Page 225 - Encyclopedia of Philosophy of Language

A semantic theory, whether for a natural language or for a formal language artificially constructed for specific clearly defined purposes, is a theory of what makes language (or some uses of it) meaningful. One familiar theory of the meaningfulness of language is that the meaning of a declarative sentence is its truth conditions, i.e., those conditions which render the sen- tence true. Thus, the meaning of Snow is white is explained in terms of what it is for that sentence to be true, captured by:
(T) Snow is white is true if and only if snow is white.
If truth conditions are the basis of meaning, the the- orems of a fully developed truth-conditional theory of meaning will be statements of the form:
(M) Snowiswhitemeansthatsnowiswhite.
1. SemanticsandTruthConditions
Classical logic tacitly presents a partially truth- conditional semantics for formal systems. The sem- antics for sentential logic begins with the possible dis- tributions of truth values over the atomic sentences. The interpretation of compound statements is then given solely on the basis of the truth conditions of their components, as given by the truth tables for the sentential connectives. Thus, according to classical semantic structures, logically equivalent sentences are semantically equivalent. The semantics for quanti- ficational and intensional logics are truth conditional to the extent that they rely on the classical semantics for the sentential connectives.
2. TruthConditionsandtheNatureofTruth
The precise nature of meaning is incompletely speci- fied by the simple statement that meanings are truth conditions. If truth is correspondence with reality, then truth-conditional semantics is the doctrine that meanings are objective metaphysical structures of the world, structures that are not wholly a function of what language users believe or have good reason to believe. If truth is the coherence of the elements in a system of belief, or the tendency to satisfy goals and purposes in a noteworthy manner, or the support by a sufficient amount of evidence, then the truth con- ditions that constitute the meanings of statements are at least partly a function of the theoretical, pragmatic, or assertibility conditions in which speakers find them- selves.
Truth-conditional semantics was proposed by Lud- wig Wittgenstein in the Tractatus Logico-Philo- sophicus where he claims that a true statement pictures or depicts a state of affairs. Components of the sen- tence structure contribute to the meaning of the whole
by referring to components of the depicted fact. J. L. Austin, Alfred Tarski, and Donald Davidson define truth as correspondence with reality by defining truth in terms of reference and the satisfaction of a predicate without relying on structured facts. These accounts provide a general basis for the semantics of classical logic. If statement meanings are truth conditions that obtain regardless of a speaker's knowledge that they obtain, then statements of the form:
pv~p Vx(Fxv~Fx)
are necessarily true.
Strict empiricists found this metaphysical account
of truth conditions objectionable and gave an alter- native semantics for logic and natural language. It is a mere terminological issue whether to describe them as rejecting truth-conditional semantics or as merely rejecting a specific formulation of the proper theory of truth. Mathematical intuitionists maintain that the truth of a mathematical statement is parasitic upon the conditions of proof of that statement and that the meaning of the logical operators is given by the conditions of constructing a proof of compound state- ments containing those operators. Thus, logical truth is identified with provability and, more generally, the meanings of statements are the conditions of their warranted assertibility. Disjunctions are accepted as true only when there is a proof of one of the disjuncts. For this reason, instances of excluded middle are not intuitionistically valid, since there may be proofs of neither disjunct. Standard reductio ad absurdum proofs are intuitionistically acceptable, however, so long as they do not involve the use of the double negation elimination rule.
See also: Intuitionism. Bibliography
Austin J L 1950 Truth. Proceedings of the Aristotelian Society 24: 111-28
Davidson D 1984 Inquiries into Truth and Interpretation. Clarendon Press, Oxford
Dummett M 1978 Truth and Other Enigmas. Harvard Uni- versity Press, Cambridge, MA
Heyting A 1956 Intuitionism: An Introduction. North- Holland, Amsterdam
Tarski A 1943/44 The semantic conception of truth. Phil- osophy and Phenomenological Research 4: 341-75
Tarski A 1958 The concept of truth in formalized languages. In: Logic, Semantics, Metamathematics: Papers from 1923 to 1938. Oxford University Press, Oxford
Wittgenstein L 1961 (trans. Pears D F, McGuinness B F) Tractatus Logico-Philosophicus. Routledge and Kegan Paul, London
Truth Conditions S. Shalkowski
Truth Conditions
203