatic. As the anti-realist may point
out, a speaker S can only display the linguistic uses by which the existence of such
disposition can be assessed if there is available evidence at the disposal of speaker S to
justify the fact that Caesar was stabbed by Brutus on the ides of March. We think we do
have that evidence in the case of proposition (6), but suppose that all traces by which the
fact could have been tracked had disappeared in the course of the centuries. Suppose, for
example, that the invasion of the hordes of Huns had been much more terrible and
destructive of the ancient culture. Atila and his heirs, suppose further, ruled over the West
for a thousand years and destroyed every single record of an independent past of the people
inhabiting the shores of the Mediterranean Sea. If proposition (6) were unverifiable, as it
seems the situation could suggest it was, then the issue might appear whether a speaker S
could really grasp the meaning of the truth-conditions of proposition (6) for –in principle
and as far as the manifestation challenge goes- there are no circumstances where S could
display linguistic behaviour by which his understanding could be assessed.
In the classical treatment of Dummett, these considerations lead to a general
scepticism concerning the ontological status of the past19. The realist is inclined to think
11
that, although one could not have evidence to affirm (or to deny) that Caesar was stabbed
by Brutus on the ides of March, it should be a fact –somewhat inscribed in the book of
time- that Caesar determinately was or determinately was not stabbed by Brutus on the ides
of March. The manifestation challenge questions this basic realist assumption remarking
the fact that a speaker S in the envisaged epistemic circumstances does not seem to grasp
such objective and independent truth-conditions for (6), for he does not know if any of
those alternatives obtain, or is in the situation to somewhat improve the epistemic situation
in order to determine whether any of the alternatives obtain. If the meaning of a proposition
is something that a speaker should grasp, then there seems to be no guarantee that there is
really a truth at all about whether Caesar was or was not stabbed by Brutus on the ides of
March.
The strategy that has been usually discussed to address the challenge has focused –
as was said above- on the possibility of “truth-value links”. A truth-value link comes to be
in this context an explanation of what it is to be true for a proposition in a tense other than
the present by resource to the understanding of what it is to be true for the same proposition
in the present tense. Consider again, in effect, proposition (6). It can be analysed in the
usual way with a core proposition in present tense and a tense-operator indicating past
tense.
(7)
In the past it was the case that: (Caesar is stabbed by Brutus)
The general idea of the truth-value link is to think of the understanding of the truth
conditions of (7) as constituted by the understanding of what are the present-tense truthconditions of Caesar being stabbed by Brutus, and “projecting” that understanding to the
past. The general strategy is to think of something like “in the past it was the case that: in
the present it is the case that: Caesar is stabbed by Brutus” (taking the last clause as
tenseless)20. In other words, the understanding of the meaning of proposition (7) comes
from the understanding that a speaker S might have of an utterance in present-tense saying
that Caesar is being stabbed by Brutus now (you should imagine someone uttering these
words on the ides of March of the year 44 BC). Under this strategy of addressing the
manifestation challenge the realist still has to face some difficulties if the requirement of
manifestation is construed as applying to complete propositions. In effect, a speaker that
understands a truth-value link relevant for the case considered should display dispositions
of correct use of: (i) the proposition in the present-tense, and (ii) the character of being past
of that present-tense proposition. Obviously, a speaker in the present and supposing –ex
hypothesi- that all or most traces of the death of Caesar have disappeared, is in no position
to display correct linguistic uses of a present-tense utterance of the proposition “Caesar is
being stabbed now by Brutus”.
But there is another strategy that is much more feasible and easy to address the
challenge21. If the requirement of manifestation is construed –as was defended above- as
bound to the structure and deliverances of a theory of truth for the language in question,
then the problem in respect to proposition (6) comes to be a problem about the
understanding of certain names, predicates, temporal locations and the past-tense operator.
It is not important to know if a speaker S can or cannot know if Caesar was or was not
stabbed by Brutus on the ides of March, but simply if this speaker S understands the
meaning of the names “Caesar” and “Brutus”. It is a question, further, of understanding
what it is “to stab”, what it is to locate an event on the ides of March (which will require
12
some acquaintance with the Roman culture in general, as well as the understanding of the
meaning of the names “Caesar” and “Brutus”). Finally, it may be a question of
understanding the past-tense operator in general. In every case, the dispositions of correct
use should be displayed with respect to the semantic components of proposition (6),
whatever they might be. If a speaker has legitimate and reasonable understanding of all
these semantic components and their mode of combination, there is no further question of
whether he really understands the meaning of the proposition. And here there appear to be
no special problems with the understanding –even by anti-realist standards- of any of those
components on the part of the speaker. It is a matter of common linguistic competence to
know how to use the past-tense in general (remember that the problem is not how to verify
if Caesar was stabbed by Brutus, but to know in general how a past-tense proposition is
verified) and all the other semantic items involved.
In this alternative strategy that exploits the compositional character of meaning, the
operation of a truth-value link may be implicit, as was originally envisaged by the previous
discussion of Dummett, but the point is that the difficulties raised by the manifestation
challenge cannot be adequately answered if not by focusing on the general understanding of
the sub-sentential components and the manner of their combination.
3.2. Other minds
A case very similar to that of the past is concerned with attribution of intentional states –or
consciousness- to other beings. The basic difficulty lies in the fact that intentional states are
accessible, in principle, from the first-person perspective. This fact seems to make those
states opaque to third-person public observation. Consider a proposition like:
(8)
Oedipus is in severe pain
Suppose that in the situation Oedipus does not manifest pain by any of what are usually
taken to be the characteristic forms of behaviour manifesting pain. Then, there appears the
question of whether a speaker uttering (8) really understands its meaning22. A truth-value
link strategy to deal also with this case has been proposed here. Under the truth-value link
strategy, the understanding of the meaning of proposition (8) comes from a dissociation in
its truth-conditions between a part open to first-person authority and a part attributing that
grasp to a third person. Hence, (8) could eventually be understood as:
(9)
(Oedipus is in severe pain) ↔ (“I am in severe pain” could be correctly uttered by
Oedipus)
This is supposed in the same way as it was in the case of the stabbing of Caesar
(10)
(Caesar was stabbed by Brutus) ↔ (“Caesar is stabbed by Brutus” could have been
correctly uttered in the past)
And, as in the case of the past, there seems to be scarce remedy for the realist predicament
in the truth-value link procedure if the requirement of manifestation is connected to
complete propositions. In effect, if the meaning of the proposition stating that Oedipus is in
severe pain is understood –and the manifestation requirement is construed in the more
13
restrictive way, affecting complete propositions- the speaker S can only understand it if he
has dispositions of correct use of that precise proposition under whatever truth-value link
analysis. If the speaker cannot verify what could be for Oedipus to utter –truthfully- that he
is in severe pain, then there will not be sufficient evidence to postulate dispositions of
correct use in S, i.e. there will not be sufficient evidence to postulate understanding of the
meaning of (8) on the part of speaker S.
Let us now turn to a compositional construction of the manifestation requirement.
Under this more relaxed construction, a speaker has to show dispositions of use only of the
semantic components of proposition (8) and of their mode of combination. In the case
considered of the severe pain of Oedipus, all that seems to be required on the part of
speaker S is understanding of what it is to be under severe pain and what is the meaning of
the name “Oedipus”. Now, understanding of the meaning of those semantic components
may come from very different sources. A speaker may manifest understanding of the
meaning of the predicate of being under severe pain making correct statements about his
own case and making also correct statements describing the mental states of other beings as
these states manifest in overt behaviour (maybe also taking into account what those beings
report linguistically about their own severe pains). It should be remarked once again, that to
attribute this understanding to speaker S it is no problem if, for example, there is no way of
verifying if Oedipus is or is not in severe pain. What really matters for the manifestation
requirement in this case is that there are some circumstances –not necessarily linked with
what happens with Oedipus- where there are criteria by which the speaker can verify if
someone is or not in severe pain and others can correct his statements if they were
inappropriate.
3.3. Inaccessible areas of space-time
It is a result of the views put forward by the theory of relativity that there are (or might be)
areas of space-time from which no signal could get to us, giving us information about what
happens in those areas. As no signal can travel faster than light, then it follows that certain
events, although not simultaneous with us, are so distant that it is physically impossible that
someone could come to “observe” them in the present. Suppose that the coordinates x, y, z,
t give the location of a space-time point inaccessible to us in the way just explained and
consider the following proposition about what happens in that space-time point:
(11)
A supernova exploded in x, y, z, t
Now, surely it happens that a speaker S cannot display correct linguistic uses of proposition
(11), no matter how astronomically sophisticated he might be. There are no recognizable
circumstances under which S could know that a supernova exploded in x, y, z, t and, hence,
could correctly assert that a supernova exploded in x, y, z, t. Following the stricter
construction of the manifestation requirement, speaker S cannot manifest his understanding
of the meaning of proposition (11) giving clues about his dispositions of language usage.
Once again, if one adopts a construction of the manifestation requirement connected
with the compositional structure of language, a feasible response is at the disposal of the
realist. In the case of proposition (11) all that he has to manifest is understanding of what a
supernova is, what is to explode and, finally what the location designated by the
coordinates x, y, z, t is. Of course, in this last case, it is not necessary that the speaker
14
should know exactly that space-time point for himself. It suffices if he knows that there is a
systematic procedure by which all these locations are singled out from a certain frame of
reference.
3.4. Unsurveyable domains
The last general case that will be considered here is concerned with domains over which
some quantifier may range but that are unsurveyable by finite procedures of effective
decision. It is supposed that a finite domain will always be “surveyable”, so the discussion
is restricted to infinite domains, at least here (doubts will be raised below regarding this
point). In this last case, there are sometimes procedures to “survey” certain domains by
means of, for example, mathematical induction. The point appears in relation with infinite
domains where –presumptively- there are no such procedures. Consider, for the sake of
argument, Goldbach’s conjecture:
(12)
∀n∃m∃r ((n is even) & (n > 2)) → ((m is prime) & (r is prime) & (n = m + r))
That is, every even number greater than 2 is the sum of two prime numbers. Currently we
have not either proved or refuted this statement. Suppose there is no inductive procedure by
which one could come to prove it. Suppose even that –given our limited mathematical
capabilities- we will never come to prove it. Suppose that coming to know about its truth is
just a matter of “checking” the validity of the principle contained in proposition (12)
individually for all the even natural numbers greater than 2, a task than could only be
accomplished by God, if it can be accomplished at all.
This is a case, where by anti-realist standards a speaker S could not have
dispositions of correct use of proposition (12), for there are no recognizable circumstances
where the correctness of his assertion of (12) could be assessed. In the case in question,
proposition (12) cannot be proved by the speaker, but it is also the case that the speaker
cannot even recognise a proof of it, if he were presented with one, for there is no such proof
at the disposal of our finite cognitive capabilities. How do the considerations coming from
the principle of compositionality work here? The compositional construction of the
principle of manifestation requires dispositions of correct use connected with the semantic
components occurring in the proposition. Here, those semantic components are the
predicates “being even”, “being prime” and “being the sum of n and m” with the logical
constants and operators. It is obvious that a normal speaker –with sufficient knowledge of
elementary arithmetic- does have the understanding of the meaning of (almost all) these
items. The concern arises, notwithstanding, in connection with the universal quantifier
operating over the entire proposition. An anti-realist might say here that it is this quantifier
that is responsible for the lack of dispositions of correct use of proposition (12), because it
alone produces the result of evidence-transcendence.
The point in debate, nevertheless, is not simply whether this quantifier makes the
proposition unverifiable, but whether this fact is a reason to think that the speaker does not
have understanding of its truth-conditions. The anti-realist is inclined to maintain that an
evidence-transcendent proposition cannot have a meaning of which there is grasp by a
speaker. It has been shown above how the inclination of the anti-realist can be resisted in
general without rejecting the principle of manifestation, but just construing it in a more
sensible way, in line with the compositionality of meaning. If there is lack of understanding
15
of the meaning of a proposition, that should reside in the specific contribution of some
semantic component of the proposition in question or in some specific mode of
combination of those semantic components going against some rule of the language for
well-formed expressions. The issue here of whether a speaker has or does not have
understanding of what is stated by (12) should be answered, then, considering whether the
speaker has or does not have understanding of one precise sub-sentential component of the
offending proposition. If the speaker has general knowledge of how to use universal
quantifications, for example, displaying that ability in cases where the universal
quantification is surveyable, then there are no remaining questions whether he understands
universal quantifications in the unsurveyable case. Certainly, there are provable statements
that have the form of universal quantifications over all natural numbers and also there are
provable statements that have the form of universal quantifications over all real numbers, so
–under strict anti-realist standards- there should be dispositions of correct use on the part of
speakers of the sub-sentential components involved in those statements. If the universal
quantifier is understood in those cases, then it can be understood generally in all the
contexts where it may occur23.
4. An anti-realist rejoinder
It is obvious that a speaker can be deemed as having dispositions of correct use of the
quantifier, for example, if he in general uses this operator correctly in linguistic uses. And
surely, any competent speaker knows how to use a universal quantifier. But an anti-realist
would eventually raise the question of whether there is a problem here in the case
considered when the quantifier ranges over an unsurveyable domain. An anti-realist may
be inclined to contend that a speaker having dispositions of correct use for a quantifier over
surveyable domains does not have dispositions of use of quantifiers ranging over
unsurveyable domains: at least, he will contend that it is not obvious that the former entails
or guarantees the latter. So the question can be restricted to quantification over an
unsurveyable domain. Does a speaker understand the meaning of this kind of
quantification? Does the understanding he does have of quantifiers ranging over surveyable
domains suffice for the unsurveyable case? Consider also, that an argument in similar lines
would be displayed by the anti-realist also in the case of a past-tense operator, or even in
the case of third-person attributions of mental states to a person. The anti-realist might
contend here that our understanding of a past-tense predication where we have reliable
methods of verification is not guarantee that we will have also understanding in the case of
past-tense predications where there are no verification procedures at our disposal. So, the
problem considered here has a general character, although the discussion will be focused in
the case of quantification over unsurveyable domains.
The reasoning –on the part of the anti-realist- for distinguishing the case of
surveyable from the case of unsurveyable domains may be along the following lines: when
a speaker has dispositions of correct use of an universal quantifier, he should have
displayed those dispositions in correct linguistic speech acts by which he could have
asserted that certain universally quantified proposition obtains. A speaker can only make
“correct” assertions of universally quantified propositions when there is evidence sufficient
for that proposition and, one may suppose, that evidence can only be gathered in the case of
a domain surveyable to our cognitive capabilities. Hence, it seems that there is no
“manifestation” in the required sense coming from the principle of manifestation construed
16
in accordance with the principle of compositionality. In the case of statements about the
past, on the other hand, the fact that a statement about the stabbing of Caesar’s is
unverifiable comes from the specific contribution of a tense operator ranging over times
over which our epistemic capabilities are seriously deficient. The anti-realist will, then, be
inclined to contend that understanding of a past-tense operator ranging over surveyable past
instants of time does not guarantee understanding of a past-tense operator ranging over
unsurveyable instants of past time. Everywhere a rift between the surveyable and the
unsurveyable should be posed by the theorist and, hence, the general compositional strategy
will fail to address the general explanatory tasks posed by the manifestation requirement.
This line of anti-realist rejoinder will be answered by two different kinds of
response. In first place, it will be argued, there seems to be a basic difficulty in the antirealist’s interpretation of what counts as a universal quantifier ranging over an
unsurveyable domain. This point relating the universal quantifier generalises to the related
cases of operators dealing with times or regions of space-time. In second place, the antirealist claim relies in a sharp distinction between operators over surveyable and
unsurveyable domains that is unwarranted and, even more, should be rejected if we are
going to understand the workings of a theory of meaning by what speakers actually
manifest about the structure of those theories.
4.1. What is “surveyable”?
A determinate notion of what could count as “sufficient evidence” is required for a
quantifier ranging over a “surveyable” domain. What is a “surveyable” domain? Is it simply
a “finite” domain? Of course, the anti-realist is thinking of rather abstruse cases in
mathematics dealing with the transfinite, but the problem comes when one considers how to
validate certain quantifications that are normally deemed non-problematic for most
philosophers. We can take the case of universal quantifications that appear in, for example,
theories of natural science, as perfectly in order both for realists and anti-realists. Consider,
for example, the following proposition:
(13)
∀x ((x is an atom) → (x has a nucleus))
It should be taken as neutral ground between the realist and the anti-realist that a speaker
sufficiently conversant with our contemporary worldview of the physical understands the
meaning of a universal quantification like (13). If a speaker S understands the meaning of
(13), by the manifestation principle, he should have dispositions of correct use of the
semantic items appearing in (13) and their manner of combination. In particular, speaker S
should have dispositions of correct use of the universal quantifier in front of proposition
(13), duly manifested in correct uses where the quantification is sufficiently justified for our
epistemic standards. Now, for our common epistemic standards, as those standards are
displayed in the rational activity of accepting and rejecting theories and hypotheses in
natural science, a certain amount of finite and limited evidence is perfectly sufficient to
justify a universal quantification like (13) where it is not the case –not at all- that the
evidence attained is exhaustive.
The problem for the anti-realist comes here when one asks whether the evidence
gathered, for example, for the universal quantification in proposition (13) is sufficient, i.e.
whether, the domain over which the quantifier is ranging in (13) is or not really
17
“surveyable”. A dilemma ensues, as both answers to this question are rather embarrassing
for the anti-realist. Suppose, in fact, that the answer of the anti-realist were “no”. Then a
common speaker could intelligibly use universal quantifications only in the limited case of
domains where a finite and quite limited survey could be taken. Natural science, almost in
its entirety, would fall into the realm of the evidence-transcendent. We will have to convict
most scientist for “not understanding” what they are talking about. Suppose, on the other
hand, that the answer of the anti-realist were “yes”. Then, the realist would be immediately
inclined to ask why this case is different from the case of the “unsurveyable” domains in
mathematics. For surely, the anti-realist must have some principled way of saying why
some domains are outside the limits of what a speaker can duly manifest in correct
linguistic uses of universal quantification. The realist could further contend that, as in the
case of the generalisations in natural science, the evidence one can gather in the case of, for
example, the domain of the natural numbers over which the quantifier in proposition (12) is
ranging, is quite limited. It is evidence limited to how a certain domain of mathematical
entities is constituted as an objective realm. This knowledge, or putative knowledge (if you
prefer), gives one reason to think of proposition (12) as having a determinate truth-value
albeit unknown or even unknowable. The general ontological conception –by whatever
means it were justified- is the ground for regarding the truth-value of proposition (12) as
definite24. This evidence is, in a sense, “incomplete”: it can be improved and defeated by
further evidence, but in any case we never have “complete” warrants for our beliefs, even
for our best entrenched theories.
Of course, the anti-realist might contend that the evidence presented by the realist
for his ontological conception of, for example, the mathematical domain of the natural
numbers is faulty, but this could be another issue and not one by which one could a priori
exclude understanding of the meaning of a universal quantification for considerations
having to do specifically with the requirement of manifestation. Consider again the entire
dialectical situation. The anti-realist is saying that there are no dispositions of correct use of
universal quantifiers when they range over unsurveyable domains, for there are no
circumstances where a speaker may display correct linguistic usage of those quantifiers.
The realist asks the anti-realist to explain what counts as an “unsurveyable” domain. The
best way to understand the notion of the “unsurveyable” is to connect it to our cognitive
powers for detecting what is going on in a certain realm. Suppose now that our cognitive
powers are sufficient to survey what is going on in the physical realm, as far as this realm is
described by natural science. Then it follows that a normal speaker understands the
meaning of quantifiers ranging over the entities in the physical realm although our beliefs
about the physical realm are neither infallible nor complete. The point now is: if incomplete
evidence is sufficient for understanding in the case of the physical realm, why not also in
the case of the domain of, say, real numbers? Here the anti-realist can only continue
defending his case criticising the grounds for accepting the ontological realm of, for
example, a non-denumerable infinity of real numbers, but he does not have an a priori
argument to say that a speaker does not understand the meaning of universal quantification
in this case. The speaker should be deemed as understanding the meaning of quantification
over real numbers in dependence of the question of whether the realm of real numbers is or
not “surveyable”, and, of course, if one knows that there is a certain objective domain of
entities of which some well defined properties and relations determinately obtain or fail to
obtain, one does have reason to think that a proposition like (12) has a definite truth-value.
In this case, the domain is –in some sense- “surveyable” and a speaker should understand
18
the meaning of (12) if he is conversant simply with the universal quantifier and with the
other semantic components there occurring. As should already be apparent, it is not the case
here that a certain domain of entities and states of affairs where those entities enter might
be dismissed for reasons having to do with our understanding of the meaning of the
propositions stating facts about the domain in question, but on the contrary, the ontological
questions about what there is are what settle the issue of whether a speaker really
“manifests” understanding of universal quantification.
In other words, the issue of whether a certain domain counts as really unsurveyable
turns finally to the usual ontological questions about the reasons there are to think that a
certain domain is objectively and independently constituted. It should be recalled that the
manifestation challenge has been devised as an argument for an anti-realist conception of
meaning and, hence, for an anti-realist ontological conception about realms of (putative)
entities. But the efficacy of the argument turns finally into the question of whether a realm
is “surveyable” in the relevant sense. And the question of whether a realm is “surveyable” in the relevant sense- finally turns into the question of whether there are reasons to think
that the realm is objectively constituted. But this was what the argument was proposed to
show to begin with! So, there are no conclusions following from the manifestation
argument, at least from it alone, in the way envisaged by the anti-realist, or so it seems25.
This strategy of response can be generalised to similar anti-realist’s rejoinders in relation
with past-tense operators or other kinds of offending evidence-transcendent statements.
4.2. Conditions of identity of an operator
The anti-realist rejoinder relies on a crucial distinction between the operator over
surveyable domains and the operator over unsurveyable domains. It seems obvious, at least
at this point, that the understanding that should be manifested by speakers is attached to the
sub-sentential components to which the workings of a theory of meaning for the language
in question are connected. It follows that a speaker that manifests how to use correctly a
semantic sub-sentential component in some contexts should be deemed as having
dispositions of correct use of that sub-sentential component in general in all contexts26. So,
to repeat again a crucial point, if it is really the same operator that is working in universal
quantifications over surveyable domains and over unsurveyable domains, then there cannot
be any further question whether the speaker really understands the operator in general, if he
displays dispositions of correct use in actual correct uses of the quantifier in cases where
the correctness can be duly assessed, v.gr. in cases where the quantifier is ranging over
domains that are surveyable by our epistemic capabilities.
The anti-realist rejoinder can only work, then, if there is a real difference in nature
between the quantifier ranging over surveyable domains and the quantifiers ranging over
unsurveyable domains so that understanding of the former does not imply understanding of
the latter. The same kind of distinction should be defended in the case of other operators
where the anti-realist may be disposed to pose the same type of criticism. But can the
distinction be defended? It seems that it cannot. The clauses of a theory of meaning in
which our understanding of names and predicates -as well as different types of connectives
and operators- is involved are designed to deliver a precise explanatory duty, that is, to
explain how it is that a speaker can, in principle, understand the meaning of a potential
infinite number of different sentences in a language from the understanding of the elements
from which the sentence has been constructed and the understanding of the mode of
19
combination of those elements. One basic semantic element requires one axiom of the
theory that rules its function and its contribution to the truth-conditions of the sentences
where it occurs. Now, if there is a real difference in nature between, e.gr. the universal
quantifier ranging over surveyable domains and the quantifier ranging over unsurveyable
domains, then there should be different axioms or different rules for those different
semantic operators.
The problem with this line of argument is that such a difference between two
different kinds of operator should manifest itself in some semantic difference of
recognisable structure. And there is no such recognisable difference. We do not make any
recognisable difference between the occurrences of “any” or “all” when talking about a
finite domain of entities or about an –let us suppose- undenumerably infinite domain. Nor
do we make any difference in the past-tense utterances involving past events about which
we have reliable information about what may have happened there and those involving past
events about which we do not have such information, or we do not have any information at
all. In other words, the anti-realist contention of a certain difference in nature between
operators over surveyable or unsurveyable domains requires overt semantic evidence in the
structure of the languages we speak that does not actually exist.
The anti-realist may reply to the foregoing that there cannot appear any overt
semantic structural difference between the operators because there is just one axiom ruling
it. The point is that that sole axiom rules an operator over surveyable domains, so it is not
strange that no special operator appears on the surface ranging over the unsurveyable. It is
possible, in fact, for the anti-realist, to contend that there is just one axiom of which
understanding can be attributed to the speaker: the axiom ruling the quantifier over
surveyable domains; there will be no other putative axiom for a quantifier over
unsurveyable domains. So it will result, as it is obvious, that the speaker will be able to
understand utterances using the former but not utterances using the latter. Now, the
problem with this anti-realist contention lies in the fact that the sole operator in question –
acceptable by anti-realist standards- can be used in statements that turn out unverifiable.
Suppose, for reductio, that there were an operator just as the anti-realist wants it to be,
ranging only over surveyable domains. Let us suppose that it is a past-tense operator
acceptable for the anti-realist “It was the case in the past that:…” Now surely there are
possible worlds where there is no way for us to coming to know whether Brutus stabbed or
did not stab Caesar on the ides of March of year 44 BC27. Surely in those situations we can
construct the sentence:
(14)
It was the case in the past that: Brutus stabbed Caesar
Now, (14) appears on the face of it as well constructed as any proposition, and not only in
relation to our cognitive situation in regarding the death of Caesar in the actual world, but
also in the situation envisaged in a possible world where our cognitive situation would be
extremely worse. The point is that just because the semantic components can be freely
combined to form sentences in the language, whatever may be the restrictions imposed by
the anti-realist, it is always possible to devise statements where those components occur
and which are unverifiable. If the anti-realist were right, then (14) should appear in the
circumstances immediately as ungrammatical, but it is not. The anti-realist, then, is not
right.
20
5. Conclusions
The manifestation challenge has been devised as an argument purported to show that there
are serious deficiencies in a realist conception of meaning in so far as this conception
embraces the possibility of propositions endowed with determinate evidence-transcendent
truth-conditions. It has been shown here that a more reasonable form of construing the
manifestation requirement in connection with the principle of compositionality of meaning
-a principle as well justified as the principle of manifestation regarding attributions of
understanding of meaning- gives the realist the resources to address the challenge in the
areas that have been usually taken as crucial. The cases of propositions about the past,
propositions about other minds, about inaccessible regions of space-time and about
unsurveyable domains appeared after examination to be perfectly explicable by all the
standards coming from the manifestation requirement.
It results, then, that the areas over which the manifestation requirement could pose a
real challenge for the realist conception of meaning appear as much more restricted and
localised than originally envisaged by the proponents of the manifestation argument. As far
as one can tell, it is restricted to cases where a certain specific semantic component cannot
have dispositions of correct use associated with it because there are no circumstances where
a speaker can recognise the obtaining of the facts expressed by a proposition where the
offending semantic component occurs. And there seems to be no such cases, as far as one
can tell.
Finally, a possible anti-realist rejoinder to the line of argument developed trying to
distinguish the cases of operators over what is verifiable and operators over what is not has
appeared after examination to be faulty. In the first place, a domain can only be deemed as
“unsurveyable” after some crucial decisions about its ontological character have been
taken, so the unverifiable character of the sentences produced by an operator cannot be
used to devise an argument designed to defend an anti-realist conclusion about that domain
that should have been duly justified already. In the second place, the purported distinction
between different semantic operators when the domain over which they range is surveyable
or unsurveyable is badly lacking the sort of evidence that may render it plausible. We have
no reasons to think that the operators are really different in nature. On the face of the issue
it appears that they are the same kind of operators, and it seems also clear that we do
understand those operators in correct uses manifesting dispositions of correct use. Hence,
under the more exacting anti-realist standards coming from the manifestation requirement,
the propositions usually taken by anti-realists as posing a challenge for realist conceptions
of meaning seems to be perfectly acceptable as having legitimate meaning and content28.
Notes
1
The terminology will be rather loose in the foregoing about “propositions” and “sentences”. In principle the
object of a theory of meaning should be the sentences of a language and not, or at least, not directly the
meaning of those sentences, v.gr. the propositions expressed by those sentences when uttered by a speaker in
a precise context. Nonetheless, the primary philosophical interest in a theory of meaning for a language lies in
the deliverances that such a theory can render regarding the question of the nature of thought and the nature of
the contents of those thoughts, v.gr. the propositions constituting those thoughts. This is the reason why
sudden transition from “sentences” to “propositions” need not concern us unnecessarily.
21
2
M. Dummett developed the manifestation challenge in many places. Cf, e.gr. Dummett (1978a), (1978b),
(1978c), (1991), (1993a), (1993b). A general presentation of the dialectic can be consulted in Hale (1997);
also Wright (1987), pp. 1-43. More detailed discussion of the structure of the argument in Tennant (1997), pp.
1-62, 159-244.
3
Cf. Kripke (1982), specially pp. 22-37.
4
A related argument is defended in Wright (1987), pp. 18-21.
5
The reference here to truth conditions should not be taken as a sort of pre-judgement in favour of realist
semantics. The difference between a realist and an anti-realist semantics can be taken to lie in the conception
of truth for the sentences in question. For the realist a sentence is true objectively and independently of our
judgement-responses. For the anti-realist a sentence is true only granted some kind of cognitive contribution
on our part. Then, in this latter case, some kind of appropriate cognitive response or appropriate epistemic
state is constitutive of the truth conditions of the sentence in question.
6
A better formulation, although less simple, would be:
(2’)
∀p∀S ((S has dispositions of correct use of p) ↔ (C → ∃s (s a correct use of p by S))
In this modified principle (2’) the correct uses of a proposition p count as “manifesting” the existence of
dispositions of correct use by the speaker S only if some condition (or conditions) C obtain(s). Those
conditions are introduced here to guarantee that the uses are indeed sufficient to render the desired result.
7
Cf. Divers (2002), pp. 11-14. Facts A might be supervenient on facts B compatible with the fact that facts B
are supervenient on facts A. Of course, the idea that one usually tries to convey by the statement of a
supervenience relation between two domains of facts is that of a sort of asymmetric dependence between
those domains.
8
It seems wiser to formulate the supervenience relation in terms more tied to “dispositions of use” rather than
use. Then, any two speakers with the same “dispositions of use” will be deemed as having the same
understanding of meaning. On the other hand, different bases of linguistic behaviour displayed by different
speaker can be considered sufficient for the postulation of a single disposition of use. There are many issues
also arising here about this –more refined- supervenience relation that shall not and should not be addressed
here.
9
For a very complete and through discussion of the nature and metaphysical consequences of a principle of
individuation as a mean to deliver a new category of entities (what is called an “abstraction principle”),
related in particular to the mathematical case, cf. Hale & Wright (2001), pp. 1-27.
10
Consider, as one of the problems that a principle in these lines should face, that the equivalence relation
between linguistic uses is defined as being the relation of being the use of a same p. Now, this means that the
equivalence relation that is giving the conditions of identity for the entities in the introduced domain seems to
be obviously dependent on the existence of some or other propositions p by which the idea of “being a use of
p” can make sense. The –supposed- principle, then, could only deliver the desired identity-conditions if,
previously, the entities for which identity-conditions are going to be given, are already there. This procedure
seems, on the face of it, to be question-begging. The principle in question should be formulated again so that
the equivalence relation defined over linguistic uses does not presuppose the previous existence of the
propositions that the principle is presumptively introducing for the first time. Of course, it is not necessary to
enter into this topic here.
11
The locus classicus for this formulation is, of course, Davidson (2001)
12
Cf. for these topics Evans, (1985), Miller, (1997).
13
Cf. Tarski, (1997), (1944).
22
14
Here I am overlooking some other alternatives by which the principle of compositionality and the principle
of manifestation can be made coherent with each other, because they seem less natural or (in some cases)
simply unfeasible as part of a sound understanding of semantic theory. For example, one may seem inclined
to think in a “No-Theory” theory by which the compositional character of a proposition may be sometimes
despised in favour of a particular context of utterance where the meaning will be interpreted differently and in
which the dispositions of correct usage are linked directly to the complete proposition and not to the semantic
components. It is not the case here that the dispositions of usage are linked always directly to complete
propositions. What a “No-Theory” will sustain is that there is no general basis by which it may be decided
when the deliverances of the compositional principles should be despised. A less radical conception may
sustain that the deliverances of the compositional clauses must be despised in certain precise contexts of
usage when some general philosophical reasons require a different interpretation. What is common to all these
alternatives is the supposition that meaning is not always a function of the semantic components of an
expression and their mode of composition. Some other factors may produce huge differences in meaning (not
coming from the explicitly indexical character of an expression), coming from the context of utterance, for
example. This general approach to semantic theory will not be considered here.
15
Cf. with the clauses of tacit knowledge of the deliverances of a theory of meaning proposed by G. Evans:
“we might say that a speaker U tacitly knows that the denotation of a is John iff he has dispositions such that:
ΠφΠψ if
(i) U tacitly knows that an object satisfies φ iff it is ψ
(ii) U hears an utterance having the form φ^a,
Then U will judge the utterance is true iff John is ψ.
Connectedly, we say that a speaker U tacitly knows that an object satisfies F iff it is bald iff he has a
disposition such that:
ΠxΠα if
(i) U tacitly knows that the denotation of α is x
(ii) U hears an utterance having the form F^α
Then U will judge that the utterance is true iff x is bald.
In these formulations, ‘Π’ is a universal substitutional quantifier, with variables having the following
substitution classes: φ, names of predicate expressions of the (object) language; α, names of names of the
(object) language; ψ, predicate expressions of our language (the metalanguage); and ‘x’, proper names of our
language.” [Evans, (1985), p. 329.]
16
A position like this in semantics is usually associated with J. L Austin. It has been now defended by Ch.
Travis. Cf. for a statement of the position, Ch. Travis, (1997).
17
Probably it should not be called a semantic theory but, instead, the simple rejection of semantic theory as a
theoretical fruitful enterprise.
18
Cf. for example, M. Dummett, (1991), pp. 221-244; C. Wright, “Can a Davidsonian Meaning-Theory be
Construed in Terms of Assertibility?” in Wright (1987), pp. 287-316.
19
Cf. M. Dummett, (1978c), pp. 358-374.
20
This is the explanation of Dummett: “If I now (2.45 p.m. 12 February 1969) say, ‘I am in my College
room’, I make a present-tense statement which is, as I say it, true: let us call this statement A. Suppose now
that exactly one year later someone makes the statement (call it B) ‘A year ago Dummett was in his College
room’. Then it is a consequence of the truth-value link that, since the statement A is now true, the statement B,
made in one year’s time, is likewise true. Now, the realist claims, it is from an understanding of the truth-
23
value link, as exemplified in such a case, that we derive a grasp of what it is for a statement in the past tense,
whenever made, for example one made now, to be true.” [Dummett, (1978c), p. 363]
21
This strategy is proposed explicitly by J. McDowell, (1998).
22
It should be noted that the problem presented here for the verifiability –and, hence, for the understandingof propositions about mental states of persons other than oneself, need not arise if the general conception of
the nature of those mental states prevents the asymmetry between the first and third person perspectives in
some form or other. For example, if mental states are conceived as identical with some physical states of the
brain, then there should not appear any problem about the public observability of mental states of a subject as
far as those physical states are publicy observable; if, on the other hand, mental states are identified with
dispositions of public behaviour or, simply, if they are identified with a certain class of public and
characteristic behaviour, then –again- the contrast between what can be ascertained from the first-person
perspective in relation with one’s own case and what can be ascertained by public criteria open to third-person
scrutiny, disappears. Here, none of these positions are prejudged. The cases considered in the text simply
consider first/third person contrast because under that supposition, a certain problem for realist semantics
arises.
23
I am grateful to Stephen Williams for this last point.
24
It should be noted here that the contention is that one can have certain evidence that a proposition like (12)
has a definite truth value, although –of course- one does not have any evidence about what is that truth-value.
If one has relevant evidence concerning the objectivity of a mathematical realm of entities, then one has also a
prima facie strong reason to sustain that proposition (12) should have a definite truth-value. This notes should
not be taken as the endorsement of any specific position in the philosophy of mathematics.
25
A useful comparison with the systematic difficulties put forward here can be made with the related,
although different, difficulties raised in Edwards (1995). The difficulties annotated by Edwards are related
with the requirements for canonical introductions of universal quantifiers in the context of a general
verificationist theory of sense, where the meaning of logical constants is fixed by the joint operation of
introduction and elimination rules. It happens that a universal quantifier can only be introduced if the a
posteriori warrants for its introduction are of the same or higher order of complexity than the introduced
proposition where the universal quantification occurs. It is needed some sort of knowledge that the instances
of the relevant predicate recognized are somehow “exhaustive” of the domain considered.
26
This requirement is what has been called the “Generality Constraint” by Gareth Evans. Cf. Evans, (1982)
pp. 100-105.
27
Suppose that in this possible world w the Huns destroyed the Roman Empire completely and ruled one
thousand years, etc. In w we –or our counterparts, if you want- speak English, and in w we can construct the
sentence saying that in the past Brutus stabbed Caesar.
28
This work has been written in execution of research Project Fondecyt 1030523 (Conicyt, Chile). I specially
thank Stephen G. Williams for his detailed comments on a previous draft of this paper. I also thank Timothy
Williamson and Bob Hale for their discussion of the topics dealt with here and many useful comments. A
previous version was presented at the XV Jornadas de Epistemología e Historia de la Ciencia organized by
Universidad Nacional de Córdoba (Argentina). I thank the audience for many suggestions. Thanks also for
many valuable suggestions to an anonymous referee.
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26