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In semantics and pragmatics, a truth condition is the condition under which a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska. Truth conditions of a sentence do not necessarily reflect current reality. They are merely the conditions under which the statement would be true. [1]
In realizability truth values are sets of programs, which can be understood as computational evidence of validity of a formula. For example, the truth value of the statement "for every number there is a prime larger than it" is the set of all programs that take as input a number , and output a prime larger than .
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 ...
The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name truth-value semantics). Game semantics or game-theoretical semantics made a resurgence mainly due to Jaakko Hintikka for logics of (finite) partially ordered quantification , which were originally investigated ...
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:
Broadly speaking, the primary motivation for research of three valued logic is to represent the truth value of a statement that cannot be represented as true or false. [8] Łukasiewicz initially developed three-valued logic for the problem of future contingents to represent the truth value of statements about the undetermined future.
It understands meaning usually in relation to truth conditions, i.e. it examines in which situations a sentence would be true or false. One of its central methodological assumptions is the principle of compositionality. It states that the meaning of a complex expression is determined by the meanings of its parts and how they are combined.
If an idea works then it must be true, to the Pragmatist. The consequences of applying a concept reveal its truth value upon examination of the results. The full meaning of an idea is self-apparent in its application. For example, the therapeutic value and effect of penicillin in relation to infections is proven in its administration.