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Truth conditions of a sentence do not necessarily reflect current reality. They are merely the conditions under which the statement would be true. [1] More formally, a truth condition makes for the truth of a sentence in an inductive definition of truth (for details, see the semantic theory of truth).
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson , and attempts to carry out for the semantics of natural language what ...
Truth or verity is the property of being in accord with fact or reality. [1] In everyday language, it is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences.
These explain how the truth conditions of complex sentences (built up from connectives and quantifiers) can be reduced to the truth conditions of their constituents. The simplest constituents are atomic sentences. A contemporary semantic definition of truth would define truth for the atomic sentences as follows:
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
One can also say S is a sufficient condition for N (refer again to the third column of the truth table immediately below). If the conditional statement is true, then if S is true, N must be true; whereas if the conditional statement is true and N is true, then S may be true or be false. In common terms, "the truth of S guarantees the truth of N ...
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It is inadequate as a criterion because it treats facts in an isolated fashion without true cohesion and integration; nevertheless it remains a necessary condition for the truth of any argument, owing to the law of noncontradiction. The value of a proof largely lies in its ability to reconcile individual facts into a coherent whole.