Nasir al-Din Tusi (1201—1274)

Nasir al-Din Tusi, by far the most celebrated scholar of the 13th
century Islamic lands, was born in Tus, in 1201 and died in Baghdad in
1274. He was apparently born into a Twelver Shi'i family. At the age
of twenty-two or a while later, Tusi joined the court of Nasir al-Din
Muhtashim, the Ismaili governor of Quhistan, Northeast Iran, where he
was accepted into the Ismaili community as a novice.Around 634/1236,
we find Tusi in Alamut, the centre of Nizari Ismaili government. He
seems to have climbed the ranks of the Ismaili da'wat ascending to the
position of chief missionary (da'i al-du'at). The collapse of Ismaili
political power and the massacre of the Ismaili population, during the
Mongol invasion, left no choice for Tusi except the exhibition of some
sort of affiliation to Twelver Shi'ism and denouncing his Ismaili
allegiances (taqiyya).

In the Mongol court, Tusi witnessed the fall of the 'Abbasid caliphate
and after a while, securing the trust of Hulegu, the Mongol chief, he
was given the full authority of administering the finances of
religious foundations (awqaf). The ensemble of Tusi's writings amounts
to approximately 165 titles on a wide variety of subjects (astronomy,
ethics, history, jurisprudence, logic, mathematics, medicine,
philosophy, theology, poetry and the popular sciences).

Nasir al-Din Tusi, Muhammad b. Muhammad b. Hasan, by far the most
celebrated scholar of the 7th/13th century Islamic lands was born in
Tus, in 597/1201 and died in Baghdad on 18 Dhu'l Hijja 672/25 June,
1274. Thomas Aquinas and Roger Bacon were his contemporaries in the
West. Very little is known about his childhood and early education,
apart from what he writes in his autobiography, Contemplation and
Action (Sayr wa suluk).

He was apparently born into a Twelver Shi'i family and lost his father
at a young age. Fulfilling the wish of his father, the young Muhammad
took learning and scholarship very seriously and travelled far and
wide to attend the lectures of renowned scholars and 'acquire the
knowledge which guides people to the happiness of the next world.' As
a young boy, Tusi studied mathematics with Kamal al-Diin Hasib about
whom we have no authentic knowledge. In Nishabur he met Farid al-Din
'Attar, the legendary Sufi master who was later killed in the hand of
Mongol invaders and attended the lectures of Qutb al-Din Misri and
Farid al-Din Damad. In Mawsil he studied mathematics and astronomy
with Kamal al-Din Yunus (d. 639/1242). Later on he corresponded with
Qaysari, the son-in-law of Ibn al-'Arabi, and it seems that mysticism,
as propagated by Sufi masters of his time, was not appealing to his
mind and once the occasion was suitable, he composed his own manual of
philosophical Sufism in the form of a small booklet entitled The
Attributes of the Illustrious (Awsaf al-ashraf).

His ability and talent in learning enabled Tusi to master a number
disciplines in a relatively short period. At the time when educational
priorities leaned towards the religious sciences, especially in his
own family who were associated with the Twelver Shi'i clergy, Tusi
seems to have shown great interest for mathematics, astronomy and the
intellectual sciences. At the age of twenty-two or a while later, Tusi
joined the court of Nasir al-Din Muhtashim, the Ismaili governor of
Quhistan, Northeast Iran, where he was accepted into the Ismaili
community as a novice (mustajib). A sign of close personal
relationship with Muhtashim's family is to be seen in the dedication
of a number of his scholarly works such as Akhlaq-i Nasiri and
Akhlaq-i Muhtashimi to Nasir al-Din himself and Risala-yi Mu'iniyya to
his son Mu'in al-Din.

Around 634/1236, we find Tusi in Alamut, the centre of Nizari Ismaili
government. The scholarly achievements of Tusi in the compilation of
Akhlaq-i Nasiri in 633/1235, seems to, amongst other factors, have
paved the way for this move which was a great honour and opportunity
for a scholar of his calibre, especially since Alamut was the seat of
the Ismaili imam and housed the most important library in the Ismaili
state.

In Alamut, apart from teaching, editing, dictating and compiling
scholarly works, Tusi seems to have climbed the ranks of the Ismaili
da'wat ascending to the position of chief missionary (da'i al-du'at).
Through constant visits with scholars and tireless correspondences, a
practice which he developed from a very young age, Tusi kept his
contact with the academic world outside Ismaili circles and was
addressed as 'the scholar' (al-muhaqiq) from a very early period in
his life.

The Mongol invasion and the turmoil they caused in the eastern Islamic
territories hardly left the life of any of its citizens untouched. The
collapse of Ismaili political power and the massacre of the Ismaili
population, who were a serious threat to the Mongols, left no choice
for Tusi except the exhibition of some sort of affiliation to Twelver
Shi'ism and denouncing his Ismaili allegiances.

Although under Mongol domination, Tusi's allegiance to any particular
community or persuasion could not have been of any particular
importance, the process itself paved the ground for Tusi to write on
various aspects of Shi'ism, both from Ismaili and Twelver Shi'i
viewpoints, with scholarly vigour and enthusiasm. The most famous of
his Ismaili compilations are Rawda-yi taslim, Sayr wa suluk, Tawalla
wa tabarra, Akhlaq-i Muhtashimi and Matlub al-mu'minin. Tajrid
al-i'tiqad, al-Risala fi'l-imama and Fusul-i Nasiriyya are among his
works dedicated to Twelver Shi'ism.

In the Mongol court, Tusi witnessed the fall of the 'Abbasid caliphate
and after a while, securing the trust of Hulegu, the Mongol chief, he
was given the full authority of administering the finances of
religious foundations (awqaf). During this period of his life, Tusi's
main concern was combating Mongol savagery, saving the life of
innocent scholars and the establishment of one of the most important
centres of learning in Maragha, Northwest Iran. The compilation of
Musari'at al-musari;, the Awsaf al-ashraf and Talkis al-muhassal are
the scholarly writings of Tusi in the final years of his life.

The ensemble of Tusi's writings amounts to approximately 165 titles on
a wide variety of subjects. Some of them are simply a page or even
half a page, but the majority with few exceptions, are well prepared
scholarly works on astronomy, ethics, history, jurisprudence, logic,
mathematics, medicine, philosophy, theology, poetry and the popular
sciences. Tusi's fame in his own lifetime guaranteed the survival of
almost all of his scholarly output. The adverse effect of his fame is
also the attribution of a number of works which neither match his
style nor has the quality of his writings.

Tusi's major works: (1) Astronomy: al-Tadhkira fi 'ilm al-hay'a; Zij
Ilkhani; Risala-yi Mu'iniyya and its commentary. (2) Ethics:
Gushayish-nama; Akhlaq-i Muhtashami; Akhlaq-i Nasiri, 'Deliberation
22' in Rawda-yi taslim and a Persian translation of Ibn Muqaffa''s
al-Adab al-wajiz. (3) History: Fath-i Baghdad which appears as an
appendix to Tarikh-i Jahan-gushay of Juwayni (London, 1912-27), vol.
3, pp. 280-92. (4) Jurisprudence: Jawahir al-fara'id. (5) Logic: Asas
al-iqtibas. (6) Mathematics: Revision of Ptolemy's Almagest; the
epistles of Theodosius, Hypsicles, Autolucus, Aristarchus, Archimedes,
Menelaus, Thabit b. Qurra and Banu Musa. (7) Medicine: Ta'liqa bar
qunun-i Ibn Sina and his correspondences with Qutb al-Din Shirazi and
Katiban Qazwini. (8) Philosophy: refutation of al-Shahrastani in
Musara'at al-musari'; his commentary on Ibn Sina's al-Isharat
wa'l-tanbihat which took him almost 20 years to complete; his
autobiography Sayr wa suluk; Rawda-yi taslim and Tawalla wa tabarra.
(9) Theology: Aghaz wa anjam; Risala fi al-imama and Talkhis
al-muhassal and (10) Poetry: Mi'yar al-ash'ar.
References and Further Reading

* Badakhchani, S. J. Contemplation and Action: The Spiritual
Autobiography of a Muslim Scholar (London, I. B. Tauris in association
with The Institute of Ismaili Studies, 1998).
* Mudarris Radawi, Muhammad. Ahwal wa athar-i Abu Ja'far Muhammad
b. Muhammad b. Hasan al-Tusi. Tehran, Intisharat-i Danishgah-i Tehran,
1345s/1975.
* Mudarrisi Zanjani, Muhammad. Sargudhasht wa 'aqa'id-i falsafi-yi
Khwaja Nasir al-Din Tusi. Tehran, Intisharat-i Danishgah-i Tehran,
1363s/1984.
* Madelung, Wilferd. 'Nasir al-Din Tusi's Ethics Between
Philosophy, Shi'ism and Sufism,' in Ethics in Islam, ed. R. G.
Hovannisian, Malibu, CA, 1985, pp. 85-101.

Prosentential Theory of Truth

Prosentential theorists claim that sentences such as "That's true" are
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.

Truth

Philosophers are interested in a constellation of issues involving the
concept of truth. A preliminary issue, although somewhat subsidiary,
is to decide what sorts of things can be true. Is truth a property of
sentences (which are linguistic entities in some language or other),
or is truth a property of propositions (nonlinguistic, abstract and
timeless entities)? The principal issue is: What is truth? It is the
problem of being clear about what you are saying when you say some
claim or other is true. The most important theories of truth are the
Correspondence Theory, the Semantic Theory, the Deflationary Theory,
the Coherence Theory, and the Pragmatic Theory. They are explained and
compared here. Whichever theory of truth is advanced to settle the
principal issue, there are a number of additional issues to be
addressed:

1. Can claims about the future be true now?
2. Can there be some algorithm for finding truth – some recipe or
procedure for deciding, for any claim in the system of, say,
arithmetic, whether the claim is true?
3. Can the predicate "is true" be completely defined in other terms
so that it can be eliminated, without loss of meaning, from any
context in which it occurs?
4. To what extent do theories of truth avoid paradox?
5. Is the goal of scientific research to achieve truth?

1. The Principal Problem

The principal problem is to offer a viable theory as to what truth
itself consists in, or, to put it another way, "What is the nature of
truth?" To illustrate with an example – the problem is not: Is it true
that there is extraterrestrial life? The problem is: What does it mean
to say that it is true that there is extraterrestrial life?
Astrobiologists study the former problem; philosophers, the latter.

This philosophical problem of truth has been with us for a long time.
In the first century AD, Pontius Pilate (John 18:38) asked "What is
truth?" but no answer was forthcoming. The problem has been studied
more since the turn of the twentieth century than at any other
previous time. In the last one hundred or so years, considerable
progress has been made in solving the problem.

The three most widely accepted contemporary theories of truth are [i]
the Correspondence Theory ; [ii] the Semantic Theory of Tarski and
Davidson; and [iii] the Deflationary Theory of Frege and Ramsey. The
competing theories are [iv] the Coherence Theory , and [v] the
Pragmatic Theory . These five theories will be examined after
addressing the following question.
2. What Sorts of Things are True (or False)?

Although we do speak of true friends and false identities,
philosophers believe these are derivative uses of "true" and "false".
The central use of "true", the more important one for philosophers,
occurs when we say, for example, it's true that Montreal is north of
Pittsburgh. Here,"true" is contrasted with "false", not with "fake" or
"insincere". When we say that Montreal is north of Pittsburgh, what
sort of thing is it that is true? Is it a statement or a sentence or
something else, a "fact", perhaps? More generally, philosophers want
to know what sorts of things are true and what sorts of things are
false. This same question is expressed by asking: What sorts of things
have (or bear) truth-values?

The term "truth-value" has been coined by logicians as a generic term
for "truth or falsehood". To ask for the truth-value of P, is to ask
whether P is true or whether P is false. "Value" in "truth-value" does
not mean "valuable". It is being used in a similar fashion to
"numerical value" as when we say that the value of "x" in "x + 3 = 7″
is 4. To ask "What is the truth-value of the statement that Montreal
is north of Pittsburgh?" is to ask whether the statement that Montreal
is north of Pittsburgh is true or whether it is false. (The
truth-value of that specific statement is true.)

There are many candidates for the sorts of things that can bear truth-values:

* statements
* sentence-tokens
* sentence-types
* propositions
* theories
* facts

* assertions
* utterances
* beliefs
* opinions
* doctrines
* etc.

a. Ontological Issues

What sorts of things are these candidates? In particular, should the
bearers of truth-values be regarded as being linguistic items (and, as
a consequence, items within specific languages), or are they
non-linguistic items, or are they both? In addition, should they be
regarded as being concrete entities, i.e., things which have a
determinate position in space and time, or should they be regarded as
abstract entities, i.e., as being neither temporal nor spatial
entities?

Sentences are linguistic items: they exist in some language or other,
either in a natural language such as English or in an artificial
language such as a computer language. However, the term "sentence" has
two senses: sentence-token and sentence-type. These three English
sentence-tokens are all of the same sentence-type:

* Saturn is the sixth planet from the Sun.
* Saturn is the sixth planet from the Sun.
* Saturn is the sixth planet from the Sun.

Sentence-tokens are concrete objects. They are composed of ink marks
on paper, or sequences of sounds, or patches of light on a computer
monitor, etc. Sentence-tokens exist in space and time; they can be
located in space and can be dated. Sentence-types cannot be. They are
abstract objects. (Analogous distinctions can be made for letters, for
words, for numerals, for musical notes on a stave, indeed for any
symbols whatsoever.)

Might sentence-tokens be the bearers of truth-values?

One reason to favor tokens over types is to solve the problems
involving so-called "indexical" (or "token reflexive") terms such as
"I" and "here" and "now". Is the claim expressed by the sentence-type
"I like chocolate" true or false? Well, it depends on who "I" is
referring to. If Jack, who likes chocolate, says "I like chocolate",
then what he has said is true; but if Jill, who dislikes chocolate,
says "I like chocolate", then what she has said is false. If it were
sentence-types which were the bearers of truth-values, then the
sentence-type "I like chocolate" would be both true and false – an
unacceptable contradiction. The contradiction is avoided, however, if
one argues that sentence-tokens are the bearers of truth-values, for
in this case although there is only one sentence-type involved, there
are two distinct sentence-tokens.

A second reason for arguing that sentence-tokens, rather than
sentence-types, are the bearers of truth-values has been advanced by
nominalist philosophers. Nominalists are intent to allow as few
abstract objects as possible. Insofar as sentence-types are abstract
objects and sentence-tokens are concrete objects, nominalists will
argue that actually uttered or written sentence-tokens are the proper
bearers of truth-values.

But the theory that sentence-tokens are the bearers of truth-values
has its own problems. One objection to the nominalist theory is that
had there never been any language-users, then there would be no
truths. (And the same objection can be leveled against arguing that it
is beliefs that are the bearers of truth-values: had there never been
any conscious creatures then there would be no beliefs and, thus, no
truths or falsehoods, not even the truth that there were no conscious
creatures – an unacceptably paradoxical implication.)

And a second objection – to the theory that sentence-tokens are the
bearers of truth-values – is that even though there are
language-users, there are sentences that have never been uttered and
never will be. (Consider, for example, the distinct number of
different ways that a deck of playing cards can be arranged. The
number, 8×1067 [the digit "8" followed by sixty-seven zeros], is so
vast that there never will be enough sentence-tokens in the world's
past or future to describe each unique arrangement. And there are
countless other examples as well.) Sentence-tokens, then, cannot be
identified as the bearers of truth-values – there simply are too few
sentence-tokens.

Thus both theories – (i) that sentence-tokens are the bearers of
truth-values, and (ii) that sentence-types are the bearers of
truth-values – encounter difficulties. Might propositions be the
bearers of truth-values?

To escape the dilemma of choosing between tokens and types,
propositions have been suggested as the primary bearers of
truth-values.

The following five sentences are in different languages, but they all
are typically used to express the same proposition or statement.

Saturn is the sixth planet from the Sun. [English]
Saturn je šestá planeta od slunce. [Czech]
Saturne est la sixième planète la plus éloignée du soleil. [French]
[Hebrew]
Saturn er den sjette planeten fra solen. [Norwegian]

The truth of the proposition that Saturn is the sixth planet from the
Sun depends only on the physics of the solar system, and not in any
obvious way on human convention. By contrast, what these five
sentences say does depend partly on human convention. Had English
speakers chosen to adopt the word "Saturn" as the name of a different
particular planet, the first sentence would have expressed something
false. By choosing propositions rather than sentences as the bearers
of truth-values, this relativity to human conventions does not apply
to truth, a point that many philosophers would consider to be a virtue
in a theory of truth.

Propositions are abstract entities; they do not exist in space and
time. They are sometimes said to be "timeless", "eternal", or
"omnitemporal" entities. Terminology aside, the essential point is
that propositions are not concrete (or material) objects. Nor, for
that matter, are they mental entities; they are not "thoughts" as
Frege had suggested in the nineteenth century. The theory that
propositions are the bearers of truth-values also has been criticized.
Nominalists object to the abstract character of propositions. Another
complaint is that it's not sufficiently clear when we have a case of
the same propositions as opposed to similar propositions. This is much
like the complaint that we can't determine when two sentences have
exactly the same meaning. The relationship between sentences and
propositions is a serious philosophical problem.

Because it is the more favored theory, and for the sake of expediency
and consistency, the theory that propositions – and not sentences –
are the bearers of truth-values will be adopted in this article. When
we speak below of "truths", we are referring to true propositions. But
it should be pointed out that virtually all the claims made below have
counterparts in nominalistic theories which reject propositions.
b. Constraints on Truth and Falsehood

There are two commonly accepted constraints on truth and falsehood:

Every proposition is true or false. [Law of the Excluded Middle.]
No proposition is both true and false. [Law of Non-contradiction.]

These constraints require that every proposition has exactly one
truth-value. Although the point is controversial, most philosophers
add the further constraint that a proposition never changes its
truth-value in space or time. Consequently, to say "The proposition
that it's raining was true yesterday but false today" is to equivocate
and not actually refer to just one proposition. Similarly, when
someone at noon on January 15, 2000 in Vancouver says that the
proposition that it is raining is true in Vancouver while false in
Sacramento, that person is really talking of two different
propositions: (i) that it rains in Vancouver at noon on January 15,
2000 and (ii) that it rains in Sacramento at noon on January 15, 2000.
The person is saying proposition (i) is true and (ii) is false.
c. Which Sentences Express Propositions?

Not all sentences express propositions. The interrogative sentence
"Who won the World Series in 1951?" does not; neither does the
imperative sentence "Please close the window." Declarative (that is,
indicative) sentences – rather than interrogative or imperative
sentences – typically are used to express propositions.
d. Problem Cases

But do all declarative sentences express propositions? The following
four kinds of declarative sentences have been suggested as not being
typically used to express propositions, but all these suggestions are
controversial.

1. Sentences containing non-referring expressions

In light of the fact that France has no king, Strawson argued that the
sentence, "The present king of France is bald", fails to express a
proposition. In a famous dispute, Russell disagreed with Strawson,
arguing that the sentence does express a proposition, and more
exactly, a false one.

2. Predictions of future events

What about declarative sentences that refer to events in the future?
For example, does the sentence "There will be a sea battle tomorrow"
express a proposition? Presumably, today we do not know whether there
will be such a battle. Because of this, some philosophers (including
Aristotle who toyed with the idea) have argued that the sentence, at
the present moment, does not express anything that is now either true
or false. Another, perhaps more powerful, motivation for adopting this
view is the belief that if sentences involving future human actions
were to express propositions, i.e., were to express something that is
now true or false, then humans would be determined to perform those
actions and so humans would have no free will. To defend free will,
these philosophers have argued, we must deny truth-values to
predictions.

This complicating restriction – that sentences about the future do not
now express anything true or false – has been attacked by Quine and
others. These critics argue that the restriction upsets the logic we
use to reason with such predictions. For example, here is a
deductively valid argument involving predictions:

We've learned there will be a run on the bank tomorrow.
If there will be a run on the bank tomorrow, then the CEO should
be awakened.
So, the CEO should be awakened.

Without assertions in this argument having truth-values, regardless of
whether we know those values, we could not assess the argument using
the canons of deductive validity and invalidity. We would have to say
– contrary to deeply-rooted philosophical intuitions – that it is not
really an argument at all. (For another sort of rebuttal to the claim
that propositions about the future cannot be true prior to the
occurrence of the events described, see Logical Determinism.)

3. Liar Sentences

"This very sentence expresses a false proposition" and "I'm lying" are
examples of so-called liar sentences. A liar sentence can be used to
generate a paradox when we consider what truth-value to assign it. As
a way out of paradox, Kripke suggests that a liar sentence is one of
those rare declarative sentences that does not express a proposition.
The sentence falls into the truth-value gap. See the article Liar
Paradox.

4. Sentences that state moral, ethical, or aesthetic values

Finally, we mention the so-called "fact/value distinction." Throughout
history, moral philosophers have wrestled with the issue of moral
realism. Do sentences such as "Torturing children is wrong" – which
assert moral principles – assert something true (or false), or do they
merely express (in a disguised fashion) the speaker's opinions, or
feelings or values? Making the latter choice, some philosophers argue
that these declarative sentences do not express propositions.
3. Correspondence Theory

We return to the principal question, "What is truth?" Truth is
presumably what valid reasoning preserves. It is the goal of
scientific inquiry, historical research, and business audits. We
understand much of what a sentence means by understanding the
conditions under which what it expresses is true. Yet the exact nature
of truth itself is not wholly revealed by these remarks.

Historically, the most popular theory of truth was the Correspondence
Theory. First proposed in a vague form by Plato and by Aristotle in
his Metaphysics, this realist theory says truth is what propositions
have by corresponding to a way the world is. The theory says that a
proposition is true provided there exists a fact corresponding to it.
In other words, for any proposition p,

p is true if and only if p corresponds to a fact.

The theory's answer to the question, "What is truth?" is that truth is
a certain relationship—the relationship that holds between a
proposition and its corresponding fact. Perhaps an analysis of the
relationship will reveal what all the truths have in common.

Consider the proposition that snow is white. Remarking that the
proposition's truth is its corresponding to the fact that snow is
white leads critics to request an acceptable analysis of this notion
of correspondence. Surely the correspondence is not a word by word
connecting of a sentence to its reference. It is some sort of exotic
relationship between, say, whole propositions and facts. In presenting
his theory of logical atomism early in the twentieth century, Russell
tried to show how a true proposition and its corresponding fact share
the same structure. Inspired by the notion that Egyptian hieroglyphs
are stylized pictures, his student Wittgenstein said the relationship
is that of a "picturing" of facts by propositions, but his development
of this suggestive remark in his Tractatus Logico-Philosophicus did
not satisfy many other philosophers, nor after awhile, even
Wittgenstein himself.

And what are facts? The notion of a fact as some sort of ontological
entity was first stated explicitly in the second half of the
nineteenth century. The Correspondence Theory does permit facts to be
mind-dependent entities. McTaggart, and perhaps Kant, held such
Correspondence Theories. The Correspondence theories of Russell,
Wittgenstein and Austin all consider facts to be mind-independent. But
regardless of their mind-dependence or mind-independence, the theory
must provide answers to questions of the following sort. "Canada is
north of the U.S." can't be a fact. A true proposition can't be a fact
if it also states a fact, so what is the ontological standing of a
fact? Is the fact that corresponds to "Brutus stabbed Caesar" the same
fact that corresponds to "Caesar was stabbed by Brutus", or is it a
different fact? It might be argued that they must be different facts
because one expresses the relationship of stabbing but the other
expresses the relationship of being stabbed, which is different. In
addition to the specific fact that ball 1 is on the pool table and the
specific fact that ball 2 is on the pool table, and so forth, is there
the specific fact that there are fewer than 1,006,455 balls on the
table? Is there the general fact that many balls are on the table?
Does the existence of general facts require there to be the Forms of
Plato or Aristotle? What about the negative proposition that there are
no pink elephants on the table? Does it correspond to the same
situation in the world that makes there be no green elephants on the
table? The same pool table must involve a great many different facts.
These questions illustrate the difficulty in counting facts and
distinguishing them. The difficulty is well recognized by advocates of
the Correspondence Theory, but critics complain that characterizations
of facts too often circle back ultimately to saying facts are whatever
true propositions must correspond to in order to be true. Davidson has
criticized the notion of fact, arguing that "if true statements
correspond to anything, they all correspond to the same thing" (in
"True to the Facts", Davidson [1984]). Davidson also has argued that
facts really are the true statements themselves; facts are not named
by them, as the Correspondence Theory mistakenly supposes.

Defenders of the Correspondence Theory have responded to these
criticisms in a variety of ways. Sense can be made of the term
"correspondence", some say, because speaking of propositions
corresponding to facts is merely making the general claim that
summarizes the remark that

(i) The sentence, "Snow is white", means that snow is white, and
(ii) snow actually is white,

and so on for all the other propositions. Therefore, the
Correspondence theory must contain a theory of "means that" but
otherwise is not at fault. Other defenders of the Correspondence
Theory attack Davidson's identification of facts with true
propositions. Snow is a constituent of the fact that snow is white,
but snow is not a constituent of a linguistic entity, so facts and
true statements are different kinds of entities.

Recent work in possible world semantics has identified facts with sets
of possible worlds. The fact that the cat is on the mat contains the
possible world in which the cat is on the mat and Adolf Hitler
converted to Judaism while Chancellor of Germany. The motive for this
identification is that, if sets of possible worlds are metaphysically
legitimate and precisely describable, then so are facts.
4. Tarski's Semantic Theory

tarskiTo capture what he considered to be the essence of the
Correspondence Theory, Alfred Tarski created his Semantic Theory of
Truth. In Tarski's theory, however, talk of correspondence and of
facts is eliminated. (Although in early versions of his theory, Tarski
did use the term "correspondence" in trying to explain his theory, he
later regretted having done so, and dropped the term altogether since
it plays no role within his theory.) The Semantic Theory is the
successor to the Correspondence Theory. It seeks to preserve the core
concept of that earlier theory but without the problematic conceptual
baggage.

For an illustration of the theory, consider the German sentence
"Schnee ist weiss" which means that snow is white. Tarski asks for the
truth-conditions of the proposition expressed by that sentence: "Under
what conditions is that proposition true?" Put another way: "How shall
we complete the following in English: 'The proposition expressed by
the German sentence "Schnee ist weiss" is true …'?" His answer:
T: The proposition expressed by the German sentence "Schnee ist
weiss" is true if and only if snow is white.

We can rewrite Tarski's T-condition on three lines:

1. The proposition expressed by the German sentence "Schnee ist
weiss" is true
2. if and only if
3. snow is white

Line 1 is about truth. Line 3 is not about truth – it asserts a claim
about the nature of the world. Thus T makes a substantive claim.
Moreover, it avoids the main problems of the earlier Correspondence
Theories in that the terms "fact" and "correspondence" play no role
whatever.

A theory is a Tarskian truth theory for language L if and only if, for
each sentence S of L, if S expresses the proposition that p, then the
theory entails a true "T-proposition" of the bi-conditional form:
(T) The proposition expressed by S-in-L is true, if and only if p.

In the example we have been using, namely, "Schnee ist weiss", it is
quite clear that the T-proposition consists of a containing (or
"outer") sentence in English, and a contained (or "inner" or quoted)
sentence in German:
T: The proposition expressed by the German sentence "Schnee ist
weiss" is true if and only if snow is white.

There are, we see, sentences in two distinct languages involved in
this T-proposition. If, however, we switch the inner, or quoted
sentence, to an English sentence, e.g. to "Snow is white", we would
then have:
T: The proposition expressed by the English sentence "Snow is
white" is true if and only if snow is white.

In this latter case, it looks as if only one language (English), not
two, is involved in expressing the T-proposition. But, according to
Tarski's theory, there are still two languages involved: (i) the
language one of whose sentences is being quoted and (ii) the language
which attributes truth to the proposition expressed by that quoted
sentence. The quoted sentence is said to be an element of the object
language, and the outer (or containing) sentence which uses the
predicate "true" is in the metalanguage.

Tarski discovered that in order to avoid contradiction in his semantic
theory of truth, he had to restrict the object language to a limited
portion of the metalanguage. Among other restrictions, it is the
metalanguage alone that contains the truth-predicates, "true" and
"false"; the object language does not contain truth-predicates.

It is essential to see that Tarski's T-proposition is not saying:
X: Snow is white if and only if snow is white.

This latter claim is certainly true (it is a tautology), but it is no
significant part of the analysis of the concept of truth – indeed it
does not even use the words "true" or "truth", nor does it involve an
object language and a metalanguage. Tarski's T-condition does both.
a. Extending the Semantic Theory Beyond "Simple" Propositions

Tarski's complete theory is intended to work for (just about) all
propositions, expressed by non-problematic declarative sentences, not
just "Snow is white." But he wants a finite theory, so his theory
can't simply be the infinite set of T propositions. Also, Tarski wants
his truth theory to reveal the logical structure within propositions
that permits valid reasoning to preserve truth. To do all this, the
theory must work for more complex propositions by showing how the
truth-values of these complex propositions depend on their parts, such
as the truth-values of their constituent propositions. Truth tables
show how this is done for the simple language of Propositional Logic
(e.g. the complex proposition expressed by "A or B" is true, according
to the truth table, if and only if proposition A is true, or
proposition B is true, or both are true).

Tarski's goal is to define truth for even more complex languages.
Tarski's theory does not explain (analyze) when a name denotes an
object or when an object falls under a predicate; his theory begins
with these as given. He wants what we today call a model theory for
quantified predicate logic. His actual theory is very technical. It
uses the notion of Gödel numbering, focuses on satisfaction rather
than truth, and approaches these via the process of recursion. The
idea of using satisfaction treats the truth of a simple proposition
such as expressed by "Socrates is mortal" by saying:

If "Socrates" is a name and "is mortal" is a predicate, then
"Socrates is mortal" expresses a true proposition if and only if there
exists an object x such that "Socrates" refers to x and "is mortal" is
satisfied by x.

For Tarski's formal language of predicate logic, he'd put this more
generally as follows:

If "a" is a name and "Q" is a predicate, then "a is Q" expresses a
true proposition if and only if there exists an object x such that "a"
refers to x and "Q" is satisfied by x.

The idea is to define the predicate "is true" when it is applied to
the simplest (that is, the non-complex or atomic) sentences in the
object language (a language, see above, which does not, itself,
contain the truth-predicate "is true"). The predicate "is true" is a
predicate that occurs only in the metalanguage, i.e., in the language
we use to describe the object language. At the second stage, his
theory shows how the truth predicate, when it has been defined for
propositions expressed by sentences of a certain degree of grammatical
complexity, can be defined for propositions of the next greater degree
of complexity.

According to Tarski, his theory applies only to artificial languages –
in particular, the classical formal languages of symbolic logic –
because our natural languages are vague and unsystematic. Other
philosophers – for example, Donald Davidson – have not been as
pessimistic as Tarski about analyzing truth for natural languages.
Davidson has made progress in extending Tarski's work to any natural
language. Doing so, he says, provides at the same time the central
ingredient of a theory of meaning for the language. Davidson develops
the original idea Frege stated in his Basic Laws of Arithmetic that
the meaning of a declarative sentence is given by certain conditions
under which it is true—that meaning is given by truth conditions.

As part of the larger program of research begun by Tarski and
Davidson, many logicians, linguists, philosophers, and cognitive
scientists, often collaboratively, pursue research programs trying to
elucidate the truth-conditions (that is, the "logics" or semantics
for) the propositions expressed by such complex sentences as:
"It is possible that snow is white." [modal propositions]
"Snow is white because sunlight is white." [causal propositions]
"If snow were yellow, ice would melt at -4°C." [contrary-to-fact
conditionals]
"Napoleon believed that snow is white." [intentional propositions]
"It is obligatory that one provide care for one's children."
[deontological propositions]
etc.

Each of these research areas contains its own intriguing problems. All
must overcome the difficulties involved with ambiguity, tenses, and
indexical phrases.
b. Can the Semantic Theory Account for Necessary Truth?

Many philosophers divide the class of propositions into two mutually
exclusive and exhaustive subclasses: namely, propositions that are
contingent (that is, those that are neither necessarily-true nor
necessarily-false) and those that are noncontingent (that is, those
that are necessarily-true or necessarily-false).

On the Semantic Theory of Truth, contingent propositions are those
that are true (or false) because of some specific way the world
happens to be. For example all of the following propositions are
contingent:
Snow is white. Snow is purple.
Canada belongs to the U.N. It is false that Canada belongs to the U.N.

The contrasting class of propositions comprises those whose truth (or
falsehood, as the case may be) is dependent, according to the Semantic
Theory, not on some specific way the world happens to be, but on any
way the world happens to be. Imagine the world changed however you
like (provided, of course, that its description remains logically
consistent [i.e., logically possible]). Even under those conditions,
the truth-values of the following (noncontingent) propositions will
remain unchanged:
Truths Falsehoods
Snow is white or it is false that snow is white. Snow is white and
it is false that snow is white.
All squares are rectangles. Not all squares are rectangles.
2 + 2 = 4 2 + 2 = 7

However, some philosophers who accept the Semantic Theory of Truth for
contingent propositions, reject it for noncontingent ones. They have
argued that the truth of noncontingent propositions has a different
basis from the truth of contingent ones. The truth of noncontingent
propositions comes about, they say – not through their correctly
describing the way the world is – but as a matter of the definitions
of terms occurring in the sentences expressing those propositions.
Noncontingent truths, on this account, are said to be true by
definition, or – as it is sometimes said, in a variation of this theme
– as a matter of conceptual relationships between the concepts at play
within the propositions, or – yet another (kindred) way – as a matter
of the meanings of the sentences expressing the propositions.

It is apparent, in this competing account, that one is invoking a kind
of theory of linguistic truth. In this alternative theory, truth for a
certain class of propositions, namely the class of noncontingent
propositions, is to be accounted for – not in their describing the way
the world is, but rather – because of certain features of our human
linguistic constructs.
c. The Linguistic Theory of Necessary Truth

Does the Semantic Theory need to be supplemented in this manner? If
one were to adopt the Semantic Theory of Truth, would one also need to
adopt a complementary theory of truth, namely, a theory of linguistic
truth (for noncontingent propositions)? Or, can the Semantic Theory of
Truth be used to explain the truth-values of all propositions, the
contingent and noncontingent alike? If so, how?

To see how one can argue that the Semantic Theory of Truth can be used
to explicate the truth of noncontingent propositions, consider the
following series of propositions, the first four of which are
contingent, the fifth of which is noncontingent:

1. There are fewer than seven bumblebees or more than ten.
2. There are fewer than eight bumblebees or more than ten.
3. There are fewer than nine bumblebees or more than ten.
4. There are fewer than ten bumblebees or more than ten.
5. There are fewer than eleven bumblebees or more than ten.

Each of these propositions, as we move from the second to the fifth,
is slightly less specific than its predecessor. Each can be regarded
as being true under a greater range of variation (or circumstances)
than its predecessor. When we reach the fifth member of the series we
have a proposition that is true under any and all sets of
circumstances. (Some philosophers – a few in the seventeenth century,
a very great many more after the mid-twentieth century – use the idiom
of "possible worlds", saying that noncontingent truths are true in all
possible worlds [i.e., under any logically possible circumstances].)
On this view, what distinguishes noncontingent truths from contingent
ones is not that their truth arises as a consequence of facts about
our language or of meanings, etc.; but that their truth has to do with
the scope (or number) of possible circumstances under which the
proposition is true. Contingent propositions are true in some, but not
all, possible circumstances (or possible worlds). Noncontingent
propositions, in contrast, are true in all possible circumstances or
in none. There is no difference as to the nature of truth for the two
classes of propositions, only in the ranges of possibilities in which
the propositions are true.

An adherent of the Semantic Theory will allow that there is, to be
sure, a powerful insight in the theories of linguistic truth. But,
they will counter, these linguistic theories are really shedding no
light on the nature of truth itself. Rather, they are calling
attention to how we often go about ascertaining the truth of
noncontingent propositions. While it is certainly possible to
ascertain the truth experientially (and inductively) of the
noncontingent proposition that all aunts are females – for example,
one could knock on a great many doors asking if any of the residents
were aunts and if so, whether they were female – it would be a
needless exercise. We need not examine the world carefully to figure
out the truth-value of the proposition that all aunts are females. We
might, for example, simply consult an English dictionary. How we
ascertain, find out, determine the truth-values of noncontingent
propositions may (but need not invariably) be by nonexperiential
means; but from that it does not follow that the nature of truth of
noncontingent propositions is fundamentally different from that of
contingent ones.

On this latter view, the Semantic Theory of Truth is adequate for both
contingent propositions and noncontingent ones. In neither case is the
Semantic Theory of Truth intended to be a theory of how we might go
about finding out what the truth-value is of any specified
proposition. Indeed, one very important consequence of the Semantic
Theory of Truth is that it allows for the existence of propositions
whose truth-values are in principle unknowable to human beings.

And there is a second motivation for promoting the Semantic Theory of
Truth for noncontingent propositions. How is it that mathematics is
able to be used (in concert with physical theories) to explain the
nature of the world? On the Semantic Theory, the answer is that the
noncontingent truths of mathematics correctly describe the world (as
they would any and every possible world). The Linguistic Theory, which
makes the truth of the noncontingent truths of mathematics arise out
of features of language, is usually thought to have great, if not
insurmountable, difficulties in grappling with this question.
5. Coherence Theories

The Correspondence Theory and the Semantic Theory account for the
truth of a proposition as arising out of a relationship between that
proposition and features or events in the world. Coherence Theories
(of which there are a number), in contrast, account for the truth of a
proposition as arising out of a relationship between that proposition
and other propositions.

Coherence Theories are valuable because they help to reveal how we
arrive at our truth claims, our knowledge. We continually work at
fitting our beliefs together into a coherent system. For example, when
a drunk driver says, "There are pink elephants dancing on the highway
in front of us", we assess whether his assertion is true by
considering what other beliefs we have already accepted as true,
namely,

* Elephants are gray.
* This locale is not the habitat of elephants.
* There is neither a zoo nor a circus anywhere nearby.
* Severely intoxicated persons have been known to experience hallucinations.

But perhaps the most important reason for rejecting the drunk's claim is this:

* Everyone else in the area claims not to see any pink elephants.

In short, the drunk's claim fails to cohere with a great many other
claims that we believe and have good reason not to abandon. We, then,
reject the drunk's claim as being false (and take away the car keys).

Specifically, a Coherence Theory of Truth will claim that a
proposition is true if and only if it coheres with ___. For example,
one Coherence Theory fills this blank with "the beliefs of the
majority of persons in one's society". Another fills the blank with
"one's own beliefs", and yet another fills it with "the beliefs of the
intellectuals in one's society". The major coherence theories view
coherence as requiring at least logical consistency. Rationalist
metaphysicians would claim that a proposition is true if and only if
it "is consistent with all other true propositions". Some rationalist
metaphysicians go a step beyond logical consistency and claim that a
proposition is true if and only if it "entails (or logically implies)
all other true propositions". Leibniz, Spinoza, Hegel, Bradley,
Blanshard, Neurath, Hempel (late in his life), Dummett, and Putnam
have advocated Coherence Theories of truth.

Coherence Theories have their critics too. The proposition that
bismuth has a higher melting point than tin may cohere with my beliefs
but not with your beliefs. This, then, leads to the proposition being
both "true for me" but "false for you". But if "true for me" means
"true" and "false for you" means "false" as the Coherence Theory
implies, then we have a violation of the law of non-contradiction,
which plays havoc with logic. Most philosophers prefer to preserve the
law of non-contradiction over any theory of truth that requires
rejecting it. Consequently, if someone is making a sensible remark by
saying, "That is true for me but not for you," then the person must
mean simply, "I believe it, but you do not." Truth is not relative in
the sense that something can be true for you but not for me.

A second difficulty with Coherence Theories is that the beliefs of any
one person (or of any group) are invariably self-contradictory. A
person might, for example, believe both "Absence makes the heart grow
fonder" and "Out of sight, out of mind." But under the main
interpretation of "cohere", nothing can cohere with an inconsistent
set. Thus most propositions, by failing to cohere, will not have
truth-values. This result violates the law of the excluded middle.

And there is a third objection. What does "coheres with" mean? For X
to "cohere with" Y, at the very least X must be consistent with Y. All
right, then, what does "consistent with" mean? It would be circular to
say that "X is consistent with Y" means "it is possible for X and Y
both to be true together" because this response is presupposing the
very concept of truth that it is supposed to be analyzing.

Some defenders of the Coherence Theory will respond that "coheres
with" means instead "is harmonious with". Opponents, however, are
pessimistic about the prospects for explicating the concept "is
harmonious with" without at some point or other having to invoke the
concept of joint truth.

A fourth objection is that Coherence theories focus on the nature of
verifiability and not truth. They focus on the holistic character of
verifying that a proposition is true but don't answer the principal
problem, "What is truth itself?"
a. Postmodernism: The Most Recent Coherence Theory

In recent years, one particular Coherence Theory has attracted a lot
of attention and some considerable heat and fury. Postmodernist
philosophers ask us to carefully consider how the statements of the
most persuasive or politically influential people become accepted as
the "common truths". Although everyone would agree that influential
people – the movers and shakers – have profound effects upon the
beliefs of other persons, the controversy revolves around whether the
acceptance by others of their beliefs is wholly a matter of their
personal or institutional prominence. The most radical postmodernists
do not distinguish acceptance as true from being true; they claim that
the social negotiations among influential people "construct" the
truth. The truth, they argue, is not something lying outside of human
collective decisions; it is not, in particular, a "reflection" of an
objective reality. Or, to put it another way, to the extent that there
is an objective reality it is nothing more nor less than what we say
it is. We human beings are, then, the ultimate arbiters of what is
true. Consensus is truth. The "subjective" and the "objective" are
rolled into one inseparable compound.

These postmodernist views have received a more sympathetic reception
among social scientists than among physical scientists. Social
scientists will more easily agree, for example, that the proposition
that human beings have a superego is a "construction" of (certain)
politically influential psychologists, and that as a result, it is (to
be regarded as) true. In contrast, physical scientists are – for the
most part – rather unwilling to regard propositions in their own field
as somehow merely the product of consensus among eminent physical
scientists. They are inclined to believe that the proposition that
protons are composed of three quarks is true (or false) depending on
whether (or not) it accurately describes an objective reality. They
are disinclined to believe that the truth of such a proposition arises
out of the pronouncements of eminent physical scientists. In short,
physical scientists do not believe that prestige and social influence
trump reality.
6. Pragmatic Theories

A Pragmatic Theory of Truth holds (roughly) that a proposition is true
if it is useful to believe. Peirce and James were its principal
advocates. Utility is the essential mark of truth. Beliefs that lead
to the best "payoff", that are the best justification of our actions,
that promote success, are truths, according to the pragmatists.

The problems with Pragmatic accounts of truth are counterparts to the
problems seen above with Coherence Theories of truth.

First, it may be useful for someone to believe a proposition but also
useful for someone else to disbelieve it. For example, Freud said that
many people, in order to avoid despair, need to believe there is a god
who keeps a watchful eye on everyone. According to one version of the
Pragmatic Theory, that proposition is true. However, it may not be
useful for other persons to believe that same proposition. They would
be crushed if they believed that there is a god who keeps a watchful
eye on everyone. Thus, by symmetry of argument, that proposition is
false. In this way, the Pragmatic theory leads to a violation of the
law of non-contradiction, say its critics.

Second, certain beliefs are undeniably useful, even though – on other
criteria – they are judged to be objectively false. For example, it
can be useful for some persons to believe that they live in a world
surrounded by people who love or care for them. According to this
criticism, the Pragmatic Theory of Truth overestimates the strength of
the connection between truth and usefulness.

Truth is what an ideally rational inquirer would in the long run come
to believe, say some pragmatists. Truth is the ideal outcome of
rational inquiry. The criticism that we don't now know what happens in
the long run merely shows we have a problem with knowledge, but it
doesn't show that the meaning of "true" doesn't now involve hindsight
from the perspective of the future. Yet, as a theory of truth, does
this reveal what "true" means?
7. Deflationary Theories

What all the theories of truth discussed so far have in common is the
assumption that a proposition is true just in case the proposition has
some property or other – correspondence with the facts, satisfaction,
coherence, utility, etc. Deflationary theories deny this assumption.
a. Redundancy Theory

The principal deflationary theory is the Redundancy Theory advocated
by Frege, Ramsey, and Horwich. Frege expressed the idea this way:

It is worthy of notice that the sentence "I smell the scent of
violets" has the same content as the sentence "It is true that I smell
the scent of violets." So it seems, then, that nothing is added to the
thought by my ascribing to it the property of truth. (Frege, 1918)

When we assert a proposition explicitly, such as when we say "I smell
the scent of violets", then saying "It's true that I smell the scent
of violets" would be redundant; it would add nothing because the two
have the same meaning. Today's more minimalist advocates of the
Redundancy Theory retreat from this remark about meaning and say
merely that the two are necessarily equivalent.

Where the concept of truth really pays off is when we do not, or can
not, assert a proposition explicitly, but have to deal with an
indirect reference to it. For instance, if we wish to say, "What he
will say tomorrow is true", we need the truth predicate "is true".
Admittedly the proposition is an indirect way of saying, "If he says
tomorrow that it will snow, then it will snow; if he says tomorrow
that it will rain, then it will rain; if he says tomorrow that 7 + 5 =
12, then 7 + 5 = 12; and so forth." But the phrase "is true" cannot be
eliminated from "What he will say tomorrow is true" without producing
an unacceptable infinite conjunction. The truth predicate "is true"
allows us to generalize and say things more succinctly (indeed to make
those claims with only a finite number of utterances). In short, the
Redundancy Theory may work for certain cases, say its critics, but it
is not generalizable to all; there remain recalcitrant cases where "is
true" is not redundant.

Advocates of the Redundancy Theory respond that their theory
recognizes the essential point about needing the concept of truth for
indirect reference. The theory says that this is all that the concept
of truth is needed for, and that otherwise its use is redundant.
b. Performative Theory

The Performative Theory is a deflationary theory that is not a
redundancy theory. It was advocated by Strawson who believed Tarski's
Semantic Theory of Truth was basically mistaken.

The Performative Theory of Truth argues that ascribing truth to a
proposition is not really characterizing the proposition itself, nor
is it saying something redundant. Rather, it is telling us something
about the speaker's intentions. The speaker – through his or her
agreeing with it, endorsing it, praising it, accepting it, or perhaps
conceding it – is licensing our adoption of (the belief in) the
proposition. Instead of saying, "It is true that snow is white", one
could substitute "I embrace the claim that snow is white." The key
idea is that saying of some proposition, P, that it is true is to say
in a disguised fashion "I commend P to you", or "I endorse P", or
something of the sort.

The case may be likened somewhat to that of promising. When you
promise to pay your sister five dollars, you are not making a claim
about the proposition expressed by "I will pay you five dollars";
rather you are performing the action of promising her something.
Similarly, according to the Performative Theory of Truth, when you say
"It is true that Vancouver is north of Sacramento", you are performing
the act of giving your listener license to believe (and to act upon
the belief) that Vancouver is north of Sacramento.

Critics of the Performative Theory charge that it requires too radical
a revision in our logic. Arguments have premises that are true or
false, but we don't consider premises to be actions, says Geach. Other
critics complain that, if all the ascription of "is true" is doing is
gesturing consent, as Strawson believes, then, when we say

"Please shut the door" is true,

we would be consenting to the door's being shut. Because that is
absurd, says Huw Price, something is wrong with Strawson's
Performative Theory.
c. Prosentential Theory

The Prosentential Theory of Truth suggests that the grammatical
predicate "is true" does not function semantically or logically as a
predicate. All uses of "is true" are prosentential uses. When someone
asserts "It's true that it is snowing", the person is asking the
hearer to consider the sentence "It is snowing" and is saying "That is
true" where the remark "That is true" is a taken holistically as a
prosentence, in analogy to a pronoun. A pronoun such as "she" is a
substitute for the name of the person being referred to. Similarly,
"That is true" is a substitute for the proposition being considered.
Likewise, for the expression "it is true." According to the
Prosentential Theory, all uses of "true" can be reduced to uses either
of "That is true" or "It is true" or variants of these with other
tenses. Because these latter prosentential uses of the word "true"
cannot be eliminated from our language during analysis, the
Prosentential Theory is not a redundancy theory.

Critics of the theory remark that it can give no account of what is
common to all our uses of the word "true", such as those in the
unanalyzed operators "it-will-be-true-that" and "it-is-true-that" and
"it-was-true-that".
8. Related Issues
a. Beyond Truth to Knowledge

For generations, discussions of truth have been bedeviled by the
question, "How could a proposition be true unless we know it to be
true?" Aristotle's famous worry was that contingent propositions about
the future, such as "There will be a sea battle tomorrow", couldn't be
true now, for fear that this would deny free will to the sailors
involved. Advocates of the Correspondence Theory and the Semantic
Theory have argued that a proposition need not be known in order to be
true. Truth, they say, arises out of a relationship between a
proposition and the way the world is. No one need know that that
relationship holds, nor – for that matter – need there even be any
conscious or language-using creatures for that relationship to obtain.
In short, truth is an objective feature of a proposition, not a
subjective one.

For a true proposition to be known, it must (at the very least) be a
justified belief. Justification, unlike truth itself, requires a
special relationship among propositions. For a proposition to be
justified it must, at the very least, cohere with other propositions
that one has adopted. On this account, coherence among propositions
plays a critical role in the theory of knowledge. Nevertheless it
plays no role in a theory of truth, according to advocates of the
Correspondence and Semantic Theories of Truth.

Finally, should coherence – which plays such a central role in
theories of knowledge – be regarded as an objective relationship or as
a subjective one? Not surprisingly, theorists have answered this
latter question in divergent ways. But the pursuit of that issue takes
one beyond the theories of truth.
b. Algorithms for Truth

An account of what "true" means does not have to tell us what is true,
nor tell us how we could find out what is true. Similarly, an account
of what "bachelor" means should not have to tell us who is a bachelor,
nor should it have to tell us how we could find out who is. However,
it would be fascinating if we could discover a way to tell, for any
proposition, whether it is true.

Perhaps some machine could do this, philosophers have speculated. For
any formal language, we know in principle how to generate all the
sentences of that language. If we were to build a machine that
produces one by one all the many sentences, then eventually all those
that express truths would be produced. Unfortunately, along with them,
we would also generate all those that express false propositions. We
also know how to build a machine that will generate only sentences
that express truths. For example, we might program a computer to
generate "1 + 1 is not 3″, then "1 + 1 is not 4″, then "1 + 1 is not
5″, and so forth. However, to generate all and only those sentences
that express truths is quite another matter.

Leibniz (1646-1716) dreamed of achieving this goal. By mechanizing
deductive reasoning he hoped to build a machine that would generate
all and only truths. As he put it, "How much better will it be to
bring under mathematical laws human reasoning which is the most
excellent and useful thing we have." This would enable one's mind to
"be freed from having to think directly of things themselves, and yet
everything will turn out correct." His actual achievements were
disappointing in this regard, but his dream inspired many later
investigators.

Some progress on the general problem of capturing all and only those
sentences which express true propositions can be made by limiting the
focus to a specific domain. For instance, perhaps we can find some
procedure that will produce all and only the truths of arithmetic, or
of chemistry, or of Egyptian political history. Here, the key to
progress is to appreciate that universal and probabilistic truths
"capture" or "contain" many more specific truths. If we know the
universal and probabilistic laws of quantum mechanics, then (some
philosophers have argued) we thereby indirectly (are in a position to)
know the more specific scientific laws about chemical bonding.
Similarly, if we can axiomatize an area of mathematics, then we
indirectly have captured the infinitely many specific theorems that
could be derived from those axioms, and we can hope to find a decision
procedure for the truths, a procedure that will guarantee a correct
answer to the question, "Is that true?"

Significant progress was made in the early twentieth century on the
problem of axiomatizing arithmetic and other areas of mathematics.
Let's consider arithmetic. In the 1920s, David Hilbert hoped to
represent the sentences of arithmetic very precisely in a formal
language, then to generate all and only the theorems of arithmetic
from uncontroversial axioms, and thereby to show that all true
propositions of arithmetic can in principle be proved as theorems.
This would put the concept of truth in arithmetic on a very solid
basis. The axioms would "capture" all and only the truths. However,
Hilbert's hopes would soon be dashed. In 1931, Kurt Gödel (1906-1978),
in his First Incompleteness Theorem, proved that any classical
self-consistent formal language capable of expressing arithmetic must
also contain sentences of arithmetic that cannot be derived within
that system, and hence that the propositions expressed by those
sentences could not be proven true (or false) within that system. Thus
the concept of truth transcends the concept of proof in classical
formal languages. This is a remarkable, precise insight into the
nature of truth.
c. Can "is true" Be Eliminated?

Can "is true" be defined so that it can be replaced by its definition?
Unfortunately for the clarity of this question, there is no one
concept of "definition". A very great many linguistic devices count as
definitions. These devices include providing a synonym, offering
examples, pointing at objects that satisfy the term being defined,
using the term in sentences, contrasting it with opposites, and
contrasting it with terms with which it is often confused. (For
further reading, see Definitions, Dictionaries, and Meanings.)

However, modern theories about definition have not been especially
recognized, let alone adopted, outside of certain academic and
specialist circles. Many persons persist with the earlier, naive, view
that the role of a definition is only to offer a synonym for the term
to be defined. These persons have in mind such examples as:
"'hypostatize' means (or, is a synonym for) 'reify'".

If one were to adopt this older view of definition, one might be
inclined to demand of a theory of truth that it provide a definition
of "is true" which permitted its elimination in all contexts in the
language. Tarski was the first person to show clearly that there could
never be such a strict definition for "is true" in its own language.
The definition would allow for a line of reasoning that produced the
Liar Paradox (recall above) and thus would lead us into self
contradiction. (See the discussion, in the article The Liar Paradox,
of Tarski's Udefinability Theorem of 1936.)

Kripke has attempted to avoid this theorem by using only a "partial"
truth-predicate so that not every sentence has a truth-value. In
effect, Kripke's "repair" permits a definition of the truth-predicate
within its own language but at the expense of allowing certain
violations of the law of excluded middle.
d. Can a Theory of Truth Avoid Paradox?

The brief answer is, "Not if it contains its own concept of truth." If
the language is made precise by being formalized, and if it contains
its own so-called global truth predicate, then Tarski has shown that
the language will enable us to reason our way to a contradiction. That
result shows that we do not have a coherent concept of truth (for a
language within that language). Some of our beliefs about truth, and
about related concepts that are used in the argument to the
contradiction, must be rejected, even though they might seem to be
intuitively acceptable.

There is no reason to believe that paradox is to be avoided by
rejecting formal languages in favor of natural languages. The Liar
Paradox first appeared in natural languages. And there are other
paradoxes of truth, such as Löb's Paradox, which follow from
principles that are acceptable in either formal or natural languages,
namely the principles of modus ponens and conditional proof.

The best solutions to the paradoxes use a similar methodology, the
"systematic approach". That is, they try to remove vagueness and be
precise about the ramifications of their solutions, usually by showing
how they work in a formal language that has the essential features of
our natural language. The Liar Paradox and Löb's Paradox represent a
serious challenge to understanding the logic of our natural language.
The principal solutions agree that – to resolve a paradox – we must go
back and systematically reform or clarify some of our original
beliefs. For example, the solution may require us to revise the
meaning of "is true". However, to be acceptable, the solution must be
presented systematically and be backed up by an argument about the
general character of our language. In short, there must be both
systematic evasion and systematic explanation. Also, when it comes to
developing this systematic approach, the goal of establishing a
coherent basis for a consistent semantics of natural language is much
more important than the goal of explaining the naive way most speakers
use the terms "true" and "not true". The later Wittgenstein did not
agree. He rejected the systematic approach and elevated the need to
preserve ordinary language, and our intuitions about it, over the need
to create a coherent and consistent semantical theory.
e. Is The Goal of Scientific Research to Achieve Truth?

Except in special cases, most scientific researchers would agree that
their results are only approximately true. Nevertheless, to make sense
of this, philosophers need adopt no special concept such as
"approximate truth." Instead, it suffices to say that the researchers'
goal is to achieve truth, but they achieve this goal only
approximately, or only to some approximation.

Other philosophers believe it's a mistake to say the researchers' goal
is to achieve truth. These "scientific anti-realists" recommend saying
that research in, for example, physics, economics, and meteorology,
aims only for usefulness. When they aren't overtly identifying truth
with usefulness, the instrumentalists Peirce, James and Schlick take
this anti-realist route, as does Kuhn. They would say atomic theory
isn't true or false but rather is useful for predicting outcomes of
experiments and for explaining current data. Giere recommends saying
science aims for the best available "representation", in the same
sense that maps are representations of the landscape. Maps aren't
true; rather, they fit to a better or worse degree. Similarly,
scientific theories are designed to fit the world. Scientists should
not aim to create true theories; they should aim to construct theories
whose models are representations of the world.
9. References and Further Reading

* Bradley, Raymond and Norman Swartz . Possible Worlds: an
Introduction to Logic and Its Philosophy, Hackett Publishing Company,
1979.
* Davidson, Donald. Inquiries into Truth and Interpretation,
Oxford University Press, 1984.
* Davidson, Donald. "The Structure and Content of Truth", The
Journal of Philosophy, 87 (1990), 279-328.
* Horwich, Paul. Truth, Basil Blackwell Ltd., 1990.
* Mates, Benson. "Two Antinomies", in Skeptical Essays, The
University of Chicago Press, 1981, 15-57.
* McGee, Vann. Truth, Vagueness, and Paradox: An Essay on the
Logic of Truth, Hackett Publishing, 1991.
* Kirkham, Richard. Theories of Truth: A Critical Introduction,
MIT Press, 1992.
* Kripke, Saul. "Outline of a Theory of Truth", Journal of
Philosophy, 72 (1975), 690-716.
* Quine, W. V. "Truth", in Quiddities: An Intermittently
Philosophical Dictionary, The Belknap Press of Harvard University
Press, 1987.
* Ramsey, F. P. "Facts and Propositions", in Proceedings of the
Arisotelian Society, Supplement, 7, 1927.
* Russell, B. The Problems of Philosophy, Oxford University Press, 1912.
* Strawson, P. F. "Truth", in Analysis, vol. 9, no. 6, 1949.
* Tarski, Alfred, "The Semantic Conception of Truth and the
Foundations of Semantics", in Philosophy and Phenomenological
Research, 4 (1944).
* Tarski, Alfred. "The Concept of Truth in Formalized Languages",
in Logic, Semantics, Metamathematics, Clarendon Press, 1956.