||Although truth might seem to be an absolute concept, in the disciplines which need or seek to define it exactly, mathematics and philosophy, it has proved more elusive than might have been thought possible. For example, until the early 19th century mathematicians accepted that Euclidean geometry was a paradigm of the absolute truth of their discipline, but then the work of Bolyai and Lobachevsky demonstrated that there was more to geometry than had been suspected, and the idea of mathematics as absolute truth became invalid overnight. In modern mathematics, the axiom of choice involves acceptance of the fact that many results are true in one system but not in another; equally, GÃ¶del\'s incompleteness theorem shows that â€˜trueâ€™ and â€˜provableâ€™ are not always the same thing in mathematical terms, as had previously been believed.
In logic, truth has a restricted meaning, and is really a label with no content at all. A sentence of the propositional calculus is either true or false, and its truth value depends on whether the individual particles that make it up are true or false. (For example, the sentence â€˜A and Bâ€™ is true if A and B are both true, but false if either of them is false.)
Such ideas underlie the various philosophical theories which attempt to answer the question â€˜What is truth?â€™. According to the correspondence theory of truth, a statement is true just if it corresponds to the facts, to how things are. Thus the statement that the cat is under the table is true just if the cat is in fact underneath the table, and is false just if the cat is not in fact underneath the table. A statement is true just if it stands in a certain relationâ€”the relation of correspondence with the facts, with how the world is independently of whatever statement may or may not be made about it. One difficulty here is to say exactly what the relation of correspondence is supposed to be.
According to the coherence theory of truth, a statement is true just if it is a member of the most coherent set of statements. Thus the statement that the cat is under the table is true just if it is a member of the most coherent set of statements about the cat, the furniture and, indeed, anything else. And a statement is false just if it is not a member of the most coherent set of statements. So a statement is true just if it stands in a certain relationâ€”the relation of coherenceâ€”with the most coherent set of statements. Truth is not a matter of the relation between statements and something elseâ€”the factsâ€”but a matter of the relation between statements. The most obvious objection to the coherence theory is that there could be two equally coherent sets of statements, both of which are more coherent than any other sets, but which contradict each other. But two contradictory sets of statements could not both be true.
According to F. P. Ramsay\'s redundancy theory of truth, when one says that a certain statement is true one is doing no more that making that statement. When one says that the statement that the cat is under the table is true, one is doing no more than stating that the cat is under the table. So it is redundant to say of any statement one makes that it is true. AJ SMcL
See also semantics.Further reading S.F. Baker, The Elements of Logic; , F. Palmer, Semantics.