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The truth value is an important idea of the contemporary logical semantics and the philosophy of logic. The notion is conceived as the natural element of the language analysis in which sentences and expressions are interpreted as a special type of name that refers to a special type of objects called the True and the False. Basically, the classical logic has the truth values, which obey the norm of bivalence. In this context, there are only two distinct logical values. The notion of truth values in semantics has been used differently in logic and philosophy. They are applied as the primitive abstract objects in which sentences are denoted in both natural and formal languages. It includes values that indicate the truth in a sentence and convey information about a specific proposition and the values preserved in a valid inference.
Historic Background of Truth Values
Based on how they are used, truth values can be treated as structured, unstructured, or unanalyzed entities. In addition, the concept of truth values as compound entities perfectly conforms to the models of truth values such as three-valued and four-valued logics (Goldblatt, 2006). Gottlob Frege explicitly introduced the concept of the truth value into logic and philosophy in 1891. Even though he was the first to make it one of the key ideas of semantics, Boole and Pierce had already anticipated the theory of semantical values. The introduction of this new notion in semantics helped in enhancing an extensive and diverse impact on the development of the modern philosophy and logic (Anderson & Edward, 2004). A sentence can be determined as true or false based on the information given. For example, the sentence “24 is divisible by 6” is true while “111 is a multiple of 8” is false.
Truth Values and Semantics
The truth value offers a means to complete the formal elements of a functional analysis of language in a uniform manner. This is achievable through the generalization of the functional concepts and introduction of a special type of functions (Goldblatt, 2006). These include propositional or truth value functions with the various values consisting of a set of truth values. Specific representatives of these functions establish both expressions and logical connections. Consequently, a powerful tool is obtained to implement a conclusive principle that helps in determining the meaning of complex expressions in terms of their components (Camp, 2002). Therefore, it is possible to differentiate between intrinsic and extrinsic logics.
The concept of truth values has been used to induce new perspectives into the philosophy of logic such as the category of truth, the idea of an abstract object and the nature of logical thinking among others. If the truth value is deemed a special object, the issues that arise determine the nature of their entities. This implies that the truth value cannot be given a general characterization. One way of providing it with specific characterization is by referring to it as an abstract object (Anderson & Edward, 2004).
The notion of Gottlob Frege about the truth value successfully became a standard component of both philosophical and logical terms used with semantics. The idea has become a crucial instrument used to achieve realistic and theoretical aspects of semantics. Truth values are essentially applicable in model theoretical semantics, especially in the areas of the knowledge and theoretical representations. In addition, considerations of the truth values create issues related to their ontological nature, facts and theories. Theoretical models have been used to explore the concept of the truth value beyond the initial idea of the True and the False developed by Frege. As a result, the notion has been developed to explain various aspects of semantics.
Anderson, D., & Edward Z. (2004). Frege, Boolos, and logical objects. Journal of Philosophical Logic, 33(1), 1-26.
Camp, L. (2002). Confusion: A study in the theory of knowledge. Cambridge, MA: Harvard University Press.
Goldblatt, R. (2006). Topoi: The categorial analysis of logic. Mineola, NY: Dover Publications.