Truth-bearer

Entities that are said to be either true or false

A truth bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth bearer is used to be neutral among the various theories. Truth bearer candidates include propositions, sentences, sentence tokens, statements, beliefs, thoughts, intuitions, utterances, and judgements but different authors exclude one or more of these, deny their existence, argue that they are true only in a derivative sense, assert or assume that the terms are synonymous,
or seek to avoid addressing their distinction or do not clarify it.

Some distinctions and terminology as used in this article, based on Wolfram 1989
(Chapter 2 Section1) follow. It should be understood that the terminology described is not always used in the ways set out, and it is introduced solely for the purposes of discussion in this article. Use is made of the type–token and use–mention distinctions. Reflection on occurrences of numerals might be helpful. In grammar a sentence can be a declaration, an explanation, a question, a command. In logic a declarative sentence is considered to be a sentence that can be used to communicate truth. Some sentences which are grammatically declarative are not logically so. A character is a typographic character (printed or written) etc. A word token is a pattern of characters. A word type
is an identical pattern of characters. A meaningful word token
is a meaningful pattern of characters. Two word tokens which mean the same are of the same word meaning

A sentence token is a pattern of word tokens. A meaningful sentence token
is a meaningful sentence token or a meaningful pattern of meaningful word tokens. Two sentence tokens are of the same sentence type if they are identical patterns of word tokens characters
A declarative sentence token is a sentence token which that can be used to communicate truth or convey information. A meaningful declarative sentence token is a meaningful declarative sentence token
Two meaningful declarative sentence tokens are of the same meaningful declarative sentence type
if they are identical patterns of word tokens. A nonsense declarative sentence token
is a declarative sentence token which is not a meaningful declarative sentence token. A meaningful declarative sentence token use
occurs when and only when a meaningful declarative sentence token is used declaratively. A referring expression
is expression that can be used to pick out or refer to particular entity. A referential success
is a referring expression's success in identifying a particular entity. A referential failure
is a referring expression's failure to identify a particular entity. A referentially successful meaningful declarative sentence token use
is a meaningful declarative sentence token use containing no referring expression that fails to identify a particular entity.

In classical logic a sentence in a language is true or false under (and only under) an interpretation and is therefore a truth bearer. For example, a language in the first order predicate calculus might include one or more predicate symbols and one or more individual constants and one or more variables. The interpretation of such a language would define a domain (universe of discourse); assign an element of the domain to each individual constant; assign the denotation in the domain of some property to each unary (one place) predicate symbol. For example, if a language L consisted in the individual constant a, two unary predicate letters F and G and the variable x, then an interpretation I of L might define the Domain D as animals, assign Socrates to a, the denotation of the property being a man to F, and the denotation of the property being mortal to G. Under the interpretation I of L, Fa would be true if, and only if Socrates is a man, and the sentence x(Fx Gx) would be true if, and only if all men (in the domain) are mortal. In some texts an interpretation is said to give "meaning" to the symbols of the language. Since Fa has the value true under some (but not all) interpretations, it is not the sentence type Fa which is said to be true but only some sentence tokens of Fa under particular interpretations. A token of Fa without an interpretation is neither true nor false. Some sentences of a language like L are said to be true under all interpretations of the sentence, e. g. x(Fx Fx), such sentences are termed logical truths, but again such sentences are neither true nor false in the absence of an interpretation.

Frege (1919) argued that an indicative sentence in which we communicate or state something, contains both a thought and an assertion, it expresses the thought, and the thought is the sense of the sentence.