prosentences that function analogously to their better known
cousins–pronouns. For example, just as we might use the pronoun 'he'
in place of 'James' to transform "James went to the supermarket" into
"He went to the supermarket," so we might use the prosentence-forming
operator 'is true' to transform "Snow is white" into "'Snow is white'
is true." According to the prosentential theory of truth, whenever a
referring expression (for example, a definite description or a
quote-name) is joined to the truth predicate, the resulting statement
contains no more content than the sentence(s) picked out by the
referring expression. To assert that a sentence is true is simply to
assert or reassert that sentence; it is not to ascribe the property of
truth to that sentence. The prosentential theory is one kind of
deflationary theory of truth. Like all deflationary theories, it
provides an alternative to explanations of truth that analyze truth in
terms of reference, predicate satisfaction or a correspondence
relation.
1. What is a Prosentence?
The prosentential theory was first developed by Dorothy Grover, Joseph
Camp, Jr., and Nuel Belnap, Jr. (1975) and Grover (1992) and has
received renewed attention due to the work of Robert Brandom (1994).
The central claim of the prosentential theory is that 'x is true'
functions as a prosentence-forming operator rather than a
property-ascribing locution. Perhaps the best way to begin an
explication of the prosentential theory is by looking at the more
familiar 'proforms' found in ordinary English usage. 'Proform' is the
generic name for the linguistic category of expressions that 'stand
in' for other expressions—pronouns being the most familiar variety.
Most uses of pronouns are 'lazy'—the antecedents of the pronouns could
have easily been used instead of the pronouns. For example,
1) Mary wanted to buy a car, but she could only afford a motorbike.
2) If she can afford it, Jane will go.
3) John visited us. It was a surprise.
4) Mary said that the moon is made of green cheese, but I didn't believe it.
'She' simply stands in for 'Mary' in (1), and 'she' stands in for
'Jane' in (2), even though 'she' appears before 'Jane.' In (3) 'it'
refers to the event of John's having visited us, while in (4) 'it'
refers to Mary's statement. Lazy uses of pronouns are convenient but
perhaps not essential linguistic conventions.
In addition to lazy uses of pronouns, there are also 'quantificational
uses,' as in:
5) If any car overheats, don't buy it.
6) Each positive integer is such that if it is even, adding 1 to
it yields an odd number.
In these cases, the pronouns do not pick up their referents from their
antecedents in the same straightforward way as pronouns of laziness
do. Replacing the 'it' in (5) by the apparent antecedent 'any car' or
the 'it' in (6) by 'each positive integer' yields the following.
5′) If any car overheats, don't buy any car.
6′) Each positive integer is such that if each positive integer is
even, adding 1 to each positive integer yields an odd number.
(5′) and (6′) obviously do not express the sense of the original
sentences. 'Any car' and 'each positive integer' cannot be construed
as referring expressions; rather, they pick out families of admissible
expressions that can be substituted into the claims. (5) and (6)
should be represented as
5″) (x)[(x is a car & x overheats) → don't buy x].
6″) (x)[(x is a positive integer & x is even) → adding 1 to x
yields an odd number].
More will be said about quantificational proforms below.
There are also many commonly used proforms that are not often
recognized as proforms. These include proverbs:
7) Dance as we do
8) Mary ran quickly, so Bill did too
proadjectives:
9) We must strive to make men happy and to keep them so
and proadverbs:
10) She twitched violently, and while so twitching, expired.
Most importantly, defenders of the prosentential theory of truth claim
that English also contains prosentences. For example,
11) Bill: There are people on Mars. Mary: That is true.
12) John: Bill claims that there are people on Mars but I don't
believe that it is true.
In these examples, 'that is true' and 'it is true' serve as
'prosentences of laziness.' They inherit their content from antecedent
statements, just as pronouns inherit their reference from antecedent
singular terms. John's use of 'it is true' is lazy because he could
have easily repeated the content of Bill's claim without using a
prosentence. John could have said the following.
12′) John: Bill claims that there are people on Mars but I don't
believe that there are people on Mars.
The relation between a proform and its antecedent is called a relation
of 'anaphora.' Defenders of the prosentential theory claim that
prosentences such as 'it is true' and 'that is true' do not have any
content of their own. Whatever content they have is inherited from
their anaphoric antecedents. Because prosentences simply stand in for
other sentences, prosentential theorists claim that utterances of 'p'
and 'p is true' always have the same content.
There are many more kinds of prosentences than 'that is true' or 'it
is true.' Each of the following sentences, for example, is also a
prosentence.
13) Goldbach's conjecture is true.
14) 'Snow is white' is true.
15) The claim that grass is green is true.
According to the prosentential theory, sentences (13), (14) and (15)
say no more than sentences (16), (17) and (18), respectively.
16) Every even number is the sum of two primes.
17) Snow is white.
18) Grass is green.
Each prosentence is formed by conjoining some expression that refers
to a sentence to the truth predicate.
Although the semantic content of prosentences and their antecedents is
the same, prosentences often differ in pragmatic respects from their
antecedents. Consider the difference between the following cases:
11) Bill: There are people on Mars. Mary: That is true.
11′) Bill: There are people on Mars. Mary: There are people on Mars.
Although Mary's utterance in (11′) asserts no more than her utterance
in (11), her utterance in (11′) does not acknowledge that Bill has
said anything. By acknowledging Bill's previous statement, Mary's
utterance of 'that is true' avoids a kind of assertional plagiarism
and has the effect of expressing agreement. Mary could have uttered
her statement in (11′) without ever having heard Bill say anything and
without, therefore, expressing any kind of agreement. Thus, the
prosentential theory takes up the point emphasized by F. P. Ramsey's
redundancy theory of truth that assertions of truth do not assert
anything new. Unlike redundancy theories, however, the prosentential
theory does not take the truth predicate to be always eliminable
without loss. What would be lost in (11′) is Mary's acknowledgment
that Bill had said something.
One of the prosentential theory's most important claims about the
truth predicate is that it is not used to ascribe a substantive
property to propositions. Grover (1992, p. 221) writes,
Many other truth theories assume that a sentence containing a
truth predication, e.g., 'That is true,' is about its antecedent
sentence ('Chicago is large') or an antecedent proposition. By
contrast, the prosentential account is that 'That is true' does not
say anything about its antecedent sentence (e.g., 'Chicago is large')
but says something about an extralinguistic subject (e.g., Chicago).
The truth predicate is not used to say something about sentences or
propositions. It is used to say something about the world. As Grover
(1992, p. 221) puts it, prosentences function "at the level of the
object language." Even when someone makes an utterance such as "John's
last claim is true"—which uses a referring expression that explicitly
mentions an antecedent utterance token—the prosentential theory still
denies that it is the utterance that is being talked about. The person
uttering this sentence "expresses an opinion about whatever
(extralinguistic thing) it was that John expressed an opinion about"
(Grover, 1992, p. 19). W. V. Quine (1970, pp. 10-11) makes a similar
claim, stating that the truth predicate serves "to point through the
sentence to reality; it serves as a reminder that though sentences are
mentioned, reality is still the whole point." The prosentential theory
uses the notion of the anaphoric inheritance of content to explain how
reality remains the focus in such cases.
2. Quantificational Prosentences
In addition to lazy uses of prosentences, there are also
'quantificational' uses. For example,
19) Everything John said is true
is a quantificational prosentence. A first attempt to translate (19)
into a language containing bound propositional variables might read
20) (p)(If John said that p, then p is true).
A natural language paraphrase of (20) which exhibits 'it is true' as a
quantificationally dependent prosentence would be
21) For anything one can say, if John said it, then it is true.
(Grover, 1992, p. 130)
Since, according to the prosentential theory, the statement 'p is
true' says no more than the statement 'p,' the truth predicate in (20)
can be dropped to yield
20′) (p)(If John said that p, then p).
If the variable 'p' ranges over objects and take names of objects as
its substitution instances—i.e., if '(p)' and 'p' are given their
ordinary interpretations—then the consequent of the conditional inside
(20′) will not be a grammatical expression. The antecedents and
consequents of conditionals must be complete sentences. In order for
(20′) to be a grammatical expression, two modifications in the
standard interpretation of variables and quantifiers must be made.
First, the variable 'p' must be understood to be a propositional
variable, taking entire propositions instead of names of propositions
as its substitution instances. Secondly, the universal quantifier
'(p)' must be understood substitutionally, since the traditional,
objectual interpretation of the quantifiers does not square well with
the use of propositional variables. A statement using the particular
(or existential) substitutional quantifier is true just in case the
open sentence following the quantifier has at least one true
substitution instance; while a statement using the universal
substitutional quantifier is true in case every substitution instance
is true (cf. David, 1994, p. 85). In order to avoid confusion between
the objectual and substitutional interpretations of the quantifiers, I
shall use '∀p' to designate the universal substitutional quantifier.
(20′), then, should read
20″) ∀p(If John said that p, then p).
If, however, we interpret the conditional in (20″) as a material
conditional, (20″) will still misrepresent the content of (19).
To see why this is so, consider the fact that universally quantified
statements can be understood as conjunctions of all their possible
substitution instances. For example, (20″) is equivalent to
22) (If John said that p1, then p1 is true) & (If John said that
p2, then p2 is true) & (If John said that p3, then p3 is true) & … &
(If John said that pn, then pn is true).
How many conjuncts make up the content of (22) will depend upon the
size of the domain of discourse in question. That is, it will depend
upon how many possible values of p there are. If the domain of the
variable 'p' is the set of all things that can be said, then (22) will
consist of an indefinitely large conjunction of substitution
instances. Most of the conjuncts will be vacuously true by virtue of
having false antecedents—i.e., there will be indefinitely many things
that John did not say. This means that each of the indefinitely many
conditionals formed from things that John did not say is just as much
part of the content of (19) as each of the conditionals formed from
things John did say. That seems counterintuitive and contrary to the
meaning of (19). Suppose that John made only the following three
statements on the occasion in question.
23) Gas prices are too high.
24) Taxes are too high.
25) Professional baseball players' salaries are too high.
It is plausible to think that (19) says something about (23), (24) and
(25) but not about (26), (27) and (28)—statements John never made.
26) Gas prices are too low.
27) Taxes are too low.
28) Professional baseball players' salaries are too low.
Yet if the quantification in (20″) remains unrestricted, then its
content consists of a conjunction of conditionals having (26), (27),
(28) and countless other statements John did not say in their
antecedents.
If quantificational prosentences such as 'Everything John said is
true' are to refer to only finite classes of claims, their quantifiers
must be restricted in some way. One way to trim down the domain of 'p'
in (20″) is to limit the universe of discourse to the set of all
statements made by John. Let 'UJ' represent some particular universe
of discourse, and let '{p|Øp}' mean 'the set of all propositions such
that 'Øp' is true.' If we limit the universe of discourse to all and
only the things that John said, then we have
29) ∀p(If John said that p, then p). UJ = {p|John said p}
'∀p(If John said that p, then p)' will then consist of a finite
conjunction of true conditionals, one for each thing said by John on
the occasion in question. This arrangement, however, has the unusual
feature that, for every grammatical subject of such a universally
quantified sentence, there will be a different universe of discourse.
For every x, there will be a unique universe of discourse for each
statement of the form
30) ∀p(If x said that p, then p). Ux = {p|x said p}
Other quantificational prosentences that would be instances of (30) include
31) Everything the Pope says about theological doctrine is true.
32) Everything Henry Kissinger says about foreign policy is true.
Following the current suggestion, (31) could be symbolized as either
33) ∀p(If the Pope said that p, then p). UP = {p|the Pope said p &
p is a matter of theological doctrine}
or
33′) ∀p(If the Pope said that p & p is a matter of theological
doctrine, then p). UP = {p|the Pope said p}
The symbolization for (32) would be analogous. It is not clear that we
will be able to capture what is common to all of these cases if each
quantificational prosentence is tied to a distinct universe of
discourse. Perhaps there is another way to limit the domain of 'p' in
(20″).
Nuel Belnap, Jr. (1973), one of the founders of the prosentential
theory of truth, introduced the notion of 'conditional assertion' to
solve the problem of restricted quantification—i.e., where one wants
to quantify over only a limited domain. All prosentential theorists
now rely upon Belnap's model to explicate the logical structure of
quantificational prosentences. Belnap introduced the notation '(A/B)'
to stand for conditional assertion. Conditional assertion occurs when
someone does not assert the conditional 'If A then B' as much as
conditionally assert B—that is, assert B on the condition that A.
Belnap formulates the following principle to capture this idea:
B1) If A is true, then what (A/B) asserts is what B asserts. If A
is false, then (A/B) is nonassertive. (Belnap, 1973, p. 50)
Quantifying into conditional assertions yields a restricted form of
quantification, regarding which Belnap offers the following principle.
B2) Part 1. (x)(Cx/Bx) is assertive just in case ∃xCx is true.
Part 2. (x)(Cx/Bx) is the conjunction of all the propositions (Bt)
such that Ct is true. (ibid., p. 66)
Applying Belnap's conditional assertion notation to (20″) yields
34) ∀p(John said that p/p).
The content of (34), then, is a finite conjunction of claims. But
notice that it is not a conjunction of conditionals of the form 'If
John said that p, then p,' each with a true antecedent. Rather, it is
a conjunction of claims p1, p2,…, pn, each of which satisfies the
condition that John said it. The focus of such a claim is on what John
said and only derivatively on the fact that it was John who did the
saying. If the only statements John made were (23), (24) and (25),
then the content of an assertion of (34) is exhausted by the
conjunction of (23), (24) and (25). As a result, Belnap's principle of
restricted quantification solves the problem of how to interpret
'Everything John said is true.' Applying Belnap's principles to (31)
and (32) yields
35) ∀p(the Pope said that p & p is a matter of theological doctrine/p).
36) ∀p(Kissinger said that p & p is a matter of foreign policy/p).
Following Belnap's interpretation of conditional assertion and
restricted quantification, prosentential theorists can explain how
quantificational prosentences have as their content finite
conjunctions of claims rather than infinite conjunctions of
conditionals, most of which are trivially true. Prosentential
theorists thereby show that quantificational prosentences contain no
more content than the anaphoric antecedents of those prosentences.
Although quantificational prosentences may contain no more explicit
content than their anaphoric antecedents, they can also be used as
implicit attributions of reliability, where such attributions do not
clearly appear in their antecedents. Cf. Beebe (forthcoming).
3. Why the Prosentential Theory is Deflationary
The prosentential theory of truth counts as a 'deflationary' theory
because it denies that any analysis of truth of the form
37) (x)(x is true iff x is F)
can be given, where 'x is F' expresses a property that is conceptually
or explanatorily more fundamental than 'x is true.' An analysis of
truth would be appropriate if the truth predicate were a
property-ascribing locution and the property that is ascribed could be
broken down into more fundamental properties. However, prosentential
theorists deny that uses of the truth predicate ascribe any property
to sentences or propositions.
A common anti-deflationist approach to truth analyzes truth in terms
of reference and predicate satisfaction. Stephen Stich (1990, ch. 5),
for example, takes the proper analysis of truth to be
38) 'a is F' is true iff there exists an object x such that 'a'
refers to x and 'F' is satisfied by x.
Instead of denying the truth of statements such as (38), deflationists
merely deny that they constitute analyses of truth (cf., e.g.,
Horwich, 1998, p. 10). Deflationists claim that the most fundamental
facts about truth are the instances of the various truth schemata used
by deflationary theorists. Consider the equivalence schemata employed
by Quine's (1970) disquotationalism:
D) 'p' is true iff p
and Paul Horwich's (1998) minimalism:
MT) The proposition that p is true iff p.
Nominalizations of descriptive items are substituted on the left-hand
sides of each biconditional schema, while the right-hand sides contain
either descriptive items themselves or appropriate translations of
them. Each of these theorists claims that there is no more to truth
than what is expressed by the substitution instances of these
equivalence schemata. Truth is not analyzed as a relation and the
instances of the equivalence schemata are taken to be the most
fundamental facts about truth. The prosentential theory claims that
each of the favored examples of these deflationary theorists is simply
a special case of the more general phenomenon of anaphora. Regardless
of the points of disagreement among deflationary theorists, they all
agree that instances of the truth schemata represent facts about truth
that are more fundamental vis-à-vis truth than any fact given in an
analysis such as (38).
Some theories, such as the correspondence theory of truth, take truth
to be a relation between propositions and the world. Where 'C'
expresses the correspondence relation, 'y' ranges over segments of
reality, and 'x' is used—for the sake of convenience—as a placeholder
for both descriptive items and the contents of descriptive items, we
can represent a common version of the correspondence theory as
39) (x)[x is true iff (∃y)(Cxy)].
(39) should read 'For any (descriptive item) x, x is true if and only
if there is a (segment of reality) y such that x corresponds to y.' If
truth cannot be analyzed at all, then it obviously cannot be analyzed
as a relation. If, however, truth can be analyzed, then perhaps it
would be appropriate to analyze it as a relation between descriptive
items and segments of the world. How should one go about deciding
between the correspondence theory and the prosentential theory?
Prosentential theorists respond by inviting readers to consider the
following facts. The correspondence theory claims that snow's being
white is necessary but not sufficient for the truth of 'snow is
white.' In addition to snow's being white, the proposition that snow
is white must stand in a relation of correspondence to the fact that
snow is white. The prosentential theory, by contrast, claims that
snow's being white is both necessary and sufficient for the truth of
'snow is white.' As Alston (1996, p. 209) puts it, "Nothing more is
required for its being true that p than just the fact that p; and
nothing less will suffice." One of the hallmarks of deflationism is
the claim that the truth of a descriptive item depends only upon the
meaning or content expressed by that item and how things actually
stand in the world. Prosentential theorists and other deflationists
hope that their readers will see that further constraints on truth are
unnecessary.
The prosentential theorist's claim that no analysis of truth can be
given should not be confused with the claim that no explanation of
truth can be given. The prosentential theory explains the function of
the truth predicate by showing how 'x is true' functions as a
prosentence-forming operator. (Because the prosentential explanation
of truth makes the story about truth depend upon a story about how we
use words and concepts, the prosentential explanation of the function
of "true" generally leads theorists to adopt a version of the 'use
theory of meaning.')
Deflationary theorists also claim that truth never performs any real
explanatory work. Suppose, for example, that Smith successfully
performs the action of attending a concert on Friday and that his
action was in part based upon his belief that the concert is on
Friday. If Smith succeeds in arriving at the concert on Friday, what
best explains the success of his action? The non-deflationist answers
that it is the truth of Smith's belief that explains his success. His
action succeeds because his belief is true. In other words, there is
an important property of his belief (or perhaps a property of the
proposition expressed by his belief)—namely, truth—that is central to
any adequate explanation of Smith's successful action. Deflationists
disagree. They reply that the reason that Smith succeeded in
performing an action based upon the belief that the concert is on
Friday is that the concert is on Friday. There is no need to implicate
a special truth property in this explanation. Why do actions based
upon the belief that oxygen is necessary for combustion generally
succeed (other things being equal)? Because oxygen is necessary for
combustion. And so on. Because prosentences never have any content of
their own, whatever explanatory burden one may wish for them to
shoulder will always fall to their anaphoric antecedents.
4. The Recognition-Transcendence of Truth
Unlike some alternatives to the correspondence theory (e.g., the
epistemic theories of truth of C. S. Peirce, Hilary Putnam, and
Michael Dummett), the prosentential theory accepts that truth can be
recognition-transcendent. Epistemic theories of truth always have
epistemic operators (e.g., 'justifiably believes that…,' 'warrantedly
asserts that…') of some sort on the right-hand side of their analyses
of truth. For example,
CSP) p is true iff the unlimited communication community in the
long run would believe that p.
HP) p is true iff one would be warranted in asserting that p in
ideal epistemic circumstances.
IJC) p is true iff it would be justifiable to believe that p in a
situation in which all relevant evidence (reasons, considerations) is
readily available. (due to Alston, 1996, p. 194)
Unlike correspondence and prosentential theories, epistemic theories
always mention the knowledge, assertions or justified beliefs of
particular people. Subjects and their beliefs do not figure into
correspondence and prosentential theories in any way.
Truth theories such as (CSP), (HP) and (IJC) have the implication that
there could not be any true propositions "such that nothing that tells
for or against their truth is cognitively [in]accessible to human
beings, even in principle" (Alston, 1996, p. 200). Summarizing a
common thread of epistemic theories of truth, Alston (1996, pp.
189-190) writes,
The truth of a truth bearer consists not in its relation to some
"transcendent" state of affairs, but in the epistemic virtues the
former displays within our thought, experience, and discourse. Truth
value is a matter of whether, or the extent to which, a belief is
justified, warranted, rational, well grounded, or the like.
According to prosentential theorists, truth theories like (CSP), (HP)
and (IJC) that focus on epistemic virtues are incompatible with the
various truth schemata used by deflationists to explicate the concept
of truth. Schemata such as
40) p is true iff p
represent facts about truth that are so fundamental and obvious that
the uninitiated often have difficulty seeing beyond their triviality
to the significance of the deflationary thesis.
According to (IJC), snow's being white is neither necessary nor
sufficient for the truth of 'snow is white' or the proposition that
snow is white. If it is possible for all relevant evidence to be
readily available and yet for this evidence to be unable to make a
belief that snow is white justifiable, then 'snow is white' will not
be true—even if snow is, in fact, white. Since this seems clearly
possible, snow's being white is not sufficient for the truth of 'snow
is white.' Moreover, if it is possible for all relevant evidence to be
readily available and for this evidence to make the belief that snow
is white justifiable even when snow is not white, then (since this
seems clearly possible) snow's being white is not necessary for the
truth of 'snow is white' either. Similar considerations apply to (CSP)
and (HP). Prosentential theorists claim that any theory which makes
snow's being white neither necessary nor sufficient for the truth of
'snow is white' is inadequate. The equivalence schemata simply do not
allow any room for the epistemic status of a proposition (or a belief
or statement) being both necessary and sufficient for that
proposition's truth. In the eyes of prosentential theorists, epistemic
theories of truth are incompatible with the equivalence schemata and
their instances.
By contrast, the prosentential theory embraces the
recognition-transcendence of truth. Truth schemata such as
40) p is true iff p
do not require that anyone be able to tell whether p is the case in
order for p to be true. In order for p to be true, nothing more is
required than p. No one has to be able to verify or warrantedly assert
it. The right-hand side of (40), then, does not limit truth to what
falls within our thought, experience and discourse. As a result, the
prosentential theory of truth is compatible with (though it neither
entails nor is entailed by) a robustly realist metaphysics. It is a
mistake to think that the correspondence theory is the only truth
theory a metaphysical realist can buy into and that any critic of the
correspondence theory will be an antirealist.
5. A Prosentential Theory of Falsity
The prosentential theory of truth can be extended to account for uses
of the predicate 'x is false.' The prosentential theory of falsity
will be strongly analogous to the prosentential theory of truth. The
prosentential theorist can claim that, just as the predicate 'x is
true' functions as a prosentence-forming operator, so does 'x is
false.' When an expression referring to an antecedent utterance is
substituted for 'x' in 'x is true,' the resulting claim will have the
same content as its anaphoric antecedent. By parity, when a referring
expression that denotes some antecedent utterance is substituted for
'x' in 'x is false,' the resulting claim will have the same content as
the denial of its anaphoric antecedent. Consider the following
example.
41) Joe: The sky is cloudy. Jane: That's true. Mark: That's false.
Jane's utterance has the same content as Joe's, namely, that the sky
is cloudy. Mark's utterance, on the other hand, has the same content
as the denial of Joe's utterance, namely,
42) The sky is not cloudy.
Mark's utterance inherits part of its content from its anaphoric
antecedent (that is, Joe's utterance), but his utterance includes an
extra bit of content not found in that antecedent: negation. Instances
of the prosentence-forming operator 'x is false,' then, will have the
same content as the negations of their antecedents.
6. The Liar Paradox
The prosentential theory of truth implies a solution to the liar
paradox. Consider the following sentence.
43) This sentence is false.
Is (43) true or false? If (43) says something true, then—since it says
that (43) itself is false—it says something false. However, if (43)
says something false, then—since it says that (43) is false—it says
something true, namely, that (43) is false. We are thus confronted
with a paradox.
Some attempts to solve the liar paradox involve extreme measures.
Tarski, for example, thought that the paradox could be avoided only by
eschewing 'semantically closed languages'—i.e., languages which
contain semantic terms that are applicable to sentences of that same
language. He maintained that a theory of truth for a language should
not be formulated within that same language. So, a theory of
truth-in-L1 must be formulated in some meta-language, L2. If we allow
the predicate 'x is true-in-L1' to be part of L1, paradoxes will
result. The predicate 'x is true-in-L1,' then, must be part of the
meta-language, L2. Since no well-formed sentence of L1 can be used to
talk about the truth value of any sentence in L1, there is no chance
for the liar paradox to arise because the basic liar sentence makes a
claim about its own truth value. Tarski succeeds in avoiding the basic
form of the liar paradox—but only at a very high price. He must
content himself with providing an account of 'true-in-Li' rather than
an account of truth. And, since natural languages like English are
semantically closed, Tarski's theory also has the weakness of applying
only to artificial languages.
Defenders of the prosentential theory claim that they can provide a
solution to the liar paradox that is more natural and comes with a
significantly lower price tag. According to the prosentential theory,
(43) is neither true nor false because it fails to pick up an
anaphoric antecedent. Just as I cannot inherit my own wealth, a
prosentence cannot inherit its content from itself. Anaphoric
inheritance is a non-reflexive relation that holds between two
distinct things. A prosentence has content only when content has been
passed to it from a content-bearing antecedent. Consequently, (43)
will have content only if its anaphoric antecedent does. But if (43)
is its own antecedent, (43) will have content only if (43) does. Since
prosentences do not have their own independent content, (43) fails to
have any content. Since it does not succeed in expressing a
proposition, the liar sentence is neither true nor false and the
paradox is avoided.
7. Objections
Philosophical objections to the prosentential theory of truth can be
divided into two main groups. One set of objections is directed
against Grover, Camp and Belnap's (1975) original version of the
theory; the other is directed against Brandom's (1994) updated
version. Originally, Grover, Camp and Belnap claimed that each
prosentence—e.g., 'it is true' or 'that is true'—referred as a whole
to an antecedent sentence token. Each occurrence of 'it' or 'that' in
a prosentence, they claimed, should not be interpreted as a referring
expression. In fact, 'it,' 'that' and '…is true' should not be treated
as having independent meanings at all. Grover, Camp and Belnap were
trying to undermine the idea that the truth predicate is a
property-ascribing locution. They thought that if 'it' and 'that' were
taken to be referring expressions, it would seem only too natural to
conclude that '…is true' ascribed a predicate to their referents.
One consequence of Grover, Camp and Belnap's commitment to the
non-composite nature of prosentences is that they are forced to find
non-composite prosentences in places where there do not seem to be
any. Consider, for example,
13) Goldbach's conjecture is true
and
14) 'Snow is white' is true.
Grover, Camp and Belnap must argue that, despite appearances, (13) and
(14) are not really composed of the referring expressions 'Goldbach's
conjecture' and ''Snow is white'' conjoined to the predicate '…is
true.' According to the original version of the prosentential theory,
the logical form of (13) is actually something like
13′) For any sentence, if it is Goldbach's conjecture, then it is true
or
13″) There is a unique sentence, such that Goldbach conjectured
that it is true, and it is true.
The logical form of (14) would be either
14′) For any sentence, if it is 'Snow is white,' then it is true
or
14″) Consider: snow is white. That is true. (Grover, Camp and
Belnap, p. 103)
(Each of these interpretations has been suggested by some
prosentential theorist.) In three of the four interpretations,
quantifiers are introduced so that the prosentence 'it is true' can
remain an unbroken unit. Universal quantifiers are used in (13() and
(14(), and an existential quantifier is used in (13″).
An obvious objection to Grover, Camp and Belnap's strategy is that it
seems quite unlikely that (13′) and (14′) or (13″) and (14″) reveal
the true logical structure of (13) and (14). There is no good reason
to suppose that the surface structure of (13) and (14) hides genuine
quantifiers below the surface. Furthermore, there are simply too many
uses of the truth predicate outside of the phrases 'it is true' and
'that is true' for Grover, Camp and Belnap's interpretation to be
plausible. (Cf. Brandom (1994, pp. 303-305) and Kirkham (1992, pp.
325-329) for more critical discussion of Grover, Camp and Belnap's
early version of the prosentential theory.)
Brandom (1994, pp. 303-305) has argued that prosentential theorists do
not need to treat 'it is true' and 'that is true' as non-composite
units. Instead, he claims that '…is true' should be treated as a
prosentence-forming operator. When it is conjoined to any kind of
referring expression, the resulting expression will have the same
content as the antecedent sentence or utterance denoted by the
referring expression. (This is the version of the prosentential theory
that I have been assuming throughout.) However, a different set of
problems confronts this version of the prosentential theory. Consider
the following example inspired by Wilson's (1990) criticisms of the
prosentential theory.
44) Steve: Boudreaux won the mayoral election. Kate: What that
conniving, good-for-nothing bum said was true.
If Brandom's version of the prosentential theory is correct, Kate's
utterance should have no more content than Steve's. Clearly, however,
Kate's remark does more than simply reassert the content of Steve's
remark. It casts aspersions on Steve's character. According to
Brandom's seemingly more defensible version of the prosentential
theory, a referring expression used at the head of a prosentence
serves only to pick out an antecedent from which the prosentence can
inherit its content. But referring expressions can be naughty or nice,
informative or dull. Once Brandom opens the door for prosentences to
be formed by conjoining any referring expression to the
prosentence-forming operator '…is true,' it seems that he can no
longer maintain that prosentences never have any more content than
their anaphoric antecedents. Referring expressions are not all like
proper names. Very often they bring with them a great deal more
content than is strictly necessary for them to succeed in referring. A
proper interpretation of prosentences cannot ignore this extra
content. (Cf. Wilson (1990) for more criticisms that apply to both
versions of the prosentential theory.)
8. Prosentential Theory vs. Other Deflationary Theories
According to F. P. Ramsey's redundancy theory, one of the earliest
deflationary theories, sentences such as
45) The earth is round
and
46) It is true that the earth is round
say exactly the same thing. The phrase "It is true" is a superfluous
addition. Ramsey did not, however, explain why phrases like "It is
true that…" or "…is true" exist at all if they serve no real purpose.
The prosentential theory incorporates Ramsey's claim about redundancy
of content in its account of the function of prosentences. Since
prosentences inherit their content from their anaphoric antecedents,
they will say the same thing as their antecedents. However, the
prosentential theory goes beyond the redundancy theory by providing an
explanation of why we have the truth predicate in our language.
Prosentences of laziness (e.g., "That's true" spoken after someone
utters "It's very humid in Louisiana"), it is argued, give us a way of
expressing agreement without having to repeat what has been said while
at the same time acknowledging that an assertion has been made. Also,
quantificational prosentences (e.g., "Everything Henry Kissinger says
is true") enable us to state generalizations when we might be unable
to state each individual instance of any such generalization.
The prosentential theory also tries to incorporates some of the
central claims of P. F. Strawson's performative theory of truth.
According to Strawson, statements such as "That's true" (uttered after
someone says that the sun is bright) or "It is true that the sun is
bright" are nonassertoric performative utterances. An utterance is
nonassertoric if it does not make an assertion. Commands (e.g., "Clean
your room") are examples of nonassertoric utterances because they do
not purport to state or describe any facts. Similarly, according to
Strawson, "It is true" (uttered after someone says that the sun is
bright) and "It is true that the sun is bright" do not assert that
some sentence or proposition has the property of being true. Rather,
these are performative utterances, which do not so much say something
as do something. In these cases the truth predicate is being used to
express agreement or to endorse some claim.
The prosentential theory follows Strawson's performative theory in
denying that the truth predicate ascribes a truth property to
propositions or statements. However, the prosentential theory does not
deny that prosentences—while they may very well be used to express
agreement—also assert something in the act of expressing this
agreement. In addition, the prosentential theory can accommodate one
type of case that causes trouble for the performative theory. Many
embedded uses of the truth predicate do not seem to be expressions of
agreement, as in "If what he said is true, we'll be out of this
building before winter." Such a use of the truth predicate may very
well not express agreement. The speaker may be unsure whether he
should endorse the claim and may be merely thinking hypothetically.
The prosentential theory does not require that every use of the truth
predicate be an expression of agreement—although they can be used to
do so. It explains that prosentences—even those that are embedded in
the antecedents of conditionals (e.g., "what he said is true")—inherit
their content from their anaphoric antecedents.
W. V. Quine's (1970) disquotational theory of truth views the truth
predicate as a convenient device of 'semantic ascent.' When, for
example,
we want to generalize on 'Tom is mortal or Tom is not mortal,'
'Snow is white or snow is not white,' and so on, we ascend to talk of
truth and of sentences, saying 'Every sentence of the form 'p or not
p' is true,' or 'Every alternation of a sentence with its negation is
true.' What prompts this semantic ascent is not that 'Tom is mortal or
Tom is not mortal' is somehow about sentences while 'Tom is mortal'
and 'Tom is Tom' are about Tom. All three are about Tom. We ascend
only because of the oblique way in which the instances over which we
are generalizing are related to one another. (Quine, 1970, p. 11)
The truth predicate, then, exists because it enables us to form
certain generalizations that would otherwise quite difficult to state
without some such device of semantic ascent. When, however, the truth
predicate is used with single sentences (e.g., "'Snow is white' is
true"), it is superfluous.
Defenders of the prosentential theory agree with Quine (1970, p. 12)
that, "despite a technical ascent to talk of sentences, our eye is on
the world" when we use the truth predicate. In other words, both
Quine's disquotationalism and the prosentential theory deny that the
truth predicate is used to ascribe a property to propositions. The
truth predicate, they claim, is used to say something about the world.
The prosentential theory also acknowledges the important role the
truth predicate plays in forming generalizations that might otherwise
be difficult or impossible to state (cf. the discussion of
quantificational prosentences above). Furthermore, both theories
explain truth by explaining the role of certain linguistic items
(e.g., devices of semantic ascent, prosentences) rather than focusing
on language-independent propositions and properties.
However, unlike disquotationalism, the prosentential theory recognizes
that there are many uses of the truth predicate in which there is
nothing to disquote. For example, in the sentence "Goldbach's
conjecture is true," there are no quotation marks to be removed.
Instead of being used in connection with an entire sentence, here the
truth predicate is joined to an expression ('Goldbach's conjecture')
referring to an antecedent sentence. It is not clear how the
disquotational theory might be extended to cover this kind of case.
The prosentential theory explains that any referring expression (e.g.,
a name, definite description, etc.) inherits its content from its
anaphoric antecedent(s) and, when such an expression is conjoined to
the truth predicate, a prosentence with the same content as the
antecedent(s) results.
Paul Horwich's minimalist theory of truth (1998)—unlike the
prosentential theory and some other deflationary theories—takes the
primary bearers of truth to be propositions rather than sentences or
utterances. Horwich claims that the conjunction of all the instances
of the schema
MT) The proposition that p is true iff p
yields an implicit definition of truth. Each instance is an axiom of
his theory. How many instances are there? There's one for every
possible proposition, including propositions no human being
understands and maybe even a few that no human being could ever
understand. In other words, there are infinitely many. Horwich claims
that there is nothing more to our concept of truth than our
disposition to assent to each of the instances of (MT).
Horwich and defenders of the prosentential theory agree in thinking
that no analysis of truth can be given. Horwich, however, thinks that
the truth predicate does expresses a property, since he believes that
all predicates express properties in some minimal sense. Although the
prosentential theory is typically described as denying that "true"
expresses a property of any sort (see, for example, Lynch, 2001, p.
4), the writings of Dorothy Grover (1992)—the primary defender of the
prosentential theory—are far from clear on the issue of predicates and
properties. Grover claims that the truth predicate is not used to
ascribe a property to propositions, but this is compatible with the
truth predicate expressing a property in a minimal sense (à la
Horwich) nonetheless. The fact that a certain Rolex is not used as a
paperweight does not mean that it lacks the property of being able to
weigh down papers. Grover also claims that truth is not a substantive
or naturalistic property, but this claim is compatible with truth
being an insubstantial or nonnaturalistic property (also à la
Horwich). Since Grover does not sufficiently explain her remarks about
substantive or naturalistic properties, it is difficult to tell how
close her prosentential theory actually is to Horwich on this issue.
Brandom's (1994, ch. 5) discussion of the prosentential theory does
not even broach the issue.
What is clear is that Horwich and defenders of the prosentential
theory disagree about the virtues of the substitution interpretation
of the quantifiers. Horwich recognizes that if he used substitutional
quantifiers, his theory would be finitely statable. He explains,
however, that substitutional quantifiers would be too costly an
addition to our language: "The advantage of the truth predicate is
that it allows us to say what we want without having to employ any new
linguistic apparatus of this sort" (Horwich, 1998, p. 4, n. 1).
Horwich also harbors doubts about whether we can spell out the notion
of substitutional quantification without circularly relying upon the
notion of truth (Horwich, 1998, pp. 25-26). In making this last
remark, Horwich is thinking of Grover, Camp and Belnap's unusual
thesis that every use of a prosentence—even "'Snow is white' is
true"—implicitly contains a quantifier. (Cf. section VII for more
discussion of this point.) Since substitutional quantifiers must be
brought in to explain every use of a prosentence, Grover, Camp and
Belnap cannot explain substitutional quantification in terms of truth.
However, Brandom's (1994) version of the prosentential theory does not
use substitutional quantification to explain the function of the truth
predicate. He argues that, although quantificational prosentences
employ substitutional quantification, lazy uses of prosentences—which
are more fundamental than their quantificational cousins—do not (cf.
section II above). Brandom, thus, avoids the problem of circularity.
9. References and Further Reading
* Alston, W. P. (1996). A realistic conception of truth. Ithaca,
NY: Cornell University Press.
* Beebe, J. R. (forthcoming). Attributive uses of prosentences. Ratio.
* Belnap, Jr., N. D. (1973). Restricted quantification and
conditional assertion. In H. Leblanc (Ed.), Truth, syntax and modality
(pp. 48-75). Amsterdam: North Holland Publishing Co.
* Brandom, R. B. (1994). Making it explicit: Reasoning,
representing, and discursive commitment. Cambridge, Mass.: Harvard
University Press.
* David, M. (1994). Correspondence and disquotation. New York:
Oxford University Press.
* Grover, D. (1992). A prosentential theory of truth. Princeton,
NJ: Princeton University Press.
* Grover, D., Camp, Jr., J., & Belnap, Jr., N. D. (1975). A
prosentential theory of truth. Philosophical Studies, 27, 73-124.
* Horwich, P. (1998). Truth (2nd ed.). New York: Oxford University Press.
* Kirkham, R. L. (1992). Theories of truth: A critical
introduction. Cambridge, MA: MIT Press.
* Lynch, M. P. (2001). Introduction: The mystery of truth. In M.
P. Lynch (Ed.), The nature of truth: Classic and contemporary
perspectives (pp. 1-6). Cambridge, MA: MIT Press.
* Quine, W. V. (1970). Philosophy of logic. Englewood Cliffs, NJ:
Prentice-Hall.
* Stich, S. P. (1990). The fragmentation of reason: Preface to a
pragmatic theory of cognitive evaluation. Cambridge, MA: MIT Press.
* Wilson, W. K. (1990). Some reflections on the prosentential
theory of truth. In J. M. Dunn & A. Gupta (Eds.), Truth or
consequences (pp. 19-32). Dordrecht: Kluwer Academic Publishers.
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